domingo, 25 de dezembro de 2016

## AN EXTRAVAGANT READING OF FREGE'S SEMANTIC (4) (on thought-contents...)

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 x 12 = 144’ in the utterance: ‘The sentence “12 x 12 = 144” expresses a true thought.’ Frege had the latter meaning in mind. In this usage, the word ‘thought’ means simply what the sentence (statement) says, which Frege has conceived of as some sort of unchanging Platonic entity. The terminology here counts, because the word ‘thought’ is the only term in ordinary language that has a sense corresponding to more technical terms like ‘proposition’ and ‘propositional content’.[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 truthful, trustworthy or reliable person, someone with integrity. But it is not always so. When we say that Sam’s belief is true, we mean firstly a subjective psychological attitude of the believer concerning a (dispositional) thought that happens to be true, which leads us again to the truth of a thought in the Fregean sense.
   One reason for preferring to say that the thought is the truth-bearer concerns the logical behavior of the concept. Our concept of truth works as a normative ideal so that the actual truth-value is conceived of as something invariant: if something is true, it is always true; if something is false, it is always false. Obviously, we can err in holding something to be true (für wahr halten), believing in a falsity instead, and vice versa – this is common. But when we discover the error, we correct ourselves, not by saying the thought was previously true but now is false, but by saying that it was always false! Our mental process of holding things to be true is fallible. However, it is fundamental to perceive that this fallibility does not affect the invariability or immutability of the truth-value as a normative ideal, even if it is beyond our fallible capacities to know whether we have reached this ideal.
   Now, if the actual truth-value is immutable, its truth-bearer must also be unchanging, able to remain the same in order to retain this same truth-value independently of the time or place where we grasped it. Indeed, for Frege a true thought (if true) remains true forever, just as a false thought (if false) remains false forever. These entities can even be abbreviated as ‘truths’ and ‘falsities’ respectively. Thus, it is deeply ingrained in our conceptual grammar that the entity that can be primarily called true or false must remain the same and with the same truth-value, so that what may change is only our cognitive grasp of it, our believing in its truth-value (unser für wahr halten). If this is so, then only a thought has the necessary stability to be a proper truth-bearer; for a thought is, according to Frege, unchangeable and eternal (atemporal), being eternally (atemporally) true or false independently of our grasping (fassen) it.
   Consider now the case of sentences as candidates for truth bearers. Identical sentences can express different Fregean thoughts, but in this case, the truth-value of the thought will accompany the expressed thought and not the sentence… This is obvious in the case of indexical sentences like ‘I am in pain’, which express different thoughts depending on the speaker. These sentences can change their truth-value when uttered by different persons, and even when uttered by the same person at different times, though in these cases the thought they express also changes. Thoughts and their truth-values are co-variant, sentences and their truth-values are not.
   One can suppose that perhaps the sentence-token would be the truth-bearer, since it would be a different one in accordance with the time and place of the utterance, changing with the truth-value. However, we still have cases in which different sentences (token or not) say the same thing – express the same thought –in this way preserving the same truth-value. Consider, for example, these statements in four different languages: ‘It is raining’, ‘Il pleut’, ‘Es regnet’, ‘Llueve’… uttered in the same context. In this case, they all have the same truth-value, while their sentence-tokens seem quite different. Indeed, the only justification for the sameness of truth-value of these three different statements is that their truth-bearer is the thought expressed by them, since what remains the same is what they say, their senses, the thought. Moreover, this is the case not only for indexical sentences, but also for synonymous eternal sentences expressed in the most diverse languages. To conclude: thoughts and their truth-values are not only invariantly related; when thoughts vary, they maintain a relationship of co-variance with their truth-values that is missing in the relationships between sentences and their truth-values. Because of this, the proper bearer of truth must be the thought or proposition, not the sentence and still less persons and things.[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 X (Df) = a given p-thought X embodied in some mind or any other p-thought Y qualitatively identical to X, embodied in the same mind or in any other mind.

