domingo, 10 de abril de 2016

CLAUDIO COSTA - PHILOSOPHICAL TEXTS (TEXTOS DE FILOSOFIA)


THIS "BLOG" HAS BEING THOUGHT OF AS A WAY TO MAKE MY WORK IN PHILOSOPHY ACCESSIBLE TO A WIDE PUBLICUM. THERE ARE NEARLY HUNDRED PAPERS, MOST OF THEM IN DRAFT FORM. SOME ARE INTRODUC-TORY. PAPERS WITH INTEREST FOR RESEARCH ARE MARKED WITH ONE OR MORE '#'. I WISH YOU HAVE SOME INTELECTUAL JOY IN READING THEM.



ESSE "BLOG" FOI PENSADO COMO UMA MANEIRA DE TORNAR MEU TRABALHO ACESSÍVEL A UM PÚBLICO AMPLO. SÃO CERCA DE CEM ARTIGOS. OS QUE FORAM ESCRITOS EM PORTUGUÊS SÃO EM SUA MAIORIA INTRODUTÓRIOS. ESPERO QUE SEJAM ÚTEIS.

 
INFORMATION ABOUT MYSELF:
I am full professor at the UFRN (Brazil) and researcher for the CNPq. My graduation was in medicine. I made my PhD in Germany and post-doctoral sabbaticals of one year in München (with Friedo Ricken), Konstanz (with Wolfgang Spohn), Oxford (with Richard Swinburne), Berkeley (with John Searle) and now in Göteborg (with Anna-Sofia Morin). I Published some papers in international journals and two books in English: The Philosophical Inquiry: Towards a Global Account  (UPA, 2002), developing a theory on the nature of philosophy, and Lines of Thought: Rethinking Philosophical Assumptions (CSP, 2014), which is a collection of papers on central issues of contemporary philosophy. Presently I am working in a book to be called  Philosophical Semantics: Towards a New Orthodoxy (CSP, 2016) aiming to defend some old ideas of the philosophy of language, which I believe are important an were falsely debunked by the philosophy of language of the last 60 years.




 
 
Photo of Magda's tree
 


SEM EXAGERO ALGUM
Minha poesia é tão hipermoderna que só daqui a mil anos, quando a espécie humana se alçar ao nível ômega, ela será capaz de compreendê-la!  Quanto à minha filosofia, essa então nem se fala. Essa vai até o osso. Sua força é como a da explosão de uma supernova. Ela é tão profunda, tão profunda mesmo, que espécimes do gênero humano, especialmente aqueles por muitos anos adestrados na miopia do academicismo cientificista da pigmeica filosofia contemporânea não conseguirão enxergar dela mais do que traços embaçados.
Por isso, ao temerário que pretender imergir em sua profundidade abissal eu previno: muito dificilmente conseguirá retornar outra vez à superfície sem explodir pelo simples efeito da despressurização cognitiva. Pois a distância entre a minha filosofia galáctica e quase toda a minúscula filosofia de nossa época é tão grande que não se mede em quilômetros, nem em léguas, nem em milhas... mas em anos-luz! Por isso resolvi denominá-la "filosofia clássica pós-analítica e anti-contemporânea."

#THE KEY TO THE HUMEAN PROBLEM OF INDUCTION


obs: this is a corrected rough draft for an Appendix of the book Philosophical Semantics: Towards a New Orthodoxy to be published by Oxford Scholars Publishing in 2016.






Appendix to chapter 5


THE KEY TO SOLVING HUME’S PROBLEM OF INDUCTION


It would be impossible to say truly that the universe is a chaos, since if the universe were genuinely chaotic there could not be a language to tell it. A language depends on things and qualities having enough persistence in time to be identified by words and this same persistence is a form of uniformity.
J. Teichman & C. C. Evans

I will first reconstruct Hume’s skeptical argument against the possibility of induction in the clearest way possible. Then I will sketch what I believe to be the best way to answer it, in order to re-establish the credibility of inductive reasoning, which is assumed throughout this book.

The Humean argument
According to Hume, our inductive inferences require metaphysical principles of uniformity of nature to support them. Although induction can be not only from the past to the future, but also from the future to the past and from one spatial region to another in the present, for the sake of simplicity I will limit myself here to the first case. The principle of uniformity from the past to the future can be stated as:

PF: the future will resemble the past.
If this principle is true, it ensures the truth of inductive inferences from the past to the future. Consider the following very simple example of an inductive argument justifying the introduction of PF as a first premise:

1. The future will resemble the past. (PF)
2. The Sun has always risen in the past.
3. Hence: The Sun will rise tomorrow.

This seems at first glance a natural way to justify the inference that if the Sun rose each day in the past, it will also rise tomorrow, an inference which could be extended as the generalization ‘The Sun will always rise in the future.’  
   It is at this point that the problem of induction begins to be delineated. It begins with the observation that the first premise of the argument – a formulation of PF – is not a true reason characterized by the inconsistency of its negation, i.e. it is not an analytic proposition. According to Hume, it is perfectly imaginable that the future could be very different from the past, for example, that trees will bloom in the depth of winter and snow will burn like fire!
   We can still try to gain the certainty that the future will resemble the past based on the past permanence of uniformities that once belonged to the future: past futures. This is the inference that at first glance seems to justify PF:

1. Already past futures were always similar to their own pasts.
2. Hence: The future of the present will also resemble its past.

The problem with this inference is that it is also inductive. That is: in order to justify the induction we need to use PF, the principle that the future will resemble the past; but PF itself needs to be justified. However, when we try to justify PF, we need to appeal to induction again, which will require PF again. Consequently, the above justification is circular.
   From such considerations Hume concludes that induction cannot be justified. Therefore, there is no rational justification either for the expectations created by the laws of empirical science, or for our own expectations of everyday life, since both are based upon induction.
   It is true that we are very willing to believe in our inductive inferences. But for Hume, this disposition is only due to our psychological constitution. We are by nature inclined to acquire habits of having inductive expectations. Once formed, they constantly make us obey them, like moths flying towards bright lights. This is an extremely skeptical conclusion, and it is not without reason that only a few philosophers followed Hume’s lead. Most think that something must be wrong somewhere in the argumentation.
   There have been many unsatisfactory attempts to solve Hume’s problem. I believe that the strategy that I follow, although only sketched out, has the virtue of facing the central core of the problem.  I want to first present a general argument and then try to show how it could influence PF.

General strategy
My general thesis has a mildly Kantian flavor, but without its indigestible synthetic a priori. It is the idea that any concept of a world (nature, reality) that we may have must be open to induction. I see this as a conceptual truth in the same way as, say, the truth of our concept that the empirical world must in some way be accessible to perception.
   Understanding any maximal set of entities compatible with each other (a minimal condition) as a world, our thesis can be unpacked as follows.
   For us an external world can only exist if it is at least conceivable. But we cannot conceive of an external world without any degree of uniformity or regularity. Now, as we can only experience what we are able to conceive, it is clear that we cannot experience any world completely devoid of regularity. However, the existence of regularity is all that is needed for at least some inductive procedure to be applicable. But if this is the case, then it is not possible for us to conceive of any experienceable world that is not open to induction. Hence, it is a conceptual fact that if a world is given to us, then some inductive procedure should be applicable to it.
   There is a predictable objection to this thesis: why should we assume that a chaotic world cannot be imagined to exist? – a world devoid of any regularity and therefore closed to induction? In my view, the widespread belief in this possibility has been a great mistake,[1] and David Hume is to blame for this. His error was to choose causal regularity as the focus of his discussion, strengthening it with selected examples. This was misleading and in what follows I want to explain why.
   Causal regularity is what I would call a form of diachronic regularity, that is, one in which a given kind of phenomenon is regularly followed by another kind of phenomenon. Such patterns constitute what we could call ‘becoming’ in a world or regular sucessions.
   However, induction applies not only to diachronic regularities, but also to something that was never considered by Hume: synchronic regularities. Synchronic regularities are what we could also call structures: states of affairs that endure over time in the constitution of anything we can imagine. Their patterns constitute the ‘remaining’ in a world that includes permanence. We can make this concept clear by conceiving of a world without any diachronic regularity, causal regularities included. This world would be devoid of change, static, frozen. It still seems as though it could be properly called a world. But even a frozen world must have regularities in order to be conceivable; it must have synchronic regularities. But if this frozen world were constituted of synchronic regularities, then it would still be open to induction: we can foresee that its structural regularities would endure for some period of time, the period of its existence, and this already permits inductive reasoning.
   Considerations like this show the weakness in Hume’s argument. By concentrating on diachronic patterns and thinking of them as if they were the only regularities that can be to be inductively treated, it becomes quite easy to imagine the real existence of a world to which induction does not apply or cannot be applicable, but still remains a world.
   Try now to imagine a world destitute of both synchronic and diachronic structures. Something close to that can be illustrated when we think of a world as made up of irregular or temporally random repetitions of a single point of light or sound.  However, even if the light or sound occurs irregularly, they will have to be repeated at times (as long as the world lasts), which demonstrates that it still has the regularity of randomly intermittent repetition. Hence, it turns out that induction could be applied even to such a minimalist world as long as it lasts.
   Indeed, a world absolutely destitute of both species of regularity is inconceivable, and therefore not accessible to experience. We cannot conceive of any set of empirical elements without giving some kind of structure to them. But if that’s the case, if a world without regularities is unthinkable, whereas the existence of regularities is all we need for some kind of inductive inference to be applicable, then it is not possible that there is for us a world closed to induction. And since the concept of a world is nothing but the concept of a world for us, there is no world at all closed to induction.
   Summarizing my argument: by focusing on causal relationships, Hume invited us to ignore the fact that the world is made up not only of diachronic but also of synchronic regularities, which in turn leads us to the illusion that we can conceive of a world inaccessible to inductive inference. If we take into account both general types of regularity to which induction is applicable, we realize that a world that is entirely unpredictable, chaotic, devoid of any regularity, is impossible, because any possible world consists of regularities, being therefore intrinsically open to induction.
   I am by no means the first to grasp this point. For example, Keith Campbell has developed an argument for the inevitability of applying inductive procedures, which is another way to say the same thing.[2]  As he noted, in order cognitively to experience a world – an objectively structured reality – we must continually reapply empirical concepts, which, in turn, if they are to be postulated, learned and used, require a re-identification of the designata of their applications as being identical. However, he thinks this is only possible if there is a certain degree of uniformity in the world, one sufficient to allow re-identification.  Indeed, if the world could lose all the synchronic and diachronic regularities implicitly referred to in Campbell’s argument, no concept would be re-applicable, and the experience of a world would cease.
   But could there not be at least a partially chaotic world with a minimum of structure or uniformity, which would therefore be insufficient for the purposes of our inductive procedures? I guess that this is a theoretical impossibility. And the reason for this is that induction has a self-adjusting nature, i.e. the application of its principles must always be calibrated in accordance with the nature of what they apply. The requirement of an inductive basis, of a repeated and varied inductive attempt, can always be made greater if greater improbability of uniformity is expected. Hence, even a system with a minimum of uniformity requiring a maximum inductive search would always end up enabling the success of induction.
   These general considerations suggest a thread of conceptual inferences, such as the following:

Possible cognitive-conceptual experience of a world ↔ applicability of inductive procedures ↔ existence of regularities in the world ↔ existence of a world ↔ possible cognitive-conceptual experience of a world…

   These things are internally related to each other in order to derive each other extensionally, so that their existence already implies these relations. By this means, contrary to what Hume believed, when properly understood the principles of uniformity should be analytic-conceptual truths, i.e., they must be truths of reason applicable to any possible world.

