26. 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 reached this result by applying his principle of compositionality of senses, whereby combined in a certain way the senses of its component expressions constitute the sense of the whole sentence. If, for instance, in the sentence ‘The morning star is a planet’ we replace for the description ‘the morning star’ the description ‘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. Indeed, the sense of the sentence ‘The evening star is a planet’ is different. Moreover, we can also say that the thought expressed by the resulting sentence is different. Consequently, the sense of a sentence must be the thought it expresses. (Frege 1892: 32)
The word ‘thought’ is ambiguous. One can use it 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 in the sentence ‘12 x 12 = 144’ in the utterance: ‘The sentence “12 x 12 = 144” expresses a true thought.’ Frege had the latter meaning in mind. In this usage, the word ‘thought’ means simply what the sentence (statement) says, which Frege has conceived of as some sort of unchanging Platonic entity. The terminology here counts, because the word ‘thought’ is the only term in ordinary language that has a sense corresponding to more technical terms like ‘proposition’ and ‘propositional content’.
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 if the word ‘yet’ expresses only an expectation regarding the arrival of Alfred without contributing to the sentence’s truth-value (Frege 1918: 64). The sentences ‘The morning star is Venus’ and ‘The evening star is Venus’ can be counted as expressing different thoughts, because although the singular terms that make up these two identity sentences all refer to the same planet, they do this by means of different modes of representation. That is, they make us follow different paths in the determination of their truth-value, or, as I prefer to think, they make us follow different combinations of semantic-cognitive rules able to produce correspondingly different verifiability procedures.
27. The thought as the truth-bearer
Another quite plausible Fregean thesis was that the bearer of truth is not the sentence, but rather 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 useful test for this is that when a word is derivatively used we can usually replace it with a more appropriate word. Hence, if we say that a diamond is false, what we mean is only that it is only an imitation diamond, deceiving us into having false thoughts about it. When we say that Socrates was ‘true’, what we mean is that he was a truthful, trustworthy or reliable person, someone with integrity. But it is not always so. When we say that Sam’s belief is true, we mean firstly a subjective psychological attitude of the believer concerning a (dispositional) thought that happens to be true, which leads us again to the truth of a thought in the Fregean sense.
One reason for preferring to say that the thought is the truth-bearer concerns the logical behavior of the concept. Our concept of truth works as a normative ideal so that the actual truth-value is conceived of as something invariant: if something is true, it is always true; if something is false, it is always false. Obviously, we can err in holding something to be true (für wahr halten), believing in a falsity instead, and vice versa – this is common. But when we discover the error, we correct ourselves, not by saying the thought was previously true but now is false, but by saying that it was always false! Our mental process of holding things to be true is fallible. However, it is fundamental to perceive that this fallibility does not affect the invariability or immutability of the truth-value as a normative ideal, even if it is beyond our fallible capacities to know whether we have reached this ideal.
Now, if the actual truth-value is immutable, its truth-bearer must also be unchanging, able to remain the same in order to retain this same truth-value independently of the time or place where we grasped it. Indeed, for Frege a true thought (if true) remains true forever, just as a false thought (if false) remains false forever. These entities can even be abbreviated as ‘truths’ and ‘falsities’ respectively. Thus, it is 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 (unser für wahr halten). If this is so, then only a thought has the necessary stability to be a proper truth-bearer; for a thought is, according to Frege, unchangeable and eternal (atemporal), being eternally (atemporally) true or false independently of our grasping (fassen) it.
Consider now the case of sentences as candidates for truth bearers. Identical sentences 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 depending on the speaker. These sentences can change their truth-value when uttered by different persons, and even when uttered by the same person at different times, though in these cases the thought they express also changes. Thoughts and their truth-values are co-variant, sentences and their truth-values are not.