   The s-thought is my empiricist version of what Frege should have meant with his f-thought (objective non-real thought). This definition reduces the supposed f-thoughts to p-thoughts without forcing them to lose their objectivity (inter-subjectivity) and expected stability or immutability by interpreting them as s-thoughts.
   The so defined s-thought, which I also call thought-content or simply proposition, though spread in space and time, has no particular spatio-temporal location and can be seen as the most proper truth-bearer. For example: the s-thought (or thought-content) expressed in the sentence ‘The Eiffel Tower is made of metal’ can be instantiated as the p-thought that I have in mind when writing this sentence. However, it can also be instantiated by, say, the p-thought that you have in mind when you read it, such as by any qualitatively identical p-thought that I, we, or any other person can have at any other time. Characterized by the disjunction between qualitatively identical thoughts embodied in any individual mind, the s-thought is regarded in abstraction from the particular human minds that causally instantiate it.
   As with model-tropes in the construction of universals, it is not necessary to have only one particular model as the object of interpersonal consideration. To the contrary. What we do is simply to alternate a variety of qualitatively identical models that are usually given to us by memory: first the one and then some other, which we recognize as being identical to the first, so that we can choose any of them as a new model. In some way language is only the vehicle of communication that allows the reproduction of a qualitatively identical psychological p-thought in the minds of hearers, insofar as they are rooted in the conventions we have attached to the words.
   With the help of the above definition, we avoid not only appealing to specific occurrences of thoughts, but also the most expected alternative, which would be to explain one s-thought in terms of a sum or class of p-thoughts qualitatively identical to each other. This could lead us not only to the problem of defining classes, but to the problem that classes have size while thoughts have not. If an s-thought were a class of p-thoughts, it would grow ever larger, the greater the number of people who grasp it.
   Under the proposed definition, in order to exist an s-thought must always have at least one psychological occurrence. The s-thought is not less psychological than any p-thought, since it cannot be considered independently of its instantiation in at least one mind. This means that when we say that we both had the same idea, or the same thought, this is merely a way of speaking. What we really mean is only that there is a qualitative identity between the psychological p-thought-contents that we have respectively instantiated in our own minds. This has the advantage of bringing Fregean thoughts out of the ethereal Platonic heaven back to the psychological realm without making a commitment to the transient psychology of particular cognitive beings. This understanding of the true nature of thought-contents explains something that Frege was unable to explain satisfactorily, namely, why and how they may have causal powers. As an open disjunction of p-thoughts, s-thoughts only exist as psychological instantiations of p-thoughts, which enables them to have causal powers: this can cause other psychological states and, combined with desires, human actions and their effects in the external world.
   At this point one could raise an objection of multiple realizability: the same p-thought could be differently realized in different human brains, making the qualitative identity of p-thoughts impossible. I agree with the very probable multiple realizability of p-thoughts but disagree that this makes their qualitative identity impossible. There is no reason why we cannot present things that can be considered qualitatively identical on a psychological level and different on a neuro-physiological level, just in the same way as different devices can have different internal mechanisms and perform exactly the same tasks.
   In my view, one of the most unyielding and deceitful philosophical errors in ontology has always been seeing numerical identity where there is only qualitative identity. It is true that we can ask for the meaning of the common name ‘chair’ using the definite article, that we can speak of the geometrical form of circularity, and that we can speak of the number 2 in the singular – but this is just for the sake of simplicity of expression. What we actually have in mind are occurrences of qualitatively identical meanings, of qualitatively identical concepts of chairs, of circles, and probably of cognitive arithmetical concepts of dualities, and nothing more.[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├p is unable to express an s-thought because an s-thought, a thought-content, a proposition, is something to which we must possibly attribute a truth-value, and without any further contextual information we are totally at a loss for the task of associating p with any appropriate truthmaker in order to assign it a truth-value.
   However, one could argue that the sentence ├p (as much as ├~p) is misleading and causes confusion, like argument A, because ├p only seems to express cognitive thought-content. The reason for this is that ├p is very easily confused with the meaningful sentence ├p*: ‘[It is likely that] a sea-battle will take place tomorrow’, when there are reasons to think so. For example: having broken the Japanese naval codes and having lured the Japanese fleet into an ambush at Midway, the Americans already knew on the night of June 3, 1942, that on June 4 there would almost certainly be a major naval battle. The sentence ├p* is easily confused with ├p, because ├p* almost always appears abbreviated as ├p: ‘A sea-battle will take place tomorrow’.
   For example: suppose that American Admiral Nimitz had said on June 3:

Tomorrow there will be a sea-battle.

Everyone would understand that he was saying that all the factual evidence was leading to the conclusion that the expected battle would begin on June 4. This probability – made explicit or not – is in this case objectively measurable in terms of verification by actual empirical evidence, so that the assertion ├p* expresses an s-thought that is held to be true, for it is true that, with the information available to us, it was very probable that a sea-battle would occur the next day. Indeed, the utterance ‘It is likely that a naval battle will occur tomorrow’ could be regarded as definitely true on the night of June 3, 1942, without breaking any principle of bivalence.
   Suppose now, by contrast, that I am on the calm beach of Praia Bonita, looking out across the Atlantic Ocean, and without any reason I say ├q*: ‘A naval battle will take place in this region tomorrow’, meaning by it ‘It is likely that a naval battle will take place in this region tomorrow’. This statement can be regarded as definitely false, since I have all kinds of reasons to believe that this kind of event is extremely improbable in this region and at this time.
   The conclusion is that taken in the absence of a context (and not in the sense of ├p* or ├q*) the sentence ├p is a linguistic bluff devoid of meaning and justification. Aristotle would be right in rejecting the application of the principle of bivalence to it, not because this principle has exceptions, but simply because it expresses no s-thought, no proposition. All that this sentence does is to induce us to imagine a naval battle that takes place tomorrow, as if there were hidden verifiability criteria. However, as much as no context is furnished, no real criteria can be given. Statements like ├p*,├~p* and ├q*, on the other hand, say something probabilistic about tomorrow that can be confirmed and made true by criterial reasons already found today.
   It seems that in principle the metaphysical problem about contingent futures can be eliminated when we consider with enough care what we are really able to mean by affirming thought-contents regarding the future.

