PHILOSOPHICAL SEMANTICS III: WITTGENSTEIN'S SEMANTICS # (advanced draft)

Retirado de um draft avançado do livro "Philosophical Semantics: Reintegrating Theoretical Philosophy" (CSP 2018) 

Chapter III

Wittgensteinian Semantics

 

 

 

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.

—Wittgenstein

 

Im Anfang war die Tat.

[In the beginning was the deed.]

—Goethe

 

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 we might suppose at first glance.[1] What I am seeking is something that in his own terminology could be called a surveillable representation (übersichtliche Darstellung) of the grammar of the concept-word ‘meaning,’ particularly concerning representative language. Before beginning, I would like to offer my views on something we could call the ‘semantic-cognitive link.’[2]

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. A fundamental point to be considered is that this link can always be seen from two contrasting perspectives: the semantic and the cognitive.[3] From a cognitive or psychological perspective, the link is usually called an idea, representation, intention, conception, thought, belief and cognition (Aristotle and Locke were 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, verifiability rule, meaning-rule (the Stoics, Frege, and Husserl were 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 natural 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 mutually exclusive. I see this assumption as a false dilemma, generating useless philosophical disputes. The psychological and semantic perspectives should be seen not as mutually exclusive alternatives, but as complementary and at the bottom inseparable.

     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 Aristotelianist) about universals. In contrast, the cognitivist perspective seems committed to some kind of nominalism or at least 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 spatiotemporally embodied in specific psycho-physical subjects (or persons).

     In order to clarify the complementarity that I am suggesting, the intermediate link can be considered as both:

 

(a)  a cognitive link, consisting of semantic elements that must be spatiotemporally realized as ephemeral cognitions experienced in specific psycho-physical subjects;

(b) a semantic link, which is referred to as the same semantic elements considered in abstraction from their spatiotemporal realization as cognitions going on in a certain specific psychological subject in a specific time and space, but not in abstraction from any spatiotemporal instantiation in at least one only particular psycho-physical 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 spatiotemporal 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 psycho-physical subject which instantiates the meaning, and focusing on the signs that can convey this meaning, insofar as they can be understood by some other psycho-physical interpreter. This is the only way to make a semantic-cognitive link semantically independent of its instantiation in occasional 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[4] image of this color that may become conscious in mine or any other mind.[5]

     In other words, contrary to the idea that our semantic link is a type that is a unique abstract Platonic or Sub-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.[6] In short, we can define a semantic link X as:

 

A semantic link X (Df.) = 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 psycho-physical subject. What we really need is for at least one psycho-physical subject, 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 those 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 ‘content of thought’ and ‘proposition.’

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. (1984c, part I, sec. 1)

Wittgenstein’s aim in this passage was to object to semantic referentialism, a theory championed by him in his first and only published book, the 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.[7]

     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.’[8]

     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 Julius Caesar was assassinated you do not intend to say that the meaning of his name was assassinated.

     Another argument is that many different 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 (trope) of Alexander’s horse Bucephalus; and the same predicate ‘…is fast’ in the sentence ‘Silver is fast’ allegedly refers to a particularized property (trope) 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 John Searle once noted, semantic referentialism ‘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). This might contain some exaggeration, but it isn’t wrong.[9]

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 (1994: 194-5; 201-2).[10]

     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 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 spatiotemporal property, and also true if it is a phenomenal appearance, a sense-datum, as Russell preferred. Indeed, if the meaning of ‘vermilion’ is nothing but a detected occurrence irrespective 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.[11] 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 other occurrences of the sense-data that would at least qualitatively be the same sense-data? Moreover, how could these logically 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 acknowledgment 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 by means of Russell’s account alone.

     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 or sub-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 here 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 resource to open sets would not be helpful since they 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} I must have a model Vm in my memory. Hence, I can say that V1 = Vm, V2 = Vm... Vn = Vm and, therefore, that V1 = Vm = Vn, etc. 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). Now, 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 qualitatively identical vermilion colors in each case. Moreover, this internal semantic cognition is produced in association with ‘vermilion’: the 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. Indeed, this convention can be created, even if in itself the semantic cognition isn’t, as a matter of fact, interpersonally accessible.[12] 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 kind of solution is the only that seems to be workable.

     However, this solution 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 recovers 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 certain linguistic practice. It is true that we always need to understand the phrase ‘simple object’ as inevitably having a non-absolute sense restricting it to a non-decomposable entity in the framework of some linguistic practice (Wittgenstein 1984c, I, sec. 45-48). And this would be the case with the sense-datum or external property of vermilion of cinnabar as a trope (a spatiotemporally particularized property). The positive conclusion is that for such ‘simple names’ to acquire appropriate 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[13] 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 now move on to a second candidate for the semantic link: use or application. Wittgenstein 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. (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 by so-called performative verbs like ‘I order,’ ‘I promise,’ ‘I quit’… However, directive meaning, together with (b) expressive meaning, which aims to express internal psychological states, though also considered by Wittgenstein, are two kinds of meaning with little relevance for us here. The focus of our research is the kind of meaning able to link our linguistic expressions with the world, something that is sometimes called (c) the referential meaning – the kind of meaning typically  required for the communication of information.

     My concern here, as was clear right from the start, is the semantic 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 semantic content should be of major philosophical importance, because by being able to relate language to the world, it should have epistemological and ontological import.

     However, the identification of meaning with use doesn’t apply so easily to the cognitive or 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 identifying meaning with in such cases 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 as p, which is not the easiest thing to do.

     It is possible to approach pure cognitive or referential meaning with an appeal to use by producing an acceptable extension of the concept of use. Consider first the cognitive meaning of p as p without judicative and assertoric force. We can isolate cognitive meaning from force by employing the Fregean device of expressing a sentence’s content only as being regarded, depriving it of any assertoric 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 cognitive content, even if not asserted – could also be seen as a use. And use could also in this case be considered to be any realization of a phonetic shape of the mental construction of a verifiability rule constitutive of the sense/meaning of the subordinate clause as conceivably (though not as really) applicable – which in fact does not identify use with meaning.

     But we can also try to approach use to the cognitive or referential 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 involve (i) the utterance in which a propositional content (cognitive meaning) is expressed, added to (ii) the assertoric 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 the hearer’s mind. In an extended sense this can also be called use: this is use as communication of the judication of a cognitive meaning, the last being what one might suppose to be a verifiability rule applied to a real-actual fact (Cf. Chapters IV and V of this book). If not the identity, we see the narrowness.

