sábado, 14 de outubro de 2017




On my CV:
After a graduation in medicine I made my M.S. in philosophy at the UFRJ (Rio de Janeiro), Ph.D. at the University of Konstanz (Germany) and post-doctoral works at the Hochschule für Philosophie (Munich) and at the universities of Berkeley, Oxford, Konstanz, Göteborg, and at the École Normale Supérieure. 
My main articles published in international journals were collected and better developed in the book Lines of Thought: Rethinking Philosophical Assumptions (Cambridge Scholars Publishing, 2014). Also from interest may be a short theory on the nature of philosophy in the book The Philosophical Inquiry (UPA, 2002). Presently I am writting a book aiming to recuperate the credibility of the old orthodoxy in analytic philosophy of language. This book, to be called Philosophical Semantics, shall be also published by CSP in 2017/2. 

I am full professor at the Department of Philosophy of the UFRN, Natal, Brazil, though with ergonomic limitation.

Advertisement of some published books (see Amazon.usa):


This is the present draft of the first pages of the book Philosophical Semantics to be published by Cambridge Scholars Publishing in the next months. Drafts of most chapters can be find in this "blogg"


This book offers an alternative systematic approach to the problems of meaning and reference, unifying in promising ways some of the best insights, not only of exponential philosophers like Wittgenstein, Frege, Russell and Husserl, but also of influential later theorists like Michael Dummett, Ernst Tugendhat, John Searle and Donald Williams. Moreover, it exposes some main errors popularized by clever but reductionist and formalistically-oriented philosophers, from Willard V-O. Quine to Saul Kripke and Hilary Putnam. In this way, it aims to show how some older major approaches could regain their central importance and how the cartography of philosophy of language could once more be redrawn.

Table of Contents


Chapter I: Introduction
1.     Ernst Tugendhat’s analysis of singular statements
2.     Virtues of comprehensiveness

Appendix to Chapter I: How Do Proper Names Really Work? (Cutting the Gordian knot)
1.     A meta-descriptivist rule for proper names
2.     Identification rules at work
3.     Objection of vagueness
4.     Signification
5.     Ignorance and error
6.     Rigidity
7.     Rules changeability
8.     Names versus descriptions
9.     Autonomous definite descriptions
10. Kripke’s counterexamples
11. Donnellan’s counterexamples
12. Explanatory failure of the causal-historical view

Chapter II: Against the Metaphysics of Reference: Methodological Assumptions
1.     Common sense and meaning
2.     Critical common-sensism
3.     Ambitious versus modest common sense
4.     Resisting changes in worldviews
5.     Primacy of established knowledge
6.     Philosophizing by examples
7.     Tacit knowledge of meaning: traditional explanation
8.     A very simple model of semantic-cognitive rule
9.     Criteria versus symptoms
10. Challenges to the traditional explanation (i): John McDowell
11. Challenges to the traditional explanation (ii): Gareth Evans
12. Non-reflexive semantic cognitions
13. Conclusion

Appendix to Chapter II: Modal Illusions: Against Supra-Epistemic Metaphysical Identities
Addendum: disposing of externalism

Chapter III: Wittgensteinian Semantics
1.     Semantic-cognitive link
2.     Why can’t reference be meaning?
3.     Failure of Russell’s atomistic referentialism
4.     Meaning as a function of use
5.     Meaning as a kind of rule
6.     Meaning as a combination of rules
7.     Meaning and language-games
8.     Meaning and forms of life
9.     Tying the threads together
10. Criteria and symptoms revisited
11. Transgressions of the internal limits of language
12. The form of semantic cognitive rules
13. What is wrong with the private language argument?
14. Concluding remarks

Appendix to Chapter III: Trope Theory and the Unbearable Lightness of Being
1.     Introducing tropes
2.     Tropes and universals
3.     Tropes and concrete particulars
4.     Tropes and formal properties
5.     Conclusion

Chapter IV: An Extravagant Reading of Fregean Semantics
1.     Reference of a singular term
2.     Sense of a singular term
3.     Reference of a predicative expression
4.     Ontological level
5.     Referring to particularized properties (tropes)
6.     Difficulties with the concept of unsaturation
7.     Unsaturation as ontological dependence
8.     Sense of a predicative term
9.     The dependence of the predicative sense
10. The concept of horse paradox
11. Existence as a property of concepts
12. Existence as a property of conceptual rules
13. Two naïve objections
14. Attributing existence to objects
15. Existence of objects and its identification rules
16. Existence of spatio-temporal locations: indexicals
17. Advantages of the higher-order view of existence
18. Ubiquity of existence
19. Answering some final objections
20. Reference of concepts again: a metaphysical excurse (Mill)
21. The reference of a sentence as its truth-value
22. Logical structure of facts
23. Ontological nature of facts
24. Church’s slingshot argument
25. Facts: sub-facts and grounding facts
26. Taking seriously the sentence’s reference as a fact
27. The riddle of identity in difference
28. No necessity of necessary a posteriori
29. Sense of sentences: the thought
30. The thought as the truth-bearer
31. Facts as true thoughts?
32. The thought as a verifiability rule
33. Frege’s Platonism
34. Avoiding Frege’s Platonism
35. Further ontological consequences
36. A short digression on contingent futures
37. Conclusion

Appendix to Chapter IV: Frege, Russell, and the Puzzles of Reference
1.     Russell’s solutions to the puzzles of reference
2.     Fregean solutions to the same puzzles
3.     Reviewing Fregean assumptions
4.     Reviewing Russellian assumptions
5.     Building a bridge between both views
6.     Conclusion

Chapter V: Verificationism Redeemed
1.     Origins of semantic verificationism
2.     Wittgensteinean verificationism
3.     Verifiability rule as a criterial rule
4.     Objection 1: the principle is self-refuting
5.     Objection 2: a formalist illusion
6.     Objection 3: verificational holism
7.     Objection 4: existential-universal asymmetry
8.     Objection 5: arbitrary indirectness
9.     Objection 6: empirical counterexamples
10. Objection 7: formal counterexamples
11. Objection 8: skepticism about rules
12. Defending analyticity
13. Conclusion

Appendix to Chapter V: The only Key to Solving the Humean Problem of Induction
1.     Formulating a Humean argument
2.     The basic idea
3.     Reformulating PF

Chapter VI: Sketch of a Unified Theory of Truth
1.     The deceptive simplicity of adequation
2.     Compatibility between verificationism and adequation
3.     Analysis of adequation: structural isomorphism
4.     Analysis of adequation: categorial match
5.     Excurse on logical form
6.     Analysis of adequation: intentionality and causality
7.     Exemplifying adequation
8.     The logical form of the adequation relation
9.     Negative truths
10. Self-referentiality
11. Pragmatics of the adequation relation
12. Retrograde procedures
13. A more complex case
14. General statements
15. Some funny facts
16. Expansion to formal sciences
17. Why can analytic truth be called true?
18. The insufficiency of coherence
19. Coherence as a mediator
20.  Roles of empirical coherence
21. What about the truth of the truth-maker?
22. Objection of the linguistic-cognitive circle
23. Answering the objection of the linguistic-cognitive circle
24. Answering the argument of illusion
25. Answering the argument of science
26. Question: How to warrant a non-mental external content?
27. Answer: A definitional criterion of external reality
28. Proving the existence of the external world
29. Skeptical scenarios
30. Verification and intentionality: Husserl
31. Solving two Husserlian problems
32. Truth and existence again
33. The rule’s structural mirroring of the world
34. The unavoidability of particularizing tropical qualities
35. Synopsis of this book

Epilogue: Discovery of Wine


Niemand weiß noch, wer künftig in jenem Gehäuse wohnen wird und ob am Ende dieser ungeheuren Entwicklung ganz neue Propheten oder eine mächtige Wiedergeburt alter Gedanken und Ideale stehen werden, oder aber – wenn keins von beiden – mechanisierte Versteinerung, mit einer Art von krampfhaftem sich wichtig nehmen verbrämt. Dann allerdings könnte für die “letzten Menschen” dieser Kulturentwicklung das Wort zur Wahrheit werden: “Fachmenschen ohne Geist, Genußmenschen ohne Herz: dies Nichts bildet sich ein, eine nie vorher erreichte Stufe des Menschentums erstiegen zu haben.”
[No one knows who will live in this cage in the future, or whether at the end of this tremendous development entirely new prophets will arise, or there will be a great rebirth of old ideas and ideals, or, if neither, mechanized petrification, embellished with a sort of convulsive self-importance. For the ‘last man’ of this cultural development, it might well be truly said: ‘Specialist without spirit, sensualist without heart; this nullity imagines that it has attained a level of humanity never before achieved.’]
Max Weber


Indem die Besinnung auf das Destruktive des Fortschritts seinen Feinden überlassen bleibt, verliert das blindlings pragmatisierte Denken seinen aufhebenden Charakter, und darum auch die Beziehung auf Wahrheit.
[In that reflection on the destructive aspect of progress is left to its enemies, blindly pragmaticized thought loses its uplifting character and thereby also its relation to truth.]
Theodor Adorno & Max Horkheimer

Making empty is the result of making small.
Malcolm Bull

Science (mainly applied science) rises, while culture (artistic, religious, philosophical) falls. Whereas culture was once a source of values, today science and technology have made cultural values seem superfluous.
  The critical theory of society has offered some explanations for this, drawing on Max Weber’s basic idea of the ‘disenchantment of the world’ (Entzauberung der Welt). According to him, history is marked by a long and inevitable process in which a scientific-technological society, characterized by increasing rationality and burocracy, gradually replaces the values, traditions and emotions of older forms of social thinking and acting. As a result, instrumental reason tends to prevail over valuing reason, promoting mass culture and furthering science and technology at the expense of the old aesthetic, mystical and humanistic culture, without having sufficient resources to fill the void left behind.
  Under the pressure of the social framework resulting from this disenchantment of the world, we should not wonder that a kind of philosophy prevails that all too often materially and institutionally mimics the ways particular scientific fields work. In fact, it often mimics sciences in a way that suggests the way much of continental philosophy has mimicked literary forms, that is, counterfeiting the most proper forms of philosophical argumentation with the effect of losing much of its relation to truth. In other words, we are assisting a process of ‘disenchantment of philosophy’: an enterprise endangered by incoherence, as far as philosophy centrally pertains to an old cultural conjectural, comprehensive, argumentative endeavor, which cannot be reduced particular sciences.
  We can feel this tension in the praxis: by taking into account only the discussions of recent years, one might pretend that philosophy is going through the same linear development as science, only to find itself some time later in a foreseeable cul-de-sac. But this inevitably segmented philosophy of the ‘last novelty’ made for ‘immediate consumption’ by and for specialists and related scientists no longer seems, as in the tradition, to be an independent conjectural undertaking making balanced use of whatever new scientific knowledge can serve its purposes. More often, it seems a busy handmaiden of science suffering from loss of identity and self-esteem: particularized proto-scientific guesswork, atomized conjectural endeavor that does not look beyond its own narrow interests and scarcely touches the central philosophical problems inherited from the tradition, or touches them in a way that is deformed by their own particularizing perspective. They forget that in its most central issues philosophy should absorve science instead of being absorbed by science.
  In pointing to this, I am far from embracing Manichaeism. I am not claiming that for science to exert great influence on philosophy is inevitably specious and unfruitful. Often particularized philosophy plays a role in furthering the development of particular sciences. Moreover, there are felicitous cases, like the rapid proliferation of theories of consciousness over the last four decades, which serves as a striking example of fruitful philosophical work very closely associated with the development of empirical science that has deepened the field of investigation – and this is only one example among others.
  Nevertheless, it is important to remember that this same intellectual movement can easily become an ideologically motivated agenda if it tempts the theoretical philosopher to import new knowledge from particular sciences – formal or empirical – in ways that cause him to lose sight of the vast and plural scope of the philosophical landscape. A possible consequence of this is what some have aptly labeled expansionist scientism: an effort to forcibly reduce some wide domain of philosophy to the scope of investigative strategies and views derived from a more or less established particular science. In order to achieve this aim, the particular (formal or empirical) scientific field must be expanded in order to answer questions belonging to some central domain of philosophy, using a reductionist strategy that under­estimates philosophy’s encompassing and multifaceted character. An earlier example of expansionist scientism was in my view Pythagoreanism, which tried to find answers to the problems of life using the new achieved science of numbers and their applications. The price one must pay for this may be that persistent, distinctive philosophical difficulties that cannot be accommodated within the new particularizing model must be minimized, if not quietly swept under the rug.
  A chief inconsistency of scientism arises from the fact that while sciences are in various ways all particular, philosophy is most properly ‘holistic’: As Wittgenstein once wrote, the difficult of philosophy is its problems are so interconnected that it is impossible to solve any one philosophical problem without first having solved all the others. Insofar as his claim is true, it means that a persistent difficulty of the central philosophical problems is that we need a proper grasp of the whole to be able to evaluate and answer them properly. Indeed, this is what can make philosophy so unbearably complex and multifarious. And the lack of this kind of comprehensiveness is what can make fragmented contemporary analytic philosophy often appear like a headless turkey running around aimlessly. Nonetheless, taking account of parts as belonging to a whole, trying to see things sub specie totius, is what the great systems of classical philosophy – such as those of Aristotle, Kant and Hegel – strove to achieve, even if paying a price that we are now better able to appreciate as unavoidably high in terms of misleading and aporetic speculation. Anyway, it would be too easy to conclude that true comprehensiveness is no longer a fundamental desideratum of philosophy (Wittgenstein was well aware of this when he called for more ‘Übersichtlichkeit’).
  A main reason for the narrowness and fragmentation of much of our present linguistic-analytical philosophy can be explained as follows. The new Anglo-American philosophy – from W. V-O. Quine to Donald Davidson, and from Saul Kripke to Hilary Putnam and Timothy Williamson – has challenged a great variety of inherited commonsensical starting points and challenged them in often undeniably insightful and imaginative ways, although in my view with ultimately unsustainable results. Because of this, a large part of theoretical philosophy has increasingly lost touch with its intuitive commonsensical grounding in the way things prima facie seem to be and for the most part really are.
  Take, for instance, the concept of meaning: the word ‘meaning’ was challenged by Quine as too vague a noise to be reasonably investigated. But an approach is inevitably limited if it, moved by insufficient arguments, starts from a kind of positivist reductionist perspective that denies or ignores commonsense certainties, like the obvious fact that meanings exist. Indeed, using this strategy of skeptically questioning all kinds of deeply ingrained truisms, scientistically oriented philosophers have sawed off the branches they were sitting on. The reason for this is that the result of the adopted strategy couldn’t be other than replacing true comprehensiveness with a superficializing positivistic fragmentation of inevitably misleadingly-grounded philosophical concerns, which ends by plunging philosophy into what has Scott Soames unwittingly called the ‘age of specialization.’
  This fragmentation can be regarded as dividing to conquer, I admit; but it may also be a matter of dividing to subjugate; and what is here to be subjugated is more often the philosophical intellect. Indeed, by focusing too much on the trees, we may lose sight of the philosophical forest and thereby even of where the trees are and how to compare them. Without the well-reasoned assumption of some deep common­sensical truisms, no proper descriptive metaphysics, to use P. F. Strawson’s expression, remains possible. And without this, the only path left for originality in philosophy of language, after rigorous training in techniques of argumentation, may turn out to be the use of new formalistic pyrotechnics of unknown value. This would have the end-effect of blocking the paths of inquiry, disarming adequate philosophical analysis and increasing the risk that the whole enterprise will degenerate into a sort of scholastic, fragmented, vacuous intellectual Glasperlenspiel.
  It may be that practitioners of reductive scientistic philosophy are aware of the problem, but they have found plausible excuses for neglecting to deal with it. Some have suggested that any attempt to do philosophy on a comprehensive level would not suffice to meet the present standards of scholarly adequacy demanded by the academic community. But in saying this they forget that philosophy does not need to be pursued too close on the heels of new advances in the sciences, which are continually producing and handing down new authoritative developments. Philosophy in itself still remains to a great extent an autonomous cultural enterprise: it is inherently conjectural and dependent on indispensable metaphorical elements intrinsic to its pursuit of comprehensiveness (Aristotle, calling his first philosophy ‘the searched science’ was well-aware of this). Indeed, most of philosophy remains a relatively free cultural enterprise with a right to controlled speculation, experimentation and even transgression, though most properly done in the pursuit of truth.
  Others have concluded that today it is impossible to develop a truly encompassing theoretical philosophy. For them this kind of philosophy cannot succeed because of the difficulties imposed by the overwhelming amount of information required, putting the task far beyond the cognitive capacity of individual human minds. We are – to borrow Colin McGinn’s original metaphor – cognitively closed to finding decisive solutions for the great traditional problems of philosophy: In our efforts to do ambitious comprehensive philosophy, we are like chimps trying to develop the theory of relativity. Just as they lack sufficient mental capacity to solve the problems of relativistic mechanics, we lack sufficient mental capacity to develop comprehensive philosophy and will therefore never succeed! Hence, if we wish to make progress, we should shift our efforts to easier tasks...
  This last answer seems specious and borders on defeatism. The very ability to initiate the discussion of broadly-inclusive philosophy suggests that we might also be able to accomplish our task. As Wittgenstein once wrote, if we are able to pose an appropriate proper question, it is because we are also in principle able to find its answer. In contrast to human thinkers, one indication that chimps could never develop a theory of relativity is that they are unable to even pose questions such as what would happen if they could move at the speed of light. Moreover, even if the total amount of scientific knowledge available to us has increased immensely, it may well be that the amount of really essential information needed to answer any given question is sufficiently limited for us to grasp and apply. As Bertrand Russell once theorized, very often the science needed to do philosophy can be limited to very general findings. Furthermore, not all philosophical approaches need to be taken into account, since they are often superimposed or displaced. The main difficulty may reside in the circumstances, strategies and authenticity of attempts, in limits on the context of discovery, rather than in the sheer impossibility of progress. In any case, it is a fact that in recent years, true comprehen­siveness has almost disappeared in the philosophy of linguistic analysis. However, my guess is that the main reason isn’t impossibility in principle, but rather loss of the proper cultural soil in which a more comprehensive philosophy could flourish.
  In this book, I begin by arguing that more fruitful soil can be found if we start with a better reasoned and more affirmative appreciation of commonsense truisms, combined with a more pluralistic approach, always prepared to incorporate the relevant (formal and empirical) results of science. Perhaps it is precisely against the unwanted return of a broader pluralistic approach that much of the mainstream of our present philosophy of language secretly struggle. This is often obscured by some sort of dense, nearly scholastic scientistic atmosphere, so thick that habituated practitioners barely notice it surrounding them. The intellectual climate sometimes recalls the Middle Ages, when philosophy was allowed, providing it left unchallenged established religious dogmas. I even entertain the suspicion that in some quarters the attempt to advance any plausible comprehensive philosophy of language against the institutional power of reductive scientism runs the risk of being ideologically discouraged as a project and silenced as a fact.
  Ernst Tugendhat, who (together with Jürgen Habermas) attempted with considerable success to develop comprehensive philosophy in the seventies, has recently seemed to be hoisting the white flag and conceding that the heyday of philosophy is past. The problem is in my view aggravated because we live in a time of widespread cultural indifference, as I noticed at the beginning, heavily influenced by a steady almost exponential development of science and technology that minimizes the role of valuing reason. Though quite indispensable from the viewpoint of instrumental reason, our scientifically shaped age tends to impose a compart­mental­ized form of pragmatic alienation on philosophical research that works against more broadly oriented attempts to understand reality.
  In the present book, I insist on swimming against the current. My main task here – a risky one – is to establish grounds for a more comprehensive philosophy of meaning and reference, while arguing against some main reductionist-scientistic approaches that are blocking the most available paths of inquiry. Hence, it is an attempt to restore its deserved integrity to the analytic philosophy of language, without offending either common sense or science; an effort to give a balanced, systematic and sufficiently plausible overview of meaning and the mechanisms of reference, using bridges laboriously constructed between certain summits of philosophical thought. In this way, I hope to realize something of the old philosophical ambition of a comprehensive synthesis, insofar as this still sounds like a reasonable undertaking.
Paris, 2017

