terça-feira, 31 de janeiro de 2017


Corrected draft. The final version will be published in the book Philosophical Semantics, Cambridge Scholars Publishing, 2017.

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 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’.[1]
   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 truthfultrustworthy 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.[2]

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).’[3]
   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.[4]
   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.[5] 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 (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.[6] 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.[7] 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.[8] 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:

      Argument A
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).[9]
   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├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 with any appropriate truthmaker in order to assign it a truth-value.
   However, one could argue that the sentence ├(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.

34. 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 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.

[1] 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).
[2] 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).
[3] 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).
[4] See Tugendhat’s verificationist correspondentialism in 1983: 235-6.
[5] See appendix to chapter 3.
[6]  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.
[7] 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).
[8] 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.
[9] For a more sophisticated alternative interpretation in which Aristotle does not reject the principle of bivalence, see Christopher Shields, 2007: 186-190.


Corrected draft for the book Philosophical Semantics to be published by Cambridge Scholars Publishing in 2017 

19. The reference of a sentence as its truth-value
Now we will leave these speculative excurses and come back to the more tangible Fregean semantics, considering what he has to say about the reference of the sentence (Satz). Here I have no compliment. Frege was the author of the unsane idea that the references of sentences are their truth-values, and the thoughts expressed by them are modes of presentation of truth-values. How did he reach this strange conclusion? There are several reasons. First, sentences are independent, saturated, closed; they work as names, and their truth-value is also closed, like the object referred to by a name. Second, he says that the search for truth is what brings us from sense to reference. Third, he notes that sentences without reference lack truth-value: ‘Vulcan is a warm planet’ has no reference and for him no truth-value, as this hypothetical planet has never been discovered. Fourth, he also noted that according to the principle of compositionality the reference must be what remains unchanged after we change the senses of a sentence’s components without changing their references. Now, this is what happens, for instance, if we replace ‘Napoleon lost the Battle of Waterloo’ with ‘Napoleon lost his last battle’; both sentences remain true. The references of the sentence-components do not change, and the reference of the whole sentence should likewise not change. The truth-value remains the same: the truth. Hence, the reference of these two sentences must be their truth-value. The conclusion of all this is that in extensional languages the references of sentences must be their truth-value (1892: 34). For Frege, all true sentences have only one reference, which is the abstract object The True (das Wahre), while all false sentences also have only one reference, which is the abstract object The False (das Falsche).
   Independently of this argument, interpreters have noted that Frege chose truth-value as the reference of sentences, because it is what gives them value for 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 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 healthy intuition, Frege’s proposal frontally contradicts the meaning we normally give to the word ‘reference’. It is intuitively obvious 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 we expect 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 even if it had, then all objects referred to by names in true sentences should be parts of The True. A further objection is that there are serious substitutability problems with Frege’s explanation of the references 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’. The result is the sentence ‘If The True, then water falls from the sky’, which should be true but is in fact unintelligible (Black 1954: 235-6). Finally, to make things still worse, a multitude of obviously false identities between true sentences should be true. For example, ‘Paris is a city = snow is white’ should be a true assertive composite sentence, since both partial sentences of it refer to the same thing: The True.
   The most charitable interpretation is that Frege uses the word ‘reference’ in a completely new, technical sense. The problem is that in spite of any theoretical advantage for the logician, this new way to use the word is gratuitous – What does it add to the plain admission that only truth-value and not how it was achieved is what counts for logical inference? Moreover, in philosophy this view can be – and in my judgment really has been – disastrously misleading from an epistemological standpoint, once we hold that truth has virtually nothing to do with anything that can reasonably be understood as the reference of our statements.

