terça-feira, 2 de agosto de 2016

## AN EXTRAVAGANT READING OF FREGE'S SEMANTICS (4)

Uncorrected draft of a chapter of Philosophical Semantics, a book to be published by Cambridge Scholars Publishing in 2016.

Final part of the chapter:

19. The reference of a sentence as its truth-value
Now we let these speculative excurse and come back to the more tangible Fregean semantics, considering what he has to say about the reference of the sentence (Satz). For Frege the references of sentences are their truth-values and the thoughts expresses by them are modes of presentations of truth-values. How came he to this strange result? There are several reasons. First, sentences are independent, saturated, closed, working as names, and the truth-value is also closed like the object refered by a name. Second, it is the search for truth what brings us from sense to reference. Third, he saw that sentences without reference lack truth-value. Fourth, he also noted that according to the principle of compositionality the reference must be what remains unchanged after we change the senses of the components of the sentence without changing 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: their truth-value. Both sentences remain true. Hence, he concludes that in extensional languages the references of sentences must be their truth-value (1892: 34).
   A first consequence of this conclusion is that for Frege 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). Independently of this argument, interpreters have noted that Frege has choosen the truth-value as the reference of sentences because it is what gives them value to us, because of its Bedeutung in the sense of semantic relevance or meaningfulness (e.g., Tugendhat 1992b: 231).[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 regarding the referring function of the sentences he is dealing with in order to evaluate inferential possibilities.
   However, there are a number of well-known embarrassing objections to Frege’s identification of reference with truth-value that in my view completely disqualify the idea. The first one is that, contrary to any healthy intuition, Frege’s proposal frontally contradicts the meaning we normaly give to the word ‘reference’. It is intuitively clear that the sentence ‘Napoleon was born on Corsica’ refers to something very different from the sentence ‘2 + 2 = 4’, even if both are true. Another objection is that it should be expected that the reference of the components of our sentences should belong to the same ontological level of the sentence’s references. But for a Fregean this would not be 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 object called The True. Moreover, one could also argue that his solution sounds false because it in fact violates Frege’s own 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 has no part; and if it has, then all objects refered by names in true sentences must be parts of The True. A further objection is that there are serious substitutibility problems with Frege’s view on the reference of sentences. If all true sentences refer to one object called ‘The true’ and the name ‘The true’ also refers to The True, 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 True, then water falls from the sky’, which should be true but is in fact unintelligible (Black 1954: 235-6). Maybe the worst 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 True.
   The most charitable interpretation consists in saying that Frege uses the word ‘reference’ in a totally new, technical sense. The problem is that in spite of any theoretical advantage for the logician, this new way to use the word is not only gratuitous (why not to say that truth-value is relevant for the logic, etc.?) but can be (and really has been) disastrously misleading from an epistemological standpoint, since it has virtually nothing to do with anything that can be reasonably understood with the word ‘reference’.

20. Church’s slingshot argument
Trying to refute the accusation of implausibility, the Fregean logician 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. Church’s argument is in my view equivocal, but telling. Its basic assumption is that if a constituent expression is replaced by another with interchangeable partial references, the reference of the whole sentence does not change. I will expose his example of a slingshot argument underlining its supposedly co-referential definite descriptions (Church 1956: 25):

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

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 (4) seems to concern a fact completely different from (1), it seems that the only thing left as the same reference is The True of both sentences. Hence, The True is the only referent of all these sentences.
   However, in my view the argument proves to be unsustainable when we pay attention to what should be the real reference of each singular term of these sentences. In the sentence (1) the proper name ‘Sir Walter Scott’ and the definite description ‘the author of Waverley’ are two singular terms expressing different modes of presentation of the same human being: Scott. In the sentence (2) again, the proper name ‘Sir Walter Scott’ and the definite description ‘the man who wrote the 29 Waverleys novels altogether’ refer both to Scott. The third sentence is the tricky one. Its reference is unclear: Scott? The number 29? Is there a clear way to paraphrase sentence (3) in a way that gives back clearly its whole informative content? In my view, the only way to expose its content in a transparently clear way without any addition or loss of sense is to split the sentence into the following conjunction of two sentences: (5) ‘29 is the number of Waverleys novels and Sir Walter Scott is the man who wrote that many Waverleys novels altogether.’ Or, for the sake o clarity, replacing ‘=’ for ‘is (the same as)’ and ‘&’ for ‘and’ we have:

1.     (29 = the number of Waverleys novels) & (Walter Scott = the man who wrote the many Waverley novels altogether).

That is: Sentence (3) confusively compresses nothing less then a conjunction of two identity sentences, each with its own proper object of reference given by the terms beside the identity sign. They are the number 29 in the first sentence and Scott in the second sentence. Finally, we come to the analysis of the sentence (4): ‘29 is the number of counties in Utah’, what means the same as the identity sentence (6) ‘29 = The number of counties in Utah’, each term that flanks the identity sign referring to the number 29. 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 altogether.
3.     (5) (29 = the number of Waverley’s novels) & (Sir Walter Scott = the man who wrote the many Waverly’s novels altogether).
4.     (6) 29 = the number of counties in Utah.

Now, although all these sentences are true, assuming a principle of compositonality, the claim that the reference remains the same loses its intuitive appeal. Sentences (1) and (2) have as objects of reference Scott under different guises. But (3) is a conjunction of two identity sentences each one with its own object of reference: the object refered to by the first one is the number 29 (as the number of Waterley’s novels), while the object refered by the second identity sentence is Sir Walter Scott (as the man who wrote the Waverley’s novels). And (4) has as object of its partial references only the number 29 (as the number of counties in Utah) without referring to Scott. This means that composed sentence (3) has as its second object of reference the same object of (1) and (2), while (4) is an identity sentence that has as its object of reference only the the first object of reference of (3). Consequently, the replacements slip equivocally the objects of reference, which change from Scott in (1) to the number 29 in (4). This means, according to the principle of compositionality applied to the reference that the references of (1) and (4) should be different. Initially the flaw isn’t easy to spot because the sentence (3) contains these both objects of reference conjoined in a grammatically confusive way. The replacements would only respect the compositionality principle, warranting the sameness of the sentences’ references, if the argument could prove that we could replace the objects of references of all the sentences without confusing distinct references in the sentence (3).
   If we take the reference of the sentence as a fact things turns much more intuitive. It seems that we need to distinguish at least two facts referred by non-tautological identity sentences. The first is the perspectival fact, the fact as it is immediately indicated by the mode of presentation expressed by the sentence. I will call it a subfact and make him responsible for the different modes of presentation constitutive of the different sentence-senses or Fregean thoughts about the same thing. This is why sentences (1) and (2) can be seen as expressing different thought-contents, indicating different sub-facts, since being Sir Walter Scott is not the same as (i) being the autor of Waverley and (ii) being the man who wrote the 29 novels of Waverley altogether. In this sense:

(1) Sir Walter Scott ≠ the author of Waverley.
(2) Sir Walter Scott ≠ the man who wrote the 29 novels of Waverley altoghether.