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.

quarta-feira, 21 de dezembro de 2016

# MODAL ILUSIONS: Objections to the new ortodoxy of Kripke, Putnam, Kaplan, Evans, Burge, Perry.

Draft for the book Philosophical Semantics, to be published by CSP in 2017.

Appendix to Chapter 2


Die Probleme, die durch ein Mißdeuten unserer Sprachformen entstehen, haben den Charakter der Tiefe. Es sind tiefe Beunruhigungen; sie wurzeln so tief in uns wie die Formen unserer Sprache, und ihre Bedeutung ist so groß wie die Wichtigkeit unserer Sprache.
[The problems arising through a misinterpretation of our forms of language have the character of depth. They are deep disquietudes; their roots are as deep in us as the forms of our language and their significance is as great as the importance of our language.]

Although exceedingly original and challenging, Saul Kripke’s philosophical application of modal logic to the problems of reference seems to me to be burdened by a disturbing web of confusion. Since many disagree, I will try to justify myself through a critical discussion of his article ‘Identity and Necessity’ (Kripke 1971), which precedes the more developed views defended in his book Naming and Necessity (Kripke 1980), since that short article takes some fundamental ideas direct from the oven. Paragraphs summarising Kripke’s article are printed in italics in order to be distinguished from paragraphs containing my own comments. To my comments on this article, in the addendum I will make some short criticisms to central ideas not only from Kripke, but also from Hilary Putnam, Gareth Evans, David Kaplan, Tyler Burge and John Perry, as part of my project of debunking the metaphysics of meaning.

Kripke begins by considering the modal argument for the necessity of statements of identity. Where is the operator of necessity, which here will be seen as de re (regardless of the mode of linguistic designation), we can consider that, given the principle of indiscernibility of identicals, according to which ‘(x) (y) ((x = y) → (Fx → Fy))’, and given the principle of identity, according to which ‘(x) (x = x)’, we can conclude that if the property F is to be necessarily applied to x, then y must also have this property, i.e. it is necessary that y equals x; in symbolic notation, (x) (y) (x = y) → ((x = x) → (x = y))’, namely: ‘(x) (y) (x = y) → (x = y)’.
   This apparently inconsequential formal result leads Kripke to the bold conclusion that, as long as there are theoretical (essential) identities, identities between names are necessary. We know that by universal instantiation ‘□(x = y) → □ (a = b)’. That is, if a and b are real names and a = b is a true identity, then this identity is necessarily true. This would concern identities like ‘Hesperus is (the same as) Phosphorus’ and ‘Cicero is (the same as) Tulius’: they must be necessary. Further, if F and G are theoretical predicates, defined as essential designators of properties, if they form a true theoretical identity of the form (x) (Fx = Gx), then this identity is also necessarily true. That is why identities like ‘Heat is molecular motion’ and ‘A state of mind is a physical state’, if true, are necessary.
   Kripke recognises that identities between names and between theoretical identities have generally been considered contingent; but he presents the reasons for it. Consider the statement ‘Hesperus is Phosphorus’. Since Hesperus is Venus seen at dusk (evening star), and Phosphorus is Venus seen at dawn (morning star), it was an important astronomical discovery that they are actually the same planet, as Frege has noted. Therefore, this seems not to be a necessary, but rather a contingent empirical truth. The same applies to theoretical identities such as ‘Heat is molecular motion’. This identity was a discovery of science and could be false, because if caloric theory (the theory that heat consists of a self-repellent fluid called caloric) were correct, heat would not be molecular motion. This seems to be a clearly contingent statement, since it could be otherwise.
   Kripke’s thesis, however, is that contrary to the appearances, all these identities, despite having been learned a posteriori, are necessary, even if they do not seem to be. To reinforce his thesis he introduces an important distinction between the rigid designator, here defined as a term that refers to the same object in all possible worlds in which this object exists or would exist, and the non-rigid or accidental designator, which can refer to different objects in distinct possible worlds. Proper names and terms of natural species, at least, are rigid designators, while definite descriptions are accidental designators. Hence, if we have an identity in which the identity symbol is flanked by proper names, this identity is necessarily true if true at all, considering that proper names cannot change their reference in different possible worlds.