sábado, 16 de setembro de 2017


Advanced draft for the book Philosophical Semantics to be published by CSP.

- III -

Philosophers constantly see the method of science before their eyes and are irresistibly tempted to ask and answer questions the way science does. This tendency is the real source of metaphysics, and leads the philosopher into complete darkness.
Go the bloody hard way.
Im Anfang war die Tat.
[In the beginning was the deed.]
My aim in this chapter is not so much to interpret Wittgenstein, as to reconstruct and sometimes develop his insights on meaning in a way that shows more coherence and relevance than it may seem to at first sight. What I search for here is what in his own terminology could be called a surveillable representation (übersichtliche Darstellung) of the grammar of the concept-word ‘meaning,’ particularly in regard to representative language. Before beginning, I would like to offer my views on something we could call the ‘semantic-cognitive link.’

1. Semantic-cognitive link
In this book, I support the most common viewpoint concerning the referential mechanism, according to which referential expressions can only refer because of some intermediary link able to associate them with their reference. This view originated in classical antiquity. In my understanding, this link has a semantic-cognitive nature, in the sense that it can always be considered from two contrasting perspectives: semantic and cognitive.[1] From a cognitive or psychological perspective, the link is usually called an idea, representation, intention, conception, thought, belief and cognition (Aristotle and Locke are models of semanticists who have adopted this perspective). From a semantic perspective, the link is more often called sense, meaning, use, application, intension, connotation, concept, informative content, belief-content, content of thought, proposition, criteria, criterial rule, verificational rule, meaning-rule (the Stoics, Frege and Husserl are models of semanticists of this last persuasion).
  At this point, an old question arises: What is the appropriate link? Which set of terms should be included or excluded? Should we exclude psychological terms, so as not to contaminate semantics with empirical contingency? Or should we abandon a possible commitment to questionable abstract semantic entities, exchanging them for the more feasible concreteness of the psychological, the only thing really able to justify mental causality? Should we read an ambiguous work like the Critique of Pure Reason from a semantic or from a psychological perspective?
  Traditionally, philosophers have dealt with this problem by assuming that one of these two alternatives must be correct. Nonetheless, this is the real mistake. They have assumed that these two alternatives are exclusive. I see this assumption as a false dilemma, generating useless philosophical confusion. The psychological and semantic perspectives should be seen not as mutually exclusive alternatives, but as complementary and at the bottom inseparable.
  In my view, the source of the illusion that these two perspectives are irreconcilable lies in the fact that the abstract character of the semantic perspective seems to be committed to some form of realism (Platonist or in a sense Aristotelian) about universals. In contrast, the cognitivist perspective seems committed to some kind of nominalism or particularism attached to the contingency of the psychological subject. Since these ontological commitments are incompatible, the two alternatives also seem incompatible.
  However, when we perceive that these ontological commitments could be avoided, it becomes easy to conclude that the intermediary link between words and things can be dealt with in these two apparently contradictory ways without a real conflict. In order to reach this conclusion, we must realize that when we consider the intermediate link from a semantic perspective, we are not necessarily committed to the appeal to the kind of abstract entities assumed by realism. What we are doing is leaving out of consideration the inescapable fact that meaning can only exist insofar as it is spatio-temporally embodied in some specific psychological subject.
  Trying to clarify the complementarity that I am suggesting. We can consider the intermediate link as both:

(a)  a cognitive link, consisting of semantic elements that must be spatio-temporally realized as ephemeral cognitions experienced in specific psychological individuals;
(b) a semantic link, which is referred to as the same semantic elements considered in abstraction from their spatio-temporal realization as cognitions going on in some specific psychological subject in a specific time and space, but not in abstraction from any spatio-temporal instantiation in a selected particular psychological subject. So considered, the semantic link can be distributed among an indeterminate number of cognitive subjects, even ones not immediately concerned, which does not make it de-psychologized or disembodied (cf. Appendix to this chapter).

In other words: the proposed abstraction cannot be achieved in a sense where the semantic link is considered as somehow transcending the realm of specific psychological and physical subjects, since it always requires some form of cognitive spatio-temporal intentional embodiment in order to be an object of consideration. In fact, the word ‘abstraction’ means here simply leaving out of consideration the natural association between a meaning and this or that specific psychophysical individual who instantiates the meaning, and focusing on the signs that can convey this meaning, insofar as they can be understood by some other psychological interpreter. This is the only way to make a semantic-cognitive link semantically independent of its instantiation in ephemeral cognitive subjects.
  A very simple example illustrates my point. When I recognize a patch of vermilion of cinnabar (a precisely characterized shade of color), it is because the patch I see matches a memory image of vermilion that I have stored in my long-term memory from earlier experiences. Now, when I speak of a general concept of vermilion of cinnabar, I intend to show that I am speaking not only of this image, which may become conscious in my mind, but also of any other qualitatively identical[2] image of this color that may become conscious in any other mind.[3]
  In other words, contrary to the idea that our semantic link is a type that is a unique abstract Platonic entity, what I am proposing is that we conceive the semantic link in the sense of an arbitrarily chosen model, ideally, as any token that stands for any other token that is qualitatively identical to it.[4] In short, we can define a semantic link as:

A semantic link X = any occurrence of X arbitrarily chosen to serve as a model for any other occurrence of some X that is qualitatively identical to the model.

Since all these possible occurrences must be psychological (and certainly also physical), we do not need to transcend the domain of the psycho-physical in order to reach the abstract semantic domain. Moreover, we do not need to have an instantiation of the semantic type in any privileged chosen psychological particular. What we really need is for at least one psychological particular, no matter which, to embody the semantic cognition. But this condition, as we will see later, can easily be accommodated in our commonsense ontological framework supplied by the particularized properties called tropes.
  We can strengthen this compromise solution, if we note that even some sub-items of (a) and (b) show an approximate correspondence to each other. Thus:

(i)                the psychological word ‘idea’ has meaning proximity to the semantic words ‘sense’ or ‘meaning,’ as well as to ‘concept’;
(ii)              the psychological word ‘representation’ has some meaning proximity to the semantic phrase ‘criterial rule’;
(iii)            the psychological phrase ‘mental image’ has meaning proximity to the semantic phrase ‘criterial configuration’;
(iv)            the psychological word ‘belief’ has meaning proximity to the semantic phrase ‘belief-content.’
(v)              the psychological phrase ‘occurrence of thought’ has meaning proximity to the semantic terms ‘proposition’ and ‘content of thought.’

2. Why reference cannot be meaning
When we consider the semantic link, words that more easily come to mind are ‘sense’ and ‘meaning’ (generally used as synonyms), here restricted to cognitive meaning or informational content. However, what is sense or meaning? Perhaps the simplest answer is what might be called semantic referentialism, a doctrine that in its crudest form holds that the meaning of a linguistic expression is its own reference. This conception either denies the existence of a semantic link between word and object or minimizes its importance. Wittgenstein described this way of understanding meaning at the beginning of his Philosophical Investigations, where he commented on the so-called ‘Augustinian conception of language’:

These words, it seems to me, give us a particular picture of the essence of human language. It is this: individual words in language name objects – sentences are combinations of such names. – In this picture of language we find the roots of the following idea: Every word has a meaning. This meaning is correlated with the word. It is the object for which the word stands. (Wittgenstein 1984c, part I, sec. 1)

Wittgenstein’s aim in this passage was to object to semantic referentialism, a theory championed by him in his classical Tractatus Logico-Philosophicus. According to his version of semantic referentialism, when completely analyzed, language proves to be composed of atomic propositions constituted by atomic names whose meanings would be the simple and indestructible objects necessarily referred to by them.[5]
  Semantic referentialism is not devoid of intuitive appeal. After all, it is usual to explain the meaning of a concrete substantive by pointing to objects that exemplify what it means. In our childhood, we learned what the word ‘chair’ means because adults showed us examples of this artifact. And we learn the name of a particular person when this person introduces himself to us with her name. Moreover, we learn what a word means or does not mean respectively through positive and negative examples of its application. All this seems to make credible the idea that meaning may be the object actually referred to. This view has at least an almost palpable simplicity: ‘Here is the name “Fido,” there is the dog that is its meaning.’[6]
  However, there are strong well-known arguments against this naive view of meaning. The most obvious is that you cannot predicate of a meaning what you predicate of an object: if a pickpocket steals your wallet, you do not say that the meaning of your wallet was stolen, and if you say that Abraham Lincoln was assassinated you do not intend to say that the meaning of his name was assassinated.
  Another argument is that many natural terms have the same reference, while their senses or meanings are obviously different: the singular terms ‘Socrates’ and ‘the husband of Xantippe’ point to the same person, although they clearly have different meanings. And it is worth noting that the opposite seems to be the case with general terms: the predicate ‘...is fast’ in the statement ‘Bucephalus is fast’ allegedly refers to a particularized property of Alexander’s horse Bucephalus; and the same predicate ‘…is fast’ in the sentence ‘Silver is fast’ allegedly refers to a particularized property of another horse, Silver. Although the speed of Bucephalus is numerically different from the speed of Silver, in both sentences the word ‘fast’ preserves precisely the same meaning.
  The most decisive well-known argument against the referentialist view of meaning, however, is the most obvious: it concerns the fact that even when a referential expression has no reference, it does not lose its meaning. The singular term ‘Eldorado’ and the general term ‘phlogiston’ do not have any reference, but by no means do they lack a meaning.
  For a long time, semantic referentialism has been criticized by natural language philosophers as based on a primitive and misleading understanding of mechanisms of reference. As Searle noted, it is ‘a good illustration of the original sin of all metaphysics, the attempt to read real or alleged features of language into the real world’ (1969: 164). He saw in its adoption a major source of pseudo-problems, although some proponents of the metaphysics of reference have more recently tried to reassert it (e.g., Salmon 1993).

3. Failure of Russell’s atomistic referentialism
Well aware of difficulties like those presented above, Bertrand Russell tried to defend semantic referentialism in a minimalist fashion, taking into account only alleged atomic elements of language and the world. It is instructive to consider his attempt. For Russell, the meaning of at least some foundational terms – called by him logically proper names – would have their objects of reference serving as their proper meanings. This could be the case, perhaps, with the word ‘red.’ After all, as he noted, a blind man is unable to learn the meaning of red, since he is unable to see the color (Russell 1994: 194-5; 201-2).[7]
  However, it is untenable that the meaning of any word can be given by its reference tout court. Changing his example a little, suppose that someone demonstratively applies the word ‘vermilion’ to an occurrence of vermilion of cinnabar, which is a shade of red that in practice the human eye cannot further subdivide (a simpler candidate for ‘simple’ than Russell’s red color, since it does not need to include gradations). Could such an occurrence be the meaning? There is an obvious reason to think that an occurrence of vermilion could not be its meaning: the absence of any identity criteria. When we consider the occurrence of vermilion, it will always be different for each new experience. This is true if the vermilion is physically considered as an externally given spatio-temporal property, or phenomenally considered as an appearance, a sense-datum, as Russell preferred. Indeed, if the meaning of ‘vermilion’ is nothing but a detected occurrence irrespectively of its relation to other occurrences of vermilion, then each new occurrence of vermilion should be a new and distinct meaning – an intolerable conclusion!
  Russell must have seen this problem, for he found a way to defend his view against it. However, as we will see, it was at the cost of becoming entangled in even worse difficulties. He suggested that the object-meaning of a logically proper name would be something immediately accessible – such as sense-data picked out by pronouns like ‘this’ or ‘that’ – only as long as we keep these sense-data present in our consciousness… This means that the meaning also lasts only as long as our personal experience of a word’s object of application! (Russell 1994: 201, 203) However, this is a desperate answer, as clearly it leads to solipsism.[8] What criteria of correction could we apply to fix this ‘meaning,’ in order to know in what cases the word ‘vermilion’ can be reapplied to another occurrence of the sense-data that would at least qualitatively be the same sense-data? Moreover, how could these logical proper names have the intended foundational role in a language? How could we insert this fugitive meaning of a proper name in our common language – a language composed of words whose meanings are permanently shared by their speakers?
  We need to acknowledge that in our language, to know the meaning of a word like ‘vermilion’ presupposes at least the ability to recognize an occurrence of vermilion as being precisely similar to other occurrences of vermilion. But this acknowledgement is not included in the idea that the meaning of a word is nothing more than the occurrence of its reference. The concept of a word’s meaning essentially requires that we should be able to unify its different applications to the same referent, which is not possible according to Russell’s account.
  It is true that if the meaning of a word like ‘vermilion’ were the vermilion-type – understood as an abstract entity common to all occurrences (tokens) – we would be able to solve the difficulty pointed out above. But this solution might commit us to accepting some form of Platonic realism, raising justified suspicion of an unintelligible reification of the type in a topos atopos. Alternatively, one would need to consider the vermilion-type as being a certain set of occurrences of sense-data that are precisely similar to each other. This reduces the danger of realism, but does not eliminate it, since sets are often seen as abstract entities, and if they are not, then they need some limiting intention. In addition, sets may be larger or smaller depending on how many members they have, while the meaning of the word ‘vermilion’ has no proper magnitude, neither increasing nor decreasing. Even the resources able to open sets would not be helpful, since open sets are abstract constructs and not what is effectively given.
  The most feasible alternative seems to be that we consider the meaning of ‘vermilion’ as some occurrence of vermilion that we are using as a model. This could be either a sense-datum or some particularized property in the outside world, able if necessary to be arbitrarily replaced by another like it or any other occurrence that is precisely similar to this model. Thus, if I recognize what is currently being offered as an occurrence of vermilion, it may be because I realize that this occurrence is qualitatively similar to others that were previously given to me as being those of vermilion. This relies on a model whose copy I have stored in my memory, giving me an awareness of it as a color qualitatively identical to colors I have previously experienced. Thus, recalling the various experienced occurrences of vermilion {V1, V2... Vn} and the model Vm recalled by my memory, I can say that {V1 = Vm, V2 = Vm... Vn = Vm} and, therefore, that {V1 = Vm = V2}, etc. And I can do this without resorting to any Platonic entity or to any multiplication of identities of identities or even to the concept of an intentionally defined set – problems often thought to burden particularistic strategies for handling universals.
  What this view amounts to is that what we could call the referential meaning of the word ‘vermilion’ must be identified with a referential connection (a true relation of remembered similarity). This referential connection is a rule that relates cognitive experiences of occurrences of a color to occurrences of color that we in some way use as models, in order to produce an awareness of what is experienced as being precisely similar vermilion colors in each case. Moreover, this internal semantic cognition is produced in association with ‘vermilion,’ a concept-word for such entities. In this way, both a reference and its name turn out to be in principle interpersonally accessible, once the qualitative identity between occurrences associated with the same word allows for interpersonal accessibility and for the kind of practical implicit agreement necessary to create a linguistic convention, even if in itself the semantic cognition isn’t, as a matter of fact, interpersonally accessible.[9] We should also point out that the semantic rule that uses recollections of models to identify any new instance of vermilion is independent of this or that particular occurrence of vermilion, for it only relates to instantiations of possible occurrences that can satisfy it. This view is the one I believe to be workable.
  However, this view has a price: we see on reflection that by adopting it we have already left behind the referentialist conception of meaning. Even to establish a meaning as simple as that expressed by the word ‘vermilion of cinnabar’ we must appeal to something that is more than a rough object of reference and is independent of it, namely, a semantic rule.
  Even if Russell’s semantic referentialism is unsustainable, there is a lesson to be learned from discussing it. Our last suggestion salvages an important idea derived from his semantic referentialism, namely, the idea that the existence of an object of reference is necessary for the names of objects taken as simple in the context of a linguistic practice. We understand the phrase ‘simple object’ as inevitably having a non-absolute sense (Wittgenstein 1984c, I, sec. 45-48) and restrict it to a non-decomposable entity in the framework of some linguistic practice. This seems to be the case with the sense-datum of vermilion of cinnabar as a trope (a spatio-temporally particularized property). The positive conclusion is that for such ‘simple names’ to acquire meaning they need to have reference.
  This is why, in an important sense, a blind man cannot learn the meaning of the word ‘red.’ Since the color red is in a sense simple[10] and knowledge of it is based on acquaintance, and since the blind cannot have this sensory experience, a blind man cannot learn and apply the conventional criterial rule for the shared referential meaning of the word ‘red.’ At least in the case of this subrogate of a logically proper name restricted to a certain linguistic practice, the existence of some object of reference is indispensable. But this obviously does not lead to the idea that a word’s reference is its meaning. What it means is only that in basic cases a given object of reference is indispensable for the formation of the semantic rule whereby a word acquires its referential semantic function.