20. Structural status of facts
The Fregean account of the references of sentences as their truth-values turns out to be still less acceptable if we consider that a much more natural alternative is available, which, as Sir Anthony Kenny has noted, was not even mentioned by Frege (Kenny 2000: 133). Since it is more plausible that the references of sentences are facts, it is important to investigate the logical structure and ontological nature of facts.
   Concerning the logical structure of facts, the most plausible hypothesis is that they correspond to the logical structure of the thoughts representing them, assuming these thoughts are expressed in declarative sentences logically analyzable in accordance with appropriate contexts. Singular empirical statements such as ‘Plato has a beard’ and ‘The cat is on the mat’ respectively represent facts that should have the logical structure Fa and bRc. The elements ab and c, as particulars, refer to clusters of appropriate compresent tropes, while F and R would be also analyzed as tropes, usually forming complex configurations dependent upon the clusters. The links b-R-c and F-a, in turn, are only pseudo-relations, since the admission of their existence as relational tropes would generate one inevitable Bradleyan regress. Individuals and their tropes are linked by ‘non-relational ties’ without any ontological addition (Cf. appendix to chapter 3).
   We should also pay attention to the somewhat obvious rule of analysis according to which we should not accept singular terms as components of predicative expressions. Thus, for instance, in a sentence like ‘Stockholm is the capital of Sweden’ we should not take ‘…is the capital of Sweden’ as a predicate, since Sweden is a proper name. The correct analysis is to take relational predicates like ‘…is the same as…’, and since we consider that ‘the capital of Sweden’ is a definite description contextually referring to Stockholm in our world, if not in all possible worlds, this is a case where ‘…is the capital of…’ would be the most appropriate relational predicate. Finally, if necessary we can analyze proper names using Russell’s device of transforming them into quantified predicative expressions, since to a limited degree this device mirrors my own defense of a neo-descriptivist theory of proper names. The structure of facts must correspond with the structure of the so-analyzed sentences that express the structure of thought (the real ‘language of thought’).

21. Ontological status of facts
If we accept that the references of sentence-senses or thoughts are facts, then from an ontological perspective the references of empirical sentences – what they represent – must be empirical facts, most typically located in the external world, though possibly also located in someone’s inner mental world. This assumption speaks for the correspondence theory of truth, according to which empirical facts are truth-makers seen as contingent complex arrangements of elements in the world, which are nothing but arrangements of tropes and things constructed from them.
   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, in a very influential article P. F. Straw­son suggested that empirical facts are mere ‘pseudo-material correlates of the statement as a whole’ and not something in the world (1950: 6).[2] According to him, empirical facts, unlike events or things, are not spatio-temporally localizable (‘the world is the totality of things, not of facts’). One reason for 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’. On the other hand, 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’. Facts are for Strawson what statements (when true) state; not what statements are about. They are ‘not, like things or happenings on the surface of the globe, witnessed or heard or seen, broken or overturned, interrupted or prolonged, kicked, destroyed, mended or noisy’ (1950: 6), the same being the case with states of affairs and situations.[3] Finally, to give a striking example, the event of Caesar’s crossing the Rubicon occurred in the year 47 BC, while the fact that he crossed the Rubicon did not occur in the year 47 BC, but it is still a fact today, since facts simply do not occur (Patzig 1980: 19-20).
   An efficacious way to dispose of this argument could be the following. As I understand him, 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 don’t we use it stipulatively in order to designate the truthmaker, whatever condition it is?[4]
   However, it seems clear 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, I am of course not saying that everything we may call a ‘fact’ is obviously empirical. The fact that 2 + 2 = 4 is not easily said to be empirical. And we can say it is a fact that the Sun is not green, although this seems only a different way to say that there is no fact that the Sun is green. What I want to defend here is that empirical facts, particularly so-called observational facts, should be considered objectively real: they exist in the external world as possible truthmakers.
   There is a simple and very decisive reason to think that facts can be constituents of the empirical world. It is the fact that of many facts we can easily say that they act 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 a holiday, the class will be canceled.
(4)  The fact that Caesar crossed the Rubicon had important historical consequences.

It does not seem possible that pseudo-material correlates (supposedly abstract contents) can be causally active in the empirical world producing these effects. The admission of the empirical nature of the facts (1) to (4) solves the problem in obvious ways. Scratching the match is a fact-event causing the flame; the situational fact created by Thomas’ forgetfulness of the gas being turned on caused his death; the fact-circumstance that today is a holiday causes the canceling of a 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, as the classical correspondence theory of truth has sustained. According to this view, empirical facts are contingent arrangements of elements in the external and/or internal world in general (basically an arrangement of more or less complex predicative or relational tropes contingently tied with clusters of compresent tropes referred to by proper names). This would be the case with facts as simple as those referred to by the sentences ‘Frege had a beard’, ‘The book is on the table’, ‘Lydia suffers from agoraphobia’.
   My argument against Strawson’s opposition between non-spatio-temporal facts and spatio-temporal events begins by showing that there is a serious confusion in his argument. He treats facts (as much as states of affairs and situations) as opposed to events. But this can easily be contested. We begin to be suspicious when we perceive that every event can be called a fact, but not every 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 Mt. Everest is more than 8,000 m. high’ by ‘the event of Mt. Everest being 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 this proposal is that we can call all these things facts, but we cannot call all these things states of affairs or events or whatever. So considered, events are sub-types of facts: Linguists should say that the word ‘event’ should is a hyponym of the word ‘fact’. Considering things in this way, it is easy to distinguish two great sub-classes of facts:

1.     STATIC FACTS: Can be formal or empirical, the latter when clearly located in space and time. As a whole, 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 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 comes to an end after a certain amount of time. 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 × 8 = 56, are static in the innocuous sense that they aren’t seen as spatio-temporally 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. Examples of static facts are my unhealthy state, the situation that I am lying in bed, the circumstance that the airport is closed, the state of affairs that Venice has many canals or that the Earth orbits the sun. The Earth’s movement of revolving around the sun counts as a static fact because it is an internal cyclical relationship that remains the same during the fact’s existence (each orbital period is 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 World War II, for instance, was marked by events like the Battle of Britain, the defeat of Stalingrad and the Normandy invasion – it had an unforeseeable 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 or a bomb blast. An example of an occurrence is a volcanic eruption. The process of global warming is a very slow natural process, slower them the economic process of globalization. We can predict the stages of many events and processes, although many are also unpredictable in such a way that (differently from static facts) we cannot entirely grasp them before they 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. Thus, 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 lying on the bed. Conclusion: that-clauses have the function to emphasize static facts and exclude 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: ‘Caesar crossing the Rubicon was an event’ as much as ‘It is a fact that Caesar 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 a 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 crossed the Rubicon? Isn’t this fact timeless? This is a good case of a philosophically misleading expression. In most cases it is 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 Roman territory, violating the law that prohibited this and forcing the Roman state to declare war against him. Only occasionally is the phrase ‘crossing the Rubicon’ 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 say that they are located in time while they last. It seems, therefore, that because philosophers such as Strawson did not realize 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 (and things) 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 Caesar’s crossing the river was far more durable, because it was a static fact, the political situation that led, as is well-known, to 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 crowning of Caesar as dictator and up until his assassination. It was not something that existed in Greenland 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. Under this view, facts are the universal truthmakers.

22. Church’s slingshot argument
Trying to refute the accusation of implausibility, the Fregean logician Alonzo Church used 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 when one constituent expression is replaced by another, so that their partial references are interchangeable, the reference of the whole sentence does not change. I will initially expose his example of a slingshot argument, underlining its supposedly co-referential definite descriptions (Church 1956: 25):[5]

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

According to him, if it is 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 truth 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, they are partial references to Walter Scott. In sentence (2) again, the nominal expression ‘Sir Walter Scott’ and the definite description ‘the man who wrote altogether the twenty-nine Waverley novels’ both refer to the same Walter Scott. The third sentence is the tricky one. Its reference is unclear: Walter Scott? The number 29? Both in one? An amalgam like Scott29? Is there a way to paraphrase sentence (3) so that it gives back in a transparent way its complete informative content? In my view, the only way to reveal 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 Waverley novels and Sir Walter Scott is the man who wrote altogether that many Waverley novels.’ Or for the sake of clarity, replacing ‘=’ for ‘is (the same as)’ and ‘&’ for ‘and’, we have:

6.     (29 = the number of Waverley novels) & (Sir Walter Scott = the man who wrote the many Waverley novels altogether).[6]

That is: Sentence (3) confusingly compresses nothing less than a conjunction of two identity sentences, each with its own proper partial references given by the terms flanking their identity signs. They are the number 29 in the first sentence and Walter Scott in the second sentence. Finally, we come to the analysis of the sentence (4): ‘29 is the number of counties in Utah’, which means the same as the identity sentence (7) ‘29 = The number of counties in Utah’. Here, each term that flanks the identity sign has the number 29 as partial reference. So analyzed, the derivation appears as:

1.     Sir Walter Scott = the author of Waverley.
2.     Sir Walter Scott = the man who wrote the altogether 29 novels of Waverley.
3.     (5) (29 = the number of Waverley novels) & (Sir Walter Scott = the man who wrote the many Waverley novels altogether).
4.     (6) 29 = the number of counties in Utah.