Reformulations of PF
To show how the just offered proposal could be applied to the reformulation of the principles of uniformity or induction, I will reconsider in some detail PF, the principle that the future will be like the past. If my suggestion is correct, then it must be possible to turn this principle into analytic-conceptual truths constituting our only possibilities of conceiving and experiencing the world. I understand an analytic conceptual proposition to be one whose truth depends only on the combination of its semantic constituents. This truth does not widen our knowledge (in opposition to synthetic propositions), and isn’t such that its denial implies a contradiction or inconsistency.
   To show how the aforementioned suggestion could be applied to the reformulation of the principles of uniformity or induction, I would like to redefine PF. If my suggestion is correct, then it must be possible to turn this principle into an analytic-conceptual truth, constituting our way of conceiving and experiencing the world. Here is my first attempt to formulate PF in this way:

PF *: The future must have some resemblance to its past.

Unlike PF, PF* can be more easily accepted as expressing an analytic-conceptual truth, for PF* can be seen as satisfying the above characterization of analyticity. Without doubt, it belongs to the concept of the future to be the future of its own past. It cannot be the future of another past belonging to some alien world. If a future had nothing to do with its past, we couldn’t even recognize it as being the future of its own past, because it could be the future of any other past... In other words: the future of our present world as Fw can only be the future of w, of the past of w, that is, of Pw; It cannot be the future of numerous other possible worlds, w1, w2, w3... that have as their past respectively Pw1, Pw2, Pw3... It is necessary, therefore, that there is something that identifies Fw as being the future of Pw, and this something can only be some degree of similarity.
   Against this we can try to illustrate the possibility of complete changes of the world by means of examples, showing that this isn’t possible. Suppose, in an attempt to imagine a future totally different from its past, a ‘complete transformation of the world’, as foretold in the New Testament book of Revelations. It is hard to imagine more drastic changes than those described there. Here is the biblical passage describing the locusts sent by the fifth angel:

In appearance the locusts were like horses equipped for battle. And on their heads were what looked like golden crowns; their faces were like human faces and their hair like women’s hair; they had teeth like lions’ teeth and they wore breastplates like iron; the sound of their wings was like the noise of horses and chariots rushing to battle; they had tails like scorpions with stings in them, and in their stings lay their power to plague mankind for five months.[3]

The problem with this example is that there is nothing in this report that puts PF* at risk. In fact, accurate examination of the example demonstrates that even PF isn’t seriously challenged. Although these biblical locusts are indeed strange creatures, they consist of combinations of parts with which we are already very familiar, horses, women, men, heads, teeth, scorpion tails with stings, faces of persons, etc. Both internally and externally they include a vast quantity of synchronic regularities, of structural associations, together with familiar diachronic associations, like the sequential causal relationship between the noise produced by wings or the sting of the scorpion and the effects of its poison on humans.
   In fact, were it not for these uniformities, the Revelation of John would not be understandable, conceivably able to be subjected of any linguistic description, and consequently it would be impossible to imagine. The future, at least proportionally to its greater proximity to the present, must maintain sufficient similarity to its past to allow an application of inductive procedures in the recognition of the continuity of the same world.
   Now one could object that maybe it is possible that at some time in a remote future we could find a dissimilarity so great between the future and our past that invalidates all reasonable inductive procedures; a future that would be radically different from its past. Indeed, it is conceivable that a continuous sequence of small changes could in the course of a very long period of time give way to something if not totally different, at least extremely different. This would not destroy PF* because its formulation is too weak, requiring only that some similarity remains. But it is clear that this weakness of PF*, though not destroying its analytic-conceptual character, makes it poor as a way to assure the accuracy of inductive forecasts.
   However, precisely this weakness of PF* indicates a way to improve it. We see that the closer we get to the point of junction between the future and the past, the greater must be the similarity between future and past, becoming both identical in their limit, which is the present. This point can be approximated when we remember the Aristotelian analysis of change as assuming the permanence of something that remains identical in a continuous way, without gains or losses.[4] In other words, the suggestion is that every change must occur upon some basis of permanence.
   This leads us to another principle, namely, that the measure of permanence must be inversely proportional to the period of time in which the change occurs. In other words: if a sequence of changes is given that are parts of a more complete change, the changes that belong to the smaller parts presuppose more permanence than the more complete change.
   This principle can be illustrated by many examples. Consider one of them: the changes resulting from heating a piece of wax. The change from the solid state to the liquid state assumes the permanence of the same wax-like material. But the next change, of the liquid wax to carbon ash, assumes only the permanence of carbon atoms. If then the heat is much more intense, carbon will lose its atomic configuration, giving place to a superheated plasma of neutrons, protons and electrons. We have here four periods of time in a row: regarding the shortest period of time from t1 to t2, we assume as remaining (i) the same wax, made up of (ii) the same carbon atoms, which in turn are composed of (iii) their same subatomic constituents, protons, neutrons and electrons. In the longer period of time from t1 to t3 we assume as identical only (ii) and (iii). And in the still longer period of time from t1 to t4 the only thing that remains the same are (iii) the subatomic constituents.
    Note that this model is not restricted to changes in the physical and material world! As Leibniz saw: Natura non facit saltus. And this can be generalized: the same examples repeat in every domain that you can imagine, psychological, social, economic, historical…[5] with the same patterns: the closer the future is to its junction with its past, the more identities must be assumed. Thus, it belongs to the very structure of the experienceable world that the changes that take place in a shorter period of time tend to presuppose more permanence than the most comprehensive changes in which they take part. One consequence of this is that the future closer to its present should in more aspects be similar to its past than the more distant futures (which, as already noticed, may become nearly unrecognizably different). Regarding induction, this principle ensures that inductive predictions become more likely, the closer the future is to which they relate.  On this basis principle PF* can be improved here as:

PF**: The closer the future is to the junction point with its own past, the more it will tend to resemble its past, the two being indifferentiable at the point of junction (the present).

For a correct understanding of PF** we need to add that this principle should be applied to a future that is sufficiently close to its past and not to an indefinitely distant future. Moreover, we need to safeguard the possibility of anomalous but possible cases in which we find sequential moments in which states of affairs of a more distant future are closer to the present than those of an earlier future. A clause clause excluding these anomalies must be added to PF**.
   This shows that PF** should be considered more carefully, allowing the addition of formal methods. But it seems to me that with the addition of the above remarks this principle already meets our understanding of analyticity.
   Moreover, it is the truth of PF** which makes it natural to think that the more distant the future, the less probable our inductive forecasts will be. This explains why our inductive generalizations about the future cannot be applied to the too distant future. When we say, for example, that induction allows us to infer that the Sun will ‘always’ rise, the word must be placed in quotation marks. It makes sense to affirm, on the basis of induction, that the sun will rise tomorrow or a thousand years from now. But it doesn't make any sense (and is astronomically false) to use the same inductive basis to say that the Sun will rise in seventeen billion years.
   Finally, PF** can ensure restricted applications of PF: If the future is sufficiently close to its junction with the past, then the future is unavoidably similar to its past. The problem, of course, is that we need to establish criteria for knowing how close we have to expect that the future to be to its past so that PF applies. We can imagine, if the response does not depend on the domain of regularities in which the change is being considered, a domain of regularities to which a whole system of sufficiently well entrenched beliefs applies.
   Looking for an example: the inductive conclusion that the Sun will rise tomorrow belongs to the domain of regularities implicated in the changes studied by astronomy, which includes a very distant future in which broader changes, such as the death of the Sun, are possible. Moreover, it is always possible that the Sun will not rise tomorrow. But this is only conceivable at the price of an immense loss of other well entrenched beliefs on regularities and, subsequently, the loss of the current intelligibility of a considerable part of the physical world that surrounds us. Still, what makes us consider as highly likely the future occurrence of regularities such as that the sun will rise tomorrow? The ultimate answer seems, based on the inevitable assumption of the world we experience, that our world as a whole will continue for a long time to exist as a system of regularities. And this assumption – I am forced to admit – is a real and inevitable gamble.  There is nothing preventing that our whole world disappear in the next second. But once we make this general assumption – that our world as a whole will remain in existence – it looks as though the rest will take place: we are inevitably forced to admit how likely the existence of certain fields of cohesive regularities remain. Conversely, if we decide to reject arbitrarily more central future regularities, we will need to put in question the future of the whole system of regularities constituting our world, something fairly improbable.
   There is no reason that makes it improbable or probable that the whole world will disappear a moment from now. But we can find reasons that make it improbable that a dependent part of the world will disappear in a moment, while others continue to exist, since this already presupposes the permanence of the world as an inductive basis.
   The crude arguments I have just presented were developed only for a single form of induction: from the past to the future. But it would not be difficult to generalize them, even if they need further development. Still, they indicate a path to be open which may be of some relevance regarding a problem that from any other angle seems to remain disorienting and intangible.




[1] Curiously the idea of a chaotic world to which induction isn’t applicable was uncritically assumed as possible in the literature on the problem from P. F. Strawson to Wesley Salmon.

[2] Keith Campbell: “One Form of Scepticism about Induction”, in Richard Swinburne (ed.): The Justification of Induction (Oxford: Oxford University Press 1974), pp. 80-83.

[3]  New English Bible: The Revelation of John, sec. 9. 7.

[4] Aristotle: Physics, 200b, 33-35.