4. Meaning as a function of use
We shall now move on to a second candidate for the semantic link: use or application. Wittgenstein has privileged this candidate, suggesting that the meaning of a linguistic expression is its use (Gebrauch) or application (Verwendung). As he wrote in a famous passage of Philosophical Investigations:

You can, for a large class of cases of use of the word ‘meaning’ – if not for all cases of its use –, explain it like this: the meaning of a word is its use in a language. (Wittgenstein 1984c, part I, sec. 43)

This suggestion applies to both words and sentences. It clearly applies to (a) what has been called directive meaning: the illocutionary forces of expressions, which establish kinds of interaction between speaker and hearer in speech acts and can be made explicit, particularly by so-called performative verbs like ‘I order,’ ‘I promise,’ ‘I quit’… Directive meaning, together with (b) expressive meaning, which aims to express internal psychological states, though also considered by Wittgenstein, are two kinds of meaning without much importance for us here. The focus of our investigation is the kind of meaning able to link our linguistic expressions with the world, something that may be called (c) referential meaning.
  My concern here, as was clear right from the start, is the content of declarative sentences, which is the kind of referential meaning we call cognitive, epistemic, informative, descriptive or factual, able to link language with the world and to be endowed with truth-value (Aristotle’s logos apophantikós). Such epistemic, informative or descriptive contents should be of major philosophical importance, because by being able to relate language with the world, they should have epistemological and ontological imports.
  However, the identification of meaning with use doesn’t apply so easily to the cognitive and referential meanings of our sentences and terms. Consider, for example, a declarative sentence like ‘The tide is high.’ It is easy to imagine an illocutionary use for this sentence, such as warning or informing. However, by doing this we would revert to meaning as force. In his theory of speech acts John Searle has distinguished in all utterances the necessary form F(p), where (explicitly or not) F expresses an illocutionary force and p (explicitly or not) expresses a propositional content (1983: 6); no speech act makes real sense without the combination of these two elements. Anyway, if we wish to approach use with cognitive meaning, with and without force we must attend to the use of p, which is not the easiest thing to do.
  The only way of approaching pure referential and cognitive meaning with an appeal to use consists in producing an acceptable extension of the concept of use. This is possible. Consider first the cognitive meaning of p as p without judicative and assertive force. We can isolate cognitive meaning from force employing the Fregean device of expressing a sentences’ content only as being regarded, depriving it of any assertive force. We can do this by making a sentence like ‘The dog has run away’ the subordinate clause of ‘It is possible that the dog has run away.’ The spelling of the complementary sentence ‘…that the dog has run away’, expressing epistemic content, even if not asserted – could also be seen as a use. And use could also be seen in this case as the linguistic expression of the mental construction of the verification rule constitutive of the sense of the subordinate clause as conceivably (though not as really) applicable.
  But we can also try to approach use to the cognitive meaning involved in the whole act of communication by means of which a speaker intends to share with a hearer his awareness of a real or possible fact. For instance: when a speaker says ‘The tide is high,’ the use may be (i) the utterance in which a propositional content (cognitive meaning) is expressed, added to (ii) the assertive force as an external expression of the judicative force. Here the speaker intends to communicatively reproduce the same judgment (the same propositional content plus its judicative force) in hearers’ minds. In an extended way, this is also use: this is use as communication of the judication of a cognitive meaning, the last being what I suppose to be a verification rule applied to a real fact (Cf. Chapters IV and V of this book).
  But what about the hearer’s understanding of a statement? The hearer is not using phonetic shapes in his understanding of its meaning. In order to maintain the view that even in this case meaning can be viewed as use, we need to resort here to a bolder extension of the word ‘use.’ It seems possible to say that we use expressions referentially or not, simply by thinking them. When a hearer really thinks the tide is high, it is possible to say that he actually uses this sentence in an epistemic mode by thinking it. Thus, if Paul understands the sentence ‘The tide is high’, or if Anne comes to believe that ‘the dog has run away,’ with or without using words, Paul is repeating and Anne is reproducing these judgments of these respective contents internally, that is, they are applying the verification rules of these sentences in thought. In normal communication, the use that a hearer gives to heard words by understanding them should consist in conceiving the construction of verification rules with their identification and ascription rules in a way similar to what the speaker should do when using words to convey cognitive meaning. My conclusion is that not only the cognitive meaning as the speaker’s thought, but also the hearer’s thought, could be viewed as internalized cognitive uses, with or without the addition of judicative force, which could also be seen as an internalized form of assertive force. Finally, if Plato was right that discursive thought is ‘a silent dialogue of the soul with itself,’ we can generalize this process of internalization and consider any cognitive act associated with language as a form of use, even without being associated with communicative action.[11] We can call this the cognitive use of an expression, of which judicative and assertive forces are dispensable complementary elements.
  It is easy to object to the relevance of the proposed extensions of the meaning of the word ‘use’ that I am employing in order to save the understanding of meaning as a function of use. Though they are not wrong or confusing, they can be considered too cumbersome to be required. However, as will become clear, the reason why Wittgenstein identified meaning with use was a pragmatic advantage, namely, that of locating meaning in its most proper place from the start: in normal linguistic praxis, in the concrete speech-act situation, even in the mental practice of thinking with words. This enables us to individuate the meaning of an expression where it exercises its proper function, so that in this way we achieve the highest level of interpersonal corrigibility, with a minimal amount of distortion and exclusion.
  This is what Wittgenstein’s identification of meaning with use is all about: It allows us to individuate meanings in the natural contexts of their existence, while in doing philosophy we are too easily prone to decontextualize meanings, excerpting and distorting them, in order to develop insights that can be highly illusory. In this sense the maxim that meaning is a function of use can help us in practicing what Wittgenstein called philosophy as therapy, which aims to untie the knots of thought tied by philosophers, insofar as it brings our words back from their metaphysical holidays to their daily chores (Wittgenstein 1984c, part I, sec 116).

5. Meaning as a kind of rule
A more basic difficulty arises when we perceive that the identification of meaning with use cannot be one of meaning and episodic use tout court, namely, a mere spatio-temporal occurrence (token) of a linguistic expression. This isn’t possible, because each occurrence differs from others in its spatio-temporal location. If it were the case, each new occurrence would be a new meaning, which would result in a semantic catastrophe by making the number of meanings of any linguistic expression unlimited.
  There is, however, a more reasonable alternative. We can understand the words ‘use’ (Gebrauch) or ‘application’ (Verwendung) as a way of use (Gebrauchsweise) or a way of application (Verwendungsweise), since the same word can be used many times in the same way. But what is the way of use? Well, it doesn’t seem to be anything other than ‘something of-the-type-of-a-rule’ (etwas Regelartiges) that determines episodic uses. Wittgenstein himself came to that conclusion in an important, though less well known passage of his last work, On Certainty:

The meaning of a word is its mode of application (Art der Verwendung) ... Hence, there is a correspondence between the concepts of ‘meaning’ and ‘rule.’ (Wittgenstein 1984a, sec. 61-62)

In fact, to use a word meaningfully is to use it in accordance with its mode or way of use or application, it is to use it correctly, and to use an expression correctly, in the right way, is to use it in accordance with those rules that give it its meaning. By analogy, we can say that we use a screwdriver according to its way of use when we use it correctly, according to a rule, turning it clockwise in order to tighten a screw. Consider the following examples of ways of use based on the Linguee online dictionary, which gives examples and translations of common phrases:

Way of Use: Apply several times to the skin and rub in for several minutes with a circular motion, until completely absorbed.
Way of Use: To color and cover up grey hair, we recommend 20 ml. 6% of a cream oxidizing agent in the proportion of 1 + 1.
Way of Use: Never dispense any pharmaceutical product without a prescription detailing way of use, site, withdrawal periods and other relevant information signed by a physician.

Of course, here ‘way of use’ means rules or sequences or combinations of rules for correctly using things. Now we see clearly that meaning can only be identified with use in the sense of ‘something of-the-type-of-a-rule’ determining episodic uses. And what holds in general for a word’s use also holds here for epistemic or referential use.
  In fact, the identification between meaningfulness and rule is more primitive. Consider the following two signs: ‘OO’ and ‘Oà.’ The second seems to us ‘more meaningful,’ since we have the tendency to link it with a rule pointing in a particular direction. Rules are the ultimate intrinsic source of meaningfulness.

6. Meaning as combinations of rules
However, why does Wittgenstein prefer to say that meaning is determined by rules? Why can’t the meaning of our linguistic expressions be identified with rules simpliciter?
In my view, at least part of the answer was also approached by him with his analogy between language and calculation. (Wittgenstein 1984f: 168; 1982: 96-97). This understanding is reinforced by the many otherwise unjustified considerations in his Brown Book of how complex sequences of rules could be followed in relatively simple language-games, understood as systems of rules. In use, linguistic expressions normally involve calculations, which should be understood as nothing more than combinations of conventional rules. And the cognitive meanings that these expressions have can consist essentially in combinations of more or less implicit, automatized semantic conventions, knowledge of which speakers tacitly share.
  Arithmetic can serve as an illustration. If the meaning of a mathematical proposition is constituted by its proof, considering that proof is a combination of rules, this meaning is also a combination of rules. Some people can do the multiplication ‘120 x 30 = 3,600,’ for instance, by combining three rules, first multiplying 100 by 30, then multiplying 30 by 20, and finally adding the results 3,000 and 600 to get the result 3,600. The meaning, understood as the cognitive content of multiplying ‘120 x 30 = 3,600,’ would be given by this and other methods of calculation. Together they should amount to essentially the same general signification, insofar as they proceed in different but complementary ways, i.e., beginning at the same starting points and reaching the same result, in some cases by direct application of a single rule.
  We see that what we called ‘something of-the-type-of-a-rule’ can be understood as possible combinations of rules that starting from some initial conditions bring us to some result. The cognitive meaning of a linguistic expression must also be the same as (i) a specific semantic-cognitive rule or (ii) one or more combinations of semantic-cognitive rules that determine a correct episodic use of the rules – which could be called a rule-complex (Regelkomplex). And the cognitive meaning of a linguistic expression is a rule or possible rule-complex that when applied or satisfied brings about a cognition of some state of affairs. – In this book, I normally use ‘rule’ in a broad sense that includes combinations of rules or rule-complexes. This is ultimately a justified extension of the term ‘rule,’ since combinations of rules that produce the same results do the same job as rules. Although irreducible to shared conventions, such combinations can still be seen as conventionally grounded, since they are constituted by elementary rules, namely, ones usually established by convention. Thus, when someone says, as Wittgenstein sometimes does, that meaning is determined by rules, what can be reasonably understood by this is that cognitive meaning may be the application of some rule-complex enabling us to reach a cognitive effect, and nothing more.
  Since we are interested in the problem of reference, the meaning that will be considered will be a content – cognitive, informative, epistemic or referential – that is, something reducible to semantic-cognitive rules responsible for our linguistic awareness of what can be objectively given, which are also criterial rules. So, we are dealing with cognitive-criterial rules responsible for the epistemic or referential significance of declarative sentences. Criteria are, in Wittgenstein’s own terms, ‘what confers to our words their ordinary meanings,’ (1958: 57). As I understand him, semantic-cognitive rules are based on criteria or criterial configurations, which are conditions generated by rules, hence parts of them, and hence part of their meaning-giving function. On the other hand, criteria (having process-product ambiguity) must also be those cognitively independent conditions that once given satisfy such criterial conditions, making us realize that something is the case. Using Wittgenstein’s own example, if someone says ‘It’s raining’ and this statement is true, this involves applying a criterial rule, a rule which requires that certain conditions must be given – say, drops of water falling from the sky – so that a cognition follows – say, awareness that it’s raining (2001: 28). And this resulting awareness, the cognition, could be understood, as already suggested at the end of the first chapter, as the availability to the system of what results from what we may consider as definitely satisfied criterial conditions.
  However, if an analysis of the appeal to use leads us to cognitive reference-rules, why appeal to use? Why not just start with an investigation of these rules and their combinations? The answer was already given. Language is primarily an instrument of action, and meaning, cognitive or not, is there mainly to facilitate action. Moreover, semantic rules are not abstract objects in any realist sense; they only exist when they are applied. Therefore, attention to correct use helps us to individuate meaning and to find the real cognitive-criterial rules or combinations of rules that must of necessity be applied in order to confer meaning.
  We can further elucidate what is at stake by appealing to a metaphor: when a post office delivers a letter, the envelope gives general indications as to the addressee’s state, city, and locality. These general indications can be compared with the grammatical meaning of a sentence. Although necessary, they are insufficient. Too many other addressees live in the same country or city, just as too many different sentences have the same grammatical structure or meaning. To reduce this vagueness, mail carriers also need the name of the street, the building or house number and if applicable the addressee’s apartment number. Without singularizing details, it is impossible to deliver mail to its proper destination. The same holds for cognitive meaning. What is decisive is the way of applying our expressions in the given context – not only the concrete, but also the whole discursive context, including even the context we find in philosophical texts. What an appeal to use does is to lead us to semantic details necessary to find what really matters. In other words: the more general traits of an expression’s way of use are less relevant in the sense that they are common to many other expressions and for this reason are not able to individuate meanings. What matters at most are the more specific traits of meaning: ways of use. These are traits that expressions can only gain in the real contexts where they are applied. Consequently, these can only be completely explored in linguistic praxis. For this reason, it is so important to explicitly consider occasions of use. These can be responsible for subtle semantic variations that an expression can have in different concrete discursive contexts. As we will see, consideration of such subtle semantic variations is of particular importance for correcting or criticizing errors in usage, since this enables us to correct misconceptions arising from philosophical attempts to use words beyond the limits of meaningful language. Particularly elaborated philosophical examples of overstepping these limits are those concerning the metaphysics of reference.