However, it seems also clear that both sentences can be understood as referring to one only grounding fact, which we could represent as ‘Scott = Scott’, expressing the self-identity of Scott as the bearer of many descriptions, including ‘the author of Waverley’ and, more definitely, ‘the man who wrote the 29 Waverley novels altoghether’. That is: it is because of the subfacts that the two sentences above express a difference in the ways the object is indicated through them, while it is because of the groundfact of Scott’s self-identity that they express identities. It is because of both, the groundfact along with the subfact, that the Fregean identities express identities in their differences.[2]
   Now, assuming the kind of descriptivism proposed in the appendix 1 of this book, we can make explicit the above mentioned duplicity of refered facts stating each of the four sentences as follows:

(1) Subfact: Being Sir Walter Scott ≠ Being the author of Waverley. (1) Groundfact: Scott = Scott.
(2) Subfact: Being Sir Walter Scott ≠ Being the man who wrote the 29 novels of Waverley altoguether. (2) Groundfact: Scott = Scott.
(3) Subfact: (Being 29 ≠ Being the number of Waverley’s novels) & (Being Sir Walter Scott ≠ Being the man who wrote the many Waverly’s novels altogether). (3) Groundfact: 29 = 29 & Scott = Scott.
(4) Subfact: Being 29 ≠ Being the number of counties in Utah. (4) Groundfact: 29 = 29.

The subfats show why not only the cognitive, but also semantic contribuition of each referential component may be different. For instance, the subfact that Scott wrote 29 Waverley novels discriminates more than the subfact that he wrote the Waverley novels, and in true sentences this discrimination isn’t only a mentally considered mode of presentation, but also something objectively, factually given (in Frege’s words, ‘the way the object gives itself to ourselves’). And these subfacts remit us all to the groundfact that shows how the different senses are in the end referring to something numerically identical.

21. Taking seriously the sentence’s reference 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 (Kenny 2000: 133). We can, as Wittgenstein, Russell and others did, suppose that the reference of a statement is always a fact, understood as a contingent arrangement of cognition-independent elements usually given in the world. Facts would satisfy the Fregean condition that the reference of a sentence is an object: they are independent, complete, closed. They would satisfy the Fregean condition that thoughts expressed by sentences are modes of presentations of their references, which may be (as subfacts) as multiple and diverse as they thoughts. Moreover, differently from truth-values, 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. Finally, as we will see, they would vary with the unlimited possible variations in the epistemic values of whole sentences with the most different senses.
   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? 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 second planet orbiting the sun.
5.     Venus is the most brilliant planet visible in the sky.
6.     Venus is the only planet in our solar system shrouded by an opaque layer of highly reflective sulphuric acid clouds.
7.     The morning star 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 tautologic, proclaiming the self-identity of the morning star, while sentence (2) and the following are informative. And the information conveyed by those sentences 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, pointing to the same fact…
   The point already touched in the last section comes back: it must be a privileged grounding fact able to be described that can be identified as the ultimate truthmaker of all these identity sentences about the planet Venus, including in some way the facts indicated by the different epistemic values of the sentences (1) to (7) above as its subfacts. My suggestion is that this task can be accomplished by the references of identity sentences between proper names, as far as they are their identifying rules considered in full, that is, including all their fundamental and complementary constituents.
   Now, assuming our proposed view of proper names meaning’s as abbreviations of bundles of descriptions applicable according to identifying rules as essentially correct, then the proper name ‘Venus’ in full (i.e., abstracting the limited knowledge of concrete speakers) includes in its most complete content all the known modes of presentation of this word. This means that definite descriptions such as ‘the morning star’, ‘the second planet orbiting the Sun’, ‘the most brilliant planet visible in the sky’ and ‘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 most of them are only symptoms and cannot be seen as necessarily applicable). In that case there is indeed a sentence that could describe the groundfact, which is the ultimate truthmaker of any identity sentence concerning the planet Venus, including the sentences from (1) to (7) above. Here it is:

8.     Venus (in full) = Venus (in full).

My suggestion is that this sentence is able to express the grounding thought able to refer to the single grounding fact, which if regarded in its entirety, is able to work as the truthmaker for any identity sentence about the planet.
   It is easy to explain why. If the full meaning of the proper name ‘Venus’ is understood as an abbreviation of a bundle of descriptions that uniquely identify our object, then this proper name includes the descriptions like ‘the second planet orbiting the Sun’, ‘the morning star’, ‘the most brilliant planet visible in the sky’, etc. Consequently, we can derive inferentially from the sentence ‘Venus = Venus’ the sentence (2) ‘The morning star = the evening star’, simply by replacing the first occurrence of the name ‘Venus’ with the definite description ‘the morning star’, which the name ‘Venus’ abbreviates, and the second occurrence with the description ‘the evening star’, which the name ‘Venus’ also abbreviates. In a similar way we can easily obtain all the co-referential identities from (1) to (7). In this way the sentence ‘Venus (in full) is (the same as) Venus (in full)’ would be ideally able to represent a fact complex enough to contain the subfacts indicated by each one of the thoughts expressed by the above sentences. (See the meaning of ‘Venus’ as it is presented in an encyclopedia.)
   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 groundfact would be here:

6.     4 (in full) = 4 (in full)

   But could the subfact expressed by the sentences from (1) to (5) be derived from (6)? The answer is obviously in affirmative, since we are handling with a deductive system. And the obvious reason is that I have written the five sentences above simply by conceiving deductive inferences from ‘4 = 4’!
   However, one could still object that a sentence like ‘Venus (in full) = Venus (in full)’ is a tautology dispensing verification: a necessary truth. How could a necessary truth ground contingent truths like ‘Venus is the most brilliant planet visible in the sky’?
   My tentative answer to this objection is that for a privileged user of the word (the Venus specialist) who is supposed to master all pertinent information about Venus, this proper name expresses the following identifying rule:

IR: In any possible world our proper name ‘Venus’ has a bearer iff this bearer belongs to the class of celestial bodies that satisfies sufficiently and more than any other the condition of being the second planet to orbiting the sun between earth and Mercury; a planet somewhat smaller than our earth (contingently associated with auxiliary descriptons like ‘the morning star’, etc.)