     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 approached to use, we need to resort to a bolder extension of the word. It seems possible to say that we use expressions referentially or not, simply by thinking what we mean when we spell 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 (or interpreting) and Anne is producing the judgments of these respective contents internally, that is, they are applying the supposed verifiability rules of these sentences merely in thought. Hence, in normal communication, the use that a hearer gives to heard words by understanding them could consist in conceiving the construction of verifiability rules with their identification and ascription rules in a way similar to what the speaker should do when using words to convey cognitive meaning. The 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 way of use, with or without the addition of judicative force, which could also be seen as an internalized form of assertoric 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 as a way of use, even without being associated with communicative action.[14] Associating it with language, we might call this the cognitive use of an expression, of which judicative and assertoric forces are only complementary elements.[15]

     It is easy to find objections to the relevance of the proposed extensions of the meaning of the word ‘use’ that I am employing in order to save a supposed identification of use with meaning. Indeed, though they do not seem to be wrong, they can be considered too confusing and cumbersome to justify themselves. However, as will become clear, the real reason why Wittgenstein viewed meaning as a function of use was a different one. It was the pragmatic advantage of locating meaning in its most proper place from the start: in normal linguistic praxis, in the concrete speech-act situation, even in the normal 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 contextual and interpersonal corrigibility, with a minimal amount of distortion and exclusion.

     This is, I believe, 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 related point arises when we perceive that a really appropriate identification of meaning with use cannot be one of meaning and episodic use tout court, namely, a mere spatiotemporal occurrence (token) of a linguistic expression. This isn’t possible, because each occurrence differs from others in its spatiotemporal location. If it were the case, each new occurrence would be a new meaning, which would result in the semantic catastrophe of 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 an abbreviation of way of use (Gebrauchsweise) or 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.’ (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 includes numerous examples of words used in sentences:

 

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 cognitive 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 cannot 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 – what I would call the same rule-complex (Regelkomplex) – insofar as they proceed in different but complementary ways, i.e., beginning at the same starting points and reaching the same final result.

     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 final 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. And the cognitive meaning of a linguistic expression is a rule, combination of rules, or a rule-complex that when applied or satisfied brings about a cognition of some state of affairs. Calling such combinations rules – as I do in the present book – is ultimately a justified extension of the term ‘rule,’ since combinations of rules and a variety of combinations of rules that produce the same final results do the same job as rules. Although irreducible to implicitly 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 combination of rules or some variable combination building a rule-complex enabling us to reach the same cognitive effect, and nothing more.

     Since we are interested in the problem of reference, the meaning that will be considered will be a content – called 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 cognitive 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 these rules, insofar parts of them, and hence part of their meaning-giving function. On the other hand, criteria (having process-product ambiguity) can also be considered those cognitively independent conditions that once given satisfy such dependent or internal criterial conditions produced by the criterial rule, 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 cognitive awareness that it is raining follows (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 criterial conditions definitely accepted as satisfied.

     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, since this is an old philosophical trap (See Appendix to this chapter). If not dispositionally considered, these rules 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 applicable, that is, applied either in reality or in imagination, in order to confer meaning to a fully contextualized linguistic expression.

     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 geographic location (city, state, country, etc.). These general indications can be compared with the grammatical meaning of a sentence and also with its logical analysis. But even if necessary, they are not sufficient. Too many other addressees live in the same country or city or street, just as too many different sentences have the same grammatical or even logical structure. To reduce this vagueness, mail carriers also need the name of the street, the building or house number… Without singularizing details, it can be almost impossible to deliver mail to its proper destination. The same holds for cognitive meaning. It can be decisive to care about the way of applying our expressions in a given context, which can be the whole discursive and practical context, including that of philosophical writings. What an appeal to use does is to lead us to semantic details. The most general traits of an expression’s way of use, though relevant, are common to many other expressions and for this reason in themselves insufficient to individuate meanings. Because of this, the more specific traits of meaning specified in ways of use are also important. And these are traits that expressions can only gain in the real contexts where they are applied. Consequently, these can only be fully explored by surveilling linguistic praxis. This is why it is so important to explicitly consider occasions of use in all their pertinent details. Indeed, the main flaw of many philosophical examples and thought-experiments consists in ignoring apparently irrelevant subtleties. These can be responsible for easily ignored subtle semantic variants that an expression can have in different particular contexts. Consideration of such subtle semantic differences is of particular importance for correcting 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 and meaning.

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 often called a language-game. To explain this we might again 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. But 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 these grammatical rules – even those of logical grammar – may not be what really matters. Often what is essential are rules, rule-combinations and rule-complexes belonging to what he called ‘deep grammar’ (1984c I, sec. 668). These may have more resemblance to semantic-cognitive rules like those we exemplified before (for the proper name ‘Aristotle’ and for 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 ‘Calphurnia urged Caesar to stay at home’ 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 Calphurnia were, where and when they lived, what relationship they had, and cannot even imagine when or why she has warned him to stay at home. Superficial grammar (or syntax) gives expression to a grammatical sense that is often the same for semantically different sentences. But the semantically relevant rules and combinations of rules that constitute what is meant by a linguistic expression are more flexible and might change not only with the sentence, but also in accordance with the particular factual and linguistic-discursive contexts.

     Furthermore, in a similar way as the rules-combinations responsible for a strategic move in chess gain their meaningfulness depending on the changeable state-context provided by the system of rules that constitutes the game of chess. And 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.

     Anyway, a chess metaphor is too liberal, insofar as it does not take account of what Wittgenstein would call the divisions of language. What he called a language-game (Sprachspiel) or a linguistic practice (sprachliche Praxis) is more adequate. A language game can be understood as any linguistic system of rules that typically includes syntactic, semantic and pragmatic rules that belong to our language.[16] 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. (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. (Cf. Costa 1990: 50)

That is: it seems that almost any semiotic chunk of our language, insofar as it is identifiable as such, 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 identifiable 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 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 properly on the often variable state-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 a maze of partially related meaning-rules.

     In support of the idea that we use and give meaning to the expressions of our own language in language-games, in his 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. (1984e: 122)

Later, in his Philosophical Investigations, he compared language 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 is surrounded by a multitude of new boroughs, with straight, regular streets and uniform houses. (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 and one part overlapping another.

     There is a noteworthy relation of dependence here: learning and teaching new scientific and technical practices, even the possibility of their understanding and creation, depends on the prior acquisition of more basic language-games governing ordinary life. This coheres with our principle of the primacy of established knowledge (Ch. II. Sec. 4), which leads us to conclude that rejecting the assumptions of our modest common sense by means of science would be a very questionable approach.

     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 into 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?!

     I believe that an affirmative answer is 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 the shareable meaning of the expression, involves what we could call identifying state-contexts, which are created by two factors:

 

(i)   the relevant factual and linguistic context determining the expression’s use, together with

(ii) the speaker’s intention in using the word, insofar as this intention is made interpersonally clear, either by spelling or in a contextualized tacit way.

 

It seems that in the normal case 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 relevant language-game in which he is using a linguistic expression and in this way, the relevant meaning 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 implying the intention and 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 a teacher told his students that the philosopher who represented the culmination of the philosophical thought of antiquity was called ‘Aristotle,’ the context shows everyone that he was playing a game of naming in which he intended to speak about the famous Greek philosopher and not about someone else with the same name, despite the fact that this game of naming is included in a game of teaching, which is included in the game of public speaking.)