It seems clear that a mathematical term can be seen as a rigid designator, insofar as it does not depend on how the world is; but is really impossible for all our empirical proper names not be rigid designators? In the attempt to show that sometimes they could be accidental designators, we can imagine the following. Suppose that it were discovered that after the early childhood of G. W. Bush an extra-terrestrial creature possessed his body, and since then has lived in it and maintained his identity, becoming in this way the president of the United States and performing all actions attributed to him. Would not in this case the proper name ‘G. W. Bush’ be used to refer to this extra-terrestrial creature instead of the son of Barbara and George Bush, being in this way an accidental designator?
   The truth is that the idea that the proper name is a rigid designator would resist to this objection. According to Kripke’s views, the reference of a proper name is determined by an act of baptism, so that the true W. G. Bush, as the holder of the rigid designator ‘W. G. Bush’, would have since long disappeared. On the other hand, a homonymous being, the embodied extraterrestrial being, whose true name is Gkw9, would have had in some remote day a baptism and the name W. G. Bush, as a nickname of Gkw9, would apply to this same extraterrestrial being in each possible world where it would exist, being therefore also a rigid designator.
   Applying my own theory of proper names summarized in the appendix of chapter 1, the results would be the similar. According to this theory, the referent of a proper name is the object that satisfies the identifying rule for the application of the proper name. What this identifying rule requires is a sufficient and better than any other satisfaction of the inclusive disjunction of the fundamental description-rules, which are the localizing and the characterizing rules. For the adult W. G. Bush (as Gkw9), for instance, the localizing description includes his spatio-temporal career in the planet Omega before his embodiment and on the Earth and after its Bush-embodiment in Washington… On the other hand the characterizing description would include his main deeds, as his election as the 43tr president from USA, the wars in Iraq and Afghanistan, and the person who earlier in the planet Omega has make the main deeds of Gkw9... In every possible world were the identifying rule is satisfied, W. G. Bush (as Gkw9) would exist. Hence, the identifying rule for the name is a rigid designator for us too. Something of the kind could be easily established for the child named W. G. Bush – the true Bush – making this name also a rigid designator.
   Something different, however, is the idea that the concept of rigid designator has the consequences that Kripke expected as a way to ensure existence of de re metaphysical necessities of identities between our usual proper names and between terms of natural species.
   Kripke believes to have warranted the necessity of this identity by having discovered some radical difference of nature between proper names, on the one hand, and definite descriptions, on the other. What his words suggest is that a proper name would reach its reference without intermediaries by means of a direct (in my view purely magic) relation instituted in the act of baptism. For him this does not really depend on any property of the object, allowing then the production of external causal chains that in the end would reach each speaker of the name who really refers to its bearer.[1] A definite description, on the other hand, is only an accidental designator: it would refer to different objects in different possible worlds, probably because it has what Stuart Mill called ‘connotation’, which is the description’s implication of an attribute that the object may have (1881, I, Ch. 2). Using Kripke’s example, this would be the case of the definite description ‘the inventor of the bifocals’, which refers to Benjamin Franklin in our world, but that could refer to any other person and even to no person in a different possible world.
   I think that this strange dichotomy, suggesting a mysterious difference in the nature of reference is completely dispensable if we apply my own neo-descriptivist theory of proper names, since this theory gives a sufficiently reasonable explanation for the rigidity of proper names versus the accidental character of definite descriptions (see appendix of chapter 1, sec. 7, 8). Partially because of this I agree with the idea that the necessity of the rigid designator is always de dicto, supporting John Searle’s view according to which the so-called de re beliefs are only a sub-class of the de dicto beliefs and there is no irreducible de re belief. [2] Clearly, this rejection of irreducible de re beliefs leads to the rejection of the kind of metaphysical de re necessity proposed by Kripke.
   The neo-descriptivism I propose makes a proper name a rigid designator because any combination of descriptions that allows its reference in accordance with its identifying rule must be satisfied in any world in which the proper name has a bearer, simply because the identifying rule defines what its bearer can be. However, two different proper names of the same object can have different identifying rules, identifying their bearer under different guises, under different ways of presentation, simply because they emphasize different perspectives in which different descriptions or groups of descriptions are satisfied. In this case, even being rigid designators, we cannot without further information know that they are referring to the same object, and it may be an empirical matter to decide if two different rigid designators are referring to the same object or to two different objects. We still do not know whether the identifying rules of two names are part of a common identifying rule, being the identity sentence at this first stage contingent a posteriori. This state of affairs endures until after empirical experience we establish by convention according to which the different ways of presentation, the different identifying rules, are constituents of the same rigid designator, building in this way a more complex identifying rule that includes both, each of them emphazising a different perspective. In this case, the identity will be indeed necessary a priori! In no moment of this process, however, we need to resort to a Kripkian necessary a posteriori identity.
   Only to illustrate the point: there is a way to express Frege’s insight according to which ‘Afla = Ateb’, in which Afla is the same mountain as Ateb, though explored from a different complementary perspective, what gives to these names different but complementary senses or modes of presentation. Since for Frege references are dependent on senses, the proper names ‘Afla’ and ‘Ateb’ are from the beginning de dicto rigid designators and not metaphysically de re rigid designators. However, some day the explorers can ask themselves whether Afla is Ateb. At first, they see this identification as a contingent matter. After they discover that they are indeed referring to the same mountain, the more complete identity sentence turns to be seem as having the implicit form ‘Afla [-Ateb] = Ateb [-Afla]’, that is: Afla and Ateb express rules identifying numerically the same object simply because they were blended in the formation of one and the same identifying rule, applicable to both sides of the same mountain under different guises.