The localizing rule is here the only fundamental one. The characterizing description of being somewhat smaller than the earth is of few importance since the information that it is a planet is already included in the localizing description. Indeed, the identifying rule for Venus must be applicable in any possible world where our planet Venus exists. For the name ‘Venus’ there is no relevant characterizing rule. It is almost like the case of the lines ‘a⁀d-b⁀e’ made to localize the center of a triangle without any further property. However, without the condition established by the identifying rule of Venus it would be impossible to identify Venus. The application of many other descriptions do not build criteria, but only 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, as the highly reflexive sulfuric acid clouds. If Venus loses its atmosphere it may cease to be the most brilliant planet but does not cease to be Venus. If the planet loses half of its mass but remains in the same orbit it still does not cease to be Venus. And if in a counterfactual situation it had been thrown out of the solar system, as far as it once was the second planet, it would still be Venus.
   What I said about identity sentences applies also to other singular predicative and relational sentences. Consider the following sentences:

1. Bucephalus was a living being.
2. Bucephalus was an animal.
3. Bucephalus was a horse.
4. Bucephalus was a black horse of the best Thessalian strain
5. Bucephalus was a massive black horse possessed by Alexandre the Great.
6. Bucephalus (355 BC – 326 BC) was the most famous horse of the antiquity; it was a massive black horse of the best tessalian strain possessed by Alexandre the Great.

One could say that each of the first five sentences refers to different subfacts by means of more and more detailed modes of presentation expressed by their respective predicative expressions. But relatively to them there is a groundfact that is more completely referred by sentence (6), since the reference of all the others can be implied from this sentence. Indeed (6) is nothing but an expression of the identification rule for Bucephalus, with the localizing and the characterizing description. The subfacts (1) to (5) are all included in the grounding fact represented by this sentence. They are the immediate satisfiers of the different modes of presentation of Bucephalus indicated by each sentence.

22. The problem of the identity in the difference
There is a final point concerning the relationship between the sub-fact and the grounding fact. It concerns the unsatisfactory way by which Frege solved the puzzle of identity. Even if the sentence of the form ‘a = b’ is informative because it refers to the same object by means of different modes of presentation, we can still ask how this identity is possible, since the modes of presentation are different and since we are not intending to speak about the mere self-identity of the reference. I call this the problem of the identity in the difference.
   To see the problem more clearly, consider again the sentence (1) ‘The morning star = (is the same as) the evening star’. A more fully unpacked cognitive sense of (1) can be presented as:

The most brilliant star in the morning understood as presenting the second planet orbiting the Sun (Venus) = the most brilliant star in the evening understood as presenting the second planet orbiting the Sun (Venus).

Here we have a kind of ‘identity in the difference’: the senses of the expressions flanking the identity sign of (1) are obviously different, but they both indirectly express a sense that is identical, which is of being the second planet orbiting the sun, namely, Venus. Note that this last sense is not the reference, but still a cognitive identifying rule constituting the sense of the name ‘Venus’. It is only because both expressions flanking the identity sign indirectly evoque the identifying rule for the planet Venus that we are allowed to put the identity sign between them! In order to make the point clearer we can build the following schema:

Sentence:    The morning star               =                  The evening star

imediate      IR: the most brilliant         ≠                   IR: the most brilliant
sense:          star in the dawn                                      star in the evening
                    ………↓………………sub-fact………………↓………...
mediated     IR: the second planet…     =                   IR: the second planet…
sense:          (Venus)                                                   (Venus)
                    ……………………...grounding fact……………………….

In sum: ‘morning star’ and ‘evening star’ are responsible for a difference of imediate senses indicating a relational sub-fact constituted by the difference between them (the subfact that the bright star seen in the morning differs in place from the bright star seen in the evening), and for the mediated senses referring to a relational grounding fact that is constituted by the self-identity expressed by ‘Venus (in full) = Venus (in full)’.
   Another example is the sentence ‘The morning star is Venus’. Here the schema is:

Sentence:        The morning star                 =            Venus
Immediate:      IR: Being the most             ≠             IR: Being the
sense                brilliant star in the dawn                   second planet
                         ..……↓………………… sub-fact……↓………………….
Mediated         IR The second planet           =            IR: The second planet
Sense:             (Venus)                                               (Venus)
                         ……..……………….Grounding fact…………………….

What identity sentences of the kind ‘a = b’ express is an identity in the difference in the sense that we in fact have two levels of sense, one indicating the phenomenal sub-fact expressing a difference (Being the brighest star in the evening really differs from being the planet) and the other referring to the the ultimate groundfact expressing the hidden identity (Venus is Venus).
   Now, how to deal with the cases in which the mediated sense responsible for the identity, like the planet Venus, lacks a proper name? Consider the identities (i) ‘Everest = Chomolungma’, (ii) ‘a⁀d = b⁀e’ (concerning Frege’s example of the different ways to name the center of a triangle), (iii) ‘Afla = Ateb’ (the two imaginary montains conceived by Frege). I would answer this by creating a conjoined sense, a conjoined identifying rule, respectively the ‘Everest-Chomolungma’, the ‘a⁀d-b⁀e’, and the ‘Afla-Ateb’ that in fact make three new nominative expressions. By the law of identity we can see that ‘Everest-Chomolungma = Everest-Chomolungma’, ‘a⁀d-b⁀e = ‘a⁀d-b⁀e’, and ‘Afla-Ateb = Afla=Ateb’. This is what sustains the identity of the sentences (i), (ii) and (iii).
   We can also apply a similar analysis to identities between concept-words: ‘F = G’. Consider the identity ‘Water is H2O’. The schema will be:

Sentence:       Water                        is                  H2O
                          ↓                                                    ↓
Immediate     aquose                        ≠           amounts of
sense:             liquid…                                  hydroxid of oxigen
                       . .↓…….………..sub-fact…………↓………….