[5] Maybe not in quantum mechanics, though I have my doubts.






segunda-feira, 7 de março de 2016

ADVERTISING FOR THE BOOK "PHILOSOPHICAL SEMANTICS: TOWARDS A NEW ORTODOXY"


THE BOOK "PHILOSOPHICAL SEMANTICS: TOWARDS A NEW ORTODOXY, shall be published by Cambridge Scholars Publishing still in 2016


The assumption of this book is that the analytic philosophy made in the first half of the XX century was much deeper and stronger than the kind of analytic philosophy that began to find its space after the WWII and that today is almost hegemonic.  The later Anglo-American philosophy of language has cumulated smart scientist-formalist objections against all kinds of truisms accepted by the old analytic philosophy: against the analytic-synthetic distinction, against the relevance of meaning, against verificationism, against the correspondence theory of truth, against cognitivist internalism, against the higher-order view of existence… with the result that the descriptive metaphysics, which is a systematic enterprise relying on such truisms and aiming comprehensibility turned to be almost impossible.  The misery of much of the present analytic philosophy results from the authority of these views, which foster the positivist fragmentation of our philosophical approaches, turning philosophy a maidservant of science stollen from its proper epistemic place. This books aims to show the force of the old ideas by reconsidering them, together with arguments bringing evidence to the ultimately fallacious character of most of the new ideas.



quinta-feira, 25 de fevereiro de 2016

(C)#AN EXTRAVAGANT READING OF FREGE'S SEMANTIC (2)

This is the continuation of the uncorrected rough DRAFT (1) for the book Philosophical Semantics to be published by CSP.

...........


The reference of a sentence as its truth-value
Now we let this speculation and come to the reference of the sentence (Satz) in Frege’s semantics. According to the principle of compositionality he understands it as being what remains unchanged when we change the senses of the components of the sentence without affecting their references. This happens when we replace ‘The Evening Star is illuminated by the Sun’ with ‘The Morning Star is illuminated by the Sun’. Here the references of the sentence-components do not change. Hence, the reference of the whole sentence should also not change. But what hasn’t changed? Frege’s reply is: the truth-value. Both sentences remain true. Indeed, ashe emphazises, it is the search for truth is what brings us from sense to reference. From this he concludes that in extensional languages the references of sentences are their truth-value. For him all true sentences have only one reference, which is the abstract object, The True (das Wahre), while all false sentences have only one reference, which is the abstract object The False (das Falsche). Frege has choosen the truth-value as the reference of sentences because it is what give to them value to us, because of its semantic relevance (Bedeutung).[1] Indeed, truth-value is of decisive importance for logic because it is what must be preserved in valid arguments; the logician does not need to know more than the truth-value about the referring function of the sentences he is dealing with.
   Nonetheless, in spite of any theoretical advantage that this suggestion can provide to the logician, it remains from the point of view of what we understand by ‘reference’ utterly implausible. Trying to refute the accusation of implausibility, the Fregean philosopher Alonzo Church mounted a slingshot argument, attempting to show that by means of intersubstitutability we can prove that the reference of the most diverse sentences must be only one, namely, their truth-value. I will guive the concrete example of a slingshot argument and then explain why it is equivocal and therefore fallacious[2]:

1.      Sir Walter Scott was the author of Waverley.
2.      Sir Walter Scott is the man who wrote the 29 Waverley novels.
3.      The number that is such that Walter Scott is the man who wrote the Waverley novels is number 29.
4.      The number of counties in Utah is 29.

   Assuming it to be plausible that sentences (2) and (3) are, if not synonymous, at least co-referential sentences, then (1) has the same reference as (4). As (1) concerns a fact completely different from (4), it seems that the only thing left as a reference is the truth of both sentences.
   However, the argument proves to be unsustainable when we consider what should be the logic subjects of these sentences. The first sentence is a relational sentence: the relation is ‘…the author of…’, while the singular terms are ‘Sir Walter Scott’ and ‘Waverley’. The second sentence is similarly relational, but containing one detailment of the singular term Waverley in the definite description ‘the Waverley’s 29 novels.’ The third sentence is the tricky one:  how to analyse ‘The number that is such that that Walter Scott is the man who wrote the Waverleys novels is 29’? Preserving the sense this sentence can be made clearer as the following conjunction of two sentences: (3) ‘The number of Waverleys novels is 29 and the man who wrote Waverleys novels is Walter Scott.’ Still preserving the sense this last sense means the following conjunction: (5) ‘29 is the number of Waverley’s novels and the man who wrote the Waverley novels is Walter Scott.’ Now, understanding ‘is’ as ‘is the same as’ or ‘=’, we can say that this sentence means: (6) ‘(29 = the number of Waverley’s novels) & (Walter Scott = the man who wrote the Waverley novels).’ We see that now we really have two identity sentences and four singular terms. Finally, we come to the analysis of the sentence (4): ‘The number of counties in Utah is 29’, what means the same as the identity sentence (7) ‘29 = The number of counties in Utah’. So analysed the argument appears as:

1.     Sir Walter Scott = the author of Waverley.
2.     Sir Walter Scott = the man who wrote the 29 novels of Waverley.
3.     (6) (29 = the number of Waverley’s novels) & (Sir Walter Scott = the man who wrote the Waverly’s novels).
4.     (7) 29 = The number of counties in Utah.

   Now, can we still sustain that these sentences have all the same reference? It does not seem because sentences (1) and (2) have as objects of reference the man, Sir Walter Scott, either as the author of Waverley or as the writer of the 29 novels of Waverley. But (3) is a conjunction of two sentences with two objects of refrence. The first has as object the number 29. The second has as object Sir Walter Scott as the man who wrote the novels of Waverley. And (4) has as object of reference the number 29 as the number of counties in Utah. It seems also that we cannot pass from sentence (2) to (3) without adding a new object of reference that is preserved in (4) when the object of reference of (2) and (1) disappears. So the argument commits a subtile form of equivocity that the analysis allows to bring to the surface.
    Moreover, if the object of reference were an object to which adding properties we build a fact, then the fact represented in sentences (1) and (2) is only one, while the facts represented in the sentence (3) are two, including selectively the fact represented in (1) and (2), while the fact represented in sentence (4) includes only the newthe first two sentences.
   Not only can the slingshot argument can be debunked, but there are a number of well-known embarrassing objections to Frege’s identification between reference and truth-value. A first one is that there are substitutibility problems with Frege’s view on the reference of sentences. If all true sentences refer to an object called ‘the truth’ and the name ‘the truth’ also refers to the truth, then in the conditional sentence ‘If it rains, then water falls from the sky’, we can replace ‘it rains’ with ‘the true’, getting the sentence ‘If the truth, then water falls from the sky’, which should be true, even though it is in fact unintelligible.[3] Another difficulty is that many obviously false identities should be true. For example, ‘Paris is a city = snow is white’ should be a true assertive sentence, since both partial sentences refer to the same thing: The Truth. Moreover, contrary to any healthy intuition, Frege’s proposal frontally contradicts the meaning we normaly give to the word ‘reference’. It seems clear that the sentence ‘Napoleon was born on Corsica’ has a reference, while the sentence ‘2 + 2 = 4’ refers to something very different, even if both are true. Furthermore, it should be expected that the reference of the components of our sentences should belong to the same ontological level as their references. But this is not the case: the reference of the name ‘Napoleon’ is the Napoleon of flesh and blood, while the reference of the sentence ‘Napoleon was born on Corsica’ must be the abstract thing called The Truth. Finally, one could argue that from the perspective of Fregean semantics, his solution sounds false because it in fact violates a principle of compositionality, whereby the whole depends on its parts, so that a change in a part produces a change in the whole. If the reference of a sentence is its truth-value, it cannot be established by its parts, since the truth-value is simple and has no part. The components of the sentence, however, have their own references, which vary enormously.
   I conclude that the most charitable interpretation consists in saying that Frege is here using the word ‘reference’ in a new, technical sense, though recognising that this way to use the word is dangerously misleading, since it has nothing to do with what we can reasonably understand with the word.

The reference of the sentence as a fact
The Fregean account of the references of sentences as their truth-values turns out to be still less acceptable when we consider that a much more natural alternative is available, which, as Anthony Kenny has noted, was not even mentioned by Frege.[4] We can, as Wittgenstein, Russell and others did, suppose that the reference of a statement is always a fact, generally understood as a contingent combination of elements given in the world. Facts would satisfy the Fregean condition that the reference of a sentence is an object: they are independent, complete, closed. Moreover, facts would satisfy the principle of compositionality: they could always vary in accordance with the variations in the references of the component parts of the sentences. Moreover, they could vary with the unlimited possible variations in the epistemic values of different whole sentences.
   If we assume this answer, questions arise. The first is the following: how do we establish what fact the thought expressed by a sentence refers to? What are the criteria of individuation of facts? Consider the following sentences:

1.     The Morning Star is the Morning Star.
2.     The Morning Star is the Evening Star.
3.     The Morning Star is Venus.
4.     Venus is the most brilliant planet visible in the sky.
5.     Venus is the second planet orbiting the sun.
6.     Venus is the only planet in our solar system shrouded by an opaque layer of highly reflective sulphuric acid clouds.