Now, although these sentences are all true – assuming a principle of compositionality requiring that the partial references cannot change – this loses its intuitive appeal. Sentences (1) and (2) have as partial references Walter Scott under different guises. However, sentence (3) is a conjunction of two identity sentences, each one with its own very distinct partial reference. The object referred to by the flanking terms of the first identity sentence is the number 29 (as the number of Waverley novels), while the object referred to by the flanking terms of the second identity sentence is Sir Walter Scott (as the man who wrote the Waverley novels). Finally, sentence (4) has as a partial reference of its terms only the number 29 (as the number of counties in Utah), without referring to Walter Scott. This means that in the composed sentence (3), the second sentence of the conjunction is the only one that preserves as its partial reference the references of (1) and (2), while (4) is an identity sentence that has as its partial reference only the partial reference of the first sentence of (3), which has clearly nothing to do with the partial references of (1) and (2) and therefore with their references. That is, the replacements slip equivocally from Walter Scott in (1) and (2) to a Walter Scott together with the number 29 in (3), and to the number 29 in (4), in a surreptitious way. This means, according to the principle of compositionality applied to the complete sentences, that the references of sentences (1) and (4) should be different. Initially the flaw isn’t easy to spot, because sentence (3) contains both these partial references conjoined in a grammatically confusing way; we have the impression that the partial references of (3) are something like an amalgam of Walter Scott and 29, say, a ‘Scott29’, while they are in fact totally distinct. In fact, the replacements would only respect the compositionality principle, warranting the sameness of the sentences’ references, if the argument could prove that the partial references of all the sentences could be replaced without surreptitiously inviting the reader to conjoin in sentence (3) partial references that are of objects completely distinct.

23. Facts: sub-facts and grounding facts
If we take the whole reference of the sentence as not a truth-value but a fact, things turn out to be much more intuitive. We can seize Church’s derivation not only to introduce facts as referents of sentences, but also to introduce a distinction between sub-facts and grounding facts. As will be seen, this distinction fills a gap in Frege’s explanation.
   We need to distinguish at least two facts referred to by identity sentences. The first is the perspectival fact, the fact as what is immediately exposed through the mode of presentation expressed by the sentence. I will call it a sub-fact and make the different sub-facts responsible for the differences in the modes of presentation constitutive of the different sentence-senses or Fregean thoughts about the same thing, as the planet Venus, Scott, the number 29. This is why Church’s sentences (1) and (2) can be seen as expressing different senses or thoughts by evoking different perspectival sub-facts. They expose different sub-facts, since (i) being Sir Walter Scott is not the same thing as (ii) being the author of Waverley and (iii) being the man who wrote the altogether 29 novels of Waverley … In this way, sentences (1) and (2) show respectively two sub-facts that contain constitutive objects of reference that differ one from the other. Here they are:

(1’) Being Sir Walter Scott ≠ being the author of Waverley novels.
(2’) Being Sir Walter Scott ≠ being the man who wrote the altogether 29 novels of Waverley.

However, it is obvious that (1) and (2) are also identity sentences. Each of these sentences can be understood as referring under different guises to only one object, justifying their ‘is’ of identity. In this sense, sentences (1) and (2) also represent identities, which can be directly expressed by ‘Walter Scott = Walter Scott’ and which express the self-identity of Scott considered in full, as the bearer of all descriptions we attach to it. Under the descriptions attached to the name ‘Walter Scott’ we can find ‘the person with the title of Sir called “Walter Scott”’ (that is, ‘Sir Walter Scott’), ‘the author of Waverley’ and, more definitely, ‘the man who wrote the altogether 29 Waverley novels’, expressions that build (1’) and (2’). This primary fact that unifies all the sub-facts shown by its multiple modes of presentation is what I call the grounding fact. It is what makes sentences with the form a = b identity sentences.
   Considering things in more details: As we saw, the mode of presentation is intentional, also subjective, considering that the reference can be absent. But when the mode of presentation isn’t empty it also exposes something objective, for instance, ‘the author of Waverley’ evokes ‘being the author of the Waverley novels’, which is, we could say, an objective sub-object mediating our reference to the object Scott. Thus, ‘the author of Ivanhoe’ (who was also Walter Scott) is a mode of presentation of the sub-object ‘being the author of Ivanhoe’, though it ultimately refers to Walter Scott. Now, the sentence

The author of the Waverley novels is the author of Ivanhoe.