Mediated       amounts of                 =           amounts of
sense              hydroxif of oxygen                 hydroxid of oxygen
                       ………………grounding fact……………..…

As it was already noted (appendix to chapter 2) the concept-word ‘water’ has two nuclei of meanings: a superficial one, of the aquose liquid (transparent, insipid, etc.), and a deep one, of a chemical substance, when it is often called hydroxid of oxygen. Regarding the immediate sense we consider the subfact of the difference: the subfact that the aquose liquid differs from an H2O composition. Regarding the mediated sense, the grouding fact that the chemical substance is the same one is refered. It is because of this deep identity that we can say that two different natural kinds: water and H2O are the same substance.
   This explains much of Saul Kripke’s illusion of the necessary a posteriori. We can under different contexts enhance or magnify or emphazise the perspectival immediate sense or thought of a sentence (referring to a subfact) or the mediated sense or thought of the sentence (referring to the groundfact).[3] Here I need to speak of contexts of interest of the linguistic agents, meaning with this their pragmatic aims. Two contexts of interest are important regarding most of the examples above: the popular context of interest and the scientific one. Thus, considering the sentence ‘The morning star is the evening star’, we can contextually emphasize the immediate senses or modes of presentation or identifying rules for the phenomenal objects morning star and evening star, which emphazise the relation of difference between the morning and the evening star and let the identity in the background. This can be the case, for instance, when we consider the beauty of the starring sky in the night and, after localizing the evening star we say for a child that it is also the same as the morning star. In this case the sentence is interpreted as contingent a posteriori, since we are all aware that it was an empirical discovery that these different celestial bodies are the same. We are emphazising a indication of the phenomenal subfact that being the phenomenal evening star isn’t the same as being the phenomenal morning star. However, in a scientific context of interest, e.g., in which we are using a telescop to look at the surface of Venus, considering the sentence ‘The morning star is the evening star’ we emphazise the identity between both stars, the mediated sense, the reference to the groundfact of the self-identity of Venus. In this case we read the statement as meaning that ‘Venus = Venus’, what is a necessary a priori statement, letting the different guises of sense in the background.
   Now, consider the statement ‘Water is H2O’[4]. In a popular context of interest of fishermen interested in digging a well to find water to drink and to wash, this sentence is readed emphasizing the subfact that the the precious watery liquid has the chemic structure H2O. Since the difference between the senses is emphasized, the statement is seen as contingent a posteriori, regarding that the deep identity was an empirical discovery. On the other hand, when the context of interest is scientific, e.g. of people messing the acidity of a portion of water, the word ‘water’ in the sentence ‘Water is H2O’ can be understood as meaning hydroxid of oxygen, and the whole sentence as referring to the groundfact expressed by the identity ‘Hydroxid of oxygen = H2O’, which is the same as ‘H2O = H2O’, that is, a necessary a priori tautology. Something similar can be said to the other examples.
    Now, in my view what Kripke misleadingly does is to conjoin the a posteriority of the emphasization of the immediate sense or thought with the necessity of the mediated sense or thought, concluding that the identity of names and concepts has a necessary a posteriori nature only metaphysically explicable. A Wittgensteinian linguistic therapeut would say that Kripke has produced a hipostasis.

23. Structural and ontological status of facts
The next point concerns the logical structure of the facts (grounding facts and their aspectual subfacts). The most plausible answer is that they have a structure that corresponds to the logical structure of the thoughts representing them. Basic empirical statements as ‘Plato has a beard’ and ‘The cat is on the mat’ represent respectively facts that have the logical structure Fa and bRc. Their elements a, b and c, as particulars, are clusters of tropes to be analysed in accordance with Simons’ nuclear trope theory with some special tropes, at least, while F and R would be analysed as tropes themselves, normaly complex configurations of tropes. The links b-R-c and F-a, on their side, are really only pseudo-relations, since the admission of their existence as relational tropes would generate an inevitable Bradleyan regress. The individuals and their tropes must be seen as forming ‘non-relational ties’ linking one with the other without any ontological addition (see appendix to chapter 3).
   If we accept that the references of sentence-senses or thoughts are facts, then from an ontological perspective the reference of empirical sentences, what they represent, must be empirical facts, often located in the external world. This assumption speaks for the correspondence theory of truth, according to which empirical facts are truthmakers seen as contingent complex arrangements of elements in the world, elements that we are prepared to call singularized properties or tropes.
   However, this assumption runs against Frege’s anti-correspondentialist view of truth. According to him a fact would be nothing more than a true thought (Frege 1918: 74). Following similar anti-correspondentialist lines, P. F. Strawson in a very influential article suggested that empirical facts are mere ‘pseudo-material correlates of the statement as a whole’ and not something in the world (Strawson 1950: 6).[5] According to him empirical facts, in opposition to events or things, are not spatio-temporally localisable (‘the world is the totality of things, not of facts’). One evidence of this is that the description of a fact usually begins with a that-clause, for instance (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 very properly ‘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.[6] 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 occured in the year 47 BC; it is still a fact today, since facts simply do not occur (Patzig 1980: 19-20).
   An efficacious way to dispose of this argument was proposed by the correspondentialist John Searle. He noted that 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 truthmaker, whatever is it? (Searle 1998).
   However, it seems clear to me that even this way to circumvent the problem is avoidable, since it is not difficult to 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 easily said to be empirical. And we can say that it is a fact that the Sun is not green, though this seems only a queer way to say that the fact that the Sun is green does not exist. What I want to defend is that empirical facts, particularly the so-called observational facts, should be considered objectively real: they exist in the external world as possible truthmakers.
   There is a very decisive 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)  Thomas 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 (supposedly a kind of abstract content) can in itself act causally in the empirical world producing an effect. Obviously, the admission of the empirical nature of the facts (1) to (4) solves the problem: scratching the match is a fact-event causing the flame; the situational fact created by Thomas’ forgetfulness of the gas turned on caused his death; the fact-circumstance that today is holyday causes the absence of class; the fact-event of crossing the Rubicon concretized a state of affairs that causally determined decisive political 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 (basically an arrangement of more or less complex attributive or relational tropes contingently tied with clusters of compresent tropes referred to by proper names, using the word ‘tie’ in a non-relational sense that lacks of ontological import.) 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 a serious confusion in his argument. Strawson treats facts (as much as states of affairs and situations) as being opposed to events. But this can be contested. We begin to distrust when we perceive that 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 the sinking of the Titanic’, but I cannot replace ‘the fact that the Everest is more than 8.000 m. high’ by ‘the event that the Everest is more than 8,000 m. high’. Hence, it is much more reasonable to consider the event as a kind of fact than to oppose both, as Strawson did. 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… 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: linguistically the word ‘event’ should be seen as a hyponym of the word ‘fact’. Considering things in this way we can distinguish 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. We will see that they are truthmakers of a static kind. And in the ordinary language there are names for them: 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 after a while comes to an end. We will see that they work as truthmakers of a dynamic kind. And 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 seen as 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, since the element of revolving around the sun is a cyclic relationship that remains the same during the fact’s existence). – One orbital period would be in turn an event.
   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 instance, 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 usually called events when their duration is comparatively shorter, occurrences when their duration isn’t as short, 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 truthmakers of a dynamic kind.
   We are now able to find what may be 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 as 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 emphasize static facts and to eschew dynamic facts. And since the hyperonymic term ‘fact’ can be applied to both – the static facts as much as the dynamic facts – it is 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 also say: ‘Cesar crossing the Rubicon was an event’ as much as ‘It is a fact that Cesar crossed the Rubicon’, referring less precisely to the event. We can summarize these relationships in a schema:

(a)  Static facts (states of affairs…): can be stated with or without that-clause.
(b) Dynamic facts (events…): cannot be stated with that-clause.
(c)  Facts in general: admit both cases because they do not differentiate between (a) and (b).

Now, what about the fact that Caesar’s crossed the Rubicon? Isn’t this fact timeless? This is a good case of philosophically misleading example: 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. Only occasionally the phrase ‘crossing the Rubicon’ is understood in the literal sense, as the physical event of crossing the river, which comprises Caesar’s sequential 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 only use to say 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 until his assassination. It was not something that existed in Australia or that endures until the present, even if we have the custom of using the present tense to speak about historical facts.
   A final point is that by having the broadest scope, the so underrated short word ‘fact’ remains the ideal candidate for the role of truthmaker in a correspondence theory of truth. Facts are the universal truthmakers.

24. 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 instance, in the sentence ‘The morning star is a planet’ we replace for the phrase ‘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. (Frege 1892: 32)
   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 the sentence ‘12 . 12 = 144’ in the utterance: ‘The sentence “12 . 12 = 144” expresses a true thought.’ Frege had the latter meaning in mind. In this usage, the word ‘thought’ means simply what the sentence (or statement) says, which Frege has conceived of as some kind of unchangeable platonic entity. The terminology here counts, because the word ‘thought’ is the only term in natural language that has a sense corresponding to more technical terms like ‘proposition’ and ‘propositional content’.[7]
   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 (Frege 1918: 64). 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 I prefer to think, by following different combinations of semantic-cognitive rules able to produce verifiability procedures that are correspondingly different.

25. 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. The test for this is that when a word is derivatively used we can usually replace it for something better. According to this, 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. When we say that Socrates was ‘true’, what we mean is that he was a truthful, reliable person; when we say that Sam’s belief is true, we mean firstly a subjective psychological attitude of the believer concering a thought, even if well-grounded, and when we say that a sentence is true, this is only a shortened way to say that the thought it expresses is true.
   One reason for preferring to say that the thought is the truth-bearer concerns the logic behaviour of the concept. Our concept of truth works as a normative ideal so that the the true truth-value is conceived as something invariant: if something is true, it is forever true; if something is false, it is forever false. Obviously, we can fail in our holding of something as true (für wahr halten) and grasp a falsity instead, and vice versa – this is frequent. But when we discover the error we correct ourselves not by saying the the truth turned to be false, but by saying that it was always false. Our holding something for true is also fallible. But it is fundamental to perceive that this does not affect the invariability or imutability of the truth as a normative ideal.
   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, for Frege a true thought (if true) remains for ever true, as much as a false thought (if false) remains for ever false. They are even shortened out as ‘truths’ and ‘falsities’ respectively. Thus, it is something deeply ingrained in our conceptual grammar that the entity that can be primarily called true or false must remain 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 (unseres für wahr halten). If it is so, then only the thought has the necessary stability to be the proper 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 case of sentences. Identical sentences-tokens can express different Fregean thoughts, but in this case the truth-value of the thought will accompany the expressed thought and not the sentence… This is obvious in the case of indexical sentences like ‘I am in pain’, which express different thoughts according to the speaker. These sentences can change their truth-values when uttered by different persons, and even when uttered by the same person in different times, but in these cases the thought expressed by them also changes. If the sentence-token were the truth-bearer, the truth-value of the same sentence wouldn’t be able to change in this form. Moreover, if the own sentence were the truth-bearer then the truth-bearer could change without a corresponding change in its truth-value. For example, the different sentences ‘Il pleut’, ‘Es regnet’, ‘Chove’… when uttered in the same context, remain with the same truth-value. Hence, the sentence does not have the kind of stability expected of a truth-bearer. Moreover, the only justification for the sameness of truth-value of these different sentences is that the truth-bearer is the thought expressed by them, since what is said by them remains the same. And this is the case not only for indexical sentences, but also for identical eternal sentences expressed in different languages. Concluding: 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, the proper bearer of truth must be the thought or the proposition, not the sentence.[8]