Kripke also considers the problem of apriority. A priori truths are those that we can know without appealing to experience. Many consider the necessary and the a priori to be equivalent. However, the concept of necessity is for him metaphysical about how the world must be – while the concept of a priori is epistemic – about how we know the world. Kripke thinks that the two classes are not equivalent. Consider, he writes, Goldbach’s conjecture, which states that any natural number above two is the sum of two primes. It may be a necessary truth without the possibility of our knowing it a priori. In this case it would have metaphysical necessity.

The suggestion that necessity is metaphysical while apriority is epistemological is highly questionable. This distinction would be justified only if there were metaphysical de re necessities, as Kripke intends, since a de dicto necessity would follow from a more trivial epistemologically established apriority, even if well grounded. Moreover, the existence of metaphysical de re necessities in the supposed sense seems to be something that escapes our cognitive faculties, since our empirical knowledge is inherently fallible, something that has been insistently repeated by philosophers of science from C. S. Peirce (1991, Ch. 7) to Karl Popper (1959). All that we can do is to postulate empirical necessities by accepting the most well-entrenched[3] and strongly inductively grounded regularities as natural laws (Tugendhat 1983; Mackie 1974). To really know if there is a necessity of a natural law beyond this well-grounded postulation (pace Armstrong), a metaphysical necessity, would require absolute knowledge – something that our epistemic fallibility makes impossible. Therefore, the necessities of natural laws are nothing but a result of a well-grounded decision to treat them as necessities. They are necessities in a weaker sense of the word. However, once we postulate them as natural laws, we have the right to treat them as basic rules of our conceptual system. We view them as necessary as long as we accept the system.
   Thus, if our analysis of necessity is correct, there seems to be at least two kinds of necessity, both of them with epistemic import:

(i)                the logical and conventional necessities that we find in formal sciences (like ‘~(A & ~A)) and in definitional sentences (like ‘brothers are persons with the same parents’), or that can be translated to the last ones;
(ii)              the empirical necessity, which is reached a posteriori, but afterwards can be simply postulated as necessary, as far as it is useful to work with them in this way.

Wittgenstein would classify empirical necessities as ‘grammatical rules’ – rules grounding a useful linguistic practice (Wittgenstein 1984a). Here is his suggestion, in which we read the word ‘rule’ involving a priori propositions:

Every empirical proposition can serve as a rule if it is fixed as the unmovable part of a mechanism, in such a way that the entire representation revolves around it, making it part of a system of coordinates independent of the facts. (Wittgenstein 1984e, part VII: 437)[4]

As for Goldbach’s conjecture, the fact that it may be a necessary truth without our being aware of it does not mean that its necessity is not a priori or has some indefinite status. It is not impossible that someone finds a proof of this conjecture, giving to it finally the status of a theorem with a priori necessity. Moreover, it is because the mathematicians hold as a heuristic rule that it is possible to reach such an a priory knowledge that they insist in searching for a proof; otherwise they would not sustain the conjecture.

Maybe the most stricking example of a necessary a posteriori statement introduced by Kripke is that of the wooden table in front of him. It starts with the question: could it have consisted since the beginning of its existence of ice from the Thames? Certainly not: It would be a different object. Thus, the statement ‘This table, if it exists, cannot be made of ice,’ is a necessary truth known a posteriori. Tables, he says, are usually not made of ice. This table seems to be made of wood, and it is not cold. Hence, it is probably not made of ice. Of course, this could be a delusion. It could actually be made of ice. But that’s not the point, writes Kripke. The point is that given the fact that the table is not made of ice, but of wood, one cannot imagine that it could be made of ice. Given the fact that it is not made of ice, he concludes, it is necessary that it is not made of ice. In other words: being P = ‘This table is not made of ice’ we know a priori the truth of ‘If P then P’. Moreover, he says, we know from empirical research that P is true... Combining these two statements, he constructs the following argument applying a modus ponens:

     1 P □P
     2 P
     3 □P

It is therefore necessary that the table is not made of ice, although this is only known a posteriori, by empirical research. The statement, ‘This table is not made of ice’ is necessary a posteriori!