From the one hand, it seems clear that each of these sentences refers to a different fact. Sentence (1) is an empty tautology, while sentence (2) is informative; and the information conveyed by the sentences that follows are all different. However, since all singular terms composing these identity sentences have the same reference, it seems that in the end all these sentences must also have the same reference, just changing their ways of representation, their expressed thoughts, depending on the varying senses of their components. Thus, from the last point of view it seems that all these sentences refer to the same fact.
   The question arises: is there a privileged grounding fact able to be described that can be identified as the same truth-maker of all the identity sentences about the planet Venus, including in some way the five facts stated above as its sub-facts? My suggestion is that this task can be accomplished by the references of identity sentences between proper names. Assuming our proposed view of proper names as abbreviations of clusters of descriptions as essentially correct, then the proper name ‘Venus’ ideally summarises in its content all the known modes of presentation of this word. This means that definite descriptions such as ‘the Morning Star’, ‘the Evening Star’, ‘the second planet orbiting the Sun’ and even ‘the only planet in our solar system shrouded by an opaque layer of highly reflective clouds of sulphuric acid’ can be at least made probable by the concept of Venus – I say made probable because they are symptoms and are not seen as necessarily applicable. Well, in that case there is indeed a sentence that could describe the grounding fact, which is the ultimate truth-maker of any identity sentence concerning the planet Venus, including the sentences from (1) to (6) above. Here it is:

7.     Venus = Venus.

My claim is that this sentence is able to express the grounding thought (in principle included in the others) able to refer to the single grounding fact, which if regarded in its entirety, is able to work as the truth-maker for any identity sentence about the planet. Indeed, if the proper name ‘Venus’ is understood as an abbreviation of a cluster of descriptions that uniquely identify our object, then this proper name replaces the descriptions ‘the Morning Star’, ‘the Evening Star’, ‘the second planet orbiting the Sun’, etc. Consequently, we can derive as probable from the sentence ‘Venus is Venus’ the sentence (2) ‘The Morning Star is the Evening Star’, simply by replacing the first occurrence of the name ‘Venus’ with the definite description ‘the Morning Star’ abbreviated by the name, and the second with the description ‘the Evening Star’ also abbreviated by the name. In a similar way we can easily get all the co-referential identities presented above. In this way the sentence ‘Venus is (the same as) Venus’ would be able to represent a fact complex enough to contain the sub-facts that are the truth-makers of each one of the thoughts expressed by the above sentences. 
   In order to reinforce what I am suggesting, we can use instead numerical identities like the following:

1.     2 + 2 = 2 + 2
2.     2 + 2 = 1 + 1 + 1 + 1
3.     2 + 2 = 4
4.     4  = √16
5.     2 + 2 = (14 – 6) / 2

   Of course, the identity sentence expressing the grounding fact would be here:

6.     4 = 4

   But could the sub-fact expressed by sentence (5) be derived from (6)? The answer is surely ‘yes’, since we are handling with a deductive system. Also because I wrote the five sentences above conceiving deductive derivations from 4 = 4.
   In the case of empirical facts, being the derivation based on symptoms, the probability is variable. It is sure the fact that Venus is the second planet of the solar system. But it is somewhat less sure the fact that Venus is the only planet in our solar system shrouded by an opaque layer of highly reflective clouds of sulphuric acid. And it is still less sure the supposed fact that the core of Venus is partially liquid. Moreover, one could object that a sentence like ‘Venus is Venus’ is a tautology dispensing verification: a necessary truth. How could a necessary truth originate contingent truths like ‘Venus is the most brilliant planet visible in the sky’?
   My answer to these objections is that for a privileged user of the word (the astronomer) who is supposed to master all pertinent information about Venus, this proper name expresses its identification rule, according to which it has been identified by astronomers during a difinite period of time as the second planet to orbit the sun (localizing and main fundamental rule). Without the application of this criterial rule it would be difficult if not impossible to identify Venus. The application of other descritiptions, however, do not make criteria, but symptoms of the existence of the planet, since they make the application of the descriptions only more or less probable. Contingent truths like ‘Venus is the most brilliant planet’ hang on these symptoms, in the case, the highly reflexive sulfuric acid clouds. If Venus loses its atmosphere it may ceases to be the most brilliant planet but does not ceases to be Venus.

The ontological status of facts
If we accept that the references of sentence-senses or thoughts are facts, then from an ontological perspective the reference of empirical sentences must be empirical facts, often located in the external world. This assumption speaks for the correspondence theory of truth, according to which facts are truth-makers seen as arrangements of elements in the world. However, this assumption runs against Frege’s anti-correspondentialist view of truth. This is a reason why according to him a fact would be nothing more than a true thought.[5] Following similar anti-correspondentialist lines, P. F. Strawson in an influential article suggested that empirical facts are mere ‘pseudo-material correlates of the statement as a whole’ and not something in the world.[6] His most incisive argument was that empirical facts, in opposition to events or things, are not spatio-temporally localisable. One evidence of this is that the description of a fact is typically anticipated by a that-clause, for example (I can say ‘the fact that the book is on the table’, but not ‘the fact of a book on the table’), while the description of an event typically lacks a that-clause (I can say ‘the event of a tsunami in Japan’, but not ‘the event that there was a Tsunami in Japan’). Moreover, in opposition to events or things, I cannot create, destruct, testimony, avoid, kick, repair, point at, see or hear a fact, the same being the case with states of affairs and situations.[7] Finally, to give a striking example, the event of Caesar’s crossing the Rubicon occurred in the year 47 BC, but the fact that he crossed the Rubicon did not occur in the year 47 BC; it is still the case today, since facts simply do not occur.[8]
   An efficacious way to dispose of this argument was proposed by the correspondentialist John Searle. For him we need a word to describe the thing in the world that makes our thoughts true. The word ‘fact’ is available. So, why do not use it estipulatively in order to designate the truth-maker, whatever is it?[9]
   However, it seems clear to me that even this way to circumvent the problem is avoidable, since we can show that the problem exists only in the imagination of philosophers. To begin with, of course I’m not saying that everything we may call a ‘fact’ is objectively real. The fact that 2 + 2 = 4 is not said to be empirical. And we can say that it is a fact that the Sun is not green, though this seems only another way to say that the fact that the Sun is green does not exist. What I want to defend is that empirical facts, particularly regarding so-called observational facts, should be considered objectively real: they exist in the external world being good candidates to truth-makers.
   There is a first and relatively obvious argument to show that facts can be constituents of the empirical world. It is the property of many of them of acting causally. Consider the following sentences:

(1)   The fact that the match was scratched caused the flame.
(2)   He died because of the fact that he forgot to turn off the gas.
(3)   Because of the fact that today is holiday, today there will be no class.
(4)   The fact that Cesar crossed the Rubicon had important historical
         consequences.

   It does not seem possible that a pseudo-material correlate – something like a propositional content – can in itself act causally in the empirical world to produce an effect. Obviously, the admission of the empirical nature of these facts solves this problem: scratching the match is a fact-event causing the flame; the situational fact created by his forgetfulness of the gas turned on caused his death; the fact-circumstance that today is holyday causes the absence of class today; the fact-event of crossing the Rubicon concretized a state of affairs that determined causally important historical changes in the Roman empire.
   Furthermore, I have a key-argument to regenerate the idea that empirical facts are correlates of true thoughts, so that the empirical facts that we represent by means of affirmative sentences may be contingent arrangements of elements in the external world or in the world (external and/or internal) in general (supposedly, a combination of more or less complex s-properties designated by predicates contingently concatenated with the combinations of s-properties referred to by proper names). This would be the case with facts as simple as those referred to by the sentences ‘Frege wore a beard’ and ‘The book is on the table’.
   My argument against Strawson’s opposition between non-spatio-temporal facts and spatio-temporal events shows that there is confusion in his argument. He treats facts (as much as states of affairs and situations) as being opposed to events. But this can be contested. Any event can be called a fact, though not any fact can be called an event. For example: I can replace ‘the event of the sinking of the Titanic’ by ‘the fact of…’, but I cannot replace ‘the fact that the Everest is more than 8.000 m. high’ by ‘the event that…’ Hence, it is much more reasonable to consider the event as a kind of fact than to oppose both. Indeed, my proposal is that the word ‘fact’ is an umbrella term that encompasses events, occurrences, processes, as much as situations, circumstances, states of affairs, etc. And the reason for my proposal is that we can call all these things facts, but we cannot call all these things states of affairs or events or whatsoever. So considered, events are sub-types of facts: the word ‘event’ should be seen as a hyponym of the word ‘fact’. The reason for my proposal is that when we treat facts as arrangements of elements, we see that there are two great sub-classes of facts:

1.     STATIC FACTS: Can be formal or empirical, the latter when clearly located in space and time. Static facts do not change while they last. Typical of static facts is that the relationships between the elements constitutive of them do not decisively change during the period of their existence. In the ordinary language they may be called ‘states’, ‘situations’, ‘circumstances’, ‘states of affairs’, etc.
2.     DYNAMIC FACTS: Are always empirical. They change while they last. The relationships between the elements constitutive of them change decisively during the period of their existence, so that they have a beginning, followed by some kind of development that comes to an end. Ordinarily they are called ‘events’, ‘occurrences’, ‘occasions’, ‘processes’, etc.