26. Facts as true thoughts?
As we already noted, 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. (Frege 1918: 74)

However, this conclusion isn’t forceful, for a scientist can also say the same thing – and maybe with more property – understanding by a fact simply what corresponds to the true thought, namely, some real complex arrangement of tropes 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 made clear that the Fregean identification does not resist some 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 (Austin 1990: 170-171). But ‘His affirmation is true’ preserves the meaning while ‘His affirmation is a fact’ is a metalinguistic sentence referring to the occurrence of his utterance, and not to the content of the affirmation anymore. The reason for this would be that even if the content of its affirmation (the Fregean thought) is true, it isn’t because of this a fact.
   The hidden reason why Frege believed that the fact is a true thought seems to be that he advocated a conception of truth as redundancy, rejecting the correspondential theory of truth. However, not only his arguments against the correspondence theory (Frege 1918: 59-60) are unconvincing (see Künne 2003: 129-133), but the correspondence view remains as always deeply influential as the most natural and plausible conception of truth, still suggesting that facts are arrangements of elements in the world, able to be in some way represented by propositions, which, when this happens, are called true (Rasmussen 2014). Moreover, the view of truth as correspondence is in conformity with our common sense methodological point of departure, what justifies my endeavour to defend it in the final chapter of this book.
   I think that I can explain the reason why some are tempted to say that facts are true thoughts. The source of confusion resides in a persistent ambiguity of our own natural language. Although dictionaries in different languages present us a variety of trivial meanings for the word ‘truth’, there are two general meanings that we always find emphasized:

(a)  Thought-truth: Truth as consisting in things being as we believe that they are, as conformity or accordance or correspondence of the thought with its fact.
(b) Fact-truth: Truth as the actual, real, existing thing or fact in the world.

In a principled sense (a) we say that a thought is true, uttering sentences like ‘His words are true’, ‘tell me the truth’, while in a factual 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 (real)’, ‘we are searching for the truth (for the real facts).’[9]
   As we already saw, philosophers found good reasons to think that the sense (a) is primary and (b) is derivative, since in this case we can replace the word ‘truth’ by more adequate ones like ‘reality’, ‘actuality’, autenticity’. However, since ‘truth’ is very often used not only as ‘correspondence with facts’ but also as ‘an existing fact in the world’, it is easy to confuse both and believe – considering that facts and thoughts can be said to be true – that facts are true thoughts. This seems to be the reason of Frege’s confusion, giving us another example of the way of transgressing the internal limits of language that I called hypostasis (ch. 3, sec. 11).

27. The thought as a verifying rule
As the application of the ascription rule (sense of the predicate) is subsidiary to the application of the identifying rule (sense of the of the nominative term), the rule for the application of the singular sentence (its sense, its thought), can be seen as a combination of semantic-cognitive rules, called by Tugendhat a verifiability rule (1976: 259, 484, 487-8). But if the thought is a combination of rules, then what results from such a combination, the verifiability rule, must also have the character of a rule, even if not of a previously conventionalised rule. Combining this with our acceptance of the correspondence view of truth this means that the thought should be a kind of integrated cognitive rule whose function is to make us aware of the fact referred to by it.[10]
   This reasoning leads us directly to the cursed word 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 the rule or method or procedure for its verification (1980: 29). This doctrine is in the present days considered by many unsustainable, even though the received wisdom against it has never been very critically scrutinized. Indeed, I intend to provide a serious criticism of this received wisdom as something corrupted by positivist-scientist formalist prejudices in the next chapter of this book, making plausible that there is nothing troublesome with this doctrine except for its intrinsic philosophical difficulties.
   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 or informative content of the sentence. Suppose that the integrated semantic-cognitive rule that constitutes the thought expressed by an assertive sentence is its verifying rule. Then if we show that this rule is effectively applicable to a fact, it makes this thought-sense-rule true, what allows us to derivatively say that the the sentence expressing it is true. If, on the other hand, we show that this rule isn’t effectively applicable to an expected fact, 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 verifiability rule able to be at least in principle aplicable, we must conclude that the sentence is devoid of meaning, lacking sense-thought, even if it may seem 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 (Frege 1918: 61); indeed, truth does not add anything to the integrated cognitive rule called thought, except its effective applicability as a verifying rule in a chosen contextual domain.
   The proposed identity between the Fregean concept of thought and the concept of a verifying rule is supported by the Fregean suggestion that the identification criterion of what belongs to a thought is for it to have at least some role in the establishment of the thought’s truth. Being the identification criterion for this thought-sense-rule (procedure, method) what allows the recognition of its truth-value, this could be whatever is able to warrant its effective applicability to the corresponding fact, and this is the work of a verifying rule.
   Assuming this, what would be the property of this verifying rule – the thought – of being true? Well, I propose here the following way of answering the question. Consider first what we have said about the property of existence of what is referred by a conceptual (ascription or identification) rule. Since this existence of a property or an object should be the metaproperty of effective (and not only supposed) applicability of the conceptual rule expressed by the conceptual word in some domain, by symmetry of reasoning, the existence of a fact should be the metaproperty of the thought-rule-content which is its verifiability rue, of being true. Truth should be the property of a verifying rule of being effectively applicable to its object, which should be the existence of the fact (groundfact or subfact) that satisfies the rule. What the assertion ‘p is true’ expresses should be thought of p, which is a verifiability rule followed by its ascription of truth, which is nothing but the higher-order ascription of the property of effective applicability of the sense-thought-rule. We could almost say, in a Hegelian fashion, that existence is the truth of the concept while the truth is the existence of the thought. According to this reasoning existence and truth are twin concepts. However, when we say that a fact exists, that it is real, true, we are applying the word ‘truth’ in its factual sense (b) of a fact-truth. What we mean is that a sense-thought-rule has the property of being effectively applicable to a certain fact, attributing existence to it.