8. Meaning and form 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. (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. (1984c, I, sec. 241)

 

What is taken for granted, the given, we could say, are forms of life (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).[17] 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 a 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 the totality of their social and physical environment.

     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. 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 spatiotemporality, 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 enabling 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 certainly that we all share a fundamentally common human nature and a similar surrounding world.

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, sub-languages and language-games or linguistic practices, 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 manufactured by a life-form and not a biological agent naturally growing within it.

     We can summarize Wittgenstein view on meaning in a formula:

 

The meaning given to an episodic use of the expression X (Df.): the compliance of this use with rules in the context of an appropriate linguistic practice (the language-game) rooted in a form of life.

 

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 the mode of use and 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; and the most relevant meaning-rules are the semantic-cognitive ones, allowing us to represent the world.

     This is what I believe we can achieve, based on Wittgenstein’s semantic views: an uncomfortably vague but sufficiently plausible and, I think, minimally distorted surveillable representation of the deep 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 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 Chapter II of this book (sec. 8), is the distinction between criteria and symptoms. Semantic-cognitive rules are criterial rules. Criterial rules are ones based on conditions called criteria.

     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 properly as given essences, insofar as criteria for the same rule can be often 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 definitional of an expression or at least takes part in its definition. They are primary criteria, while symptoms are also called secondary criteria (Cf. 2001: 28).

     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 the patient has malaria. But if all we find is that the person has a cyclically high fever, we have only a symptom of malaria, perhaps a secondary criterion, something that makes it probable that the patient has contracted the disease.

     Insofar as criteria are also understood as internal constitutive conditions of the semantic-cognitive rules for the referential use of a conceptual expression (Ch. II, sec. 8), 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’ (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 (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 trivial example: consider peoples’ facial and bodily features. 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 if we look more closely, we clearly see 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 more plausible thought-experiments show that people’s facial and bodily appearances are not primary criteria at all, but only symptoms able to make their personal identification probable in an easy and immediate way. To find the ultimate criteria of personal identity is still today a controversial philosophical problem.[18] However, physical appearances will be treated as criteria in the context of some practical language-game, like that of taking attendance in a school class.

11. Transgressions of the internal limits of language

In the Tractatus, Wittgenstein was interested in ascertaining what David Pears has 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 also wrote, ‘The place of a word in grammar is its meaning’ (1984d, sec. 23), a place that cannot be fixed beforehand, since it may circumstantially change. Now, when an expression is used simultaneously in different practices, where it should receive a different meaning or meaning-modulation, it turns out to be easier to confuse what we mean with it.

     In Wittgenstein’s philosophy, we can find two forms of confusion or misleading uses of expressions, which we may call equivocity and hypostasis.[19]

     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 worthwhile to explain this process here very briefly. According to Freud, our thinking 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, in particular, 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 creation, religion, and… philosophy! In all 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 deeply explained in Freud’s Interpretation of Dreams (1900, Ch. VI).

     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 could not 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 was the idea of giving herself to him in love. The emotional charge passes from the repressed representation to the non-threatening one, which is able to outwit censorship, becoming conscious as a dream. This makes it possible for the charge to be released into the dreamer’s consciousness, bringing relief to 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 if the woman had dreamed 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 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 does not exists, and there is no justification to initiate it.

     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 (of predication) from the ‘is’ of identity. We can distinguish a linguistic practice of type A – in which the verb ‘to be’ means ‘is the same as’ (e.g., ‘Socrates is Socrates.’) – from linguistic practices of type B – in which the verb ‘to be’ is used as a copula (e.g., ‘Socrates is wise.’). However, Stilpo recognizes the verb ‘to be’ as having only one correct use: that which is found in state-contexts of type A practices. 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 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 have 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 supposedly neutral state-context. However, 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 an example of multiple ambiguity; but since the philosopher is claiming to have discovered a way to achieve the primordial sense of Being in a factually arbitrary way, the diagnosis 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 sufficient reasons, by reductionist means, usually influenced by the greater success of natural science (1975: 18). We can now suggest that here as well the frequent case of equivocity may also 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 some kind of failure. Wittgenstein concedes that the philosophically unavoidable bumps up against the walls of language have the mark of profundity (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 to avoid 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 the therapeutic critique of language.

12. The form of semantic-cognitive rules

In an approximative way, we can now expose the general form of a cognitive or criterial semantic rule, anticipating what will be considered in more details in the next chapters. 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, by the result ‘A’ I mean the (usually non-reflexive) meaning-awareness regarding the rule’s application and linguistically expressible by a declarative sentence. 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 should give place to a meaning-awareness, a judgment expressible by an assertoric 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 applicability of the rule-combination or rule-complex. I believe this could be explained by theories of consciousness such as those briefly summarized at the end of chapter II. It would be, 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 full consciousness of what the meaning of a declarative sentence represents.

     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 consequences (as the transmission of content to the global workspace of mind), we can summarize a typical common form of a semantic-cognitive rule added to its cognitive effects as follows:

 

[{C1 ˅ C2 ˅… ˅ Cn} ~> A] > E

                                  Semantic-Cognitive Content

                                                                                               

To this, we should add that when the semantic-cognitive rule is the verifiability rule, the cognitive content is the thought-content expressible by a declarative sentence, as the whole summarized in square brackets.

     In order to better understand this representation of a criterial rule, suppose that C2 is assumed as the given criterion for the meaning awareness of what can be expressed by the statement ‘Calphurnia urged Caesar to stay.’ The understanding that Calphurnia urged Caesar to stay at home is a meaning awareness. A regarded application followed by conscious effects E that can be silently thought or spelled out.[20] 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 at least potentially applicable. This act of regarding is an imaginary rehearsal of the true application. Here the cognitive meaning, for instance, e.g., the verifiability rule, is ‘put under consideration.’ But this does not mean that propositions or thoughts are statically regarded as abstract entities – this does not exist! What is meant is that they are known as applicable or even 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 semantic-cognitive content as a possible occurrence of a rule-in-its-concrete-application. This already makes us to a certain extent aware of the foreseeable effects E, once we are using it as an instrument in a search for possible utilitarian consequences.

(b) When a criterion, such as C2, is contrastively seen as actually satisfied; then we have an application of the semantic-cognitive rule, which can be symbolized as C2 & [{C1 ˅ C2 ˅… ˅Cn} ~> A] ~> E. This fulfilled, A inevitably produces a true referential awareness, which should bring about E as 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 really given factual content. Here we say that the semantic-cognitive rule is effectively applied or applicable. In this case, we add to the meaning-awareness A a judicative value, and if we associate this cognitive application of the rule with its spelling, we have an assertion, namely, a statement spelling out a sentence whose content is accepted as true, having as C2 its verifier. 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 will gradually become clear 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 name 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, even if I believe my interpretation is the one most faithful to the central line of Wittgenstein’s thought. 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 as it is currently understood and as it has been understood in the 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 ostensively: 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 child) 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 to confirm our way of application by interpersonal checking.