Formal facts, like the fact that 7 × 7 = 49, are static in the innocuous sense that they aren’t spatio-temporaly located. They are not our major concern here. Many facts are empirical and static, since the relationships between the elements constitutive of them do not change during their existence. Static facts are usually called ‘states’, ‘situations’, ‘conditions’, ‘circumstances’, ‘states of affairs’, with different nuances of meaning. For example, my unhealthy state, the situation that I am lying in bed, the circumstance that the airport is closed, the state of affairs that Venice is full of canals or that the earth orbits the sun (which counts as a static fact, as the element of revolving around the sun is a cyclic relationship that remains the same during the fact’s existence...).
   Dynamic facts, on the other hand, are defined by irrevocable changes in the relations among their elements during the period of their existence; the process of the World War II, for example, was marked by events like the war of Britain, the defeat of Stalingrad and the invasion of Normandy – it had an imprevisible history. Dynamic facts are called normaly events when their duration is shorter, occurrences when their duration isn’t as short, and processes when their duration is longer. Examples of events are a lightning flash under dark clouds, the explosion of a bomb. Example of an occurrence is the eruption of a volcano. The process of global warming is a very slow natural process, slower then the economic process of globalization. We can predict the stages of many events and processes, although many are also unpredictable in a way that (differently from static facts) we cannot have an entire grasp of them before their end. Important is to see that all these things can not only be called events, occurrences, occasions, happenings, processes… but also facts, since they are nothing but empirical facts and truth-makers of a dynamic kind.
   We are now able to find the real reason why we use a that-clause in the description of facts but not in the description of events. When we speak of dynamic facts, we do not use a that-clause. So, we can speak about the event of Caesar’s crossing the Rubicon, but not about the event that he crossed the Rubicon. We can speak about the process of climate change, but not about the process that the climate changes… But this isn’t the case regarding static facts, which are typically (though not necessarily) described beginning with that-clauses. So, I can speak about the state of affairs that my book is on the table or that I am lying on the bed, but I can also speak about the state of affairs of my book being on the table and of my being lying on the bed. Conclusion: that-clauses are used to emphasise static facts and to exclude that they are dynamic. And since the hyperonymic term ‘fact’ can be applied to both – the static facts as much as the dynamic facts – it seems plausible to think that the term ‘fact’ inherits the property of being used indifferently, with or without the that-clause: you can say ‘It is a fact that Mount Vesuvius is located near Naples’ (referring to a state of affairs), as much as ‘It is a fact that Mount Vesuvius has erupted’ (referring to an event). And you can say: ‘Cesar crossing the Rubicon was an event’ as much as ‘It is a fact that Cesar crossed the Rubicon’, referring to the event.
   Caesar’s crossing the Rubicon is in turn a very misleading statement: it is usually not understood as the description of an event, but as an illustrative way of referring to a static social fact: the state of affairs established by the movement of Caesar’s army onto Italian territory, violating the law that prohibited this and forcing the Roman state to declare war against him. Rarely is ‘crossing the Rubicon’ understood in the literal sense, as the physical event of crossing the river, which comprises Caesar’s locations in relation to the river from t1 to tn.
   Due to the nature of dynamic facts like events and processes, we say that they not only are, but also occur in time, while of static facts we say only that they are located in time while they last. It seems, therefore, that because philosophers such as Strawson did not realise that events are sub-types of facts, seeing only that we may say of events that they occur in time, they hastily concluded that only events are located in time, opposing them to timeless facts. But that this isn’t true can be shown even by inter-substitutivity salva veritate: it is not incorrect to say that the event, the occurrence of Caesar’s crossing the Rubicon was a fact and that this fact occurred in 47 BC, as a concrete dynamic fact. On the other hand, the political state of affairs established by the crossing of the river was far more durable, because it was a static fact, the political situation that produced, as is well-known, the fall of the Republic. However, it seems clear that the state of affairs brought about by the crossing of the Rubicon was spatially limited to the Roman Empire and temporally limited to the time from the crossing of the Rubicon to the empowerment of Cesar as a dictator. It was not something that existed in Australia or that endures until the present, even if we may use the present tense to speak about historical facts.
   Having the broadest scope, the concept-word ‘fact’ remains the ideal candidate for the role of truth-maker in the correspondence theory of truth. In this case, the fact given in the empirical world could be seen as composed of a static or of a dynamic arrangement of elements build up by s-properties able to satisfy criterial configurations demanded for the application of some kind of verifiability rule, as conceived by epistemic subjects. And it doesn’t seem implausible to think that this satisfaction depends on some kind of structural isomorphism between compositions of criterial configurations demanded by the rule, on the one hand, and compositions of combinations of s-properties belonging to the fact in the world, on the other hand.
   With all its difficulties the argument for structural isomorphism, which will be explored later, is in my view transcendental because we are unable to conceive another way to explain representation. This suggestion, like others presented here, is such that one could erect a wall of pigmy arguments against it which could not possibly be answered in the present text. However, since what I have suggested isn’t intuitively implausible, and since in philosophy there is no revealed truth, it is my right to go ahead.

Sense of sentences: the thought
Now it is time to go on to the sense of the sentence. Here Frege scored well! He was lucky in suggesting that the meaning of the whole sentence is the thought (Gedanke) expressed by it. He came to this result by applying his principle of compositionality of senses, whereby the sense of a complex expression is formed by the senses of its component expressions combined in a certain way. If, for example, in the sentence ‘The Morning Star is a planet’ we substitute for the expression ‘the Morning Star’ ‘the Evening Star’, which is co-referential, although having a different sense, the reference of the sentence does not change; but the sense of the sentence must change. And indeed, the sense of the sentence ‘The Evening Star is a planet’ is a different one. But what we have changed with the change of the sense of the sentence is the thought that the sentence expresses. Consequently the sense of a sentence must be the thought expressed by it.
   The word ‘thought’ is ambiguous. It can be used to describe a psychological process of thinking, as in the utterance ‘I was just thinking of you!’ But it also seems to designate something independent of specific mental occurrences – a content of thought – as expressed by the utterance: ‘The sentence ‘12 . 12 = 144’ expresses a true thought.’ Frege had the latter meaning of the word ‘thought’ in mind. In this usage, the word means simply what the sentence (or statement) says, which Frege has seen as an unchangeable platonic entity. The terminology here counts, because the word ‘thought’ is the only term in natural language corresponding to more technical terms like ‘proposition’ or ‘propositional content’.[10]
   Frege has a criterion for deciding what belongs to a thought. For him everything that contributes to determining the truth-value of a sentence should belong to its thought. Thus, using his own example, the sentences ‘Alfred hasn’t arrived’ and ‘Alfred hasn’t arrived yet’ express the same thought, once the word ‘yet’ expresses only an expectation regarding the arrival of Alfred without contributing to its truth-value.[11] On the other hand, the sentences ‘The Morning Star is Venus’ and ‘The Evening Star is Venus’ can be counted as expressing different thoughts: the singular terms that make up these two identity sentences all refer to the same planet, but by means of different modes of presentation, that is, by following different paths in the determination of their truth-value, or, as we could finally suggest, by following different combinations of semantic-cognitive rules producing verification procedures that are correspondingly different.

The thought as the truth-bearer
Another quite plausible Fregean thesis was that the bearer of truth is not the sentence, but the thought expressed by it. Although we can say that sentences, beliefs and even things and persons are true, they all seem to be true in a derived sense. According to this reasoning, when we say that a diamond is false, what we mean is only that it is inauthentic, deceiving us and making us having false thoughts about it, and when we say that Socrates was ‘true’, what we mean is only that he was a person used to tell the truth, that he was reliable; when we say that Sam’s belief is true, we mean a subjective psychological attitude of the believer, even if well-grounded, and when we say that a sentence is true, this is only a dependent way to say that the thought it expresses is true.
   One rason for preferring to say that the thought is the truth-bearer is that our concept of truth works as a directive ideal so that the concept of truth is of something invariant. We can fail to grasp the truth and grasp a falsity instead; our holding something as true is fallible. But this does not affect the invariability or imutability of the truth. Now, if it is so, the truth bearer must also be something invariable, able to remain the same in order to retain the same truth-value independently of the time of our grasping of it. And indeed, a true thought remains true, as much as a false thought remains false. They are even shorted out as ‘truths’ and ‘falsities’ respectively. So, it is something deeply ingrained in our conceptual grammar that the entity that can be primarily called true or false remains the same and with the same truth value, so that what may change is only our cognitive grasp of it, our believing in its truth-value. If it is so, then only the thought has the necessary stability to be the truth-bearer; for the thought is, according to Frege, unchangeable and eternal (atemporal), being eternally (atemporally) true or false in the independence of our grasping (fassen) of it.
   Consider now the sentences. Identical sentences can express different thoughts, but in this case the truth-values of the thought will accompany the thought and not the sentence… This is the obvious case of indexical sentences like ‘I am in pain’, which express different thoughts depending on the speaker. These sentences-token can change their truth-value when uttered by different persons, and even by the same person in different times. If the sentence were the truth-bearer, the truth-value of the sentence would be able to change at least in all cases in which indexicality were present. Moreover, if the sentence were the truth-bearer then the truth bearer could change without changing its truth-value. For example, the different sentences-token ‘Il pleut’ ‘Es regnet’, ‘Chove’, when uttered in the same context, remain with the same truth-value. Hence, the sentence does not have the stability expected of a truth-bearer. Moreover, the only justification for the truth-value of these sentences remaining the same is that their bearer is the thought expressed by them, since the thought remains the same. And this is valid not only for indexical sentences, but also for identical eternal sentences expressed in different languages, etc.[12] Concluding: the thought and the truth-values not only are invariants but have a relationship of co-variance that is missing in the relationship between sentences and truth-values. Because of this we conclude that the proper bearer of truth must be the thought (or the proposition) and not the sentence.
   Frege also suggested that what we call a fact is the the same as a true thought, because when a scientist discovers a true thought, he claims to have discovered a fact. As he writes:

‘Facts! Facts! Facts!’ exclaims the researcher of nature, when he wants to proclaim the need for a secure basis of science. What is a fact? A fact is a thought that is true.[13]

   However, this conclusion isn’t forceful, for a scientist can also say the same thing – and with more property – understanding by a fact simply what corresponds to the true thought, namely, some real arrangement of elements in the world. After all, it is natural to think that if someone discovers a true thought, it is because a fortiori he has discovered the fact corresponding to it. Moreover, J. L. Austin has shown that the Fregean identification does not resist linguistic replacements, showing changes in meaning. If the sentence ‘What he affirms is true’ had the same sense as ‘What he affirms is a fact,’ then the replacement of ‘what he affirms’ to ‘his affirmation’ should be allowed without change in the sense.[14] But while ‘His affirmation is true’ preserves the meaning, ‘His affirmation is a fact’ is a metalinguistic sentence referring to the fact of his utterance and not to the content of the affirmation anymore. The reason for this seems to be that even if the content of its affirmation – the Fregean thought – is true, it cannot be in itself a fact.
   The reason why Frege believed that the fact is the true thought is, indeed, that he advocated a conception of truth as redundancy, rejecting the correspondential theory. But not only his auments against correspondence are unconvincing,[15] but the correspondence view remains the most natural and plausible conception of truth, suggesting that facts are combinations of elements in the world, able to be at least aspectually represented by their thoughts, which, when this happens, are called true. Moreover, the view of truth as correspondence is in conformity with our common sense methodological point of departure, and in the final chapter of this book I will endeavour to defend it.
   Finally, it is worth to note that a source of confusion between true thoughts and facts seems to reside in our natural language. Although dictionaries present us a variety of meanings for the word ‘truth’, there are two pervasive meanings that are the most emphazised:

(a)  Truth as consisting in things being as we believe that they are, as conformity with facts: the correspondence to reality.
(b) Truth as the actual state of affairs: the real thing or fact.[16]

   In sense (a) we say that a thought is true, uttering sentences like ‘His words are true’, while in sense (b) we say that the fact in the world is true in the sense of being real, uttering sentences like ‘the mentioned occurrence was true (it was real)’, ‘we are searching for the truth (for the real facts)’, or ‘In truth (in reality) she respects your work.’ This shows that the sense (b) of the world ‘truth’ is derivative, since facts in the world makes us to have true thoughts about them in the same way as true objects like the authentic diamond and true persons like the the reliable Socrates. Now, since ‘truth’ can mean not only ‘correspondence with facts’ but also ‘a fact in the world’, it is easy to confuse the first and proper sense of the word with the second derivative sense and believe, considering that facts and thoughts can be said to be true, that facts are true thoughts.