One can suppose that perhaps the sentence-token would be the truth-bearer, since it would be a different one in accordance with the time and place of the utterance, changing with the truth-value. However, we still have cases in which different sentences (token or not) say the same thing – express the same thought –in this way preserving the same truth-value. Consider, for example, these statements in four different languages: ‘It is raining’, ‘Il pleut’, ‘Es regnet’, ‘Llueve’… uttered in the same context. In this case, they all have the same truth-value, while their sentence-tokens seem quite different. Indeed, the only justification for the sameness of truth-value of these three different statements is that their truth-bearer is the thought expressed by them, since what remains the same is what they say, their senses, the thought. Moreover, this is the case not only for indexical sentences, but also for synonymous eternal sentences expressed in the most diverse languages. To conclude: thoughts and their truth-values are not only invariantly related; when thoughts vary, they maintain a relationship of co-variance with their truth-values that is missing in the relationships between sentences and their truth-values. Because of this, the proper bearer of truth must be the thought or proposition, not the sentence and still less persons and things.
28. Facts as true thoughts?
As already noted, Frege also proposed that what we call a fact is 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 is not forceful, for a scientist can also say the same thing – and possibly with more justification – understanding by a fact simply what corresponds to the true thought, namely, some given arrangement of tropes and constructions out of them. After all, it is natural to think that if someone discovers a true thought, it is because he has a fortiori discovered the fact corresponding to it. Moreover, J. L. Austin made it clear that Fregean identification does not resist certain linguistic replacements. 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’ with ‘his affirmation’ should be allowed without any change of sense. 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 itself (Austin 1990: 170-171). The reason for this can only be that the true content of an affirmation – the Fregean thought – cannot really be identified with 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 correspondence theory of truth. However, on the one hand, his arguments against correspondence theory (Frege 1918: 59-60) are unconvincing (see Künne 2003: 129-133). On the other hand, correspondence theory still remains highly influential as the most natural and plausible conception of truth, suggesting that propositions or thoughts are true when they correspond to facts as arrangements of elements in the world (Rasmussen 2014). Moreover, the view of truth as correspondence is commonsensical and therefore in conformity with our methodological point of departure. These are reasons that justify my endeavor to defend this theory in the final chapter of this book.
I think I can do something more, explaining 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. Dictionaries in the most different languages present us a variety of trivial meanings for the word ‘truth’. However, two general meanings are always emphasized:
(a) Thought-truth: Truth as consisting of things being as we believe 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 the most proper sense (a), we say that a thought is true in sentences like ‘His words are true’, ‘Tell me the truth’. In the factual sense (b), we say that the fact in the world is true in the sense of being real, and we use sentences like ‘The mentioned occurrence was true (real)’, ‘We are searching for the truth (for the real facts).’
As we have already seen, philosophers have found good reasons to think that sense (a) is primary while sense (b) is derivative, since in this case we can replace the word ‘truth’ with more adequate ones like ‘reality’, ‘actuality’, authenticity’. However, since ‘truth’ is very often used not only as ‘correspondence with facts’ but also as ‘an existing fact in the world’, it is very easy, if one is so moved, 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 origin of Frege’s confusion, giving us another example of the way of transgressing the internal limits of language that I call hypostasis (Ch. 3, sec. 11).
29. 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 applying the singular sentence (its sense or thought), can be seen as a combination of semantic-cognitive rules, called by Ernst Tugendhat a verifiability rule (1976: 259, 484, 487-8). However, 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 conventionalized rule. Combining this with our acceptance of the correspondence view of truth, this means that the thought should be a kind of combined semantic-cognitive rule whose function is to make us aware of a corresponding fact to which it is applied.
This reasoning leads us directly to a cursed word called ‘verificationism’, more precisely (and still worse) 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). Many now consider this doctrine unsustainable, even if they do not stop to critically review the received wisdom and to consider the potential alternatives at hand (see Misak 1995). Indeed, in the next chapter of this book I intend to offer a decisive criticism of this received wisdom as something corrupted by positivist-scientistic formalist prejudices, showing that there is nothing troublesome with this doctrine except for its intrinsic philosophical difficulties.