     Consider now what happens when we try to identify internal mental entities of a phenomenal nature (sensations, emotions). 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, that is, 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.’ (1984c, sec. 244) Nevertheless, he concedes the existence of these mental states, rejecting behaviorism. This is in my view a clearly incoherent move, since under his assumptions real mental states should be beyond the reach of linguistic rules and therefore cognitively inaccessible, not expressible in language and in the end senseless… once he also writes that something about which nothing can be said has as much value as nothing (1984c, sec. 304).

     The problem, as Ernst Tugendhat once noted, is that the private language argument is too counter-intuitive to be correct. The point, however, is to discover where the argument’s weakness 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 be corrected. 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 beyond doubt 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.

     An objection that could be made to this interpretation is this: 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 common sense certainty that there are too many rules that we follow that have not 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 these are too implausible to persuade anyone.

     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 what I have done. 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 definitely 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). Now, this kind of consideration leads to a dogma generally assumed by earlier Twentieth Century analytical philosophers: the thesis that phenomenal states are logically non-shareable.[21] If this thesis is correct, then interpersonal corrigibility of phenomenal language would be logically impossible, which seems to be a reasonable ultimate foundation for the private language argument.

     At this point is understood, all we need, if we wish to destroy the private language argument’s ultimate 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 afterward 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 before selecting relevant data! This would, in fact, be the simplest and most direct method. Why should we think that in an analogous 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 are able to share some functioning of parts of their brains. Suppose that their limbic system is in some way tuned essentially the same, while the cortical regions of A* and B* remain distinct. Now, it seems conceivable that a mental state of pain that occurs in relevant parts of this one and same limbic system could be shared by subjects A* and B*, even though their conscious interpretation of pain, made in their distinct cortical regions, are qualitatively 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.[22]

     The thought-experiments considered above suggest that it is logically possible to distinguish:

 

(a)  the subjective interpretation of a phenomenal mental state X

from

(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 not to feel a real pain. We know 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 maybe physically and practically possible as well, which at least in principle warrants the possibility of the interpersonal checks of identification rules for mental states. In this case, the private language argument fails because the logical non-shareability of phenomenal states is a false principle. In this case, the rules of phenomenal language acquire an epistemic status that does not essentially 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 correction of rules for the identification of phenomenal states is 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 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. Against this kind of reasoning, Wittgenstein imagines a situation in which when he believes he has the (non-perceptible) particular sensation P the manometer always shows that his blood pressure has increased. This assures a correlation between his subjective thinking that 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 a 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, what we normally make is a well-grounded reasoning by analogy, allowing us in the end to reach a very high probability of associating something like the belief that we are having what we call ‘pain’ with the pain that we really feel. The difference is that in normal cases of reasoning by analogy we can do a final check to prove that the inference was correct, while in the case of subjective, inner feelings this seems impossible. But if we can do this in principle – if the principle of the logical unsharability of mental phenomena is not true – there is no justification to question our reasoning by analogy regarding our feelings.

     It seems clear that our reference to internal phenomenal states is not essentially different from the case of the conclusion based on a large amount of convincing circumstantial (indirect) evidence, that a certain woman was in fact murdered by Jack the Ripper, even though the true identity of this serial killer was never and might never be proved. Even if no one actually saw the woman being murdered, the details of the murder and all the circumstantial evidence that taken together point to this very peculiar murderer are already highly convincing.[23]

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 psycho-physical particularities are left aside. 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.[24]

     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 a needlessly equivocal way. The semantic aspect is conventionally grounded and grammatically necessary; the psychological aspect is spatiotemporally given and in its psycho-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 of rules, 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.[25]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

                                                                                                                                                

Appendix to Chapter III

Trope Theory and the Unsustainable Lightness of Being

 

 

 

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…), such as the redness of this sofa, the hardness of that wall, the property of a shirt of being made of cotton… Many traditional philosophers, however, would say that these things cannot really be properties in the true sense of the word. For in this true 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 realism, particularly in the form of Platonism is opposed to the ontological starting point of ordinary people and even of our own modest common sense. Common sense begins by considering as prototypical examples of properties the spatiotemporal properties directly given to us in perceptual experience, only afterward considering those properties that are in some way derived from perceptual experience. The contemporary ontology that shares this commonsense view is called trope theory. Properties are for trope theorists spatiotemporally 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 spatiotemporally 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 rise 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 1953 did an American philosopher named D. C. Williams conceive of the bold idea to assign tropes metaphysical place of pride as the universe’s only fundamental ontological building-blocks.[26] His central aims were to use the notion of tropes 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 my assumed methodological perspective seems more plausible, namely, a methodology that gives primacy to established knowledge (Ch. II, sec. 5).

1. Introducing Tropes

First, what are tropes? Although tropes (or properties) considered as simple cannot be intrinsically defined, they can in my view be clearly characterized as follows:

 

Tropes (Df): are properties localizable in space and enduring in time, regardless of their vagueness.

 

As such, these particularizing 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 heat of that stove, the smell of a particular daisy at a certain time and the song sung by a particular blue whale 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 that 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, emotion, purpose, love affair, act of contrition or expression of impudence (called by Williams mixed tropes); and they can be events like a smile, sneeze, election, cold snap, triangle, circle, shape or 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 multifarious. This is the case of biological properties like that of a certain cat being a mammal. This is the case with some psychological properties like Céline’s idiosyncratic personality. And this is also the case with 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 on the country, the individual entity called ‘India,’ though this trope is surely a very complex one. And there are complex and diversified cultural properties like the socio-cultural traits emphasized in the ancient Spartan state. In all these cases, the tropes are in various ways spatiotemporally located, and they are properly referred to with predicative expressions (they are at least logically repeatable).

     Tropes contrast with what I prefer to call individuals (objects): these are things that are seen as unique and non-repeatable and are referred to by singular terms like ‘this daisy,’ ‘that blue whale,’ ‘the Golden Gate Bridge,’ ‘Socrates’ and ‘India.’ In the standard case they are what can be 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 or of a cloud in the sky. And there are individuals that are constituted by the absence of tropes, for instance, a particular shadow.

     Moreover, there are complex tropes like a performance of Beethoven’s Fifth Symphony, which are homogeneous in the sense that they consist of only one kind of trope comprising a great diversity of sound-tropes. They can be designated by means of a predicative expression, as in the statement ‘The orchestra performed the Fifth Symphony.’ Considering that the Fifth Symphony can be performed over and over by many different orchestras at different times and in different places, it is clear that it is better classified as a repeatable complex homogeneous trope and not as an additional individual; moreover, it is dependent on an orchestra (an individual) to be performed, while individuals (e.g., the Vienna Philharmonic Orchestra) are relatively independent in their uniqueness.

     Finally, one can consider 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. The fact that these forces are indirectly accessible is only a contingent one (some birds navigate using the earth’s magnetic field). This is how things are, even if from the perspective of physical science the origins could be reversed.