Clearly, the covert mistake in Kripke’s argument concerns the epistemological status of P in the second premise. In this premise, the truth of P is affirmed in disregard to the fact (earlier confusionist way referred to by Kripke) that P, as any empirical statement, can only be known as true by inevitably fallible epistemic subjects. However, if it is so P can in principle be false. In order to show this clearly, we first understand a statement as practically certain when it is extremely likely to be true, that is, when we can assign to its truth a probability very near to 1. Considering this, we can rather say that the statement P of the second premise should be more precisely written as (2’): ‘It is practically certain that P (that this table isn’t made of ice)’. Indeed, (2’) must be correct because only God – the infallible and omniscient epistemic subject – could know with absolute certainty the truth of the statement P (that is, would be able to assign it the probability 1). God could know for sure the factual existence of P, giving in this way to the affirmation of P a truly metaphysically de re necessity. Unfortunately, we cannot appeal to God in this matter. Consequently, all that we can know is that P is practically certain in the already pointed sense of being, under the assumption of all our present body of information, extremely likely to be true. This must be so, since our empirical knowledge is never absolute[5] (it is always possible, for instance, that for some reason I believe I am standing before a hard wooden table, as much as all the beholders, although it is actually made of ice[6]).
   Assuming this, consider now the first premise. The same cannot be said of it, since it is a conditional. It is fully acceptable that given the fact that P – or, more precisely, if the fact that P is really given – then P follows by necessity. Thus, what P → P says is (1) ‘If it is really the case that P, then it is necessary that P,’ and this, I concede, is a logical truth. However, what the antecedent requires is that P implies □P only under the assumption that the truth of P is absolutely certain, for instance, knowable by God’s omniscience. Hence, the most complete analysis of premise (1) would be (1’): ‘If it is absolutely certain that P is the case (if P has the probability 1), then it is necessary that P’. Surely, premise (1) could not be analysed as (1’’) ‘If it is practically certain that P is the case (that is, if P has a probability near to 1), then P is necessary’, since the mere probability of P, no matter how high, if less than 1, would not warrant the necessity of P. Once we admit the changes of premise (1) to (1’) and (2) to (2’), Kripke’s argument can be made completely explicit as saying:

1’. If it is absolutely certain that P, then it is necessary that P.
2’. It is practically certain that P.
3’. It is necessary that P.

Obviously, the argument (B) is non-valid, since the modus ponens cannot be applied to (1’) and (2’) in order to give us (3’). The reason is that the antecedent of (1’) does not say precisely the same thing as (2’), what makes the argument equivocal, hence fallacious. We conclude that under a better scrutiny Kripke’s argument does nothing to convince us that we can know that the utterance ‘This table is not made of ice’ is a metaphysically necessary a posteriori truth.
   Now, the reason for Kripke’s misleading view that the conclusion of his own argument must be necessary a posteriori becomes clear. He ignores the fine semantic differences made explicit by means of the argument (B), and by doing this he jumps to a conclusion that unduly joins the necessity of the first premise of his argument with the aposteriority of its second premise, building what he calls a necessary a posteriori truth in the conclusion 3.

Kripke comes then to the analysis of identities between proper names such as ‘Hesperus is Phosphorus’ and ‘Cicero is Tulio.’ These are empirical identities, generally considered contingent. For Kripke they are identities between rigid designators, which make them necessary, since in the most diverse possible worlds these names will refer to the same object, a situation not possible where Hesperus isn’t Phosphorus or Cicero isn’t Tulio. We could, he says, have identified Hesperus and Phosphorus with two different celestial bodies, but in this case the sentence ‘Hesperus is Phosphorus’ would have a different meaning. This would be the case, for example, if Martians had once populated the Earth and had identified Hesperus with Venus and Phosphorus with Mars... The same is true with the identity ‘Cicero is Tulio.’ According to him it seems that this statement is contingent because sometimes we learn these names with the help of definite descriptions, like ‘the greatest Roman orator,’ which are accidental designators, thinking that we identify the object through properties, when in fact such names are not synonymous with descriptions, but rather with rigid designators.