This sentence evokes two different sub-objects that together form the contrastive sub-fact that being the author of Waverley ≠ (isn’t the same as) being the author of Ivanhoe. But this sub-fact also has two modes by which the same object is given, whose identity is the grounding fact that can be directly represented by the sentence ‘Scott [in full] = Scott [in full]’.
   In other words: when I say ‘The author of Waverley is the author of Ivanhoe’, I am saying two things. First, by the intentional modes of presentation I am evoking an objective difference that can be represented by the sentence ‘Being the author of Waverley ≠ (isn’t) being the author of Ivanhoe.’ Indeed, it is a objective factual difference that a person writing Waverley is not the same as a person writing Ivanhoe, even if they are both the same person (he was writing different stories at different times). However, since when I say ‘The author of Waverley is the author of Ivanhoe’ I use an ‘is’ of identity, I also mean ‘The author of Waverley = the author of Ivanhoe’, so that under different guises I am representing the grounding fact that ‘Walter Scott = Walter Scott’. It is because of the two – the grounding fact along with the sub-fact – that identities of the kind a = b are able to express what I somewhat romantically call the identities in their differences.[7]
   Now, assuming the kind of neo-descriptivism proposed in appendix 1 of this book, we can make explicit the above mentioned duplicity of the represented facts by stating each of the four sentences of Church’s reasoning as follows:

(1) Sub-fact: Being Sir Walter Scott ≠ being the author of Waverley. (1) Grounding fact: Walter Scott = Walter Scott.
(2) Sub-fact: Being Sir Walter Scott ≠ being the man who wrote the altogether 29 Waverley novels. (2) Grounding fact: Walter Scott = Walter Scott.
(3) Sub-fact: (Being 29 ≠ being the number of Waverley novels) & (Being Sir Walter Scott ≠ Being the man who wrote altogether the many Waverley novels). (3) Grounding fact: (29 = 29) & (Walter Scott = Walter Scott).
(4) Sub-fact: Being 29 ≠ being the number of counties in Utah. (4) Grounding fact: 29 = 29.

The sub-facts show why the semantic-cognitive contribution of each referential component may be different. For instance, the sub-fact that Sir Walter Scott wrote 29 Waverley novels discriminates more than the sub-fact that he wrote the Waverley novels, and in true sentences this discrimination isn’t just a mentally considered mode of presentation, but also something objectively, factually given (in Frege’s words, ‘the way the object gives itself to us’). The evocation of these sub-facts all send us to the grounding fact that all the different senses in the end refer to something numerically identical.

24. Taking seriously the sentence’s reference as a fact
I hope I have shown that the most plausible option concerning the nature of reference is to follow Russell and Wittgenstein, assuming that the reference of a statement is always a fact, understood as a contingent arrangement of cognition-independent elements usually given in the external world. Facts would satisfy the Fregean condition that the reference of a sentence is an object: they are independent, complete, closed. They would satisfy his condition that thoughts expressed by sentences are modes of presentation of their references, the last ones being (as sub-facts) as multiple and diverse as their thoughts. Finally, unlike truth-values, facts would clearly satisfy the principle of compositionality: they would always vary in accordance with variations in the references of the component parts of the sentences.
   If we assume this answer, questions arise. The first is the following: how do we establish what fact the thought expressed by a sentence refers to? 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 sulfuric acid clouds.
7.     The morning star is the only planet in our solar system shrouded by an opaque layer of highly reflective sulfuric acid clouds. …