     As particularized properties, tropes have identity conditions. As an attempt to clarify this, I propose an ontological condition (a) followed by a linguistic indicator (b):

 

Tropes are identified:

(a) By their spatiotemporal existence to the extent that they display sufficient continuity over space and time and are amenable to certain direct or (often) indirect experiential ways and conditions of access, and

(b) By being linguistically designated by predicative expressions of singular statements whose nominal terms refer to individuals.

 

So understood, tropes contrast mainly with individuals such as material objects referred to by means of nominative expressions, particularly proper names.

     The linguistic indicator (b) has a guiding function: as spatiotemporally located properties most properly linked with individuals, tropes are usually designated by means of predicative expressions like ‘…is red.’ This isn’t always so straightforward: in statements beginning with demonstratives like ‘This is a daisy’ or ‘There is the Matterhorn’ it is preferable to take the nominal terms (indexicals) ‘this’ and ‘there’ as referring to spatiotemporal places, as localizing rules for the identification of the individuals daisy and mountain, which justifies the non-application of the linguistic requirement (b) to its supposed predicates, whose owners are in fact individuals and not tropes. Better to analyze these sentences relationally as ‘<This place is> where <a daisy> is located,’ and ‘<That is the place> where <the Matterhorn> is located,’ sentences in which the predicate designates the property-trope ‘x where y is located.’

     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 of 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 maybe even the same duration as its brown color. Does this mean that this brown and this smooth are the same trope? No, since they are accessed through different forms of perception and under different conditions. This is the most natural way to identify properties, although there is much more to be considered on this point.

     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 very helpful (Cf. Campbell 1990: 136-7). Because of this, and again drawing on common sense and natural language, it seems better to say that the unity of a trope – which we can rightly call a property – is usually better established by the natural limits of its spatiotemporal 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 the usual linguistic 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 spatiotemporally located. 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, maintaining its spatial continuity.

     I mention all these seemingly trivial 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., socio-historical tropes) can be highly dispersed in space and time. This makes their boundaries still less determinate.

     Since tropes are any spatiotemporally situated properties, they are also existent particulars. This is 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 spatiotemporally locate a trope or a set of tropes. Moreover, tropes are said to have proper existence, though I must disagree with Keith 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. However, the blue sky above must be identified against the landscape below, and the colors of the rainbow are intransitively related one another and form an arc against a certain background, and all these things are, according with our definition, tropes. Therefore, I would prefer to say that tropes have rather 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 continued existence of some tropes or clusters of tropes... Campbell, disagreeing with Williams, did not consider forms as tropes because of their dependence upon other tropes (Campbell 1998: 360-361).[27] However, as I noted above, his examples are inadequate: tropes have to be always to some extent interdependently considered. If we hold this view together with our definition of a trope as any spatiotemporally localizable property, 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 spatiotemporally located, though often only in a rather vague way, and since relations are designated by means of dyadic or polyadic predicative expressions, it seems clear that relations are tropes, even if their existence is subsidiary to the existence of their relata. Although there are different kinds of relations with different strengths, particularly important 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 (Campbell 1990, Ch. 5.15). The relational predicate ‘x causes y’ is not between the objects stone and window but between a cause, such as throwing (a stone), and an effect, such as breaking (a window). Cause and effect are here located events associated with different individuals, which can be represented by means of statements (‘The stone was thrown,’ followed by ‘The window was broken’), being all made of tropes according to our identity conditions. It is doubtful if a causal relation is internal. We define an internal relation as a relation that exists as a consequence of the existence of their relata, so that if the relation does not exist the relata will be different. But a trope-event x will only be a cause of y if the right contextual conditions are added, what must be extrinsic to the relata. A straightforward case of an internal relation, however, is that of strict similarity between two tropes, which I understand as a relation of qualitative identity. 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 as easy to admit, but the relation of strict similarity is also not just predicatively designated; it is also spatiotemporally 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. Like causality, strict similarity is in this way a dependent trope.

     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. We can argue against this objection by first noticing 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 regress, 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 preposterous! The strangeness becomes clearer when we replace the symbols with words and see that we fail to give a sense to these new relations. It does not make sense to say ‘The Earth is related to its roundness,’ instead of saying ‘The Earth is round.’ Hence, it is more reasonable to see the link between subject and predicate as what some philosophers called a ‘non-relational tie’ (Strawson 1959, part II, Searle 1969: 113), something like the invisible link of a chain, to use Wittgenstein’s metaphor. They are not tropes but pseudo-additions in a literal sense of the word. Thus, 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 the kind of relation is that of friendship. 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 we can apply a single 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 supposed 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 ‘Platonist’ or the semi-Platonist ‘Aristotelian’ versions of realism 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. However, this view was never satisfactorily rescued from unsolvable problems.[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 supposedly causal relation between these abstract entities and our minds. Finally, as we already noted, 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 an otherworldly Platonic realm.

     This contrast leads us to the suspicion that only a disposition originating from the pressure of some mystical or quasi-mystical belief could lead to a committed Platonic solution. It exemplifies the consolation of what a Nietzschean philosopher would call a ‘world of beyond’ (Überwelt). Philosophers are particularly susceptible to this sort of thinking; they are to some extent unworldly creatures, and it may be a temptation to adjust their minds to see properties in such an idealized way.

     The Aristotelian solution was an attempt to bring the Platonic archetypal ideas down from their heaven (the topos hyperuranion) 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 universals. Now it seems completely impossible to understand how the universal can preserve its unity if its only reality consists in being multiply instantiated by entities belonging to the real world.[30]

     Dialectically opposed to realism was 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. This and similar counter-intuitive views were justly nicknamed ‘ostrich nominalism.’ A more sophisticated form is the contemporary 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 since they form the same set. 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 the objection of identities of extensions of different general terms because there are possible worlds where some animals with kidneys have no hearts and vice versa… 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 possibly 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 set or class; 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 to appeal to an open set, since even open sets also have their sizes, though unknown and also variable… 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 assumed before. It must be a case of 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 the case of an identity between differently spatiotemporally located things (differing from numerical identity, which is 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 (in the case of blue it is what we identify as corresponding to wavelengths between 450 and 495 nanometers).

     Now, according to the kind of reasoning adopted 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 known by appealing to the abstract idea of identity, it must be by appealing to another trope of qualitative 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 the wrong solution. And the reason why I think so is that this seems not to be 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 much better way I propose to build universals only from particulars is inspired by just the kind of treatment that particularist philosophers like Berkeley and Hume gave to ideas or impressions in order to ensure their unity. 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, sec. 12)[31]

 

Following a similar line of thought, 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 model trope, T* in no way needs to remain always the same trope. On the contrary, one can choose any trope T strictly similar to a chosen T* and then use it as a new T* in order to make new comparisons. Each speaker is free to use his own T* as a model to build the universal. Moreover, what we normally know of T* in real life is only some recollection in our memory.[32]

     Accepting this definition, we do not need to appeal to sets or classes 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 how many tropes are qualitatively identical to T* is a matter of indifference. 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 (recalled in the person’s memory) or any other strictly 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 any other trope strictly similar to Tc*, as the wider pattern of the 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,… T_n individually with some chosen trope T*. Instead of possibly generating an infinite pyramidal regress, the sequence of our comparisions will take the form T₁ = T*, T₂ = T*… T_n = T*, without any need to consider the totality of T’s. In other words, as long as all we need to do to get a universal is the ability to compare any given trope with our chosen model trope T*, there is no need to compare similarities with similarities, thereby generating further similarities of similarities. Russell’s problem does not arise because our particularist definition makes universals mere potentialities instead of actualities.