7. Meaning and language-games
There is more to be said about meaning as a function of use. The first thing to note is that a linguistic expression only makes sense when used within a system of rules, within a language-game. To explain this we may appeal to a metaphor. We can compare a linguistic expression with a chess piece, and its use with a move in playing chess. When we move a chess piece, the meaning of the move is minimally given by the rule that governs the piece’s move. What the move fundamentally means will depend on the game situation. It will be given by the contextually determined tactic, by the calculation of possible combinations of rules in anticipation of possible moves by the opponent and responses that could be made.
  Something not very dissimilar occurs with linguistic use. The linguistic rules governing what Wittgenstein called ‘superficial grammar’ could be compared to the rules for moving chess pieces. But grammatical rules – even those of logical grammar – may not be what really matters. Often what is essential are rules or rule-complexes belonging to what he called ‘deep grammar’ (1984c I, sec. 668). These may have more resemblance to semantic rules like those we exemplified before (for the proper name ‘Aristotle’ and the concept-word ‘chair’). Their combination would justify moves that suggest chess players’ tactical calculations, which is particularly clear when we consider dialogical speech.
  To give an example, one knows that the sentence ‘Caesar visited Calpurnia’ is grammatically correct, and one may even know that its logical form is aRb. But this will be of no help if one does not know who Caesar and Calpurnia were, where and when they lived, what relationship they had, and cannot even imagine when or why he could have visited her. Superficial grammar (or syntax) gives expression to a grammatical sense that is often the same for semantically different sentences. The rules and combinations of rules that constitute what is meant by a linguistic expression are more flexible, changing in accordance with the concrete and linguistic contexts.
  Furthermore, in a similar way as the rules responsible for a strategic move in chess gain their meaningfulness depending on the changeable context provided by the system of rules that constitutes the game of chess, the rules determining the application of linguistic expressions are able to produce meaningful utterances only when combined in the changeable context furnished by the system of rules constitutive of the language-game.
  What Wittgenstein called a language-game (Sprachspiel) or a linguistic practice (sprachliche Praxis) can be more precisely characterized as a linguistic system of rules that typically includes syntactic, semantic and pragmatic rules that belong to our language.[12] Examples of language-games given by Wittgenstein are:

Giving orders and acting according to them, describing an object by its appearance or measures, informing… speculating about an event, making and testing hypotheses… making up a story, reading… solving a riddle, telling a joke, describing a landscape, acting, asking, thanking, cursing, greeting, praying, etc. (Wittgenstein 1984c, sec, 23)

But he also uses the same idea in a wider sense, pointing to more extended domains of language like:

The language of colors, the language of proper names, or even the important  ‘knowing games’ from On Certainty, like the game of doubt and the languages of history, physics, chemistry and arithmetic. (Costa 1990: 50)

That is: it seems that almost any chunk of our language can be seen as a language-game. Language-games include themselves, one within another, like the case of Cantor’s theory of infinite numbers within the theory of numbers and the language of mathematics, and they can partially overlap one another, as when someone describes a scenario and simultaneously tells a joke, insofar as we remain able to distinguish them (Wittgenstein 1984c, sec. 46-48). Fundamental is that the language-games remain distinguishable at the interpersonal level.
  The concept of language-game or linguistic practice contains the concept of the speech act, systematically studied by J. L. Austin and John Searle, but it is much wider. This is why Wittgenstein was not so mistaken when he wrote that there are countless language-games (1984c I, sec. 23).
  By making the meanings of expressions the result of rule combinations belonging to rule-systems typified by language-games, Wittgenstein was endorsing what was later called semantic molecularism: What we call the meaning of an expression does not depend on the expression in isolation (semantic atomism), nor on its insertion in language as a whole (semantic holism). It depends more essentially on the often variable contexts of the linguistic practice in which it is inserted (a molecular subsystem of language).
  Finally, it is a mistake to believe that meaning is a matter of all or nothing. It is much more reasonable to think that when used according to the rules of a language-game, something of a word’s meaning gradually merges into the group of games to which this game belongs.
  In support of the idea that we use and give meaning to our expressions in language-games, in the Brown Book Wittgenstein described natural language as a great nebula of language-games:

The language of the adult presents itself to our eyes as a massive nebula, natural language, surrounded by more or less defined language-games, which are technical languages. (Wittgenstein 1984e: 122)

Later, in his Philosophical Investigations, he compared it to a great old city:

Our language can be seen as an ancient city: a maze of little streets and squares, of old and new houses, and of houses with additions from various periods; and this surrounded by a multitude of new boroughs, with straight, regular streets and uniform houses. (Wittgenstein 1984c, sec. 18) 

The nebula, the city, begins with what was built in its original center: the practices of ordinary language, expressing our ordinary commonsense wisdom. To this, there come new insights, like those better organized language-games arising with the emergence of new scientific fields. As with games, the great old city can be subdivided in many distinct ways, one part including another, one overlapping another.
  There is a noteworthy relation of dependence here: learning and teaching new scientific practices, even the possibility of their understanding and creation, depends on prior acquisition of more basic language-games governing ordinary life (Ch. II, sec. 5). This coheres with our principle of the primacy of modest common sense: Rejection of its proper assumptions by means of science is a questionable approach, and it would be logically incoherent to reject them as a whole based on science.
  A question that now arises is: in such circumstances, what criteria would we have for identifying meaning variations, or, less ambitiously, what criteria would we have for identifying the language-game in which an expression is used or even misused? Considering that language can be subdivided in multiple and varied ways, it seems that we can apply different criteria to the same linguistic move, insofar as we are able to interpersonally identify and share the criteria we are applying... But in this case, what guides us in choosing a criterion? Is this identification really possible?
  My tentative suggestion is that the identification of a language-game according to the criteria for the use of an expression (term, phrase, sentence), which also establishes its meaning, involves identifying state-contexts created by two factors:

(i)                the relevant factual and linguistic contexts in which the expression is used, together with
(ii)              the speaker’s intention (cognitive or not) in using the word, insofar as this intention is made interpersonally clear, either by spelling or in a tacit way, in the case in which (ii) conflates with (i).

It seems that in the normal case the awareness of these two factors, namely, of the state-context of the words’ application by the speaker is what allows the public identification of the language-game in which he is using a linguistic expression and in this way the relevant semantic-cognitive rules meant by him. On the other hand, it seems that if the hearer correctly identifies the speaker’s state-context – the right given context, possibly complemented by the spoken intention – he identifies the language-game the speaker has in mind and will be able to understand correctly what the speaker means. (A simple case: if I tell my students Aristotle said that friendship is only possible among equals, the context shows everyone that I am playing a game of naming in which I intend to lecture on the famous Greek philosopher and not about some homonym.)

8. Meaning and forms of life
There is a last important concept in the understanding of Wittgenstein’s explanation of meaning. The linguistic practices that form the nebula find their ultimate raison d’être as constituents of what Wittgenstein called a form of life (Lebensform). As he wrote in his few passages on this concept:

…the word ‘language-game’ is used here to emphasize the fact that speaking a language is part of an activity, or of a form of life. (Wittgenstein 1984c, I, sec. 23)
Right or false is what human beings say; and in the language they agree on. This is no agreement in opinions, but in form of life. (Wittgenstein 1984c, I, sec. 241)
What is taken for granted, the given, we could say, are forms of life (Wittgenstein 1984c, II: 572)

He arrived at this foundational idea probably influenced by an article written by the great anthropologist Bronislaw Malinowski, who suggested that in order to learn the language of a primitive people one needs to share life with them in their society (Malinowski 1989).[13] One example used by Malinowski to illustrate this point can be revealing here: when fishermen in the Trobriand Islands use the phrase ‘paddling in a place,’ they mean they are navigating close to an island village. The waters around the islands are so deep that it is not possible to use a pole to propel the canoe, so they need to paddle their boats to reach the village. Only by knowing speakers’ life circumstances can we find the information needed to understand what their expressions mean.
  The relevance of much that Wittgenstein wrote consists in his having seen the importance and comprehensiveness of some ideas. For him the phrase ‘form of life’ means the way of life in a society. More precisely: the complex of regularities that govern the lives of people in a social environment considered in its totality.
  We can compare the idea of a form of life with what is involved in two technical terms introduced by J. R. Searle. These are (a) the network of meanings involved in the determination of an intention, and (b) the background of abilities, skills, dispositions and ways of doing things that are linked with the corresponding network (Searle 1983, Ch. 5). Though including what Searle means by network and background, the concept of form of life is more comprehensive, since even the landscape in which a tribe lives should be comprehended by the concept and may have some influence on the meaning.
  More auspicious is a comparison between the concept of form of life and Husserl’s concept of life-world (Lebenswelt), which for the latter author can be the whole of our shared communal world of human activity (Husserl 1954, Vol. VI: 105 f.), grounding in this way all possible knowledge. The life-world is able to undergo changes. For Husserl, the life-world, which can be subdivided into a multiplicity of different home-worlds (Heimwelten), forms the holistic framework within which all knowledge is acquired, serving therefore as the ultimate foundation of all human cultural endeavors, gradually extending into scientific ones. Furthermore, although there are different life-worlds, they must have grounding commonalities: aspects, like spatio-temporality, materiality, life, birth, death, instincts, hunger, thirst, etc.
  Wittgenstein would probably share this view, at least in its non-theoretical aspects. The comparison shows us something important: we now see that there must be something common in the most basic levels of our different forms of life. For there must be the share of grounding commonalities that serves as a condition that allows us to accommodate ourselves to different forms of life and be able to learn and incorporate other cultures’ languages. What enables us to do this is presumably that we all share a common human nature (a generally uncontroversial assumption).

9. Tying the threads together
We can now summarize. Language appears in Wittgenstein’s philosophy as an immensely complex system of syntactic, semantic and pragmatic rules: a system we can subdivide in many ways into subsystems called languages, linguistic practices and language-games, which are in turn rooted in a wider ground: the life-form made up of regularities that determine the lives of people in social groups. Linguistic practices constituting our natural language originate spontaneously from our form of life and depend upon it. Here again, we see that creating and learning the specialized language-games of science is only possible because of the assumption of more central practices of natural language ultimately entrenched in life-forms. This is also why an inorganic computer will never be able to give meaning to the signs with which it operates: a silicon-based machine is a by-product of a life-form and not a biological agent naturally growing within it.
  We can synthesize our considerations so far in the following formula:

A meaning of an expression X = any episodic use of X made in accordance with the rules of an appropriate linguistic practice (the language-game) rooted in a certain life-form.[14]

This is a characterization of meaning as something that belongs to the praxis of language as it is understood and to our extensions of the concept of use as what is cognitively meant. This assimilation of cognitive meaning to action by means of an extended notion of use as a rule-in-its-application is what makes it unnecessary to hypostasize semantic rules as abstract objects in any Platonist sense. Meaning is what we think of or speak about as being meaningful; and what we think or speak is meaningful insofar as it is correctly used, namely, used in accordance with the meaning-rules of linguistic practices rooted in our life-form.
  This is what I believe we can achieve, based on Wittgenstein’s views, an uncomfortably vague but sufficiently plausible and, I hope, minimally distorted surveillable representation of the grammar of the concept of meaning. This kind of representation is important insofar as it plays a role as a semantic foundation for philosophy as therapy. This is also why a surveillable representation of the grammar of meaning is central to Wittgenstein’s later thought: it is the sustaining core of his philosophy, as much as the doctrine of ideas was the sustaining core of Plato’s philosophy.

10. Criteria and symptoms revisited
Another important distinction that we owe to Wittgenstein, already introduced in the chapter II of this book (sec. 9), is the distinction between criteria and symptoms. Semantic-cognitive rules are criterial rules. Criterial rules are ones based on conditions called criteria. As we have also noted, words like ‘criteria,’ ‘symptoms’ and ‘conditions’ involve process-product ambiguity. Often they mean the internal conditions belonging to the semantic-cognitive rule (criterial rule) that we are able to consider independently of its effective application in the world and hence belong to meaning. But criteria can also mean the cognitively independent external conditions that, once really given, make possible the application of a semantic-cognitive rule. When criteria are understood in this last way, they can be seen as particularized properties or tropes or configurations of them, as we will see. Moreover, as we will also see, as criteria, tropes are understood as necessitating the application of the correspondingly semantic-cognitive criterial rule and, when this rule is the verifiability rule of a statement, they are also what necessitate its truth – what we call its truthmaker.
  There is, as we have also noted, a fundamental difference between criteria and symptoms. Criteria are conventionally grounded conditions that, once accepted as really given, warrant for us the application of a semantic-cognitive rule. Symptoms, on the other hand, are conditions that, once accepted as really given, make the application of a semantic-cognitive rule only more or less probable. A criterion should establish the sufficient conditions for the application of an expression, though not essentially, insofar as criteria for the same rule can be multiple and varied, as our investigation of proper names has shown. Because of this sufficiency, Wittgenstein also called them definitional criteria, since their description is definitory of an expression or at least takes part in its definition. They are primary criteria, while symptoms are also called secondary criteria (cf. Wittgenstein 2001: 28). In this book, I will use the expression ‘secondary criteria’ to qualify those stronger forms of symptoms able to considerably increase the probability of their bearers’ existence.
  One example makes Wittgenstein’s distinction clear: a criterion for the application of the concept-word ‘malaria’ is actually finding a bacterium – plasmodium falciparum – in a patient’s blood. Once we assume that we have found this, by definition we are warranted in saying that in some way the patient has malaria. But if all we find is that the person has cyclically high fever, we have only a symptom of malaria, something that makes it probable that the patient has contracted the disease.
  Insofar as criteria are understood as internal constitutive conditions of the semantic-cognitive rules for the referential use of a conceptual expression, they must belong to its meaning, since these rules (whether effectively applied or only imaginatively regarded in their possible application) are constitutive of meaning. When Wittgenstein wrote that criteria ‘give words their common meanings’ (Wittgenstein 1975: 57), he was referring to criterial rules.
  Finally, criteria play the role of criteria only in the context of the language-games to which they belong. This is the main reason why Wittgenstein says that there can be a grammatical oscillation between criteria and symptoms. With the alternation of linguistic practice, criteria can become symptoms and vice versa (Wittgenstein 1983c, sec. 79, 354). That is: the same condition that works as a criterion in one practice can serve only as a symptom in another practice and vice versa. And similar changes can also occur as a result of the evolution of language, which may change and improve our conventions, often turning criteria into symptoms by replacing them with new conditions.
  The distinction between criteria and symptoms is also important for the critique of language. Philosophers are all too often inclined to treat symptoms as though they were criteria. To give a very simple example: consider peoples’ facial features and physique. These are the physical characteristics by means of which we are able to immediately identify people we know. At first sight, it seems that they are the real criteria for identifying persons – and within some superficial language-games they may work in this way. But in a deep way it is obvious that they aren’t. If a person, as happens in fairy tales, were transformed into a donkey, but continued to behave no differently than before, talking to us and in full possession of his memories, personality, knowledge and abilities, we would be forced to admit that he remained the same person, even though in a different body. This and other similar thought-experiments show that people’s bodily appearances are not primary criteria at all, but only useful symptoms that make their identification very probable in an easy and immediate way. To find the ultimate criteria of personal identity is still today a controversial philosophical problem.[15]

11. Transgressions of the internal limits of language
In the Tractatus, Wittgenstein was interested in ascertaining what David Pears called the external limits of language and its transgressions (1970, Ch. 5). This is relatively easy to spot: a logical contradiction is an external transgression. However, he came to see that most philosophical confusions are caused by the more subtle transgressions of the internal limits of language. These transgressions happen because many of our expressions can be used in different linguistic practices, undergoing in this way more or less subtle changes in meaning. As Wittgenstein wrote, ‘The place of a word in grammar is its meaning’ (1984d, sec. 23), a place that cannot be fixed beforehand, since it may change. Now, when an expression is used simultaneously in different practices, where it should receive a different meaning or meaning-nuance, it turns out to be easier to confuse what we mean with it.
  According to Wittgenstein’s philosophy, we can find two forms of confusion or misleading uses of expressions, which we may call equivocity and hypostasis.[16]
  These two forms of transgression have a striking similarity to the psychoanalytic distinction between the two mechanisms of the primary process (primärer Vorgang), called by Sigmund Freud displacement (Verschiebung) and condensation (Verdichtung). Hence, it is interesting to explain this process here very briefly. According to Freud, our thought can involve two distinct processes: the secondary process (sekundärer Vorgang) and the primary process (primärer Vorgang). The secondary process is the typically conscious process of rational thought, particularly scientific thought. In this process, affective or emotional charges (Besetzungen) are firmly associated with their respective representations (Vorstellungen). The primary process, on the other hand, is found in dreams, neurotic symptoms, humor, artistic creations, religion, and… philosophy! In these cases, emotional charges are not rigidly associated with their respective representations (or thoughts) and can be transferred to different representations, insofar as the latter can easily be associated with the former representations. The primary process is what produces the conscious manifestation of unconscious or pre-conscious thoughts, in the latter case understood as non-repressed and consequently always able to become conscious.
   The two fundamental mechanisms of the primary process, displacement and condensation, are more clearly illuminated in Freud’s Interpretation of Dreams (Freud 1900, Ch. 7).
  Displacement occurs when the emotional charge of a repressed representation is transferred to another representation, which is able to elude censorship and become conscious, thereby releasing its endo-psychic tension into consciousness. We have displacement when representation R1, repressed and therefore unable to become conscious, has its charge transferred to representation R2, able to evade censorship and become conscious. A Freudian example of displacement is the story of a Jewish woman who couldn’t marry the man she loved because he was a Christian. However, she dreamed that she gave him her comb. This is her conscious representation in the dream; but in her unconscious, the repressed representation is the idea of giving herself to him in love. The emotional charge passes from the repressed representation to the innocuous one, which is able to outwit censorship, becoming conscious as a dream. This makes it possible for the charge to be released in the dreamer’s consciousness, diminishing the endo-psychic tension.
  The mechanism of condensation is somewhat different. Here a representation (or group of associated representations) transfers its affective charges to a partial representation belonging to it, which becomes liberated in consciousness. We can represent this by saying that the charges belonging to the representations {R1, R2… Rn} are usually condensed in one of them, say, R2, which enters into consciousness, in this way allowing the release of emotional charges into consciousness. One example of condensation would be a case in which a similar woman dreams that the man she loves forgot his scarf at her home... The scarf is part of the whole representation of the man, and the emotional charges associated with the whole are condensed in this partial representation and released into consciousness.
  It is worth remembering that according to Freud, displacement requires full unconsciousness by being a product of repression, while condensation requires only pre-consciousness (i.e., its representations are potentially but not actually conscious), since it isn’t necessarily a product of repression.
  Now, an investigation of the two mechanisms by which the internal limits of language are transgressed brings into sharper focus the sometimes noted relation between philosophy as therapy and psychoanalysis (e.g., Wisdom 1969), for it shows that philosophical activity is affected not only by a lack of semantic awareness, but also by affirmative unconscious motivations.
  Let us see now how the primary process works in cases of confusion arising from linguistic transgressions of normal uses of expressions. By using an expression equivocally, a philosopher shifts the use of this expression, applying it in a state-context of a linguistic practice B, though following the semantic rules that this expression should have in linguistic practice A. This equivocity amounts to displacement, since the emotional charges associated with the first use are transferred to a new representation. On the other hand – in what we call hypostasis – the philosopher tries to apply an expression that can be used according to the rules of two or more linguistic practices, say, A, B, C, etc. simultaneously in a neutral state-context. It is as if there were a single linguistic practice able to bring together these different uses, adding their emotional charges, when in fact this practice neither exists nor has any justification to be created.
  Philosophical examples of these mechanisms can be complicated and difficult to describe, since philosophers, being masters of deception (and self-deception), construct their spider webs of far more abstract and complex material than ordinary mortals can imagine. Hence, I will consider only two very simple examples.
  For the case of displacement, consider the following skeptical paradox attributed to the Megarian philosopher Stilpo, denying the possibility of predication. For Stilpo, if I say that Socrates is wise, this is a contradiction, because I am denying that Socrates is Socrates. That is: I can say of something that it is what it is, but if I want to say something more than this, I fall into a contradiction, for I am denying that it is what it is… The upshot is that all that we can do is to express the identity of a thing with itself or remain silent.
  We can explain Stilpo’s fallacy as due to a failure to distinguish the ‘is’ of copula (predication) from the ‘is’ of identity. We can distinguish a linguistic practices of type A with its identifying state-contexts – in which the verb ‘to be’ means ‘is the same as’ (e.g., ‘Socrates is Socrates.’) – from linguistic practices of type B with their own identifying state-contexts – in which the verb ‘to be’ is used in as copula (e.g., ‘Socrates is wise.’). However, Stilpo recognizes the verb ‘to be’ as having only one correct use: that which is found in practices of type A. As a result, each time he observes people using the verb ‘to be’ in state-contexts of practice B, he understands their use as following the rule of use that the verb has in practice A – meaning ‘is the same as.’ In this way, he equivocally and systematically displaces the real use from practice A to practice B. Since he sees that in all these state-contexts of practice B he cannot apply the ‘is’ of identity typical of practice A, he falsely concludes that true predication is impossible.
  I will now offer an easy example of hypostasis in philosophy. Consider this suggestion made to me by a philosopher, according to whom the verb ‘to be’ must have a truly primordial sense, which is not only that of copula, but also of identity and of existence together! To justify this, he considered the sentence: ‘To be is to be’ (Sein ist Sein). This sentence says not only that ‘to be’ has the property of being, but also that ‘to be’ is the same as ‘to be,’ and finally that ‘to be’ has the property of existing (of being).
  Against this folie metaphysique, a critique of language will tell us that it is much more plausible to think that what the philosopher seeks with the ‘is’ in the sentence ‘To be is to be,’ although grammatically correct, is semantically only an incoherent mixture of different uses of the verb ‘to be.’ These were created for different practical purposes but attain no justification when mixed together, except the satisfaction of an ad hoc philosophical claim. It is a hypostasis: a condensation arbitrarily mixing three very distinct modes of use – meanings – of the same word in a neutral state-context. These three modes of use belong to three actually distinct practices, say, the identifying practice A, the predicative practice B, and the practice of attributing existence C. In the best case, this is multiple ambiguity; but since the philosopher is claiming to have discovered a way to achieve the primordial sense of Being in an arbitrary way, the diagnostic is of mere incoherence and illusion.
  I offer these explanations because in criticizing the metaphysics of reference, we very often denounce equivocity and hypostasis. Wittgenstein suggested that philosophical maladies have their origins in a ‘craving for generality’; in efforts to achieve generalization without enough fundament, by reductionist means, generally influenced by the greater success of natural science (Wittgenstein 1975: 18). We can now suggest that here as well the frequent case of equivocity may also here work as a compensatory byproduct of repressing some kind of undesirable awareness.
  An additional point is that striving for generalization is inherent in the philosophical endeavor (particularly as revisionary metaphysics) even if it may be ultimately doomed to fail. However, Wittgenstein concedes that the philosophical unavoidable bumps up against the walls of language has the mark of profundity (Wittgenstein 1984c, sec. 111). The reason for this concession is that these confusions, when able to strike us, have the potential to point to relevant issues insofar as they might force us to search for the right way out of the illusions they produce in us. As I intend to show, much of the metaphysics of reference is grounded upon the forms of confusion described above, particularly equivocation (displacement), which makes them the right target for a therapeutic critique of language.