The thought as a verifying rule
If we analysed Frege’s senses of singular and general terms as semantic-cognitive rules, thoughts, as the senses of sentences, must be for us combination of semantic rules. But if the thought is a combination of rules, then what results from such a combination must also have the character of a rule, even if it is not a previously conventionalised rule. Combining this with our acceptance of the correspondence view of truth this means that the thought is also a kind of rule, whose function is to make us aware of the fact referred to by it.[17]
   This reasoning leads us directly to a curse word of scientism called ‘verificationism’, more precisely (and still worst), to semantic verificationism: the doctrine first proposed by Wittgenstein, according to which the (cognitive, informative) sense of a sentence is its rule or method or procedure of verification. This doctrine, which in the present days is considered by many unsustainable, even though the received wisdom against has never been very deeply scrutinized. Indeed, I intend to provide the first serious criticism of this received wisdom as something corrupted by positivist-scientists prejudices in the next chapter of the present book, making plausible that there is nothing wrong with this doctrine except for its intrinsic philosophical difficulty.
   Anyway, I will introduce this view here speculatively, as an alternative and in fact as the most natural way to analyse what can be meant by Frege’s discovery of the thought as the sense or epistemic value of the sentence. Suppose that the semantic-cognitive rule that constitutes the thought expressed by an assertive sentence is its verifying rule. If we show that this rule is effectively applicable to a fact, it makes the thought-sense-rule true, and we may also derivatively say that the sentence expressing it is true. If, on the other hand, we show that this rule isn’t effectively applicable, it makes the thought-sense-rule false and we may derivatively say that the sentence expressing it is false. Finally, if we cannot build up a verifying rule able at least in principle aplicable, we must conclude that the sentence is devoid of meaning, that is, devoid of thought-sense-rule, even if it may seems to have a sense. I think that this way to understand the truth of a thought is in line with Frege’s remark that although treating truth as the property of a thought it does not seem to be a property in the usual sense of the word[18]; indeed, truth does not add anything to the thought-sense-rule, except its effective applicability in its proper domain.
   The proposed identity between the Fregean concept of thought and the concept of a verifying rule is in my view supported by the Fregean suggestion that the criterion for the identification of what belongs to a thought is for it to have at least some role in the establishment of its truth. That is, the thought rxpressed be a sentence is the same as its epistemic sense or the informative content, which should be its rule of verification. And the identifying criterion for this thought-sense-rule (procedure, method) must be that it allows the recognition of its truth-value, what should be whatever is able to warrant it its effective applicability to the corresponding fact.
   But what is the property of this verifying rule – the thought – of being true? Well, there are two ways of answering the question. First, we can get an answer by reflecting on what we have said about the property of existence of what is referred by a conceptual (ascription or identification) rule. Since this existence should be the property of the effective (and not only supposed) applicability of the concept expressed by the conceptual word, by symmetry the same should be said about the property of thoughts of being true. Truth could be the property of a verifying rule of being effectively applicable to its object, which should be the fact (or sub-fact) that satisfies the rule. What the sentence ‘p is true’ expresses should be the thought p, which is a verification rule, followed by its ascription of truth, which is nothing but the higher order ascription of the property of effective applicability to the sense-thought-rule. We could even say, in a Hegelian fashion, that existence is the truth of the concept and the truth is the existence of the thought. Existence and truth are zwilling concepts.
   However, we can get a seemingly alternative way of explaining the property of the verifying rule or thought of being true, which is by appealing to the correspondence view of truth. If the thought is the bearer of truth, and the thought is the verifiability rule of a sentence, then this verifiability rule is also the bearer of truth. And since what makes a thought true (assuming the correspondence theory) is its correspondence with the fact, what makes the verifiability rule true must be the sufficient match between the criterial configurations demanded by this rule and what is able to satisfy these configurations, as the diverse ways of manifestation of the corresponding fact in the world. If the verifying rule has the metaproperty of being satisfied by a corresponding configuration of s-properties that can be considered as the aspectual presentation of a fact given in the world, this rule has the metaproperty of being true; if the verifying rule lacks this metaproperty, it is false. If the supposed verifying rule cannot have this metaproperty, it is no verifying rule at all, it is the kind of thoughtless thought that a senseless sentence in the best case only seems to express.
   What alternative is the most plausible? My guess is that considering truth as a property of applicability or a sense-thought-rule and as a property of this rule of corresponding with a fact are only different ways of saying the same. They would be the same because to say that a verifying rule is true when it can be satisfied by the matching of its criterial configuration with a configuration of s-properties that can be considered as the aspectual presentation of a fact given in the world is the same as to say that this verifying rule is effectively applicable to the sub-fact given in a certain domain and, indirectly, to the whole fact given in the world.
   It also may be reasonable to think that the combination of elements constitutive of a fact must satisfy the verifiability rule when at least some aspect of it, some s-property, in some sense corresponds sufficiently to the criterial configurations demanded for the effective application of the verifiability rule that constitutes its thought. This also seems to combine verificationism with correspondentialism. What we call a judgment, in turn, is our acceptance of a thought-sense-rule as true, which contains our recognition of the effective applicability of a verifiability rule, of its correspondence with the fact.

The existence of a fact as the truth of its thought?
We have seen that existence in the world should be the effective applicability of a semantic-cognitive rule. And we also saw that if this idea works for concepts, it should work also, by symmetry, to the combinations of semantic-cognitive rules called thoughts or verifiability rules. Now, if the existence of an s-property is the metaproperty of effective applicability of its ascription rule, the existence of the fact should be the metaproperty of effective applicability of its verification rule. Now, considering that truth is the property of a thought, and that the thought is a verifiability rule, truth should also be a property of the verifiability rule; but what property? Of course, the property of being effectively applicable, for this is clearly what makes the verifiability rule – the thought – true. However, since

1.     The truth of a thought = the effective applicability of a verifiability rule

and

2.      the effective applicability of a verifiability rule = the existence of a fact

we are lead by transitivity to the conclusion that

3.     The truth of a thought = the existence of a fact

This seems to give right to Frege, when he writes that

4.     A fact is a thought that is true.

   This would be a very undesirable conclusion, since it seems to reinforce Frege’s redundance view of truth, which I cannot accept, since it means the rejection of the correspondence theory of truth, which is in full harmony with our methodological commonsensical principle.
   However, in a nearer consideration we see that the views are different, since (3) does not imply (4). When I say that the true of a thought is the existence of a fact, I am not identifying true thoughts with facts, but only saying that when I attribute truth to a thought I am ipso facto attributing existence to the fact that that the thought represents.  In other words, when I admit the effective applicability of the verifying rule I am admitting the existence of the fact that satisfies this rule, what is compatible with the idea that the correspondence of the verifiability rule with a fact is nothing but its effective applicability to this fact.

Frege’s Platonism
It is important to remember that for Frege thoughts (including the senses that compose them) are Platonic entities belonging to a third ontological realm, which is neither psychological nor physical. For him, taking as the criterion of objectivity the intersubjectivity and independence of will, and taking as the criterion of reality existence in space and time, we get three ontological realms:

1. Realm of the objective and real
2. Realm of the subjective and real
3. Realm of the objective but non-real

   The first realm is that of physical entities, such as concrete objects, which are objective and real. These entities are objective, since they are intersubjectively accessible and independent of our will; and they are real, since they are located in space and time. The second realm is that of psychological entities, mental states that he calls representations (Vorstellungen, a word that we could today translate as qualia). These entities are subjective and real. They are subjective by not being interpersonally accessible and are often dependent on the will. However, they are still real, because they are in the heads of those who have them and, consequently, in time and space. There is, finally, a third realm, that of thoughts (understood as propositions) and their constitutive senses. This realm is objective but not real. It is objective, because thoughts, true or false, are inter-subjectively accessible; we can all agree, for example, that the Pitagorean theorem expresses a true thought. But this third realm of thoughts isn’t real, because according to him as abstract entities thoughts cannot be found in space or time. Thus, the thought (the sense) of Pythagoras’ theorem is according to him objective but non-real.
   Indeed, for Frege thoughts are timeless (eternal), immutable, forever true or false, and not created but grasped (gefasst) by us. Thoughts must have some kind of indirect causal effect: by grasping them we must be able to make judgements, and by making judgements we are able to act in the external world.  How this is possible remains unexplained.
   The reason Frege has to introduce this third realm of thoughts is that thoughts are communicable and, to be effectively communicable, they need to be objective, that is, in some way interpersonally accessible. Representations (Vorstellungen), on the other hand, are rather subjective psychological states, which can vary in dependence of the personal psychology. Thus, for Frege the only way to explain how it is possible that we are able to share the same thought is to distinguish it strictly from mere psychological representations. Without this objectivity, thoughts would remain on the psychological level and would be able to vary from person to person. Moreover, if thoughts were on the level of representations, they would be dependent on personal psychology and would lack the required stability of truth-bearers.

Avoiding Frege’s Platonism
Despite the above suggested arguments, very few would today accept Frege’s appeal to Platonism. After all, the Fregean form of Platonism not only commits us to an infinite multiplication of objective entities (all the infinite true and false thoughts), but also seems to lack intelligibility. The price that Frege was willing to pay in order not to fall into psychologist subjectivism seems to us today too high.
   In my view, Frege’s Platonist solution is unnecessary, simply because the whole problem was wrongly formulated. For there is a way to conform the view that thoughts have a psychological nature to the view that as a truth-bearer they must have stability and the possibility of being communicated. In order to show this, I want to apply a strategy inspired by the ontological particularism of the English empiricists from Locke to Hume, for whom the universal does not exist beyond the similarities among mental ideas.[19] In order to do this, I wish to show that Fregean thoughts (objective non-real truth-bearers…), which I will call f-thoughts (‘f’ from Fregean), can be defined in terms of psychological p-thoughts (‘p’ from psychological). I suggest that can warrant the existence and stability of s-thoughts without hypostasising them as Platonic entities and even without resorting to classes of p-thoughts by means of the following definition:

An s-thought X (Df) = a given p-thought X embodied in some mind or any other p-thought Y qualitatively identical to X, embodied in the same mind or in any other mind.