     Furthermore, we can also construct the universal ‘strict similarity’ requiring that some chosen trope Ts* (a model 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 sequency of comparisions would be Ts₁ = Ts*, Ts₂ = Ts*… Ts_n = Ts*, where Ts* can remain the same while other tropes of strict similarity are changing. This means that we have second-order strict similarity tropes referred to by the third-order strict similarity signs ‘=’ occurring 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 could in principle refer to an indefinite number of higher-order strict similarity tropes by taking this ascending path.

     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, which is not possible with vicious infinite regresses. A similar consequence results from Platonic realism. As H. H. Price noted (1953, Ch. 1): the idea of ideas constantly used in Plato’s doctrine of ideas is a second-order idea. He also needs to consider the idea of the idea of ideas in his dialogues. But then he stops, not because he must, but simply because there is usually no explanatory advantage in going further. In the same way, we can find no explanatory soundness in going beyond the trope of precise similarity between two other tropes.[33]

     Finally, it is worth noting that strict similarity is not a trope like others. To begin with, it is what we have called 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 color-tropes. Campbell suggested that strict similarity is only a supervenient pseudo-addition that does not add any being to what already exists (1990: 37).

     Nonetheless, if we take seriously our identifying condition for tropes, the fact that we are dealing with an internal relation does not make strict similarity or even higher-order strict similarities quasi-tropes or a non-tropes, as some theorists think. 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 an essential condition for the existence of a (simple or not, homogeneous or not, external or not) trope is its spatiotemporal localizability, established by the application of its ascriptive predicative expression, we can argue that similarity is also spatiotemporal, 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, this likeness would be somewhere in this place, which may include myself, but not in a distant place. My house 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 house or the Taj Mahal disappear, the color likeness also disappears, which means that the similarity also exists in time. Furthermore, when someone considers the similarity 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 localizable. But as great as this distance may be, it remains insignificant 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. This spatial relation isn’t internal, insofar as it is independent of the relata only. This makes easier to classify it as a trope, but it is not because of this that it satisfies our identifying condition for tropes as spatiotemporally 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 seriously 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 the relational view originated from Leibniz, space could be constructed by means of relations, and this conception can easily be extended to include 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.

     The attempt to explain absolute space and time in terms of tropes seems to be condemned to failure. If space as a whole is a trope, it cannot be located in space, and the same holds for time, contradicting our definition of tropes. However, it seems there is a good chance of explaining space and time relationally in terms of tropes if we begin with a modest commonsense approach. It seems clear that in primeval times people understood space by thinking of relations such as above, below, 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. Originally time would also be relationally understood, by means of relations like earlier, present (simultaneous with the act of observation) and later. One can say that event x occurred three times as long ago as event y in relation to event z. Moreover, in order to make measurements, the plain man appealed to regularities as patterns: a foot to measure distances in feet, a day to measure periods of days… And one could with the aid of these regularities calculate speeds in order to conclude, for example, that Pheidippides could run more than 160,000 Greek Steps in one day before dying of exhaustion. This is how our usual concepts of space and time worked and still works in everyday life, where they do not demand a further explanation. The main point here is that all these relations should be tropes since they are also spatiotemporally located. However, since quality-tropes and material objects are also spatiotemporally located entities, it seems that we would end up in circularity: space and time would be defined as relations of spatiotemporally located property-tropes and objects as clusters of property tropes.

     The answer to the circularity objection in this modest commonsense approach is that space and time are constituted by a network of spatiotemporal relations among spatiotemporal entities that can be quantitatively compared. For instance, consider the following rough description of the Southern Cross against the horizon: star c is seen twice as far below the smaller star b than b 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 spatiotemporal relation, for instance between a and b, could be located in the spatiotemporal network and because of this could be defined as a trope. And the same could be said of the individual star b as a spatiotemporally located cluster of tropes.

     Of course, it is an entirely open question how such a rough commonsensical view could be developed, extended and transformed in order to comprehend the sophisticated and often controversial theories of contemporary physics. However, nothing could be more distant from the truth than to commit the naïve mistake of believing that the above account is so primitive and superficial that it could effortlessly be dismissed based on the discoveries made by modern science.[34]

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 a kind of artichoke consisting only of its leaves, which are tropes.

     The key-concept here is that of compresence (also called concurrence, togetherness, etc.), which can be understood as the sameness or near-sameness of the spatiotemporal 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 space, leaving aside when each of them comes to be located. 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 has been pointed out, a material object can be identified by means of an indexical added to a sortal predicate, as in the statement ‘This is a chair’ (Tugendhat 1983, Ch. 9).[35] Now, the necessary tropes are those typically specified in the definition of the sortal. Thus, ‘a chair’ is defined as a non-vehicular 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 non-vehicular and designed to be used by only one person at a time are constituted by dispositional tropes, variations and alternations of tropical relations that complete the definition. There are also contingent tropes, like those constituting the sub-clusters of armrests or four legs, since there are chairs without armrests and chairs without legs; and there are still more variable tropes associated with a chair, like its color, the relation to a certain 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 dense, yellow, 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 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.). Moreover, Simons accepts the possibility of variations: a concrete object formed only by kernel-tropes, etc.

     Here a much more precise definition seems to be simply impossible. Stones, for instance, are material objects that can be composed of very different materials, having few tropes to individualize the object-kind stone, with the exception of hardness, solidity, weight, volume, and color, all of them compresent. However, based on this cluster of properties, often combined with spatiotemporal 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 of a very complex property-trope, as it seems. These tropes appear to have compresence, since they all seem to be located where Socrates is. Moreover, they could be individuated by a sortal predicate delimiting the spatiotemporal location of Socrates (‘There comes Socrates again with his inconvenient wisdom!’). Finally, they can have a kernel: the ‘peculiar core of the inconvenient Socratic wisdom.’ But it is not a material object, not even an individual, insofar as it is said to belong to the individual Socrates and others could in principle, at least, 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 – jointed together in a structured 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 as an individual. 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:

 

 volume,

 form,

 hardness or solidity (measured by resistance to pressure),

 weight (depending on the presence of a gravitational field),

 mobility in space…

 

This already excludes the property of Socratic wisdom and individuals like the rainbow and the holographic projection. But liquids, although they are material substances, do not have a specific form or solidity, unlike a stone, a tree or a table. For example, water takes the form of its container, and additional water can be added to a given quantity 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: its droplets have minimal resistance to pressure and it has no fixed and necessarily defined form. And what about supposed material entities like bacterias, viruses, atoms quarks or hypothetical super-strings?