One could produce here an argument parallel to the argument applied by Kripke to the indexical case of the table made of wood in the attempt to demonstrate the metaphysical necessity that Hesperus is the same as Phosphorus, since these names are rigid designators that must pick out necessarily the same object in any possible world. Calling Hesperus h and Phosphorus p we can build up the following Kripkian argument:

     (h = p) → (h = p)
     h = p
     (h = p)

However, here too the modus ponens does not apply because although the first premise is true, the second premise would only conjoin with the first one assuring us the conclusion ‘(h = p)’ if it were able to give us an absolute assurance of the truth of ‘h = p’. But this is not the case. In order to get the absolute assurance that ‘h = p’ that enables us to reach the conclusion this truth must be discovered, not by inevitably fallible human epistemic subjects, but again only by God, the omniscient and infallible epistemic subject. Because of this, ‘h = p’ can here only be seen as an empirically achieved fallible conclusion, saying that it is practicaly certain (extremely probable) that ‘h = p’, which is still not the same as its absolute certainty. The following formulation demonstrates again the hidden failure of the argument:

       If it is absolutely certain (with probability 1) that h = p,
       then (h = p).
       It is practically certain (with probability near to 1) that h = p.
       (h = p)

Since the absolute certainty required by the identity of the second premise with the antecedent of the first is not available, the equivocity of the argument is clear. We cannot use the modus ponens to derive the a posteriori necessity of h = p. The statement ‘Hesperus is Phosphorus’ is in this interpretation contingent a posteriori. It cannot be metaphysically necessary because being this identity only highly probable it remains always possible that Hesperus is not Phosphorus: it does not belong to these two identifying rules that they become necessarily unified into a same convention. For instance: although extremely unlikely, it is logically possible that the gods have produced a great illusion of knowledge in the human minds, and that the planets are nothing more than a swarm of fireflies that every night assemble to decorate the celestial Vault. In this case, Hesperus would have a different location than Phosphorus when seen by the naked eye, but it would look identical to Phosphorus when viewed through a telescope – not because it is the same planet or a planet at all, but as a result of an unknown kind of witchery.
   The second example given by Kripke is very different and it would be misleading to confuse it with the example above. It concerns the utterance ‘Cicero is Tulio.’ Assuming my neo-descriptivist theory of proper names, the localizing description for his identification is (shortly) ‘Born in Greece in 3.1.106 BC and died in Rom 7.12.43 BC’, while the characterizing description is (shortly) ‘the greatest Roman orator, a politician, jurist and philosopher.’ His whole name was ‘Marcus Tullius Cicero.’ Since the proper name does not belong to the fundamental descriptions, but to the auxiliary ones (he could receive another name in a different possible world), Kripke is only relying on the fact that not all speakers know that Cicero and Tulio are parts of a same proper name as a point of convention in our actual world, assuming that they know who is the bearer of the fundamental descriptions implied by each part of the whole name.
   As a consequence the question is a trivial one, namely, whether the speaker knows an auxiliary convention. Hence, the right answer is that ‘Tulio is Cicero’ is necessary a priori as a linguistic definition, since the convention that the whole name is ‘Marcus Tullius Cicero’ is something a priori, as much as the convention that a triangle is a trilateral figure. Moreover, to say that the statement ‘Cicero is Tulio’ is a posteriori would be to confuse its belonging to a definition in our actual world – which is a question of being informed about conventions – with the possible names that the same reference could have received in different counterfactual situations. Indeed, it is possible that Cicero would not have been also called Tullius, but Tittus, making ‘Cicero is Tulio’ false. However, this is as trivial as to say that in a different possible world one could give a different name for the word ‘triangle’.

The next of Kripke’s examples concerns the identity between kinds of things, as in the already discussed statement Heat is molecular movement. Many think that this expresses an a posteriori truth, because it is the result of empirical scientific research. But for Kripke this is a necessary a posteriori identity because the heat (in gases) cannot be anything other than molecular kinetic energy. It may be, he says, that the Earth could at some time be inhabited by beings who feel cold where we feel heat and vice versa, so that for them heat would not be identical with molecular motion. However, this would not be the case, since heat is understood as molecular motion as we feel it. For Kripke the terms heat and molecular motion are rigid designators, which make the identity between them unavoidable. For him the fact that molecular motion produces the sensation of heat is used to fix the reference, making the identity necessary. The illusion of contingency arises from the fact that we confuse this fixing the reference with the fact that our identification of molecular motion with the sensation of heat is contingent.