On the one hand, it is linguistically correct to say that each of these sentences refers to a different fact. Sentence (1) is tautological, proclaiming the self-identity of the morning star, while sentence (2) and the following sentences provide different information on different factual contents regarding the planet Venus. On the other hand, since all singular terms composing these identity sentences have the same ultimate reference, the planet Venus, it also 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: in such cases there 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. This grounding fact must in some way include the facts indicated by the different cognitive values of sentences (1) to (7) above as its perspectival sub-facts. My suggestion is that this task can be accomplished by the references of identity sentences between proper names, insofar as they are their identifying rules considered in full, that is, including all their fundamental and complementary constituents.
   Now, assume our proposed view of proper names’ meanings as abbreviations of bundles of descriptions applicable according to identifying rules as essentially correct. Then the proper name ‘Venus’ in full (i.e., considering all its assumed descriptions and abstracting the limited knowledge of concrete speakers) includes in its most complete content all of those already known modes of presentation. This means that definite descriptions such as ‘the morning star’, ‘the second planet orbiting the Sun’, ‘the most brilliant planet visible in the sky’, etc. can at least be made probable by applying the concept of Venus in full (I say ‘made probable’ because according to the identifying rule any description of the bundle may be empty). If so, then there is indeed a sentence that could describe the grounding fact. This is the ultimate truthmaker or verifier 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 contention is that rightly understood this sentence is able to express an ideal 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 Venus.
   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 identifies its object, then this proper name must include descriptions like ‘the morning star’, ‘the second planet orbiting the Sun’, ‘the most brilliant planet visible in the sky’, etc. Consequently, we can inferentially derive 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 inductively infer all the other co-referential identities. 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 sub-facts indicated by each of the thoughts expressed by the above sentences, which may be seen here as contingent a posteriori. (Cf. the meaning of ‘Venus’ as presented in an encyclopedia.)
   In order to reinforce what I am suggesting, I can instead use 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, here the identity sentence expressing the grounding fact would be:

6.     4 [in full] = 4 [in full]

   But could the sub-fact expressed by sentences (1) to (5) be derived from (6)? The answer is obviously in the affirmative, since we are dealing with a deductive system. The obvious reason for this 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: a necessary truth. How could a necessary truth ground contingent truths like ‘Venus is the brightest 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 satisfy sufficiently and more than any other the condition of being the second planet orbiting the sun, located between Mercury and the Earth (making probable the application of auxiliary descriptions like ‘a planet somewhat smaller than the earth’, ‘the morning star’, etc.)

This is a one-foot identifying rule. The localizing rule is here the only fundamental description-rule. If Venus loses its atmosphere or an important part of its mass, insofar as it remains the second planet, it will be our Venus. Indeed, so understood the identifying rule for Venus must be applicable in any possible world where the planet Venus exists. The Venus’ case is somewhat like the case of the lines ‘a⁀b-a⁀c’ made to localize the center of a triangle without any further property. No characterizing description is relevant. However, without the localizing condition established by the identifying rule of Venus it would be impossible to identify Venus. The application of many other descriptions does not create criteria, but only symptoms of the existence of the planet, since they make the application of the descriptions only more or less probable. Auxiliary descriptions like ‘the brightest planet in the sky’ are symptoms, like ‘the highly reflective clouds of sulfuric acid’ that cause this brightness. If Venus loses its reflective atmosphere, it may cease to be the brightest planet, but will 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. This will occur only if it becomes an asteroid; for an asteroid is not a planet. If in another possible world the second planet had been hurled out of the solar system thousands of years ago (Kripke 1980: 57-58), it would still with right be recognized as our Venus.
   What I said about identity sentences also applies 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 Thessalonian strain.
5. Bucephalus was a massive black horse of the best Thessalonian strain, owned by Alexander the Great.
6. Bucephalus: (355 BC – 326 BC) was the most famous horse of Antiquity; it was a massive black horse of the best Thessalonian strain, owned by Alexander the Great.

One could say that each of the first five sentences refers to different sub-facts by means of increasingly detailed modes of presentation expressed by their respective predicative expressions. However, relative to them there is a grounding fact that is more completely referred to by sentence (6), since the truth of all the others can be implied by the truth of this sentence. Indeed (6) is nothing but a shortened expression of the identifying rule for Bucephalus, with a localizing and a characterizing description. The sub-facts represented by sentences (1) to (5) are all included in the grounding fact represented by sentence (6). These facts are the immediate satisfiers of the diverse modes of presentation of Bucephalus indicated by each sentence.

25. The problem of identity in difference
There is a final point concerning the relationship between the sub-fact and the grounding fact. It concerns the deficient way by which Frege solved the puzzle of identity. As he writes, differently from a sentence of the form a = a, a sentence of the form a = b is informative because it refers to the same object by means of different modes of presentation, different senses (1892: 26). However, 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, as Frege also acknowledged. I call this the riddle of identity in 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 brightest star in the morning sky, understood as representing the second planet orbiting the Sun (Venus) = the brightest star in the evening sky, understood as representing the second planet orbiting the Sun (Venus).