12. The form of semantic-cognitive rules
In an approximate way, we can now expose the general form of a cognitive or criterial semantic rule (basically the identification rule of singular terms, the attributive rule of general terms, and the verification rule of declarative sentences). This rule is constituted, on one hand, by a relation that can be summarized in the sign ‘~>,’ which means either a strong inductive inference (p > 0,5, for empirical knowledge) or a deductive inference (p = 1) for logico-conceptual knowledge). By ‘C’ I mean the criteria to be satisfied and, furthermore, by the result ‘A’ I mean (a usually non-reflexive) meaning-awareness. Here is the basic schema:

C ~> A

This schema of a semantic-cognitive rule is too simplified, for the criteria are usually multiple, varied and staggered in complex procedures. The satisfaction of a (definitional) criterion under the state-context of a certain practice gives place to the occurrence of the meaning-awareness A, which in the case of a statement could be expressed by a declarative sentence. The cognitive content or meaning or sense is the whole procedure of rule-following, including still unverified criteria, insofar as they also belong to the same ramified rule.
  Complementing what was said, there is a second cognitive element associated with the semantic-cognitive rule, which is the awareness of the consequences of the satisfied content – of the rule or rule-complex. That is, what I believe can be explained by theories of consciousness such as those briefly summarized at the end of chapter II. It is, for instance, what has been called the ‘availability of content to reasoning and action’ (Block), the ‘transmission of content for the mind’s global workspace’ (Baars), ‘brain celebrity’ (Dennett), etc. It is the consciousness of a meaningful reference.
  Calling the meaning or cognitive content [{C1 ˅ C2 ˅… ˅ Cn} ~> A], where each criterion is seen as sufficient for the meaning awareness A, and calling E its cognitive effect (like transmission of content to the global workspace of mind), we can summarize a more common form of a semantic-cognitive rule added to its conscious effects as follows:

[{C1 ˅ C2 ˅… ˅ Cn} ~> A] > E
In order to better understand the rule, suppose that C2 is the assumed criterion for the meaning awareness of what can be expressed by the statement ‘Caesar visited Calpurnia.’ The conclusion that Caesar visited Calpurnia is a meaning awareness followed by conscious effects that can be silently thought or spelled out.[17] Now, we can consider two semantically relevant situations:

(a)   When we add informative content to the verbal formulation of A, associating it at least potentially with some conventional procedure from which it results, for instance, C1 ~> A. Then we have semantic-cognitive meaning; the rule is regarded as potentially applicable. This regarding is an imaginary rehearsal of the true application. Here the cognitive meaning, say, the verifiability rule can already be considered. But this does not mean that propositions or thoughts are statically regarded as abstract entities. What is meant is that they are applied in our imagination, even if in a limited way, only felt as potentially applicable in a real situation, with the result that we make ourselves aware of the semantic-cognitive content as a possible occurrence of a rule-in-its-application. This already makes us to a certain extent aware of the foreseeable effects E. Since we are using it as an instrument in a search for possible consequences of its satisfaction, we need not be reflexively aware of the relation A ~> E.
(b)  When a criterion, say, C2, is seen as actually satisfied; then we have the application of the semantic-cognitive rule, which can be symbolized as C2 & [{C1 ˅ C2 ˅… ˅Cn} ~> A] ~> E. This fulfilled A inevitably produces a referential awareness, which could be nothing other than A’s availability for reasoning and action, its transmission to the mind’s global workspace, brain celebrity, etc. given by theories of consciousness, since it is what results from consciousness of a real state of affairs. Here the semantic-cognitive rule is effectively applied. In this case, if as a result we spell a sentence, adding to it a judicative value and we associate this cognitive application of the rule with its spelling, we have an assertion: a statement spelling out a sentence whose content is accepted as true. Notice that what is judged or asserted is the whole content: the verifiability rule along with the satisfaction of its criteria.

It is interesting to note that there is some proximity between our conclusion and inferentialist approaches to meaning. If we say that a content, a semantic-cognitive rule, is available for reasoning and action, we also mean that the content – which is in itself inferential – would be inferentially open to those related contents. This is what I believe can be understood as the cognitive effect of the satisfaction of the semantic-cognitive rule. However, I will not risk mixing this inferential openness proper of the cognitive awareness of content with the real meaning, because this openness is only a consequence of the instantiation of referential or cognitive meaning won through the application of its semantic-cognitive inferential rules.
  The usefulness of these sketched formulations isn’t clear now, but I think that it will gradually justify itself in the course of this book.

13. What is wrong with the private language argument?
I do not believe that there is only one possible interpretation of the so-called private language argument (Wittgenstein 1984c, I, sec. 244-271), a term that isn’t even present in Wittgenstein’s text. There are a variety of more or less interesting interpretative alternatives. In fact, to interpret Wittgenstein is like trying to assemble a jigsaw puzzle, knowing from the start that some pieces will inevitably be left over.
  This isn’t a problem for me, insofar as my aim here is not properly interpretative.[18] What I want is to reconstruct Wittgenstein’s ‘argument’ in a way that makes its consequences as philosophically strong as is reasonably possible. This philosophically strong formulation will be important, because if it is right it means the destruction of all our human subjectivity, not only as it is currently understood, but as it has been understood in all of traditional philosophy (e.g., in the cogito or regarding sense-data). A private language argument with trivial conclusions would be of scant interest.
  I can begin with the contrasting case: public physicalist language. How do we learn to identify and distinguish different types of physical objects? For example: how does a child learn to identify references of the word ‘ball’? This doesn’t happen by means of verbal definitions, but ostensibly: adults point to examples and say things like, ‘This is a ball’ or ‘That isn’t a ball’... and the child eventually learns what types of objects are round balls. But this learning is only confirmed when a new ball is presented and the child shows adults that it is able to re-identify the object as belonging to the ball type. In this case, based on agreement among other speakers of the language regarding correct re-identification, it is possible for everyone (adults and the children) to know that the child has learned the rule for identifying ball-type objects. That is, the only way to know that we have learned a rule is ultimately if our way of application is confirmed by interpersonal checking.
  Consider now what happens when we try to identify internal mental entities of a phenomenal nature. In this case, we cannot do any checking of interpersonal re-identifications. Suppose that a person is expected to learn to identify an internal state, for example, a feeling of pain. Other people cannot teach him to do this, because they cannot know if and when he feels pain or how it feels to him. But let’s suppose that independently of any public language a person decides to point inwardly to some feeling and identifies his feeling through a sign that he himself has invented. Suppose this sign is ‘P’ (for ‘pain’). Imagine now that the next time he feels pain, he says to himself ‘P,’ intending to point to the same internal mental state. In this case he won’t be able to know if he is really pointing to the same phenomenal state that he initially pointed to, because there are no other speakers who can check the correctness of his rule application, i.e., who are able to confirm or refute his identification. As Wittgenstein realized:

‘I impress it on myself’ can only mean: this process brings it about that I will remember the connection correctly in the future. But in this case, I have no criterion of correctness. One would like to say: whatever seems right to me is right. And that only means that here we cannot talk about ‘right.’ (1984 sec. 258)

Where interpersonal correctness criteria cannot be found, we cannot distinguish between following a rule and the mere impression of following a rule. However, this distinction is indispensable, because without it we have no way to construct something that we may effectively call ‘a rule.’
  Since language is a system of rules, the generalization of this result leads us to the radical conclusion that there cannot be a language whose objects of reference are internal phenomenal states. For Wittgenstein the only construable psychological language seems to be the one based on behavioral expressions of internal states, transforming expressions like ‘Ouch!’ into ‘I feel pain.’ Nevertheless, he concedes the existence of these mental states, rejecting behaviorism. This is in my view an incoherent move, since if behaviorism weren’t the case, mental states would be beyond the reach of linguistic rules and therefore cognitively unspeakable and in the end senseless… once he also writes that something about which nothing can be said has as much value as nothing.
  The problem, as Ernst Tugendhat once told me in conversation, is that the private language argument is too counter-intuitive to be correct. The point, however, is to discover where the weakness of the argument lies. In order to find this, we need to make two things clear. The first is that we will probably only stop regarding a rule as a rule if we conclude that it is logically impossible to correct it. A rule does not cease to be a rule just because for some contingent reason it was not in fact interpersonally checked. After all, it is an indisputable fact that many of the rules we follow, for one reason or another, have never been interpersonally checked. I can invent for myself the rule of never eating creamed spinach, and nobody needs to be informed of this rule. There are rules that for merely circumstantial reasons cannot be checked, such as those made by a shipwrecked sailor who is never rescued and consequently lives and eventually dies alone on a remote uninhabited island.
  The objection that could be made to this interpretation is that Wittgenstein’s argument demands that any rule, in order to be a rule, must be publicly checked for correctness, and not just be able to be publicly corrected (correctable). Even if this interpretation were true, it would be utterly uninteresting. For it expresses only an extremely implausible and methodologically anti-Wittgensteinian idea, jeopardizing our commonsense certainty that there are too many rules that we follow that have not yet been checked by others. In fact, if we wish to overstate skepticism, we could also argue that no rule can be applied in situations where it cannot be subjected to simultaneous interpersonal correction – after all, there is no guarantee that in the absence of this control the rule will be correctly interpreted and applied... However, gratuitous forms of skepticism like that are too implausible to persuade us.
  With this in mind, let us now interpret Wittgenstein’s argument as assuming that the rules of a phenomenal language must be logically incorrigible. Let’s suppose that every morning when waking up I unintentionally follow the rule to remind myself of the first sentence of Dante’s Divine Comedy, but that I always immediately forget doing this. Here we are already close to nonsense, and we would reach total nonsense if it could be proved to be logically impossible to know if this happens.
  We conclude that it is the assumed logical incorrigibility of phenomenal language that convinces us of the plausibility of the private language argument: it seems very plausible to assume that a rule that logically cannot be corrected cannot be considered a rule. If the rules of our (supposedly) private phenomenal language are logically incorrigible, it seems that they cannot, ultimately, be distinguished from mere impressions of rules.
  This reconstruction of Wittgenstein’s argument is not only the most interesting and reasonable. It also uncovers what I believe to be an important implicit assumption made by him. Once he noted, for instance, that even though person A’s nervous system could be connected to that of person B, so that A could feel a wasp stinging B’s hand, only the location of pain would be shared, but not the pain itself. This is because pain felt by A would be A’s pain, while pain felt by B would still be B’s pain (Wittgenstein 1975: 54). In his most famous article, surely read by Wittgenstein, Frege noted that if another person could enter our minds to observe a visual representation, the representation he experienced would be his own and not ours (Frege 1892: 30). Such considerations lead us to a dogma generally assumed by earlier Twentieth Century analytical philosophers: the thesis that phenomenal states are logically non-sharable.[19] If this thesis is correct, then interpersonal corrigibility of phenomenal language would be logically impossible, which seems to be a reasonable foundation for the private language argument.
  At this point, all we need to destroy the private language argument’s main foundation is to show that the logical non-shareability of phenomenal states is a false principle. That is, we need to show that although the rules of a phenomenal language have never been interpersonally corrected, they are – contrary to what Wittgenstein and many philosophers assumed – logically corrigible from an interpersonal perspective, this being the hidden flaw that tacitly supports the private language argument.
  It’s hard to imagine a thought-experiment able to prove that phenomenal states are logically shareable. We can begin by making an analogy with computers. Suppose A and B are updated versions of the primitive kind of automata called by Grey Walter machina speculatrix, which fed on light and spent all their time in search of it. Suppose automaton A meets automaton B, and that A is able to read the information content that B has accumulated in its searching. Although automaton A can copy these data first, and only afterwards read them in its own system, so that such ‘contents of experience’ become an unshared part of itself, there is no contradiction in thinking that A can read these ‘contents’ directly in B, as if they were its own, thereby sharing them with automaton B! This would in fact be the simplest and most direct method. Why should we think that in a similar situation we humans would need to be different from machines?
  Perhaps it is even possible to imagine that someday there will be two human beings, A* and B*, who somehow share some functioning of parts of their brains. Suppose that their limbic system is in some way tuned essentially the same, while the neocortical regions of A* and B* remain distinct. Now, it seems conceivable that a mental state of pain that occurs in relevant parts of the same limbic system could be shared by subjects A* and B*, even though their conscious interpretation of pain, made in their distinct neocortical regions, are quantitatively different. If we understand pain as essentially a process occurring in a limbic system, then A* and B* really could share the same pain, demonstrating possible interpersonal checking of the same internal phenomenal state.[20]
  The thought-experiments considered above suggest that it is logically possible to distinguish:

(a)   the subjective interpretation of a phenomenal mental state X
   (b) the phenomenal mental state X in itself.