28. 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 (Frege 1918). 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 interpersonally 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 also 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 and, consequently, in time and (why not?) in space. There is, finally, a third realm, that of thoughts (usually called propositions) and their constitutive senses. This realm is for Frege objective but not real. It is objective, because thoughts, true or false, are interpersonally 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 objective but non-real.
   There are, however, problems. One of them is that though for Frege thoughts are eternal (timeless), immutable, forever true or false, and not created but grasped (gefasst) by us, they must have some kind of causal effect: they must be able to cause our grasping of them in order to make judgements and act in the external world.  But how this interaction is possible remains a mistery to be explained.
   Frege was aware of the difficulties, but the reason Frege he had to introduce this third realm of thoughts is that thoughts are interpersonally accessible, that is, they are objective, what make them effectively communicable. Representations (Vorstellungen), on the other hand, are rather subjective psychological states, which can vary in dependence of the personal psychology and are not interpersonally accessible, objective, communicable. Thus, for him the only way to explain how it is possible that we are able to share the same thought is to distinguish strictly the thoughts from mere psychological representations placing them in a supposedly shareable Platonic realm. As well, if thoughts were on the level of representations, they would be dependent on the changeable personal psychology and would lack their required stability as truth-bearers.

29. Avoiding Frege’s Platonism
Despite the above suggested arguments, only 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 and their constitutive senses), but also seems to lack intelligibility. The price that Frege was willing to pay in order not to fall into psychologist subjectivism seems for us now too high.
   In my view, Frege’s Platonist solution is unnecessary because the whole problem was wrongly formulated. For there is a way to conform the view that thoughts have a psychological-empirical nature to the view that as a truth-bearer they must have stability and also 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.[11] In order to do this, I wish to show that Fregean Platonic thoughts (objective non-real truth-bearers…), which I call f-thoughts (‘f’ from Fregean), can be defined in terms of psychological p-thoughts (‘p’ from psychological). I suggest that we can warrant the existence and stability of the f-thoughts by means of what I call s-thoughts (‘s’ from spreadable) without hypostasizing 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 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 interpretating them as s-thoughts.
   The so defined s-thought, which I will prefereably call thought-content or simply proposition, though spread in space and time has no particular spatio-temporal location and can be seen as the truth-bearer. For example: the s-thought (or thought-content) 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 qualitatively identical p-thought that I, we, or any other person can have at any other time, provided the qualitative identity. 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 help of this definition 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 not only to the problem of defining classes, but to the problem that classes have size while thoughts haven’t. If an s-thought were seen as 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 occurrence of it. 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, this is nothing but a way of speeking. What we really mean is only that there is a qualitative identity between the psychological p-thought-contents that we have respectively instantiated in our own minds. This has the advantage of bringing the Fregean thoughts from the ethereous Platonic heaven back to the psychological realm without commitment to the transient psychology of particular cognitive beings. This understanding of the true nature of the thought-contents explains something that Frege was unable to explain satisfactorily, namely, why and how they may have causal powers (1918: 77). As an open disjunction of p-thoughts, s-thoughts only exist as psychological instantiations of p-thoughts, what enables them to cause others psychological states and finally human actions and their effects in the external world.
   At this point one could rise an objection of multiple realizability: the same p-thought could be differently realized in different human brains making the qualitative identity of p-thoughts impossible. I agree with the probable multiple realizability of p-thoughts, but disagree that this makes their qualitative identity impossible. There is no reason why we cannot present things that are qualitatively identical in a psychological level and different in a neurophysiological level just in the same way as different devices can have different internal mechanisms and perform exactly the same task.
   In my view, one of the most unyelding and deceitful philosophical errors in ontology has always been seeing numerical identity where there is only qualitative identity. It is true that we we can ask for the meaning of the common name ‘chair’ using the definite article, that we can speak of the geometrical form of circularity, and that we can speak of the number 2 in the singular – but this is just for the sake of simplicity of expression. What we actually have in mind are occurrences of qualitatively identical meanings, of qualitatively identical geometrical concepts of circles[12], of cognitive arithmetical concepts of dualities, and nothing more. In the same way, we can talk about the thought expressed by ‘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 havinh to specify which occurrence or in what mind. We speak in the singular of the thought that 7 + 5 = 12 when there is no reason to consider any individual person who thinks it.
   The adoption of the definition of s-thoughts proposed above, which is easily generalisable to all kinds of Fregean senses, 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.
   At this point the Fregean question turns back: 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 interpersonal acessibility 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. However, the need that Frege feels to admit that thoughts belong to a third realm of Platonic entities is too hasty. First, there is no doubt that what Frege calls representations (phenomenal mental contents) have a limited possibility of interpersonal communications.[13] However, senses and s-thoughts are something more than mental states: they are rules or conventions or combinations of conventions made with help of public signs that are in the end interpersonally established, even if implicitly, and precisely because of this are also easy to be interpersonally corrected. Although s-thoughts can possibly invoque mental imagery, they are verificational rules rooted in interpersonal conventions, what satisfies Frege’s demand of objectivity as interpersonal accessibility and evaluation.
   Concerning s-thoughts, as with the model-tropes in the construction of universals, it is also important to remember that it is not necessary to have one only particular model as the object of interpersonal consideration. On the contrary. 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 choose any of them as the new model and so on. And language is only the vehicle of communication that allows the reproduction of a qualitatively identical psychological p-thought in the minds of hearers as far as they are grounded in the conventions that we have attached to the words.
   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 attached to our words. However, compare this case with the case of genetic information able to indefinitely reproduce the same characteristics in successive biological individuals:[14] why the conventions and the ways they can be combined in the constitution of p-thoughts could not render the same? In addition (as probably also in the case of genetic information) it is easy to suppose that there are correcting mechanisms able to interpersonally and intra-personally correcting deviances of the conventioned standards. There is no reason, except an anti-empiricist bias, to think that things could 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 (Searle 1999: 43-45) to the objectivity of s-thoughts. 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 enduring social effects of the Napoleonic wars – without ceasing to be epistemically subjective, because it is difficult 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 of the kind can be said regarding the nature of s-thoughts. They are in themselves 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 interpersonally agree about them and their truth values. We can agree that an objective assertive sentence like ‘The Eiffel Tower is made of metal’ expresses a true s-thought that is ontologically subjective though epistemically objective. Moreover, the sentence ‘I am having a knife-like pain in my abdomen’ can express an ontologically subjective true thought about an ontologically subjective event without letting to be epistemologically objective. Like any s-thought, these thoughts remain epistemologically objective, given that they are grounded on conventions associating words with things in the world which make them fully measurable and communicable. 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 non-conventional subjective colouration, being susceptible only to an aesthetic appreciation with variable degrees of interpersonal agreement.
   Frege was in this point no exception: like Husserl, Bolzano and several others continental philosophers with mathematical training, he believed that the ontologically subjective character of psychologically conceived thought-contents would be inevitably condemned to epistemic subjectivity. But this was a mistake.