Here we have the hidden reason for the riddle of identity in difference: the senses of the expressions flanking the identity sign in (1) are obviously different, but they both evoke a sense that is identical, which is that of being the second planet orbiting the sun, namely Venus. It is important to note that this last sense is not yet the reference, but still a cognitive identifying rule (expressed by the underlined definite descriptions) constituting the core sense of the name ‘Venus’. It is only because both expressions flanking the identity sign indirectly evoke 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 use the following schema:

Sentence:    The morning star          = (is)           the evening star.

immediate   IR: the brightest            ≠                 IR: the brightest
sense:          star in the morning                           star in the evening
                                 ↓                  sub-fact:                  ↓
                   Being the morning star isn’t being the evening star

mediated     IR: the second planet…     =              IR: the second planet…
sense:          (Venus)                                               (Venus)
                                    ↓              grounding fact:           ↓
                                     Venus [in full] is Venus [in full]

In sum: the singular terms ‘morning star’ and ‘evening star’ are responsible for a difference in what I call immediate senses, evoking a relational sub-fact showing the difference between them. Indeed, the sub-fact is that being the brightest star seen in the morning sky differs in place and time from being the brightest star seen in the evening sky. Furthermore, the word ‘is’ (the same as) indicates the identity of the implicitly mediated senses pointing to a relational grounding fact that is constituted by the fact of Venus’ self-identity, here expressed by the statement ‘Venus [in full] = Venus [in full]’.
   A somewhat different example is the sentence ‘The morning star is Venus’. Here the schema is:

Sentence:        The morning star            =         (is)      Venus.

Immediate:      IR: the brightest             ≠          IR: the second
sense                star in the down                               planet
                                        ↓                 sub-fact:           ↓
                         Being the morning star isn’t being Venus

Mediated         IR: the second planet      =          IR: the second planet
Sense:             (Venus)                                               (Venus)
                                         ↓           grounding fact:      ↓
                                       Venus [in full] is Venus [in full]

In this way, the identity expressed by sentences of the kind a = b is an identity in difference. This means that in fact we have two levels of sense. The first exposing the phenomenal sub-fact expressing a difference (Being the morning star isn’t the same as being the second planet). The second, intermediated by the first one and indicated by the ‘is’ of identity (is the same as), represents the ultimate grounding fact that Venus is the same as Venus.
   Now, how should we deal with 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⁀b = a⁀c’ (concerning Frege’s example of the different ways to name the center of a triangle), (iii) ‘Afla = Ateb’ (the two names of the same imaginary mountain conceived by Frege). I would answer this by creating a conjoint sense, a conjoint identifying rule, respectively the ‘Everest-Chomolungma’, the ‘a⁀b-a⁀c’, and the ‘Afla-Ateb’, which in fact produce three new nominative expressions. By the law of identity it is now obvious that ‘Everest-Chomolungma = Everest-Chomolungma’, ‘a⁀b-a⁀c = ‘a⁀b-a⁀c’, and ‘Afla-Ateb = Afla=Ateb’ represent the three different grounding facts. This is what maintains the identity of sentences (i), (ii) and (iii).
   We can apply a similar analysis to identities between concept-words: (x) (Fx = Gx). Consider the identity ‘Water is H2O’. The schema will be:

Sentence:       Water                        = (is)     amount of H2O.
                          ↓                                                    ↓
Immediate     aqueous                      ≠           amount of
sense:            liquid…                                   hydroxide of oxygen
                          ↓                        sub-fact:              ↓
                      Being water isn’t being an amount of H2O

Mediated       amount of                   =            amount of
sense             hydroxide of oxygen                 hydroxide of oxygen
                              ↓               grounding fact:        ↓
                              Water [in full] is water [in full]