In fact, this separation seems possible. We know cases of hypnosis where people are led to feel pain even though a source of this pain is absent, or the case of a patient at the dentist who, because he is afraid of treatment, believes he feels pain when he really only feels the sensation of friction…
  Now, if we accept that it is logically possible to separate (a) and (b), then the interpersonal sharing of mental phenomenal states turns out to be logically and probably physically possible as well, which at least in principle makes possible interpersonal checks of identification rules for mental states. In this case, the private language argument fails because the logical unshareability of phenomenal states is a false principle. In this case, the rules of phenomenal language acquire an epistemic status that does not differ from that of the rule I made for myself of never eating creamed spinach; in principle, both rules could be checked. Consequently, we are entitled to assume that what we now believe to be the rules of our phenomenal language may in fact be the actual rules, since they are at least logically susceptible to interpersonal correction.
  Furthermore, we are also entitled to say that the rules for the identification of phenomenal states are highly probable, since this probability is very well confirmed in an indirect way by a multitude of systematically related associations between interpersonally accessible physical phenomena and reports of internal phenomenal occurrences. For example: if wrinkling the forehead is often associated with repeating the statement ‘I feel pain’ when one believes one has a feeling x, wrinkling the forehead indirectly reinforces the probability that when applied the words will really refer to the same feeling – even if only minimally.[21] Our case is not different from the case of concluding, based on a large amount of convincing circumstantial (indirect) evidence, that a certain woman was in fact murdered by Jack the Ripper, though the true identity of this serial killer could never be discovered. Even if no one actually saw the woman being murdered, the details of the murder and all the circumstantial evidence taken together pointing to this very peculiar murder are highly convincing. (cf. Costa 2011, Ch. 5)

14. Concluding remarks
Returning to our initial question about the nature of the intermediate link, we can now see more clearly why and how the intermediate link between words and things can be read in two different complementary modes. These are the psychological mode, which considers some particular cognitive bearer of the link, and the semantic mode, in which particular bearers of a link with their psychological particularities are left aside.[22] That is: cognitive meanings are semantic-cognitive rules that can be considered in their possible or effective application and that when regarded from the viewpoint of their conditions of satisfaction, can be seen as semantic-cognitive criterial rules. As will be made plausible in chapter V, the cognitive meaning of a statement should be nothing but a verifiability rule that really applies when some criterial configuration required by it is adequately satisfied, making the statement true; it being otherwise false.[23]
  Nonetheless, it is important to maintain a clear distinction between the semantic and the psychological aspects of the intermediate link, as philosophers like Frege and Husserl insisted, even if they did it in an unnecessarily misleading way. The semantic aspect is conventionally grounded and grammatically necessary; the psychological aspect is spatio-temporally given, and in its physical particularities contingent. But contrary to what these philosophers have supposed, nothing semantic can really exist outside of cognitive instantiations. Semantic entities are nothing more than conventional structures that exist only when embodied in mental acts, in applications, even if considered in abstraction from their contingent bearers. To assume that semantic entities can exist without any psychological basis is to hypostasize their nature.[24]

Appendix to Chapter III

Trope Theory and the Unbearable Lightness of Being OriginalEla provém da consideração de que na definição da existência do pensamento não entra em questão a mente singular que o tem, nem a pessoa na qual ele ocorre.

Any possible world and, of course, this one, is completely constituted by its tropes.
D. C. Williams

‘Could you show me some properties (qualities, characteristics…) of the things around us?’ Asked in this way, any normal person would surely point to a few nearby objects, naming their properties (qualities, characteristics…), e.g., the redness of this sofa, the hardness of that wall, this property of a shirt of being made of cotton… Many traditional philosophers, however, would say that these things cannot really be properties in the most proper sense of the word. For in this strict sense, properties are abstract entities, universals accessible only to our intellect, not to our senses.
  This comparison suggests that the ontological starting point of traditional ontological realism, particularly in the form of Platonism, is opposed to the ontological starting point of the common people and even of our own modest common sense. Common sense begins by considering as prototypical examples of properties the spatio-temporal properties directly given to us in perceptual experience, only afterwards considering those properties that are in some way derived from perceptual experience. The contemporary ontology that sustains this commonsensical view is called trope theory. Properties are for trope theorists spatio-temporally located entities called ‘concretized properties,’ ‘particularized qualities,’ ‘individual accidents,’ ‘quality-bytes,’ ‘abstract particulars’ or simply ‘tropes.’ According to trope theory, universal properties should follow from the ontological building blocks that are the spatio-temporally particularized properties or p-properties called tropes, and not the other way round.
  One reason for the importance of trope theory resides in the fact that since the development of nominalism already in the Middle Ages, this might turn out to be the only really groundbreaking advance in ontology. Although the concept of trope as a particularized property has been known at least since Aristotle, only in the 1950s did an Australian philosopher named D. C. Williams have the bold idea of assigning tropes metaphysical pride of place as the only fundamental ontological building-blocks of the universe.[25] His central aims were to use the notion of trope to solve (or dissolve) the traditional problem of universals and to explain the nature of concrete particulars. In fact, pure trope-theory is a one-category ontology. Because of this, my hunch is that the theory of tropes is so revolutionarily simple in its fundamentals that it could produce an upheaval in ontology similar to that caused by the introduction of new physicalist theories to solve the mind-body problem in the second half of the twentieth century.
  In what follows, instead of doing the hard work of discussing different versions of trope theory, I will take the easier and more direct route of outlining the view that from our methodological perspective – which gives primacy to established knowledge (modest commonsense plus science) – seems the most plausible.

1. Introducing Tropes
First, what are tropes? Although simple tropes are primitives and as such cannot be intrinsically defined, they can be elucidated as being properties individually located in space and enduring in time, whereby properties are here understood in the ordinary sense of particular properties or p-properties. As such, p-properties can be identified as the empirical designata of predicative expressions. The most obvious tropes – fundamental from a genetic-epistemological perspective – are those accessed by direct perceptual experience, like qualities. Examples of quality-tropes are the yellowness of this sofa, the smell of a particular daisy at a certain time and the snorting of a particular rhino trying to attract a female. Other tropes would be the red color of the Golden Gate Bridge, its weight, hardness, form, height above sea level… These are all what we could call external (third-personally accessible physical) tropes. However, tropes can also be internal; they can be psychological properties, like a feeling of pain, sorrow, love and pleasure and even a whole mind, insofar as not understood as a thinking substance (Williams 1953 I: 17). They can be partly internal and partly external like a belief, an emotion, a purpose, a love affair, an act of contrition or an expression of impudence (called by Williams mixed tropes); and they can be events like a smile, a sneeze, an election, a cold snap, triangles, circles, shapes, a bodily form (Williams 1953 II: 171 f.). We can prove the reality of tropes by considering that they can be removed like the color of a cloth (Campbell 1998: 352) and can be objects of selective attention (Loux 2002: 86): gazing at the ocean, one can alternately concentrate on its color-tropes, the form-tropes of its waves or their sound-tropes. Simple tropes appear in combination with other tropes, and some conglomerates of different kinds of tropes are highly complex and varied, as in the case of dispositional and psychophysical traits. This is the case of Socrates’ psychological character, of biological properties like that of a certain cat being a mammal, of social properties like that of India being a democratic country. If I say that India is a democracy, ‘being a democracy’ is a property-trope dependent of the individual India, though surely a very complex and varied one. In all these cases, the tropes are in variable ways spatio-temporally located.
  Tropes contrast with what I prefer to call individuals: things that are seen as unique, and are referred to by singular terms like ‘this daisy,’ ‘that rhino,’ ‘the Golden Gate Bridge,’ ‘Socrates’ and ‘India’. In the standard case they are what is called ‘material objects’ and, as we will see, nothing but compositions of tropes. However, some compositions of tropes are individuals without being material objects. This is the case of a rainbow, of a cloud in the sky. And there are individuals that are constituted by the absence of tropes, for instance, a certain shadow.
  Moreover, not all tropes are individuals in the considered sense. There are complex tropes like a performance of Beethoven’s Fifth Symphony, which consists of only one set of tropes, of sound-tropes, and can be designated by means of a predicative expression, as in the statement ‘The orchestra has performed the Fifth Symphony.’ Considering that the Fifth Symphony can be performed many times, it is better to consider it a complex trope than an additional individual; moreover, it is dependent on an orchestra (an individual) or something of the kind to be performed. There are property-tropes that not only complex but also varied in the kind of their constituent tropes.
  Finally, one can suggest the existence of indirectly accessible derivative tropes. This would be the case of fundamental physical forces: in order to have a clue about them, we need to begin by experiencing our more modest perceptible quality tropes. This may be so even if from a physical perspective we can ask whether our common tropes are not in a sense grounded on them (cf. Campbell 1990, Ch. 6).
  As particulars, tropes have identity conditions. As such, I propose an ontological condition (a) followed by a linguistic indicator (b):

Tropes are identified by:
(a) Their spatio-temporal existence to the extent that they display continuity over space and time and are amenable to certain direct or (mostly) indirect experiential ways and conditions of access, and
(b) Being linguistically accessible as designated by predicative expressions of singular statements whose nominal terms refer to individuals.

So understood tropes contrast mainly with material objects referred to by means of nominative expressions, particularly proper names.
  The linguistic indicator (b) has a guiding function: as spatio-temporally located properties normally related to individuals, tropes are usually designated by means of predicative expressions. In statements beginning with demonstratives like ‘This is a daisy’ or ‘There is the Golden Gate Bridge’ it is preferable to take the nominal terms (indexicals) ‘there’ and ‘this’ as referring to spatio-temporal regions, as localizing rules for the identification of the daisy and the bridge, which justifies the non-application of the linguistic requirement (b) to its predicates, which are individuals and not tropes. As we already saw, spatio-temporal location is often a complement to the individual’s identification.
  Regarding the ontological condition (a), I have something more to say. Consider the following example: the pair of shoes I am wearing is brown. The right shoe’s property of being brown can be seen as a trope, since it displays continuity and is located on my right shoe, and the left shoe’s property of being brown can be seen as another trope, since it displays continuity and is located on my left shoe. Because these shoes have different spatial locations, we can regard them as displaying two tropes of the color brown. And because the relatively homogeneous continuity of the right shoe’s color, this color can be said to be only one trope – a (located) property. The smoothness of my left shoe is also a trope that has the same location, homogeneity and possibly even the same duration of its brown color. Does this mean that this brown and this smooth are the same trope? No, since they are different kinds of tropes, accessed through different perceptual ways and conditions.
  To the further question of how much my left shoe’s trope of brown can be subdivided, one possible answer would be: into as many unities as we can distinguish. However, since depending on perceptual distance and acuity we can distinguish different amounts, this does not seem to be elucidating (cf. Campbell 1990: 136-7). Because of this, and again drawing on common sense and our natural language, it seems better to say that the unity of a trope – which we can rightly call a property – is better established by the natural limits of its spatio-temporal continuity, and what is considered as being the same, disregarding its possible divisions. Thus, for instance, the whiteness of a wall would be a myriad of tropes if any visible point of whiteness were considered a trope; but considering a trope of whiteness to be a continuous whole, we are not only being economical but also following natural language practice. Indeed, we would rather say that this wall ‘has the property of being white’ than that it has a myriad of punctiform properties of whiteness. The size and form of the wall, on the other hand, also deserve to be called tropes, since they can be spatio-temporally located. And the same could be said about the more complex color, size and forms of a human body. A related question concerns the duration of tropes. How long will my left shoe’s brown trope last? A reasonable answer is: it will probably survive no longer than my left shoe. A trope lasts as long as it remains essentially the same, while maintaining its spatial continuity.
  I mention all these things because hasty considerations can easily give rise to attempts to discredit identity conditions for tropes, for example, by pushing precision beyond its contextually reasonable bounds. The vagueness of our identity conditions for tropes is as much a direct consequence of the way we experience the world as of the way the world is supposed to be under our assumed practices, enabling us to define a  conceptual system with a suitable degree of precision. Moreover, many complex tropes (e.g., social tropes) can be highly dispersed in space and time. This makes their boundaries still less determinate.
  Since tropes are any spatio-temporally situated properties, they are also existent particulars. Because existence – as we will see later in this book – can be seen as the effective applicability of a predicative ascription rule to at least one thing, by asserting existence we assume a need to spatio-temporally locate a trope or a set of tropes. Moreover, tropes are said to have proper existence, though I must disagree with Campbell’s view that their existence is independent (1998: 353). He gives as examples the blue of the sky and the colors of the rainbow; but the blue of the sky depends on the existence of an atmosphere consisting of gases, and the colors of the rainbow depend on the existence of water droplets, both of them constituted by tropes. Tropes do not have an independent, but an interdependent existence.
  Are spatial forms and duration in time tropes? Well, these things cannot be found without being associated with tropes, a shape with a color, a volume with a weight, a duration in time with the continuous existence of some tropes or clusters of tropes... Keith Campbell, disagreeing with D. C. Williams, did not consider forms as tropes because of their dependence upon other tropes (Campbell 1998: 360-361).[26] However, as I noted above, his examples are inadequate; tropes have interdependent existence. If we hold this view, we can see forms and durations as limitations in space and time respectively. They would arise from limitations imposed by standard quality-tropes. Hence, it seems that we could view forms and durations as kinds of tropes – let us call them limiting tropes.
  Another question is whether relations are tropes. Since relations are spatio-temporally located, though often only in a rather vague way, and since relations are designated by means of dyadic or polyadic predicative expressions, it seems that relations are tropes, even if their existence is subsidiary to the existence of their relata. There are different kinds of relations with different strengths and I cannot develop this point here. Particularly distinguished is the causal relation. For instance: ‘The throwing of a stone broke the window.’ As Williams and Campbell have noted, a causal relation should be analyzed as a relation between tropes (1990, Ch. 5.15). The relational predicate ‘x causes y’ is not between the objects stone and window, but between a cause, as the throwing (of a stone), and the effect, as the breaking (of the window). Cause and effect are here events that can be designated by means of predicates (as in ‘The stone was thrown’ and ‘The window was broken’), being therefore tropes according to our identity conditions. Moreover, we call the causal relation internal, since we define an internal relation as a relation that exists as a consequence of the existence of their relata, given adequate conditions. A clearer case of an internal relation is that of strict similarity between two tropes. For instance, ‘The blue of this ocean is like the blue of the sky above it.’ Once these two blues are given, the similarity follows. Moreover, it may not be easy to admit, but the relation of strict similarity is also not just predicatively designated; it is also spatio-temporally located: it is in-between and not out there. Therefore, it should also be classified as a relational trope, even if subsidiary to its relata.
  One objection to the idea that relations are tropes could be that if relations are tropes then the relational trope and its relata must be related by a new relational trope, and so on ad infinitum.[27] I will argue against this objection by first noting that the same problem comes up again in a stronger form in the case of one-place predications. In other words, if a refers to an individual and b refers to another individual, and there is a relation aRb so that this relation produces an infinite regression, then the same should be true of a one-place predication of the form Fa, as in the statement ‘The Earth is round.’ That is, we would need a relation R to relate the object referred to by the nominal term ‘the Earth’ and the trope of roundness designated by the predicate ‘…is round,’ symbolizing it as FRa. Being related to the relata F and a, this relation R would require two new relations ‘FR1RR2a’, and so on ad infinitum. But this seems senseless! The lack of sense becomes clearer when we replace the symbols with words and see that we fail to give any sense to these new relations. It does not make sense to say ‘The Earth is related with its roundness,’ instead of saying ‘The Earth is round.’ Hence, it is better to see the link between subject and predicate as a ‘non-relational tie’ (Strawson 1959, part II, Searle 1969: 113), or as something like the invisible link of a chain, to use Wittgenstein’s metaphor. They are not tropes but pseudo-additions – now in the true sense of the word. Thus, my view is that we do not need to postulate FRa in order to explain Fa.[28] And if this seems obviously true of the monadic links represented by singular predicative sentences, there is no reason not to extend this result to the relations said to produce a regress. After all, relations must be seen as linked with their relata in the same way as non-relational properties are linked with their objects. To see this clearly, consider the following example: (i) ‘Socrates is a friend of Plato.’ Since friendship is a relation, one would be entitled to replace sentence (i) with (ii): ‘Socrates has a relation of friendship with Plato,’ which still says the same thing by being interpreted as specifying that friendship is a relation. But if we try to go ahead, deriving from (ii) the sentence (iii) ‘Socrates relates himself to his relation of friendship, which is itself related to Plato,’ which is an instantiation of aR1RR2b, we again wind up speaking nonsense.