I will introduce this view here speculatively, as an alternative and in fact as the most natural way to analyze Frege’s discovery of the thought as the sense (epistemological value, informative content) of the sentence. Suppose the combined 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, this makes this thought-sense-rule true, which allows us to say derivatively that the sentence expressing it is true. If, on the other hand, we show that this rule isn’t effectively applicable to its expected fact, this makes the thought-sense-rule false and likewise the sentence expressing it. Moreover, if we cannot formulate a verifiability rule able to be at least in principle applicable to the fact, we must conclude that the sentence is devoid of meaning, lacking sense or 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 combined cognitive rule called ‘the thought’, except its effective applicability as a verifying rule in an appropriate context. Moreover, the proposed identity between the Fregean concept of sense-thought and the concept of a verifying rule is also supported by the Fregean proposal that the identification criterion for what belongs to a thought is that to belong to a thought it must have at least some role in the establishment of the thought’s truth-value.
However, there is another way to understand the property of applicability of the verifiability rule, which is to identify it with the existence of the fact. To achieve this, we need only consider that if the higher-order property of effective applicability of a conceptual rule is the existence of an object or a property (bundle of tropes, trope), then by symmetry the higher-order property of effective applicability of the verifiability rule should be the existence of the fact to which it applies. 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 argument, existence and truth are twin concepts.
We are before a dilemma. We have two readings of truth:
1) Truth is the property of a verifiability rule of being effectively applicable to a fact, which seems to be a way to understand the correspondence theory.
2) Truth is the property of the verifiability rule of being effectively applicable to a fact, which amounts to the attribution of existence to a fact.
These two interpretations of truth may be equivalent, but they are not the same. Which is the correct one? The seemingly paradoxical provisional answer that I am able to give is that (1) and (2) take into account different senses of the word truth. Sense (1) is of truth-thought, truth as a property of the thought or the verifying rule corresponding to the fact, while sense (2) is that of truth-fact, truth as the higher order property of the thought or verifying rule of being effectively applicable to the fact, which means the same thing as to attribute existence to the fact. However, if this is the case, why is the truth-thought more fundamental? The answer is that regarding the fact-truth we can replace the word ‘truth’ with words like ‘existence’, ‘reality’, even more suitable, while in the case of the thought-truth we cannot replace the word ‘truth’ with any other word. Finally, how can 1) and 2) have different senses, if they are (or seem to be) identically defined? For an answer to this last question, we will need to wait until the last chapter.
30. 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 (a) the criterion of objectivity inter-subjectivity and independence of will, and taking as (b) 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 satisfy criteria (a) and (b): they 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 here translate as qualia). These entities satisfy criterion (b) but not (a): they 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 mind 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 satisfies criterion (a) but not (b). For Frege thoughts are objective but not real. Thoughts are objective, because, true or false, they are interpersonally accessible: we can all agree, for example, that the Pythagorean theorem expresses a true thought. However, this third realm of thoughts is not real, because according to him thoughts are abstract things that cannot be found in space or time. Thus, the thought (the sense) of Pythagoras’ theorem is objective but non-real.
There are, however, problems here. 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 them in order to make judgments and act in the external world (Frege, 1918: 77). However, how this interaction is possible remains an unexplained mystery.
Frege was aware of the difficulties, but the main reason he felt he had to introduce this third realm of thoughts is that thoughts are interpersonally accessible, that is, they are objective, which makes them effectively communicable. Representations (Vorstellungen), on the other hand, are rather subjective psychological states, which can vary depending on personal psychology and according to him are not interpersonally accessible and therefore not communicable. Thus, for him the right way to explain how it is possible that we are able to share the same thoughts is to strictly distinguish thoughts from mere psychological representations, placing thoughts in a supposedly shareable Platonic realm. In addition, if thoughts were on the level of representations, they would be dependent on changeable personal psychology and would lack their required stability as truth-bearers.
31. Avoiding Frege’s Platonism
Despite the above-suggested arguments, today few would 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 too high for us today.
In my judgment, there is a way to bring the empiricist view of thoughts as having a psychological-empirical nature in line with the view that as truth-bearers they must have stability and the possibility of being communicated. In order to show this, I want to apply again the same strategy inspired by the ontological particularism of English empiricists from Locke to Hume, which I used in the construction of universals by means of tropes. This is understandable, since according to trope ontology, a thought must be made up of tropes. In order to accomplish this, I need only 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). Hence, I suggest that we can warrant the existence and stability of 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. We can do this by means of the following definition, which is as simple as afficacious:
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 empiricist 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 (inter-subjectivity) and expected stability or immutability by interpreting them as s-thoughts.