30. Further ontological consequences
Our ultimately psychological reformulation 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? The answer is that being at least one occurrence of thought, or any other qualitatively identical occurrence, regardless of the bearer, something as the Pythagorean teorem acquires an existence that is dependent on minds, what does not mean that it is dependent 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 scattered over space and time. It must be 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. This is what gives the impression that ‘the thought’ is something abstract, beyond the psychological realm.
   A consequence from this view is that unlike the Platonic entity that Frege has 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 may sond 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 an 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 in a world of no cognitive beings.
   This remark brings us to the following objection. Imagine a possible world Wo similar to our, with planets, stars and galaxies, but without thinking beings. In Wo the s-thoughts of the Pythagorean teorem, or that there are planets, stars and galaxies, 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 there are planets, stars and galaxies would be true...
   Our answer is that we are here victims of the confusion between the primary bearer of the truth – which is the s-thought – and a derived but as we already saw very common bearer of the truth – the real existent thing or fact in the world, which is reported in any dictionary. Indeed, that there would be planets, stars and galaxies in a mindless world 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 their s-thoughts would not exist neither their truth as correspondence. 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 inversely 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 a derived 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 or verifiers. 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 that the thought couldn’t be true, since it didn’t exist. But we still can say that it was a true, a real 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 be its truthmaker. And this seems to be all that we can really mean when we say that it is true that the Moon would still be white even if there were no cognitive 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 who think it.

31. A short digression on contingent futures
Before we finish, it is curious to examine the Aristotelian problem of contingent futures in the light of our conclusions. According to Aristotle (1984, vol. I, ch. 9), 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 cannot agree with this, since I believe that any s-thought must obey the principle of bivalence. Suppose that outside any context we consider the s-thought expressed by the sentence ‘There will be a sea battle tomorrow’, which we can abbreviate as ├p. Is this statement true or false? The answer is: taken literally├p is unable to express an s-thought because an s-thought, a thought-content, a proposition, is something to which we must possibly attribute a truth-value and without any further contextual information we are totally helpless for the task to associate p with any truthmaker in order to assign it a truth-value.
   However, one could argue that the sentence ├p is misleading and brings us to confusions like the argument A because ├p only seems to express cognitive content. The reason for this is that ├p is very easily confused with the sentence ├p*: ‘[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 ├p* is easily confused with ├p, because ├p* 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 actual empirical evidence, so that the assertion ├p* expresses an s-thought hold as true, for it is true that, with the information disponible, it is probable that a sea-battle will occur tomorrow. Indeed, the utterance ‘It is likely that a naval battle will occur tomorrow’ could be hold as definitely true in the night of June 3, 1942 without breaking the principle of bivalence. In contrast, if I am on the beach of Praia Bonita looking at the Atlantic Ocean and say without any reason ├q* ‘A naval battle will take place in this region tomorrow’, meaning by it ‘It is likely that a naval battle will take place in this region tomorrow’, this statement will be seen as definitely false, since I have all kinds of reasons to believe that this kind of event is extremely improbable in this region and time.
   The conclusion is that taken in absence of context (and not in the sense of ├p*) the sentence ├p is a linguistic bluff devoid of meaning and justification, and Aristotle was right in rejecting the application of the principle of bivalence to it, not because this principle has exceptions, but simply because it expresses no thought-content, no proposition. All that this sentence does is to induce us to imagine a naval battle taking place tomorrow, as if there were hidden veriability criteria. However, as much as no context is furnished, no such criteria can be given. The statement ├p*, on one hand, says something probabilistic about tomorrow that can be confirmed and made true by criterial reasons already established today.
   It seems that the whole metaphysical trouble about contingent futures can be eliminated when we consider with enough care what we are really able to mean by affirming thought-contents regarding the future.

32. 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 giving some explanation for 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 more plausible than Frege’s own original views.





























[1] Also Frege, Letter to Russell from 28.12.1912.
[2] What I call subfact can be approximated with what defenders of the two-dimensionalism obtain through their primary intention and what I call groundfact is what they obtain through their secondary intention. I believe that the natural distinctions I am proposing avoid the often confusive formal apparatus of two-dimensionalism, which inherites the artificialities of Carnap’s modal semantics and its Fregean origins (see Chalmers 2002).
[3] The concept of emphasization was fruitfully applied in Jürgen Habermas excelent work on universal pragmatics (Habermas 1976).
[4] Already discussed in the adendum of the appendix of chapter 2 in this book.
[5] For him ‘a situation or state of affairs is, roughly, a set of facts, not a set of things’ (1950: 8).
[6] For counterexamples, see J. L. Austin, ‘Unfair to Facts’. 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.
[7] 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’ (Burge, 2005: 227-8).
[8] For Frege in the case of indexical sentences the context of the utterance belongs to the expression of the thought. I believe to have shown the real consequences of this in my 2014c.
[9] Normaly in dictionaries we find ‘truth (principle): that which is true in accordance with the fact or reality’; ‘truth (fact): the actual fact about the matter’, and ‘truth (quality): the quality of being true, like veracity, honesty’. (See Oxford-Cambridge Dictionaries).
[10] See my exposition of Tugendhat’s verificationist correspondentialism in the first chapter of this book.
[11] 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 1710, Introduction, section 12. See the more sophisticated but also less clear view of David Hume 1738, Book I part 1, section VII.
[12]  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, of course, in negative, 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 does not work with actual perfect circles, but with potential perfect circles.
[13] Against Frege we could hold that even the representations can be to a great extent 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 instance, some epileptic aura, isn’t communicable, except indirectly, metaphorically. But it seems an unquestionable fact that typical 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 reforced by interpersonally accessible physical states strongly intermingled with them (Costa 2011, ch. 3).
[14] Biological mutations are accidents whose incidence should be evolutionarily calibrated. Only species that are able to mutate in the right amount at the right period of time can survive. An unchanging species with no relevant mutation is probably possible, but would lack the adaptability necessary for survival under changing external conditions.



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