     My final condition is based on the already discussed assumption that our commitment to modest common sense does not exclude science.[36] 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[37]). This seems to me the most pertinent characteristic of what we call matter. Energy also has mass, but it isn’t inertial mass.

     I conclude that in an inevitably vague characterization, having the expected inertial mass, some size… and compresence of its definitional tropes would 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 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 a historical tropical event like the Battle of Hastings was a spatio-temporal tropical event, not a material object. They are all complex structures made up of tropes, including mental tropes like intentional states and depending on material entities to be spatiotemporally located, even if only in a vague way. Since these tropical entities are independent and unequal and identified by nominal terms, they are individuals (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 analogous 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 to answer 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 spatiotemporal delimitations that remind us of the already considered cases of form and duration. They are all dependent relational tropes that must be considered sui generis, behaving 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. Concurrence is a sui generis non-self-predicating limiting trope. Strict similarity is also a sui generis non-self-predicating dependent relational trope because one cannot say of the strict similarity between T₁ and T₂ that it is strictly similar without rising questions like: ‘what would strict similarity be similar to?’

4. Formal Tropes

What should we say about formal entities like natural numbers? Numbers are often seen as Platonic or semi-Platonic universals. And they would not be tropes since they do not seem to be spatiotemporal. However, this isn’t so uncontroversial! Much of our empirical world is made up of countable things. Would the number 3 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 would be a primary quality (a trope), together with solidity, extension, figure, motion or rest, which are accessed by diverse senses and should remain the same independently of the perceiver (1690, Book II, Ch. VIII). Indeed, I can perceive one, two, even six things at a glance and these seem to be spatiotemporally located tropes; and some savants are able to perceive hundreds of things at a glance. To use an example borrowed from Penelope Maddy, it seems that the ten fingers of my two hands are in some way here (1990: 87). It seems that even a thousand grains of wheat scattered in the wind remain spatially and temporally located, though in a diffuse way. And if the insufferable rock band called ‘The Fevers’ flies from São Paulo to Rio de Janeiro, it seems that the number of their members has also moved. However, it is important to note that these trope-numbers are dependent on countable entities of our choice.

     One can associate this dependency with Frege’s account of numbers as properties of concepts, since as he has taught us, things to be counted must be first conceptualized. The question ‘How many?’ only makes sense if followed by a conceptual expression. For instance, if the concept is of the fingers of my hands, they are ten, but if the concept is of my hands, they are only two. The property of the concept of those grains of wheat scattered in the wind is that there are a thousand. And the movable property of being five is a property of the concept of The Fevers. Moreover, as Frege famously wrote, the attribution of existence is the negation of the number zero (1892, sec. 54).

     So it seems that the concepts of number and existence are related. In fact, one can suggest that the property of existing and the property of being a number are higher-order tropical-properties because, like tropes, they are in a vague way spatiotemporally located: this black spot on the carpet exists here and now and not somewhere outside in a remote time. And it seems plausible that when I say ‘This is my one and only nose,’ ‘these are my two hands,’ ‘these are my ten fingers,’ the number one I am applying is located where my nose is, the number two is where my hands are, and the same with my ten fingers. The naïve error would be only to confuse these ethereal tropes with those qualities primarily constitutive of the nose, the hands, and the fingers. Indeed, numbers, as much as the existence of things, do not seem to be in outer space or in ancient times or in the solely intelligible realm of abstract ideas.

     These considerations seem to be valid for applied arithmetic, insofar as numbers are first used to count empirical objects. After all, we learn numbers by counting material things: ‘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 distinct objects, attributing physical existence to each of them and showing in the process of counting that the rule has the higher-order trope-property of being applicable three times in an additive way.

     In the view defended in this book (See Ch. IV) a concept is a rule, which means that the attribution of existence is here the second-order property (or trope) of a dispositional first-order conceptual rule (always understood as a trope) of being satisfied by at least one thing. And in a similar way, an applied natural number would be the second-order property (or trope) of a dispositional first-order conceptual rule (or trope) of being satisfied by means of an idealized counting procedure, where counting originally results from the distinguishable applications of a first order conceptual rule to things like material objects or events or qualities attributing existence to them n times...[38]

     Using Fregean devices it is easy to formalize this suggestion using only countable tropical applications of (tropical) concepts and the (tropical) concept of existence. The affirmation of the number 0 is the negation of existence.[39] Thus, using V in place of the conceptual expression ‘moons of Venus,’ we can symbolize the idea that there are 0 moons of Venus as ~Ǝx (Vx), saying that the conceptual rule expressed by V isn’t applicable at all. Using E to symbolize the conceptual expression ‘moons of Earth,’ we can symbolize the idea that there is 1 moon of Earth as Ǝx [Ex & (y) (Ey → y = x)]. Here E is applied only once. And using M to symbolize ‘moons of Mars,’ we can symbolize the idea that there are 2 moons of Mars as Ǝx [(Mx) (My) & (x ≠ y) & (z) (Mz → (z = x) v (z = y))]. Here M is applied twice. It is the application of a tropical ascription rule for two and only two moons of Mars.

     Above we considered first order conceptual tropes together with higher order existence tropes and applied numbers as higher order numerical counting-tropes. However, I think we can separate or abstract the numerical trope from these other concepts. We can do this by representing these tropes of countability by means of localizable sets. Thus, I propose that we can represent the 0 in ‘the moons of Venus’ as the located non-countability (non-applicability) of a concept symbolized by ~a. Instead of the 1 of ‘the earth’s moons’ we can speak of a set that has as its only member a located higher-order applicability trope or {a}. Instead of the 2 of ‘the Mars’ moons,’ we can speak of a set that has two located higher-order numerical tropes as members, as follows: {a, {a}}. In this way we can represent an applied number 3 by the localizable set {a, {a}, {{a}}} and so on. Note that this 3 has the right complexity by containing {a, {a}} (=2) and {a} (=1). But the fundamental point here is that we are explaining applied numbers by means of spatiotemporally localizable sets of countability-tropes and by convention the null set. The set of Mars moons numerical tropes is spatiotemporally located in our solar system and not in the Andromeda galaxy or in the origin of time. And such sets are not Platonic or sub-Platonic entities!

     At this point, one can object that we have until now explained only natural numbers applicable to things. One could, however, instead point out that what really matters is the number of abstract arithmetic, the universal independent of its satisfaction by countable material objects or events. The suggested construction has indeed this limitation since it represents only one number among many identical numbers. The natural number 3, formulated as {a, {a}, {{a}}}, is a triad and not what is common to all triads, namely, the abstract universal three, the three-in-itself. Indeed, the only way to represent what is common to all triads seems to be the appeal to a Russellian set of all sets of the same kind, which has its own shortcomings like the axiom of infinitude, overpopulating our world with an infinite number of objects.