The so defined s-thought, which I also call thought-content or simply proposition, though spread in space and time, has no particular spatio-temporal location and can be seen as the most proper 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. However, it can also be instantiated by, say, the p-thought that you have in mind when you read it, such as by any qualitatively identical p-thought that I, we, or any other person can have at any other time. Characterized by the disjunction between qualitatively identical thoughts embodied in any individual mind, the s-thought is regarded in abstraction from the particular human minds that causally instantiate it.
As with model-tropes in the construction of universals, it is not necessary to have only one particular model as the object of interpersonal consideration. To 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 recognize as being identical to the first, so that we can choose any of them as a new model. In some way language is only the vehicle of communication that allows the reproduction of a qualitatively identical psychological p-thought in the minds of hearers, insofar as they are rooted in the conventions we have attached to the words.
With the help of the above definition, we avoid not only appealing 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. This could lead us not only to the problem of defining classes, but to the problem that classes have size while thoughts have not. If an s-thought were a class of p-thoughts, it would grow ever larger, the greater the number of people who grasp it.
Under the proposed definition, in order to exist an s-thought must always have at least one psychological occurrence. The s-thought is not less psychological than any p-thought, since it cannot be considered independently of its instantiation in at least one mind. This means that when we say that we both had the same idea, or the same thought, this is merely a way of speaking. 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 Fregean thoughts out of the ethereal Platonic heaven back to the psychological realm without making a commitment to the transient psychology of particular cognitive beings. This understanding of the true nature of thought-contents explains something that Frege was unable to explain satisfactorily, namely, why and how they may have causal powers. As an open disjunction of p-thoughts, s-thoughts only exist as psychological instantiations of p-thoughts, which enables them to have causal powers: this can cause other psychological states and, combined with desires, human actions and their effects in the external world.
At this point one could raise 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 very 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 can be considered qualitatively identical on a psychological level and different on a neuro-physiological level, just in the same way as different devices can have different internal mechanisms and perform exactly the same tasks.
In my view, one of the most unyielding and deceitful philosophical errors in ontology has always been seeing numerical identity where there is only qualitative identity. It is true that 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 concepts of chairs, of circles, and probably 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 having to specify which occurrence and in what mind. We speak in the singular of the thought that 7 + 5 = 12 because there is no reason to consider the individual persons who think it.
The adoption of the definition of s-thoughts proposed above, which is easily generalizable to all kinds of Fregean senses, is in my judgment the only plausible abstraction we can arrive at without committing any of 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 psychologically dependent definition of s-thoughts suggested above could be able to ensure the objectivity of s-thoughts, their interpersonal accessibility or communicability? As we saw, Frege thought that if we regarded thoughts as psychological representations, as is the case with p-thoughts, they would unavoidably be subjective, and we could not compare them with each other. However, it still seems that Frege was too hasty when he admitted that thoughts belong to a third realm of Platonic entities. One could note that there is no doubt that what Frege calls representations (phenomenal mental contents) have in fact limited possibilities of interpersonal communication. But more important is to note that senses and s-thoughts, without being Platonic entities, are something more than subjective mental states: they are rule-complexes built upon combinations of interpersonally agreed upon conventions made with the help of public signs that precisely because of their interpersonal character are communicable. That is, because s-thoughts are verifiability rules rooted in interpersonal conventions, they can well be able to satisfy Frege’s demand for objectivity as the interpersonal accessibility followed by the possibility of communication and evaluation.
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 recognizable instantiation of a combination of conventionally established semantic rules attached to our words. However, compare by analogy this case with the case of genetic information able to endlessly reproduce the same characteristics in successive biological individuals. Why can’t the conventions and ways they can be combined in the constitution of p-thoughts do the same thing? More than this (and probably also in the case of genetic information), it is easy to suppose that there are corrective mechanisms able to interpersonally and intrapersonally impose a limit on divergence from conventional 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 epistemologically objective/subjective (Searle 1999: 43-45) to the objectivity of s-thoughts. Searle noted that we have a strong tendency to take what is epistemologically subjective for what is only ontologically subjective. However, one thing can be ontologically objective – for instance, ‘How much was the First World War justifiable?’ – without ceasing to be epistemologically subjective, because it is not easy to reach common agreement about the issue. In contrast, a phenomenon can be ontologically subjective without ceasing to be epistemologically 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, even if the patient alone knows exactly how it feels.