   The s-thought (‘s’ from spreadable) is my version of what Frege should have meant with his f-thought (objective non-real thought). This definition reduces the supposed f-thoughts to p-thoughts without forcing them to lose their objectivity (intersubjectivity) and expected stability or imutability by interpreating them as s-thoughts.
   The so defined s-thought has no particular spatio-temporal location and can be seen as the truth-bearer. For example: the s-thought expressed in the sentence ‘The Eiffel Tower is made of metal’ can be instantiated as the p-thought that I have in mind when writing this sentence, but also by, say, the p-thought that you have in your mind when you read it, or yet again, by any p-thought that I, we or any other person can have at any other time. Characterised by the disjunction between the qualitatively identical thoughts embodied in any individual mind, the s-thought comes to be regarded in abstraction from the particular human minds that casually instantiate it. With this we avoid not only the appeal to specific occurrences of thoughts, but also the most expected alternative, which would be to explain one s-thought in terms of a sum or class of p-thoughts qualitatively identical to each other, which could lead us to a petition of principle given that classes are also candidates for abstract entities, along with the problem of the size of the thought: thoughts have no size; but if a thought were a class it would be made bigger and bigger the greater the number of people that would have been grasped it.
   Under the proposed definition, in order to exist an s-thought must always have at least one psychological instantiation. The s-thought is no less psychological than any p-thought, since it cannot be considered independently of its instantiation in at least one mind. Thus, when we say that we both had the same idea or have reached the same thought, what we mean is only that there is a qualitative identity between the psychological p-thought-contents that we have respectively instantiated in our minds. This has the advantage of bringing the Fregean thoughts from the Platonic heaven back to the psychological realm, without commitment to a transient psychology of a particular cognitive being. This understanding of the true nature of the s-thoughts explains something that Frege was unable to explain satisfactorily, namely, why they may have causal powers. As an open disjunction of p-thoughts, s-thoughts only exist as psychological instantiations of p-thoughts, and as such they can cause others psychological states and even human actions and their effects in the external world.
   In my view, one of the most ingrained and deceitful philosophical errors in ontology has been seeing numerical identity where there is only qualitative identity. It is true that we can speak of the number 2 in the singular, that we can speak of the geometrical form of circularity, and that we can ask for the meaning of the common name ‘shoe’ using the definite article – but this is just for the sake of simplicity of expression. What we actually can have in mind are instances of qualitatively identical cognitive arithmetical concepts of the number 2, of qualitatively identical geometrical concepts of circles[20], of qualitatively identical meaning occurrences of the word 'chair’ and nothing more. In the same way, we can talk about the thought ‘7 + 5 = 12’, but if we do not intend a specific occurrence of this thought, we are only referring to some occurrence, but without taking into account or specifying which occurrence it is. The true reason why we speak in the singular of the thought ‘7 + 5 = 12’ is that there is no reason to consider the individual persons who think it.
   The adoption of the definition of s-thoughts (which is easily generalisable to all kinds of Fregean senses) proposed above is in my judgment the only plausible abstraction that we can arrive at without falling into any of the various forms of reification that have infested ontology throughout its long history.
   Here arises, however, the Fregean question: how is it possible that the above suggested psychologically dependent definition of s-thoughts could be able to ensure the objectivity of s-thoughts, their intersubjective accessibility or communicability? As we saw, for Frege if thoughts were regarded as psychological representations, as is the case for p-thoughts, they would unavoidably be subjective, unable to be compared with each other. In my view, the need that Frege feels to admit that thoughts belong to a third realm of Platonic entities is too hasty. There is no doubt that what Frege calls representations, psychological mental contents, can largely be expressed through language and by its means be able to be subjectively identified and re-identified as being the same. It is true that a mental state that only one person is capable of having, for example, some epileptic aura, isn’t communicable, except indirectly, metaphorically. But it seems an unquestionable fact that most mental states, such as feelings, images, sensations, are things that all of us are able to communicate and learn to identify in ourselves, through induction by exclusion in some cases, and, in others, through induction by analogy based on interpersonally accessible physical states strongly intermingled with them. [21]
   It is true that there are important philosophical arguments against the traditional epistemological response to our learning of an auto-psychic and hetero-psychic language and knowledge shortly indicated above. But this is one of those points which only philosophers would put in question, as in the famous private language argument refuted in the last chapter. As paradoxical arguments, they have a heuristic value, which does not mean that they should discredit common sense. To do this is like using a sorites paradox to prove that heaps of sand do not exist or that there is no baldness. If we fill the whole domain of philosophy with smart paradoxes and they are taken too seriously, they make plausible systematic philosophy impossible. If internal representations can be saved from the subjectivity of psychology, thought can be saved even more.
   Concerning s-thoughts it is also important to remember that it is not necessary to have a particular model as the object of interpersonal consideration. What we do is simply to alternate a variety of qualitatively identical models that are usually given to us by memory: first the one and then some other, which we recognise as being identical to the first, and then we can use the second one as the model and so on. Important is to remember that none of these models can exist without being psychologically embodied. And language is only the vehicle of communication that allows the reproduction of a qualitatively identical psychological p-thought in the minds of hearers.
   It may at first sight seem implausible that language is capable of repeatedly reproducing in other minds and even in the same mind the same subjective pattern, the same thought content, the same recognisable instantiation of a combination of conventionally established semantic rules. However, compare this case with the case of genetic information able to indefinitely reproduce the same characteristics in successive biological individuals:[22] why the conventions and the ways they can be combined in the constitution of p-thoughts could not render the same? In addition, it is easy to suppose that there are correcting mechanisms able to interpersonally and intra-personally correcting deviances of the standard. There is no reason, except an anti-empiricist bias, to think that things should not be that way.
   Finally, let us apply the distinction made by John Searle between what is ontologically objective/subjective and what is epistemically objective/subjective to the objectivity of s-thoughts.[23] Searle noted that we have a strong tendency to take what is epistemically subjective for what is only ontologically subjective. However, one thing can be ontologically objective – for example, the justification of the World War I – without ceasing to be epistemically subjective, because we are not able to reach common agreement about it. In contrast, a phenomenon can be ontologically subjective without ceasing to be epistemically objective – for example, the knife-like pain caused by a seizure of acute pancreatitis – because everyone (doctors and patients) will agree on the form and existence of this pain. Something similar can be said about the nature of s-thoughts. They are ontologically subjective, since we admit that they are psychological events instantiated in one or other mind. But even so, they do not cease to be epistemically objective. After all, we are capable of both intersubjectively agree about them and their truth values. We can agree that the utterance ‘I am having a knife-like pain in my abdomen’ is true in the case of a patient with a diagnostic of acute pancreatitis. And an objective assertive sentence like ‘The Eiffel Tower is made of metal’ expresses an s-thought that we all also recognise as being true. This thought, like any other s-thought, is ontologically subjective, since it can only be psychologically instantiated. However, like any s-thought, it remains epistemologically objective, given that both the thought-content and its truth-value are fully measurable and reportable, since they are structured by our conventions and based on our knowledge of the facts. On the other hand, a sentence like ‘Love is the Amen of the universe’ (Novalis), unlike an s-thought, has no truth value. It has only colouration, being susceptible only to an aesthetic appreciation with a variable degree of interpersonal agreement.
   Frege was no exception: like Husserl, Bolzano and many other continental philosophers with mathematical training, he believed that the ontologically subjective character of the psychologically conceived contents of thought would inevitably be condened to epistemic subjectivity. But this was a mistake.

Further ontological consequences
This ultimately psychological reconstruction of the Fregean thoughts has interesting ontological consequences. If the thought of the Pythagorean teorem isn’t an eternal (timeless) entity of a Platonic realm, always true or false, where and when is it? Surely it is not in the individual mind, disappearing with its death. However, being at least one occurrence of thought, or any other qualitatively identical occurrence, regardless of the bearer, the Pythagorean teorem acquires an existence that is dependent on minds, although remaining independent of any of the many minds that eventually think it. Since this thought was thought by both you and me, and certainly by many others in the past, its existence must be extended over space and time. This existence can be seen as distributed over the space and time occupied by the heads of mathematicians starting with Pythagoras himself, and perhaps ending in the head of some cognitive being at some unknown future time.
   A consequence from this view is that unlike the Platonic entity that Frege called ‘thought’, our s-thought of the pytagoric theorem in fact did not exist before Pythagoras had it for the first time (supposing he was the first), and will cease to exist when it ceases to be thought by anyone. The Pythagorean theorem certainly exists, has existed and will exist in the sense that it is thought, has been thought and will probably be thought in the future, referring to occurrences of this thought, but without having to take into account who thinks it. One reason why this sounds strange is because nobody can truly think so. One cannot think: ‘The theorem according to which the sum of the squares of the shorter sides of a right triangle equals the square of the hypotenuse is something which existed in the past and now no longer exists’, for this judgment will already date the occurrence of the thought of the Pythagorean theorem and insofar falsify what is said. Nevertheless, it remains the outcome that the s-thought of this theorem would not have come into existence if nobody had ever thought it, if the world had no cognitive beings.
   This brings us to the following objection. Suppose that in the possible world Wn with no thinking being, though it would have stars and planets. In Wn the Pythagorean teorem and the s-thought that there are stars and planets could not have been thought and, as the primary bearers of the truth, could not be true. But it seems obvious that also in this world not only the Pythagoren theorem but also the fact that the sun is a star would be true...
   Our answer is that there is here confusion between the primary bearer of the truth – which is the s-thought – and a secondary but as we already saw very usual bearer of the truth – the real thing or fact in the world, which is reported in any good dictionary. Indeed, that there are planets and stars would be still true as a fact in Wn, and the applicability of the Pythagorean teorem would still be true as a fact in Wn, though not the truth of their s-thought. It is the flexibility of natural language that once again misleads us.
   Still one objection that could be made against the idea that the bearers of truth are non-Platonic s-thoughts is the following. Many truths are discovered. Pythagoras discovered the theorem that bears his name; Archimedes was one of the discoverers of the law of the lever, according to which magnitudes are in equilibrium at distances reciprocally proportional to their weights. But if something is discovered, it logically must have existed before being discovered. Consequently, the above described thoughts already existed before they were discovered.
   Again, the answer is that this objection results from a confusion between the thought as the primary bearer of truth on the one hand, and the fact as the secondary bearer of truth on the other. It seems clear in the case of empirical truths: that the law of the lever was always applicable is true... but the thought of it first came into the world when scientists like Archimedes conceived of it. Similarly, the fact expressed by the Pythagorean teorem has always existed, but our s-thought of it only came into existence after the theorem was thought by Pythagoras and since then by many others. Such facts, however, as long-lasting as they may be, are in the most proper sense not the bearers of truth, but the supposed makers of truth. They are what occurrences of their thoughts represent, which means that the truth of their thoughts cannot have existed before them. In the most proper sense, no truth or falsehood would exist if there were no minds to think of them.
   However, would this mean that before conscious beings appeared on Earth the thought that the Moon is white wasn’t true? The answer is yes and no. The thought couldn’t be true, since it didn’t exist. But we can say that this was a true fact. And we could even say, I believe, that it was true that the Moon was white in the sense that if the thought of the Moon being white were thought it would be true because it would correspond to a fact that would make it true. And this seems to be all that we can really mean when we say that the Moon would still be white even if there were no human being to think it.
   An s-thought that has never been thought does not exist and thus cannot be true. The same with falsities: suppose that the thought ‘The Colossus of Rhodes is floating in the Sargasso Sea’ had never been thought before. As soon as we think that it has never been thought before, we are already thinking it, and we see that it is surely false. Even the s-thought ‘The world could exist, even though there were no minds to think about it’ is only true because there are minds to think it.
   Nevertheless, one could still argue, we can imagine that if we didn’t think that it is true that the world could exist without minds to think it this fact would still remain true. To this the answer would be again that we are using the word ‘true’ here not in the philosophical sense in which the bearer of truth is an s-thought, but in the derivative sense in which the bearer of truth is a thing or fact in the world. As already noted, in this case the word ‘truth’ is means the property of the existence or reality of things or facts; in the case of a world without consciousness it is the property of the existence of the unconceivable multiplicity of facts constituting the external world. This truth as a property of facts is independent of minds indeed. Moreover, in our interpretation the existence of this world would be the same as the effective applicability of the verifiability rules to its facts, even in the case in which these rules do not exist in our minds. For these rules do not need to be instantiated in order to be effectively applicable. They do not need to exist as actuality, but only as a possibility, once that only the application of the rules requires their existence, not their applicability.