2. Tropes and Universals
The theory of tropes is important because it promises a parsimonious solution for at least two perennial ontological problems: the problem of universals and the problem of concrete individuals.
  I begin with the problem of universals. Linguistically stated, this problem consists in the question of how can we apply the same general term to many different individuals; ontologically stated, it consists in the question of how it is possible that many different individuals can share the same property. Traditional realist philosophers suggested that the only possible solution to this problem is to postulate that a general term refers to a universal understood as an abstract entity (existing ante rem or even in rebus, according to the ‘Platonic’ or the ‘Aristotelian’ version respectively) that in some obscure way can be instantiated in many individuals.
  For the Platonic realist we can think and see that this rose and that strawberry are red because they instantiate or exemplify the idea (universal) of redness (‘red-in-itself’). For Plato the world was real only insofar as it instantiates ideas. This answer was never satisfactorily rescued from unsolvable difficulties.[29] After all, universal properties must be non-empirical abstract objects accessible only to the intellect. This duplicates the world: we have our empirical world and a world with an infinite number of abstract entities whose intelligibility is highly questionable and for which we have no identity criteria. Moreover, the realist is left with unsolvable problems of how to explain the relation between these abstract entities and our cognitive minds. Finally, if you ask a layman where properties are, he will answer by pointing to the blue of the sky, the hardness of a table, the softness of jelly… and not to a Platonic realm.
  This contrast leads us to the suspicion that only a disposition originating from the ideological pressure of some mystical belief could lead to a committed Platonic solution. It exemplifies the consolation of what a Nietzschean philosopher would call a ‘world of beyond’ (the Überwelt). Philosophers are particularly susceptible to this; they are unworldly creatures and it may be a true temptation for some of them to set their minds to see properties in such an idealized way.
  The Aristotelian solution is an attempt to bring Platonic ideas from the heaven of ideas (topos hyperuranios) to the concreteness of the earth. However, this seems an incoherent middle way. For him universals exist in the visible world, so that if there were no world there would be no universal. Now it seems completely impossible to understand how the universal can preserve its unity if its only reality is in being multiply instantiated by entities belonging to the real world.[30]
  Dialectically opposed to realism is nominalism. According to the philosopher Roscelin (XI century), called the originator of nominalism, a universal is a mere flatus vocis (emission of a sound), since a general term has no designatum. Similar views are counter-intuitive, being justly nicknamed ‘ostrich nominalism.’ A more sophisticated form is set-nominalism: a predicative expression designates the set of individuals to which it applies. This is less counter-intuitive than strange. One problem with this view is that predicative expressions with the same extension – like ‘…animals with kidneys’ and ‘…animals with hearts’ – must mean the same thing. One alternative is to suggest that a predicative expression designates the sets of individuals to which the predicative expression applies in all possible worlds (Lewis, 2001: 51). This liberates us from a strong identity of extensions of different general terms because there are possible worlds where some animals with kidneys have no hearts and vice versa, etc. However, it also leads to implausibility, like accepting the reality of merely possible worlds and assuming the existence of unicorns...
  As the solution to the problem of universals by means of realism is too obscure and by means of nominalism is too implausible, trope-theory appears to be the safest lifeboat. To solve the problem of universals by appealing to tropes, we need to introduce the idea of similarity, or resemblance or likeness between tropes, which conceivably could be understood as a kind of relational trope. Philosophers like D. C. Williams (1953 I: 9) and Keith Campbell (1998: 358) saw universals as classes or sets of precisely similar tropes.
  Thus, the universal ‘red’ refers to the set of all tropes of red, which are unified by the fact that these tropes all have the internal relation of being precisely similar, one with the other. For Williams, when we say, ‘This rose is red,’ we mean that this rose has a red trope that belongs to the set of red tropes; and when we say ‘Red is a color,’ we mean that the set of all tropes of red (universal-R) is included in the set of all tropes of color (universal-C).
  However, there are problems with this view. First, there is a problem with the notion of class or set; if we see a set as an abstract object, it seems that we are abandoning the great advantage of trope theory. Second, there is a problem with size: a set can become larger or smaller; but a universal cannot change its size, for it has no size. It does not help the appeal to an open set, since even open sets also have sizes, though unknown or open to variation… Third, we can develop objections of regress concerning precise similarities based on Russell’s criticism of Berkeley’s and Hume’s nominalism. According to Russell, two patches of the same color have a relation of color-likeness that seems to be a universal or abstract idea… It is true that a nominalist can decide to consider applying the same analysis to color-likeness, considering it a particular. But then he will face the following problem:

We may take a standard particular case of colour-likeness, and say that anything else is to be called a colour-likeness if it is exactly like our standard case. It is obvious, however, that such a process leads to an endless regress: we explain the likeness of two terms as consisting in the likeness which their likeness bears to the likeness of two other terms, and such a regress is plainly vicious. (Russell 1994: 111-112)

To offer a more detailed explanation, I begin by assuming that likenesses or strict similarities are also tropes, as I have argued before. It must be what I prefer to call ‘strict similarity,’ because mere similarity or resemblance or likeness lacks transitivity: If trope T1 is only similar to trope T2, and T2 is only similar to T3, then it is possible that T3 is not similar to T1. The solution is to appeal to strict similarity understood as the same as qualitative identity, which is in the case an identity between differently located things (differing from numerical identity as the identity of a thing with itself). Qualitative identity does not need to be perfect: our cars are both yellow, but your car’s color is faded. We must, however, establish a corrigible limit to the differences. Corrigible differences are usually found within the range of a concept’s applicability (e.g., turquoise blue and cobalt blue are both called blue) insofar as we have a correction criterion (e.g., wavelengths between 450 and 495 nanometers).
  Now, according to the kind of reasoning suggested by Russell, in order to construct the set of strictly similar tropes, we need to know that a first trope of identity is like a second trope of identity. But how do we know this? Well, since it cannot be by appealing to the abstract idea of identity, it must be by appealing to another trope of qualitative identity or strict similarity. Since the same question can be posed regarding the strict similarities between these strictly similar tropes, it seems clear that this leads to a kind of pyramidal infinite regress.
  Russell would see this regress as plainly vicious. Even if this is not the case, I see this as a pseudo-problem born from a pseudo-solution. And the reason why I think so is because this is not the real way in which we conceive universality. In fact we can overcome Russell’s objection in a much easier way simply by dispensing with his fixation on classes. The way I propose to build universals only from particulars is inspired by just the kind of treatment that particularist-nominalist philosophers like Berkeley and Hume gave to ideas or impressions in order to ensure their unity.[31] According to this view, we can symbolize as T* any trope that we wish to use as a pattern or model. Then we can define the universal in a disjunctive way as:

Universal (Df.) = A given trope T* or… any further trope T that is strictly similar to T*.

To explain this definition better, we must note that used as a pattern trope, T* in no way needs to remain always the same. On the contrary, one can choose any trope strictly similar to a chosen T* and then use it again as T* in order to make new comparisons. Moreover, what we normally know of T* is some recollection in our memory.[32]
  Accepting this definition, we do not need to use sets of strictly similar tropes or some mereological sum to explain universality, since the definiens covers any trope strictly similar to T*. The problem of size disappears, since the definition does not require us to ask how many tropes are qualitatively identical to T*. When a person utters the sentence ‘This rose is red,’ he means that this rose has a trope of red Tr1 that is identical to some trope of red Tr* taken as a pattern (as retained in the person’s memory) or any other similar trope. When he utters the sentence, ‘Red is a color,’ he means that any trope strictly similar to Tr* is also a Tc* or anything strictly similar to Tc*, as the wider pattern of a color trope. Finally, Russell’s problem also disappears, since we don’t need to compare one identity trope with another, but only the tropes {T1, T2… Tn} individually with some chosen trope T*. Instead of possibly generating an infinite pyramidal regress, the schema will typically take the form {T1 = T*, T2 = T*… Tn = T*}. In other words, as long as all we need to do to get a universal is to compare any trope with a chosen model trope T*, there is no need to compare similarities with similarities generating similarities of similarities. Russell’s problem does not arise because our definition makes universals potentialities instead of actualities.
  Furthermore, we can also construct the universal ‘strict similarity’ requiring that some chosen trope Ts* (trope of strict similarity) is taken as a standard and allowing it to be compared with any other trope of strict similarity strictly similar to Ts*. Our schema will be: {Ts1 = Ts*, Ts2 = Ts*… Tsn = Ts*}, where Ts* can always remain the same. This means that we have second-order strict similarity tropes referred to by the strict similarity signs between Ts1 and Ts*, between Ts2 and Ts*, and so on – call them Tss1, Tss2, etc. Thus, in order to make reference to the universal composed of these strict similarities of strict similarities, we need to appeal to a standard trope of strict similarity of strict similarity Tss*, and it is easy to predict that we can refer to an infinite number of higher-order strict similarity tropes in this way.
  Would this be a vicious regress? I don’t think so. For nothing prevents us from stopping where we wish, insofar as we see no reason for going further – a point that can be understood in terms of explanatory demand. If we do not see any explanatory advantage in going further, we can simply stop where we choose. A similar consequence results from Platonic realism. As H. H. Price noted (1953 Ch. 1): the idea of the ideas constantly used in Plato’s doctrine of ideas is a second-order idea. But Plato stops with the idea of the ideas, not because he must, but simply because there is no explanatory advantage in going further, considering, for instance, the idea of the idea of the ideas. In the same way, we can find no explanatory soundness in going beyond the trope of precise similarities among first-order tropes.[33]
  Finally, it is worth noticing that strict similarity is not a trope like others. To begin with, it is what one could call a dependent trope: it depends on the existence of things considered alike. Color-similarity, for instance, is an internal relation depending on the existence of colors. Campbell suggested that strict similarity is only a supervenient pseudo-addition that does not add any being to what already exists (1990: 37). However, if we take seriously our identifying condition for tropes, the fact of being an internal relation does not make strict similarity a quasi-trope or a non-trope. As already noted, the identity condition for the reality of similarities as tropes is satisfied, even if distinguishing strict similarity from other more primary kinds of tropes. If the condition for the existence of a (simple or complex) trope is its spatio-temporal location, established by the application of its denoting predicative expression, we can argue that similarity is also spatio-temporal, though in a broad way. For example: when I consider the strict similarity between the colors of two shoes I see in a store window, the likeness would be somewhere in this place, which may include myself, but not in a distant place. My home and the Taj Mahal have a color-likeness: both are white. Nevertheless, I can swear that this likeness is situated on the planet Earth and not on the surface of the sun. Moreover, if my home or the Taj Mahal disappears, the color likeness also disappears, which means that the similarity also exists in time. On the other hand, when someone considers similarities between the form of our Milky Way galaxy and the form of the Andromeda galaxy, this coarse grained qualitative identity must have to do with the total distance between them, which is still located. As great as this distance may be, it remains ridiculously minuscule if compared with the immensity of the cosmos.
  Problems for the theory of tropes do not stop here. What about other spatial relations? For example, the Golden Gate Bridge is (on the average) 67 m. above sea level. Certainly, this spatial relation is there and can even be measured. And this relation is located in space and time, enduring as long as the bridge exists and the average sea level does not change. Even if this spatial relation is internal, depending on the existence of its relata, it can be classified as a trope, since it satisfies our identifying condition for tropes as spatio-temporally localizable entities.
  But what about space and time in themselves? Normally we admit that only tropes and space-time exist. Even in realist ontologies, a separate existence of space and time was never questioned. However, could space-time in some way consist of tropes or something derived from tropes? Imagine that all the world’s objects and properties disappeared. Would space and time remain? We have the intuitive tendency to answer in the negative. However, according to a Newtonian theory of absolute time and space, the answer should be in the affirmative: space and time would be individual-like entities. Space would be like a great container with material objects within it and would not cease to exist even if all the matter and energy ceased to exist and disappeared. On the other hand, according to a Leibnizian relational view, space could be constructed by means of relations, which can easily be extended to time. In the latter case, space and time could not exist in themselves, because being constructed of relations they require the existence of the relata (not necessarily material things). Both answers have always been controversial, and the discussion has been intensified by contemporary physics.
  It seems there is a chance of explaining space and time relationally in terms of tropes, if we begin with a modest commonsensical approach (Cf. Waismann 1986). It seems clear that people began to consider space by thinking of relations such as above, under, in front of, behind, inside and outside. We can localize an object x as being twice as far above object y as is object z.’ Time would be initially defined relationally, by means of relations like earlier, present (simultaneous with the act of observation) and later. One can say that event x occurred three times later that event y in relation to event z.’ Moreover, in order to make measurements, the ordinary man appeals to regularities as patterns: a foot to measure distances in feet, a day to measure periods of days… This is how our naïve concepts of space and time work; this is what they mean. The main point here is that all these relations should be tropes, since they are spatio-temporally located. However, since quality-tropes and material objects are spatio-temporally located entities, it seems that we would end in circularity: space and time would be defined as relations of spatio-temporally located properties.
  The answer to the circularity objection in this very modest commonsensical approach could be that space and time are constituted by a network of relations among entities that can be quantitatively compared. For instance, consider the following rough description of the Southern Cross: star c is seen twice as far below the smaller star b than below star a, while stars d and e are seen on opposite sides of b and (approximately) at the same distance from b as a is from b. With a similar approach, any particular spatial relation could be located in the spatial network and because of this be defined as a trope. Likewise, we could locate the terms of these relations as tropes or clusters of tropes (the same holds for time-relations).
  Of course, it is an entirely open question how such rough intuitive notions could be developed and extended in order to comprehend the sophisticated and often controversial theories of contemporary physics. However, this isn’t a primitive approach to be discarded merely on the grounds of any superficial examination.

3. Tropes and Concrete Particulars
The second major problem is that of constructing concrete individuals by means of tropes. For D. C. Williams, a material object is a set or sum of different conjoined tropes (1953: 11 f.). The advantage of this view is that it enables us to abandon the old, obscure concept of substance understood as some hidden substratum of properties. For the trope theorist, the material object turns out to be like an artichoke consisting only of its leaves, which are the tropes.
  The key-concept here is that of compresence (also called concurrence, togetherness, etc.), which can be understood as the sameness or quasi-sameness of the spatio-temporal location of tropes. The concept of compresence can easily be analyzed as composed of two other concepts: co-location and co-temporality. The co-location of tropes is their joint location in a certain part of space, leaving aside when each of them is placed in this part. Thus, two persons who take turns sleeping in the same bed can be said to be co-located in this place. The co-temporality of tropes is their simultaneous existence during the same time-interval. Thus, my friend Magda and I are co-temporal, though not co-located, since we are very distant in space. The compresence of tropes arises only when they are co-located and co-temporal.
  A naïve but instructive objection to the view according to which concrete objects are clusters of tropes is that if it is true, then all predication turns out to be tautological: the utterance ‘This chair is yellow’ would be tautological, because yellow is predicated of a subject that already has the trope yellow as a constituent (Loux 1998: 103). This objection is easy to refute. We just need to distinguish necessary from contingent tropes. As Ernst Tugendhat has reminded us, a material object can be identified by means of an indexical added to a sortal predicate, as in the statement ‘This is a chair’ (1983, Ch. 9).[34] Now, the necessary tropes are those typically specified in the definition of the sortal. Thus, ‘a chair’ is defined as a moveable seat with a backrest, designed to be occupied by only one person at a time. The seat is constituted by one sub-cluster of tropes, the backrest by another, and the conditions that this complex object is moveable and designed to be used by only one person at a time are constituted by dispositional tropes or sequences of tropes that complete the definition. There are also contingent tropes, like those constituting the sub-clusters of armrests or four legs (there are chairs without armrests or without legs); and there are still more casual tropes associated with a chair, like its color, the relation with a person sitting on it, its distance from a table… The concept of a chair is one of an artifact. But we can consider natural kinds in a similar way. Gold is defined as an element with the atomic number 79, a yellow, dense, precious metal. However, its having a determinate atomic number is a necessary trope, though gold does not have to be yellow or even considered a precious metal, since these are contingent tropes.
  Peter Simons gave a helpful answer to the question of the nature of material objects by pointing out that they should not be seen as an unstructured cluster of compresent tropes. A material object is typically made up of a nuclear kernel of necessarily interdependent tropes giving a foundation to an accidental halo of contingent tropes. The halo-tropes can be replaced by tropes of other kinds, but the kernel-tropes cannot (they can be approximated to the objects referred to by Tugendhat’s sortal predicates). A consequence of Simons’ view is that the halo-tropes are specifically founded on the kernel-tropes, while the kernel-tropes only generally found the halo-tropes (1994: 376 f.). Simons admits the possibility of variations: a concrete object formed only by kernel-tropes, etc.
  A very precise definition is difficult, if not impossible. A stone, for instance, is a material object that can be composed of very different materials, having few tropes to individualize it, with the exception of a tight connection of form, hardness, solidity, weight, volume, and color, all of them compresent. However, based on this bunch of properties, often combined with spatio-temporal determinations, we are already able to re-identify the stone as the same one.
  Unhelpfully, compresence and kernel-tropes are still not enough to define material particulars. Socrates’ wisdom is a dispositional property consisting in a complex and varied trope, as it seems. These tropes seem to have compresence, since they are all located where Socrates is. Moreover, they could be designated by a sortal predicate delimiting the spatio-temporal location of Socrates (‘There comes Socrates again with his inconvenient wisdom!’). Finally, they can have a kernel: the ‘peculiar core of inconvenient Socratic wisdom.’ But they are not a material object, not even an individual, insofar as it is said to belong to the individual Socrates and others could in principle share strictly similar qualities of Socratic wisdom. A common rainbow is constituted by co-located and co-temporal tropes of colors and forms – the seven colors of the spectrum – as its kernel, but it is less than a material object. The holographic projection of a teacup also has a proper compresent set of colors and forms. They belong to its kernel. But despite having colors, spatial extension and form, it is no material object.
  One strategy to deal with this problem is to add to the core of compresent tropes some tropes necessary for the identification of our typical material objects like:

 hardness or solidity (measured by resistance to pressure),
 weight (depending of the presence of a gravitational field),
 mobility in space…

This already excludes Socratic wisdom, the rainbow and the holographic projection. But liquids, although they are material entities, do not have a specific form or solidity, unlike a stone, a tree, a table. For example, water takes the form of its container, and water can be added to a given amount of water, increasing its volume. In a frozen state or as water vapor it ceases to be liquid. Resistance to pressure can be lower or higher. The water in a glass is already a material entity and an individual, though not properly a material object, since it lacks definite form, is not solid, and has only limited resistance to pressure. A cloud has a low level of materiality, and its droplets have minimal resistance to pressure; but it has no fixed and necessarily defined form. But what about individuals and supposed material entities like viruses or atoms and the hypothetical strings in string theory?
  My final condition bases itself upon the assumption that our commitment to modest common sense does not exclude science.[35] We can refine the idea of hardness or resistance to pressure by proposing that a necessary trope constitutive of the core of any physical object is a derived trope that physicists call inertial mass. In physics, the inertial mass of a body is broadly defined as its inertial resistance to acceleration when forces are applied to it (an idea accepted in both Newton’s and Einstein’s mechanics[36]). This seems to me the most pertinent characteristic of what we call matter. Energy also has mass, but it isn’t the same as inertial mass.
  I conclude that in an inevitably vague characterization, having some inertial mass, some size… and compresence of its definitional tropes seems to be necessary for singling out a material object. This excludes electromagnetic, gravitational, weak and strong forces, which are better seen as tropes. However, one cannot generalize this result to any individual. Consider the already noted cases of a cloud, a rainbow and a shadow. Consider the case of a crowd or the British Empire. These individuals do not form a material object or a physical body. Unlike material objects, a crowd and the British Empire are composed of tropes that are at least partially grounded on material, not tightly connected physical entities. And historical entities like the Battle of Hastings are in themselves not material objects that existed in the past. They are all complex structures made up of tropes, mental tropes like intentional states depending on material entities to be spatio-temporally located, even if only in a vague way. Since these tropes are independent and unequal and identified by nominal terms, they are particulars (see Ch. IV, sec. 7).
  A more technical difficulty arises from the alleged fact that the idea that particulars are clusters of tropes is vulnerable to a regression argument parallel to the third man argument used against the abstract objects assumed by a Platonist ontological view. Thus, suppose that a concrete particular were constituted only by the tropes T1, T2, and T3. Since the relation of concurrence could not be an abstract entity, it must be a trope. Call this relation Tc. In this case it seems that we need a new concurrence for T1, T2, T3 and Tc, which will be Tc’, and so on infinitely (Daily 1997: 158).
  My proposal against this objection takes a form similar to what realist philosophers have applied in defense of their own abstract properties. Compresence is made up of co-location plus co-temporality, which are spatio-temporal delimitations that remind us of the cases of form and duration. They are sui generis tropes, since they behave somewhat like Platonic ideas with their resistance to self-predication. In other words: although you can meaningfully say that this red is red, and even that this triangle is triangular, you cannot meaningfully say that a concurrence is concurrent (or that a co-location is co-located or that a co-temporality is co-temporal or even that identity is identical). Concurrence is a sui generis non-self-predicating limiting trope, requiring no new trope of concurrence to warrant its own co-location and co-temporality together with other tropes. Strict similarity is also a sui generis non self-predicating trope, because one cannot say of the strict similarity between T1 and T2 that it is strictly similar without falling into nonsense (what would strict similarity be similar to?).