     However, I think that in the same way as we have constructed universal quality-tropes without appealing to abstract sets, we can also construct universal number-tropes without appealing to abstract sets. I think we can derive the universal concept of number, the number-in-itself, from our spatiotemporally located tropes of counting. As we have seen above, an applied number can be understood as a trope, since it is spatiotemporally localizable as a second-order property of a potential conceptual rule resulting from its at least ideally countable applications. Consequently, in order to account for the universal as a set of equinumerous sets of applied numbers, we can appeal again to our disjunctive model.

     In this case, for instance, it is conceivable that the number 2 in itself would be a disjunction between a located dispositional higher order trope-set of countable applications used as a model (e.g., the number 2 in the statement ‘I have 2 hands’) or any other strictly similar (equinumerous) located set of countable tropical applicabilities. Now, in order to get the number 2 as the ‘abstract universal,’ the ‘two-in-itself,’ all we need is to apply to the separated set of tropical applicabilities the same procedure we have applied to get universals from our usual quality-tropes. For instance:

 

Number 2 (Df.) = a located model set of tropes of countable applicabilities {a, {a}}*, or… any further located set of tropes of countable applicabilities strictly similar (equinumerous) to {a, {a}}*.

 

In this sense, the number as a universal (or ‘abstract entity’) can be defined as:

 

The higher-order property of a conceptual rule of being a located set of tropes of (at least ideally) countable applicabilities taken as a model or of any higher-order located set of tropes of (at least ideally) countable applicabilities strictly similar (equinumerous) to the first one.

 

Note that such constructed universals remain empirical since they are higher-order disjunctive property-tropes that can be found scattered across our whole spatiotemporal world. This makes graspable why something abstract like mathematics applies to the empirical world.

     Assuming a definition like that, we neither stumble over controversial infinite sets of objects (as in Russell’s definition) or over pure sets (as in von Newmann’s and Zermelo’s definitions) nor remain unintentionally limited to particular instances or directly committed to any differentiating concrete feature (as in naïve empiricist views). The conclusion is that even the abstract world of arithmetic (hence, 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 can also be seen as dispersed over the world and able to be meta-predicatively designated. Finally, I would not be surprised if even logical properties were susceptible to similar treatment!

     Now one could object: aren’t such formal properties not too thin to be tropes? A dependent trope like a conceptual rule might be a thin trope. But a trope that is dependent on other possible dependent tropes will be still thinner so that 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? There is no quasi-trope.

5. Conclusion

In this section, we have seen how trope theory can turn Platonic realism upside down. Much of what I have written here is speculative, still requiring a great deal of additional work and refinement. In this short space, I could do no more than offer a sketch of what seems the most consequent and plausible way to deal with the one-category ontology chosen to play a central role in this book.

 

 

 

 

 

 

 

---

[1] As will be clear, 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.

[2] The word ‘semantics’ is understood here in a broad sense that includes pragmatics as the study of words in use, insofar as it is able to influence truth-values of statements.

[3] 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.)

[4] Qualitative identity is the identity between different things; it is opposed to numerical identity, which is the identity of a thing with itself.

[5] 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 merely complementary role of memory.

[6] 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 this class does not belong to the definition and does not need to be an object of awareness.

[7] As Wittgenstein wrote in the Tractatus: ‘The name means its object. The object is its meaning.’ (1984g, 3.203)

[8] The view was ironized by Gilbert Ryle as the ‘Fido-Fido’ theory of meaning (1957).

[9] Metaphysicians of reference have more recently attempted to reassert this primitive form of semantic referentialism (Cf. Salmon 1993).

[10] As Russell recognized, logical atomism was first suggested by Wittgenstein, who defended it in a full-fledged way in his Tractatus Logico-Philosophicus.

[11] This kind of difficulty was already raised in the 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.)

[12] See my discussion of Wittgenstein’s private language argument at the end of this chapter.

[13] 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 we have parameters to distinguish it from the blurred borders with the other two colors.

[14] Language not only has 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 ways of 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.

[15] In insisting that the content of p is a communicable kind of meaning, I distinguish this analysis from the Gricean psychological theory of meaning. H. P. Grice suggested that to display what he calls a non-natural meaning (our semantic-cognitive meaning) of p the speaker must have the intention (i) 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 of (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; see also Tugendhat 1976, Ch. 14).

[16] There are also experimental, simplified or artificial language-games that the philosopher invents to make comparisons… But I am interested here in the language games really constitutive of our natural language.

[17] Although Wittgenstein expressly disliked K. Ogden and I. A. Richards’ book ‘The Meaning of Meaning,’ he must have appreciated the short supplement to the book in which Malinowski presents these ideas.

[18] An outline of what I believe to be the most plausible solution is given in Costa 2011, Ch. 5.

[19] These two forms were also noted by Anthony Kenny (1973).

[20] 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, it is plausible that in having these non-linguistic thoughts we are using non-linguistic mental signs, like imagistic and emotivist ones.

[21] See, for instance, A. J. Ayer 1972: 196.

[22] In fact, I think we are not very far from 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 as well for the person who is having these states: you can see your own mental images (visual sense-data) represented on a screen, and others can see your represented images on the same screen. (e.g., Nishimoto 2011) Even if they are not the images (visual sense-data) in themselves, the experiment already suggests that your consciousness of these images is detachable from them.

[23] Costa 1997, 433-448; Cf. also Costa 2011, Ch. 5.

[24] Note that there are non-referential rules: we can not only have rules that relate (a) the empirical data to cognitions, but also (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 cognitive/referential meaning.

[25] 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 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).

[26] 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.

[27] 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 forceful since a conventionally charged intromission of epistemic subjects is inevitable in any conceptual application.

[28] In Russian, there is no proper verb for the copula. One uses expressions like ‘Me nice,’ ‘You beautiful’… Thus, it seems that Russian speakers are less susceptible to such worries.

[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] Although traditionally 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 substantial form or 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] See also the more sophisticated but also less clear view of David Hume (1738, Book I part 1, sec. 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, so that they can compare these patterns with any trope they come across. Moreover, the templates can have the most varied shades of a single color, say, blue. They may call the possibilities that might result from their comparisons ‘the universal of a blue color-trope.’

[33] As Anna-Sofia Maurin remarks, in a vicious infinite regress a considered statement (trigger) is dependent on the subsequent steps, while in a virtuous infinite regress, the subsequent steps depend on the considered statement, which makes them unnecessary (2007).

[34] There is no prima facie reason to believe that a relational view cannot in principle be made compatible with general relativity theory.

[35] 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.

[36] J. L. Austin objected that terms like ‘material object,’ ‘material thing’ and ‘sense-data’ do not originally belong to our ordinary language (Austin: 1962). Against this, we can only repeat that there are gaps left unexpressed by ordinary language, later filled by new philosophical terms (See Ch. II, sec. 6 of this book; see also Grice 1989: 227).

[37] 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.

[38] Of course, there are large numbers that are uncountable for us. But they remain at least ideally countable. And they can be seen as later extensions that can be calculated by means of symbolic manipulation alone.

[39] I argue for a higher-order view of existence in chapter IV, sec. 11 to 19.