A short digression on contingent futures
Before we finish, it is curious to examine the Aristotelian problem of contingent futures in the light of these conclusions. According to Aristotle,[24] the following argument is valid:

 Argument A:
1.     Necessarily now it is true or false that there will be a sea-battle tomorrow.
2.     If (1) is true then the future is fixed and there is no chance.
3.     Therefore, the future is fixed and there is no chance.

For Aristotle this conclusion would be unacceptable because if the future is fixed then there is no chance, and if there is no chance there is no free will. Hence, he thought that although this argument is sound, the premise (1) is false because it exemplifies the principle of bivalence and the principle of bivalence isn’t applicable to future events (only to present and past ones).
   I think that we can get a better light into what is wrong in this reasoning if we consider what is said by a sentence in terms of an s-thought. Suppose that outside any context we consider the thought expressed by the sentence ‘There will be a sea battle tomorrow’, which we can abbreviate as ├p. Is this true or false? The answer is: taken literally├p is unable to express today an s-thought, a proposition, because an s-thought must possibly have a truth-value and without any further contextual information we are totally unable to assign to it a truth-value. That is, the declarative sentence p is unable to express in an spatio-temporaly undetermined ‘today’ a cognitive value, since we cannot correlated it with truth-makers, what can be extended to the instantiation of the principle of bivalence as ├ (p ˅ ~p), which now means nearly as few as ├ (@ ˅ ~@). (This point is made clearer when we suppose that ├p is affirmed to something that will occur in a very remote time in the future.)
   However, there is a reason to the suspiction that it could be otherwise. One could argue that the sentence ├p is misleading and brings us to confusions like the argument A because ├p seems to express cognitive content. The reason for this is in my view that ├p is very easily confused with the sentence ├q: ‘It is likely that a sea-battle will take place tomorrow’, when there are reasons to think so. For example: having broken the Japanese naval codes and having lured the Japanese fleet into an ambush at Midway, the Americans already knew on the night of June 3, 1942, that on June 4 there would almost certainly be a major naval battle. The sentence ├q is easily confused with ├p, because ├q appears almost always abbreviated as ├p: ‘A sea-battle will take place tomorrow’.
   For example: suppose that American Admiral Nimitz had said on June 3:

Tomorrow there will be a sea-battle.

   Everyone would understand that he was saying that all the factual evidence was leading to the conclusion that the expected battle would begin on June 4. This probability – made explicit or not – is in this case objectively measurable in terms of verification by empirical evidence expressing nothing more than a measurable probability that the assertion ├q is expresses a probabilistic true s-thought that is si considered in the light of empirical actual verificational evidence. Indeed, the utterance ‘It is likely that a naval battle will occur tomorrow’ was true in the night of June 3, 1942, the utterance without breaking the principle of bivalence. In a similar way, if I look at the Atlantic Ocean in my home in Praia Bonita and say ‘A naval battle will take place tomorrow’, meaning by it ‘It is likely that a naval battle will occur tomorrow’, this statement will be with the best seen as false, since I have all kinds of reasons to believe that this kind of event is very improbable in this place and time.
   We see that taken literally (and not in the sense of ├q) the sentence ├p is a bluff devoid of meaning and justification and Aristotle was right in rejecting the application of the principle of bivalence to it. All that this sentence does is to induce us to imagine a naval battle taking place tomorrow, giving us the illusion of having verification criteria. However, as much as no context is furnished, no such criteria can be given. The statement ├q, on one hand, says something probabilistic about tomorrow that can be confirmed or rejected by criterial reasons already given today.
   Finally, we should also distinguish the level of thought and the real ontological level assigned to facts. It may be that, because of unknown causal determinism, the present state of the world has today made inevitable the occurrence of a naval battle tomorrow near to Praia Bonita. But it would be a mistake to think that this state of affairs undoes the assertive bluff made by the utterance of ├p, making it the expression of a real s-thought.
   The whole metaphysical trouble about contingent futures can be eliminated when we consider with enough care what we are really able to mean by using a sentence on the future.

Conclusion 
My first aim in this chapter was to insert in the framework of the Fregean semantics the results of my reading of Wittgenstein’s view of meaning as use in accordance with rules, in order to distinguish and give some explanation of the most relevant forms of semantic-cognitive rules. This required strong corrections in Frege’s own framework. Even if some results are admittedly vague and speculative, they nonetheless seem to me no less plausible than Frege’s own original views.






[1] Frege, Letter to Russell from 28.12.1912.
[2] See Alonzo Church, ‘Review of Carnap’s Introduction to Semantics’, in Philosophical Review 52, 1954, pp. 298-304. The argument was restarted later by Donald Davidson in a purely formal mode generating what I believe to be too much ado about nothing.
[3] See Max Black, ‘Frege on Functions’, in his Problems of Analysis: Philosophical Essays (London: Routledge and Kegan Paul, 1954), pp. 235-6.
[4] A. Kenny: Frege: An Introduction to the Founder of Analytic Philosophy (Oxford: Blackwell, 2000), p. 133.
[5] Gottlob Frege, ‘Der Gedanke: Eine logische Untersuchung’, p. 74 (original pagination).
[6] P. F. Strawson, ‘Truth’, in Logico-Linguistic Papers (Aldershot: Ashgate, 2004), p. 151. See ‘Reply to John Searle’, p. 402 in The Philosophy of P.F. Strawson (New York: Open Court, 1999).
[7] For counterexamples, see J. L. Austin: ‘Unfair to Facts’, in his Philosophical Papers (Oxford: Oxford University Press, 1990). It seems to me at least curious that the posthumously published arguments of J. L. Austin against Strawson’s view have had so little impact.
[8] Günter Patzig, ‘Satz und Tatsache’, in Tatsache, Normen, Sätze (Stuttgart: Reclam, 1980), pp. 19-20.
[9] J. R. Searle: ‘Truth: the Reconsideration of Strawson’s Views’, in The Philosophy of P.F. Strawson, ibid.
[10] As Tyler Burge in ‘Sinning against Frege’ wrote, ‘the word “thought” is the best substitute for ‘proposition’ for the naturalness of its semantics within the scope appropriate to the linguistic philosophy’, in Burge: Truths, Thoughts, Reason: Essays on Frege (Oxford: Oxford University Press, 2005), pp. 227-8.
[11] G. Frege: ‘Der Gedanke: Eine logische Untersuchung‚ p. 64 (original pagination).
[12] If instead of sentences-token we appealed to sentences-type as truth-bearers, the problem would be worst, since the same sentence-type could be true and false, infringing the law of non-contradiction.
[13] Gottlob Frege: ‘Der Gedanke: Eine logische Untersuchung’, p. 74 (original pagination).
[14] J. L. Austin, ‘Unfair to Facts’, in Philosophical Papers, a.a.O., pp. 170-171.
[15] Gottlob Frege, ‘Der Gedanke: Eine logische Untersuchung’, pp. 59-60. See the answer to Frege’s major argument in Wolfgang Künne’s, Conceptions of Truth (Oxford: Clarendon Press, 2003), pp.129-133.
[16] If you search the word ‘truth’ in any good dictionary in different languages (even non Indo-European) these two senses – truth as correspondence and truth as the real thing or fact – are always enphazized.
[17] See my exposition of Tugendhat’s verificationist correspondentialism in the introduction of this book.
[18] Gottlob Frege: ‘Der Gedanke: Eine logische Untersuchung,’ p. 61 (original pagination).
[19] In its plain form the insight is clearly expressed by 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.’ George Berkeley: Principles of Human Knowledge, introduction, section 12. See the more sophisticated but also less clear view of David Hume in A Treatise of Human Nature, book I, part 1, section VII.
[20]  One could object: how can we deal with the geometrical circles of geometry if we are always dealing with imperfect empirical circles? Don’t we need a Platonic ideal pattern? The answer is no, because in principle we can make a circle more perfect than the last one, and another still more perfect, and this process can continue without end. The perfect circle is like the actual infinite, it does not exist. It is nothing more than the projection of our awareness of the possibility of making more and more perfect empirical circles without any end in sight. Geometry only works as if a perfect circle existed and uses it as a limiting concept. For we clearly see that ‘qualitatively identical’ cannot mean ‘absolutely qualitatively identical’. The identity here depends on our ability to discern identity and our practical aims. My car has for me (qualitatively) the same colour as yours, but this identity cannot withstand a sufficiently close inspection.
[21]  As a developed defense of the argument by analogy for the existence of other minds from an epistemological point of view, see my paper ‘Linguagem privada e o heteropsíquico’, in Paisagens Filosóficas: Ensaios Filosóficos (Rio de Janeiro: Tempo Brasileiro 2011).
[22] Biological mutations are accidents whose incidence should be evolutionarily calibrated. Only species that are able to mutate in the right amount at the right time can survive. An unchanging species with no relevant mutations is probably possible, but would not have the adaptability necessary for survival under changing external conditions.
[23] John Searle, Mind, Language, and Society, pp. 43-45.

[24] See Aristotle, On Interpretation, chapter 9.