4. Tropes and formal properties
What should we say about formal entities like numbers? Numbers are not seen as consisting of tropes, since they do not seem to be spatio-temporal. However, this isn’t so obvious! The empirical world is made up of countable things. Would the number three exist if the world did not exist? Though this is an odd question, the tendency is to answer in the negative. For an empiricist like Locke, the number belong to the idea of primary qualities (= properties = tropes) together with solidity, shape, size and motion. Using an example of Penelope Maddy, it seems that the ten fingers of my two hands are in some way here (1990: 87). If an insufferable band called ‘The Fevers’ flies from São Paulo to Rio de Janeiro, it seems that the number of their components has also moved. Moreover, it seems that even a thousand grains of wheat scattered in the wind remain spatially and temporally located, though in a diffuse way.
  One can think so without denying Frege’s account of numbers as properties of concepts. The number ten is a property of the concept of the fingers of my two hands, the moveable property of being five is a property of the concept of The Fevers, and the number one thousand is a property of the concept of the grains of wheat scattered in the wind. Moreover, as Frege famously wrote, the attribution of existence is the negation of the number zero. Hence, the concepts of number and existence are related. In fact, it may be possible to consider ‘the property of being a number’ and ‘the property of existing’ as higher-order trope-properties because, like tropes, they are in a vague way spatio-temporally located, though their existence depends on the application or applicability of predicative expressions. And I believe that when I say ‘This is one chair’, ‘these are my hands’, ‘these are my fingers’, the numeral one is located where we find a chair, two hands and ten fingers, as much as their existence, without being confused with the quality tropes constitutive of the chair, the hands and the fingers. Indeed, these numbers and the existence of these things cannot be in outer space or in primeval times or nowhere. These considerations may be valid for applied arithmetic, where numbers (I call them in the case numerals) are used to count empirical objects. After all, we learn numbers by counting material objects: ‘There are two apples and one pear in the basket, totaling three pieces of fruit.’ In this case, the ascription rule of the predicate ‘…fruit in the basket’ was applied to three three distinct objects, attributing physical existence to each of them and showing in the process of counting that it has the higher-order property of being applicable to five different objects.
  In our view (contrasting with Frege) the concept is a rule, which means that the attribution of existence is here the second-order property (or trope) of a first-order conceptual rule (or trope) of being satisfied by at least one thing. In a similar way, a numeral would be the second-order property (or trope) of a first-order conceptual rule (or trope) of in a temporal process of counting being satisfied. For instance, I can say (i) ‘This hat has three corners’, meaning by this that this hat has the second-order property or trope that the first-order identification rule of corner is applicable to the hat three times. Furthermore, this countable property or trope of the numeral three can be analyzed and detached from the object, which can be better represented by a Zermelo’s set. Thus, it seems that instead of (i) I can say (ii) ‘This hat has {{{{}}}}} corners.’
  It is true that Zermelo’s construction (like Von Newmann’s) has the the undesirable property of been one number three among many. This is undesirable insofar as what we are searching for as the number three is what is common to all triads: the universal three. Insofar, the number three must be like Russell’s the set of all sets of the same type. Anyway, even with this deficiency, von Newman’s definition is already quite satisfactory in applied arithmetic, as a way to express a numeral as the trope of the number three exemplified in this or that enumeration.
  But what about the natural number in itself, as considered in pure arithmetic, as in the number 3? Is this, as some have believed, an abstract object like a Platonic universal? Or is this a further Platonist illusion? I think we can derive the universal concept of a number from our concept of numeral, that is, from the higher-order numerical trope picked out through the application of a concept. As we have seen above, numerals could be seen as tropes, since they are originally spatio-temporally located properties of properties determined as resulting from the countability of particular applications of conceptual rules. Consequently, regarding the universal, that is, the number as an ‘universal,’ we can try to define it by again applying our disjunctive model. In this case, it is conceivable that the number two would be a disjunction between a set instantiated by a chosen higher-order trope (pattern/model) of effective application of some conceptual rule (e.g., ‘that bull’s horns,’ ‘this three cornered hat’) or any other strictly similar (equinumerous) set. Thus, calling the numeral one the unity trope formed by the application trope of some ascription rule, we can (using Zermelo’s construction) symbolize zero as the empty set {}, namely, the uncountable trope of the concept of a thing being different from itself, one as the set that contains only the empty set {{}}, namely, the countable trope of application of a concept-word like this chair, two as the set {{{}}}, namely, the countable trope of the application of the conceptual rule expressed by that bull’s horns, three as the set {{{{}}}}, namely, the countable trope of the applicabilities of the conceptual rule of this three cornered hat. As we noticed, this isn’t what is common to all instances of 1, of 2 and of 3, unlike the old Russellian view of a number as the class of all classes of the same kind. But now we have the answer before our eyes! For all that we need to do to get the number as the ‘abstract object,’ or ‘universal’ called the number three, for instance, is to apply to numerals the same procedure we have applied to get universals from our usual tropes. For instance:

Number 3 (Df.) = a model set of tropes {{{{}}}}*, or any further set of tropes that is strictly similar to {{{{}}}}*.

In this sense the number as a universal (or ‘abstract object’) can be defined as:
The higher-property (trope) of being the Zermelo’s set of applications of a conceptual rule taken as model or of any set of tropes strictly similar to the first one.

Note that such a universal or abstract object remains empirical, since it is a higher-order disjunctive property-trope that can be found scattered over the whole spatio-temporal world.
  Assuming a definition like that, we neither stumble over Russell’s set paradox nor are limited to particular instances (Zermelo, Von Newmann) or directly committed to any differentiating concrete feature (Locke). If such an answer proves to be viable, one could conclude that even the abstract world of mathematics is made up of some sort of thin higher-order tropes. Such tropes, like some others, would be situated at the peak of a building whose originating genetic-epistemic foundations are our more feasible perceptually given quality-tropes, so that numerical tropes that can be univocally named in this way are also dispersed over the whole world and able to be meta-predicatively designated. Finally, there is nothing wrong in guessing that logical properties are also susceptible to a similar treatment!
– But are such formal properties not too thin to be tropes? A dependent trope is a thin trope; but a trope that is dependent on other dependent tropes will be still thinner, and formal tropes are simply too thin to be real tropes! However, isn’t it a foolish prejudice to reject tropical properties only because of their thinness?

5. Conclusion
In this section, we have seen how trope theory turns Platonic realism upside down. Much of what I have written here is speculative, awaiting for a great deal of work and refinement. In this short space, I could do no more than offer a sketch of what seems to me the most plausible way to deal with the one category ontology that will play a central role in this book.

[1] This semantic versus cognitive dichotomy can be traced at least as far back as Aristotle. The latter viewed the intermediary link as an affectation of the soul (ton en têi psychêi pathêmáton) or thought (noêmata) – a psychological perspective – while the Stoics, who appealed to ‘what is said’ (lectón) or ‘what is meant’ (semainómenon), associated the intermediary link in some way with language – a semanticist view. (Manetti 1993: 93 ff.)
[2] Qualitative identity is the identity between different things; it is opposed to numerical identity, which is the identity of a thing with itself.
[3] Of course, one could also do the same thing without drawing on color memory: suppose that people carry with them templates of vermilion, so that whenever necessary they compare the patches of color they see with these templates. This shows the importance of some empirically given model, as much as the complementary role of memory.
[4] It is true that this last ‘any’ allows us to infer that there is a class, called the class of all tokens that are qualitatively identical, but that this class does not belong to the definition and does not need to be an object of awareness.
[5] As Wittgenstein wrote in the Tractatus: ‘The name means its object. The object is its meaning.’ (1984g sec. 3.203)
[6] The view was ironized by Gilbert Ryle as the ‘Fido-Fido’ theory of meaning (1957).
[7] As Russell recognizes, logical atomism was first suggested by Wittgenstein, who defended it in a full-fledged way in his Tractatus Logico-Philosophicus.
[8] This kind of difficulty already arises in the last public discussion of Russell’s speech in ‘The Philosophy of Logical Atomism,’ 1994: 203. (For criticisms see Tugendhat 1976: 382 and Kripke 2013: 15-16.)
[9] See my discussion of Wittgenstein’s private language argument at the end of this chapter.
[10] One could object that since there are many different shades of red (one of them being vermilion), red cannot be simple. But with Wittgenstein we can answer that what we call ‘simple’ depends on whatever linguistic system we have adopted: we can use an old linguistic practice with only three basic colors: red, yellow and blue. Here red will be considered simple; and in this case, distinct shades of red will not be taken into account, even if they are perceptually distinguishable. Instead of being qualitatively identical to the pattern, a new red patch must only be sufficiently identical, insofar as it is possible to determine its blurred borders with the other two colors.
[11] Language has not only a communicational function, but also an organizational function, in the sense that we also use it to think, to organize our ideas and our plans of action (Vygotsky). At first sight, the identification of meaning with use doesn’t seem to do justice to its organizational function. But this doesn’t have to be so. It makes sense to say that when I think that the Leaning Tower of Pisa could come crashing down, I am using this name referentially in my mind, in thought, that is, in an internal dialogue with myself.
[12] There are certainly experimental, simplified or artificial language-games that the philosopher invents to make comparisons, but I am interested here in the language games constitutive of our language.
[13] Although Wittgenstein expressly disliked K. Ogden and I. A. Richards’ book ‘The Meaning of Meaning’, he must have appreciated the short supplement of the book written by Malinowski where these ideas are presented.
[14] See (Costa 1995, Ch. 1). The assumption that guides my reconstruction is that Wittgenstein was not making repeated attempts to explain the nature of meaning that always ended in some kind of failure, erratically followed by new attempts, as some interpreters seem to believe. What he did was to develop different, often analogical approximations, each addressing the approximated issues from new perspectives, such suggestions being largely complementary. In this way, it is possible to find enough continuity in Wittgenstein’s semantic conceptions, which began with the Notebooks 1914-1916 and ended with On Certainty.
[15] An outline of what seems to me the most workable solution is given in Costa 2011, Ch. 5.
[16] These two forms were already noted by Anthony Kenny (1973).
[17] C. S. Peirce’s view, according to which all thought is in signs, seems to be wrong, considering that we are surely able to think without using words. But on second thought, we see that it is plausible that in having these non-linguistic thoughts we are using non-linguistic mental signs, like imagistic and emotivist ones.
[18] Although I still believe my interpretation is the most faithful to a central line of Wittgenstein’s thought.
[19] See, for instance, A. J. Ayer 1972: 196.
[20] In fact, I think we are nearer to this result than some might believe. Computational fMRI brain reading is already close to being able to reconstruct mental states (images, intentions, memories), making them interpersonally graspable, also for the person who is having these states: you can see your own mental images (vulgo sense-data) represented on a screen, and others can see your represented images in the same screen. (e.g., Nishimoto 2011) Even if they are not the images (the sense-data) in themselves, the experiment already suggests that your consciousness of these images is detachable from them.

[21]  Against this, Wittgenstein imagines a situation in which when he believes he has the (invisible) particular sensation P the manometer always shows that his blood pressure has increased. This assures a correlation between his subjective thinking he has the feeling P and an increase in his blood pressure; but it does not guarantee that the rise in his blood pressure will be correlated with the same sensation on various different occasions (1984c, sec. 270). Indeed, it does not guarantee that the last correlation will be the same, but we feel that in small measure it increases the probability that P is being correctly correlated with the same feeling. As we normally have a very great interweaving of such correlations, in the end we reach a very high probability of associating the belief that we are having e.g., ‘pain’ with the pain that we really feel.
[22] While semantic theories like that of Davidson fall short of the mark, the Gricean psychological theory of meaning overshoots the mark. H. P. Grice suggests that to display what he calls a non-natural meaning (our semantic-cognitive meaning) of p the speaker must have (i) the intention that the hearer should come to believe that p, (ii) that the hearer should recognize the intention (i) of the speaker, and (iii) that by means of the recognition (ii) the hearer will come to believe that p. However, what Grice thereby analyzes is not the non-natural meaning in itself, but only the standard procedure by which the non-natural meaning is communicated. (cf. Grice 1991).
[23] Note that there are non-referential cognitive rules: we can have rules that relate (a) the empirical data to cognitions, (b) cognitions to other cognitions, and (c) cognitions to actions. But concerning the issue of reference, what matters is the first kind of rule, which is responsible for referential meaning.
[24] As I see it, there is a great variety of ways to make this hypostasis. One of them is to identify sense/meaning with Platonic entities (Frege, Husserl); another (already criticized in the Appendix to Chapter II) is to identify linguistic meaning with something external like essences of things (Putnam); another is to identify meaning with minimum units of reference (Russell); and yet another is the attempt to identify meaning with psychological communicative intentions (Grice).

[25] This groundbreaking work was D. C. Williams’ paper ‘The Elements of Being’ (1953), because he was the first to propose constructing the whole world using only tropes as elementary building blocks. The most relevant attempt at a systematic development of trope theory remains in my view Keith Campbell’s book, Abstract Particulars (1990). Since then, the discussion devoted to this view has grown steadily. For access to the literature, see Anna-Sofia Maurin’s 2013 article in the Stanford Encyclopedia of Philosophy.
[26][26] In his book on tropes, Campbell writes, ‘because boundaries in space need to be drawn rather than revealed it is perhaps best to view individual specimens of each of the shapes as quasi-tropes rather than as genuine tropes.’ (1990: 91) This argument is not very convincing, since a conventionally charged intromission of epistemic subjects is inevitable in any conceptual application.
[27] This objection is to some extent related to Bradley’s argument that reality is an indivisible unity because there can be no ontologically real relations (Cf. Maurin 1992: 134 f.).
[28] In Russian there is no proper verb for the copula. One says something like ‘Me nice’, ‘You angry’… Thus, they seem to be less susceptible to such concerns.
[29] Plato was the first to see some main difficulties of the doctrine in the first part of his dialogue Parmenides. Others were added by Aristotle in the Metaphysics (book VII) and by later critics.
[30] Though by tradition labeled ‘Aristotelian’, this is the most simplistic interpretation. More sophisticated interpretations tend to see Aristotle as identifying his forms (ideas) as ‘this so-and-so,’ the species building the form-substance-essence of the individual (to be distinguished from its matter). According to medieval interpreters, such a form cannot really be a universal; consequently, it is a work of the intellect to abstract the universal from the particular, so that it exists only post rem. (Copleston 1993, vol. I: 306; see also Shields 2007, Ch. 6.6)
[31] In its plain form the insight is clearly expressed by George Berkeley in the following passage: ‘...an idea, that if considered in itself is private, becomes general by being made to represent or be in the place of all other particular ideas of the same type. ... a private line becomes general by being made a sign, so that the name line, which considered absolutely is private, to be a sign is made general.’ (1710, Introduction, section 12.) See also the more sophisticated but also less clear view of David Hume (1738, Book I part 1, section VII).
[32] We can imagine circumstances in which people are unable to retain memories of the color-trope, but bring with them templates with patterns T* of this color-trope, comparing these patterns with any found trope. The templates can have the most varied tonalities of a single color. They may call the possibilities resulting from the comparisons the universal of a color-trope.
[33] See Anna-Sofia Maurin, 2007. As she remarks, in a vicious infinite regress a considered statement (trigger) is dependent on the subsequent steps, while in a virtuous regress the subsequent steps depend on the considered statement, which makes them unnecessary.
[34] Tugendhat defines a sortal as a predicate that has criteria for the spatial delimitation of the object, allowing us to distinguish what does or does not belong to it.
[35] J. L. Austin has objected that terms like ‘material object’, ‘material thing’ and ‘sense-data’ do not originarily belong to our ordinary language (Austin: 1962). Against this we can note that we are only reasonably feeling the gaps let unexpressed by ordinary language (see Ch. II, sec. 6 of this book; see also Grice 1989: 227).
[36] As is well known, the reason why according to relativity theory a body cannot reach the speed of light is that at this speed its mass would become infinite, requiring infinite force to accelerate it.