Something of the kind can also 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 mind or another. But even so, they do not cease to be epistemologically objective. After all, we are capable of interpersonally agreeing about them and their truth-values. We can agree that an objectively assertive sentence like ‘The Eiffel Tower is made of metal’ expresses a true s-thought that is epistemologically objective even though, as an s-thought, ontologically subjective, since it is scattered among the minds of those who think it. Like any s-thought, it remains epistemologically objective, given that it is grounded on conventions associating words with things in the world, which makes it 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 is only expressive. It has only non-conventional subjective coloration, being susceptible only to aesthetic appreciation with variable degrees of interpersonal agreement.
On this point Frege was no exception: like Husserl, Bolzano and several other continental philosophers with mathematical training, he believed that the ontologically subjective character of psychologically conceived thought-contents would inevitably be condemned to epistemological subjectivity. But this was a mistake.
32. Further ontological consequences
Our ultimately psychological reformulation of Fregean thoughts has some interesting ontological consequences. If the thought of the Pythagorean theorem isn’t an eternal (timeless) entity belonging to a Platonic realm, always true or false, where and when does it exist? The answer is that being at least one occurrence of thought, or any other qualitatively identical occurrence, regardless of the bearer, something like the Pythagorean theorem acquires an existence dependent on minds, which does not mean that it is dependent on any of the many minds that will eventually think it. Since this thought has been 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.
Another consequence of the proposed view is that unlike the Platonic entity that Frege called a ‘thought’, our s-thought of the Pythagorean theorem, did not in fact exist before Pythagoras thought it for the first time (supposing he was the first), and will cease to exist if 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 sound strange is that nobody can truly deny it. 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 be an occurrence of the thought of the Pythagorean theorem and insofar falsify what it states. Nevertheless, the s-thought of this theorem would not have come into existence if nobody had ever thought it. Thus, it would not exist in a world without cognitive beings.
This remark suggests to us the following objection. Imagine a possible world Ww similar to ours, with planets, stars and galaxies, but without any cognitive being. In Ww the s-thoughts that there are planets, stars and galaxies could not have been thought and, as the primary bearers of truth, could not be true. Nevertheless, it seems obvious that in this world the fact that there are planets, stars and galaxies would still be true, even though there would be no sentient beings to think this.
Our answer is that here we are again victims of the confusion between thought-truth and fact-truth. The first is the truth applied to the primary bearer of the truth, which is the s-thought. The second is a derived but as we already saw very common application of truth to the real existent thing or fact in the world, as a secondary bearer of truth. Indeed, that there would be planets, stars and galaxies in a mindless world would be still true as a fact, and the applicability of the Pythagorean theorem would still be true as a fact in Ww, even though neither their s-thoughts nor their truth in the form of correspondence would exist. The flexibility of natural language once again misleads us.
Still another 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. However, if something is discovered, then logically it must have existed before being discovered. Consequently, the above-described thoughts must already have 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. This seems clear in the case of empirical truths. That the law of the lever was always applicable in principle is surely true. However, this is a fact-truth; the thought-truth of it first came into the world when scientists like Archimedes conceived it. Similarly, common sense tells us that the fact expressed by the Pythagorean theorem must always have existed. However, our s-thought of it only came into existence after the theorem was thought by Pythagoras and since then has been thought by many others. Facts, in their turn, as long-lasting as they may be, are not the primary bearers of truth, but their truthmakers or verifiers. They are said to be true only in the sense (b) of fact-truths, not in the sense (a) of thought-truths. They are what occurrences of their thoughts represent. Hence, in the most precise sense, no truth or falsehood would exist in a world where there were no minds to think them. The most that we could think of in this direction is to say that if the law of the lever were thought in Wt, it would be recognized as truth.