As already noted (appendix to chapter 2), the concept-word ‘water’ has two nuclei of meaning: a superficial one, of the aqueous liquid (transparent, insipid, odorless, etc.), and a deep one, of a chemical substance often called hydroxide of oxygen. Regarding the immediate sense, it exposes the sub-fact of the difference: the sub-fact that being an aqueous liquid isn’t the same thing as being a quantity of H2O molecules. Regarding the mediated sense, the grounding fact indicated is the self-identity of the chemical substance, which remains the same independently of its mode of representation. It is because of this deep identity that we can say that the two different modes of representation of an aqueous liquid and of H2O are those of the same substance.
   This duplicity of sense levels explains much of Saul Kripke’s, in my view illusory, discover of the necessary a posteriori. In different contexts we can enhance or magnify or emphasize the immediate Fregean perspectival sense or thought of a sentence (representing a sub-fact) or the mediated sense or thought of the sentence (representing the grounding fact).[8] Here I need to speak again of the contexts of interest of the linguistic agents, meaning by this their pragmatic aims. Two contexts of interest are important regarding several 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 (modes of presentation, identifying rules) for the phenomenal objects the morning star and the evening star, considering the difference between being the brightest star in the morning and the brightest star in the evening, leaving the identity in the background. This can be the case, for instance, when we contemplate the beauty of the starry sky in the night and, after localizing the evening star, we say to a child that it is also the same thing as the morning star. In this case, we read the thought as contingent a posteriori, since we are well aware that we are emphasizing the difference between the two modes of representation, which is an empirical phenomenal sub-fact. We are emphasizing our representation of the phenomenally given sub-fact. However, in a scientific context of interest, e.g., in which we use a telescope to study the surface of Venus, in considering the sentence ‘The morning star is also the evening star’, what we emphasize is the identity between both stars, the mediated sense representing the grounding fact of the self-identity of Venus. In this case we read the statement as meaning that ‘[in full] Venus = Venus [in full]’, what is a necessary a priori statement, leaving the different guises of sense in the background as secondary effects of an astronomical theory that is already assumed to be true.
   Now, consider the statement ‘Water is H2O’[9]. In a popular context of interest of fishermen interested in digging a well to find water to drink and to wash, this sentence is read as emphasizing the sub-fact that the word ‘water’ means a precious aqueous liquid, a transparent, tasteless, odorless, drinkable fluid, and this is not exactly the same as saying it is constituted by H2O. Since what is emphasized here is the difference between senses, the statement is seen as contingent a posteriori treating the deep identity as an irrelevant empirical discovery. On the other hand, when the context of interest is scientific, e.g. chemists measuring the acidity of a quantity of water, the word ‘water’ in the sentence ‘Water is H2O’ can be read as meaning the same thing as hydroxide of oxygen. In this case, the whole sentence is seen as representing the grounding fact expressed by the identity ‘Hydroxide of oxygen = H2O’, which is the same as ‘H2O = H2O’, that is, a necessary a priori tautology. A similar emphasization can be found in other examples.
    Now, I think Kripke is misleadingly conjoining the a posteriority of emphasizing 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. If these names or concept-words have a work as rigid designators, applying to the same entities in all possible world, this is explained by their mediated senses, which are of the king a = a, and not b. A Wittgensteinian therapist would say that Kripke is victim of a linguistic hypostasis. Finally, as far as the singular terms in such identity sentences are seen as rigid designators, applying to the same ultimate object in all possible worlds in which it exists, this also justify the self-identity of the grounding fact.

[1] See Frege, Letter to Russell of 28.12.1912.
[2] For him ‘a situation or state of affairs is, roughly, a set of facts, not a set of things’ (1950: 8).
[3] For a relevant reply see J. L. Austin, ‘Unfair to Facts’ (1961: Ch. 5). 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.
[4] John Searle once proposed something similar to this: ‘…we neither have nor need a thick metaphysical notion of “fact”. Anything sufficient to make a statement true is a fact. Thus the fact that there are no three-headed cats is as much a fact as the fact that the cat is on the mat’ (1998: 392).
[5] I take the following better ordered formulation from Marco Ruffino, 2004: 25.
[6] This also gives back the whole sense of the original still more convoluted sentence of Church: ‘The number such that Sir Walter Scott is the man who wrote that many Waverley Novels altogether is twenty-nine’.
[7] It seems that the mode of presentation of the sub-fact can be approximated with what defenders of two-dimensionalism call primary intention, while the mode of presentation of the grounding fact can be approximated with what they call secondary intention. (see Chalmers 2002).
[8] The concept of emphasization was fruitfully applied in Jürgen Habermas’ excellent work on universal pragmatics (Habermas 1976).
[9] An example is already discussed in the addendum of the appendix to chapter 2 in this book.