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 the present moment. The moment we think that it has never been thought before, we are already thinking it, and we can attribute falsity to it. Even the s-thought ‘The world could exist, even if there were no minds to think about it’ is only a true thought because there are minds to think it.
33. 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 a plausible interpretation of Aristotle (1984, vol. I, Ch. IX), the following argument is valid:
1. Necessarily, it is true or false that there will be a sea-battle tomorrow.
2. If (1) is true, then the future is predetermined and there are no chance events.
3. Therefore, the future is fixed and there are no chance events.
It seems that for Aristotle this conclusion would be unacceptable, because if the future were predetermined, then there would be no chance events, and if there were no chance events, there would be no free will. Hence, according with the most accepted traditional interpretation, he thought that although this argument is sound, 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 we should preserve the principle of bivalence for s-thoughts. But (1) can be questioned from a different perspective. 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 at a loss for the task of associating p with any appropriate truthmaker in order to assign it a truth-value.
However, one could argue that the sentence ├p (as much as ├~p) is misleading and causes confusion, like argument A, because ├p only seems to express cognitive thought-content. The reason for this is that ├p is very easily confused with the meaningful 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* almost always appears 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 that is held to be true, for it is true that, with the information available to us, it was very probable that a sea-battle would occur the next day. Indeed, the utterance ‘It is likely that a naval battle will occur tomorrow’ could be regarded as definitely true on the night of June 3, 1942, without breaking any principle of bivalence.
Suppose now, by contrast, that I am on the calm beach of Praia Bonita, looking out across the Atlantic Ocean, and without any reason I say ├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 can be regarded as definitely false, since I have all kinds of reasons to believe that this kind of event is extremely improbable in this region and at this time.
The conclusion is that taken in the absence of a context (and not in the sense of ├p* or ├q*) the sentence ├p is a linguistic bluff devoid of meaning and justification. Aristotle would be right in rejecting the application of the principle of bivalence to it, not because this principle has exceptions, but simply because it expresses no s-thought, no proposition. All that this sentence does is to induce us to imagine a naval battle that takes place tomorrow, as if there were hidden verifiability criteria. However, as much as no context is furnished, no real criteria can be given. Statements like ├p*,├~p* and ├q*, on the other hand, say something probabilistic about tomorrow that can be confirmed and made true by criterial reasons already found today.
It seems that in principle the metaphysical problem 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.
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 better distinguish the most relevant forms of semantic-cognitive rules. This required strong corrections in Frege’s own framework. Even if most results could only be sketched here, they nonetheless seem to me much more plausible than Frege’s own original views.
 As Tyler Burge wrote in ‘Sinning Against Frege’, ‘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).
 For Frege, in the case of indexical sentences, the context of the utterance belongs to the expression of the thought. I believe I have shown the real consequences of this in (2014c).
 Often in dictionaries we find accentuated: ‘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).
 See Tugendhat’s verificationist correspondentialism in 1983: 235-6.
 See appendix to chapter 3.
 One could object: haven’t we learned that geometry deals with perfect circles, that arithmetic deals with entirely abstract numbers? Take the case of circles. The answer is, of course, in the negative, because we can make a new circle more perfect than the last one, and another even 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 a projection of our awareness of the possibility of making increasingly perfect empirical circles without any end in sight. Geometry does not work with actual perfect circles, but with potentially perfect circles.
 Against Frege, we could hold that to a great extent even representations can 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 instance, a sort of epileptic aura, is not communicable, except indirectly, metaphorically. But it seems very plausible 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 reinforced by interpersonally accessible physical states strongly intermingled with them (Costa 2011, Ch. 3).
 Biological mutations are accidents whose incidence should be evolutionarily calibrated. Only species that mutate in the right amount in the right period of time and in the proportion of the environmental changes are likely to survive. Too many mutations, as much as too few, would be dangerous. So it seems that an unchanging species with no relevant mutations is conceivable, but they would be unable to adapt to changing external conditions.
 For a more sophisticated alternative interpretation in which Aristotle does not reject the principle of bivalence, see Christopher Shields, 2007: 186-190.