As it was already noted in the appendix to chapter 1, since we have ways to translate rigidity in descriptive terms regarding proper names, we have reasons to guess that the same can be done with general terms. That is, we could link the two ascription rules of heat in gases and kinetic molecular energy, building a unified ascription rule that has two different guises: two different but interchangeable criteria of identification. I do not intend to provide an analysis of this rule here, but only show how to employ to concepts a reasoning similar to those applied above to the identity of proper names.[7] Thus, considering heat in gases and molecular movement as rigid designators that necessarily designate the same essence, we could build the following Kripkian argument calling heat in gazes H and molecular motion M:

     (x) ((Hx = Mx) → (Hx = Mx))
     (x) (Hx = Mx)
     (x) (Hx = Mx)

Clearly, the same kind of difficulty returns. The first premise says only that if it the identity (x) (Hx = Mx) is really the case, then it is necessarily the case that all heat is molecular motion, or, from an epistemic perspective, if it is absolutely certain that all heat in gases are molecular motion, then it is necessary that all heat in gases are molecular motion. However, as those who conclude the identity expressed in the second premise are always fallible epistemic subjects, even if they have the best reasons to believe it to be true, the following paraphrase of the above argument would be inescapable:

    (x) If it is absolutely certain (with probability 1) that (Hx = Mx),
          then (Hx = Mx).
    (x) It is practically certain (with probability near to 1) that (Hx = Mx).
    (x) (Hx = Mx)

Here again the more explicit formulation shows an equivocal and consequently fallacious argument. Because the antecedent of the first premise is different from the second premise, we cannot apply the modus ponens and the conclusion does not follows. The result is that we cannot by this way conclude that the statement ‘Heath (in gazes) is the same as molecular kinetic energy’ is a necessary a posteriori truth. However, if Kripke were right, this conclusion should follow.

The last of Kripke’s examples should be the most important one. It is intended as a refutation of the type-type identity theory of the mind-body relation, according to which ‘Pain is (the same as) such and such a brain state’ would be a contingent a posteriori scientific discovery, yet to be made. But, writes Kripke, ‘pain’ and ‘such and such a brain state’ are here rigid designators, because they refer to essential properties. However, if that’s the case, the identity theorist is in trouble, because the identity needs to be necessary, which clashes frontally with the fact that whenever you feel pain you do have a pain, while no one is denying that it is possible to conceive that we have pain without having the corresponding brain states. For a devout philosopher like Kripke this makes identity theory improbable.
I find this argument puzzling. First, one can feel pain without being in pain as a matter of fact – this can be done, for instance, with hypnotized people. However, even if we correct this, saying that we cannot feel pain without having the qualitative state of feeling pain, why this forces us to think that a future neuroscience cannot show us that speaking of such and such a brain state we make a rigid reference to pain in Kripke’s own terms?
   In my view in most cases Kripke confuses the a posteriori element of a contingent a posteriori discovery with the necessary element of an identity of the reference with itself implied by each flank of the identity sign, what leads him to believe in a mystical, metaphysically de re grounded necessity a posteriori. In doing so, he assigns to an ontologically unknowable identity the same status of an epistemologically alleged identity. He thinks as if we could assert ontological (metaphysical) truths without regarding our epistemic capacities and their limits. He refuses to accept that we cannot ever separate completely the epistemic from the ontic. In doing so, he denies a point that modern philosophers after Descartes were already aware, namely, that we lack access to transepistemic truths.

There is a considerable variety of arguments from Kripke and other externalist philosophers deserving close examination. In what follows I will be short, as a more careful analyses would exceed the scope of this book.

1. There is a variety of supposed examples of necessary a posteriory truths later suggested by Kripke and others. Consider, for instance, the statement (i) ‘Cats are animals’ (Kripke 1980: 181-2). For Kripke this is a necessary statement, since we cannot conceive a cat that isn’t an animal; but this is something discovered a posteriori. My answer is that statement (i) can be interpreted in two ways. As a mere result of an inductive inference it should be clearly read as a contingent a posteriori statement. However, (i) can also be read as a necessary a priori statement under the assumption of the truth of our contemporary taxonomy, according to which the cat is classified as an organism belonging to the kingdom animalia.[8] In this case, we are dealing with an analytic statement since (i) should be interpreted as (ii) ‘Animals called cats are animals’.

2. Another kind of necessary a posteriori later suggested by Kripke concerns the origin. For him, rigidity makes true parenthood necessary. Consider the statement ‘Ismael Lowenstein is the son of Abel and Berta Lowenstein.’ According to a Kripkian philosopher this statement should be necessary a posteriori because even if this is known a posteriori, a person with different parents coming from a different ovulo and a different spermatozoid, would not be Ismael Lowenstein. (See Kripke 1980: 112 f.).[9] 
   However, suppose that the adult Ismael makes the shocking discovery that his parents are not his parents; there was a mistaken change of babies in the hospital where he was born and the DNA analysis has proved that he is instead the actual son of Amanda and Mario Belinzoni. Of course, this is no reason to think that Ismael ceases to be called Ismael. It is even written in his personal identity card. If asked, he could insist in answering that his name is Ismael Lowenstein, probably with the agreement of others.
   Anyway, concerning the main point, namely, the whole statement ‘Ismael is the son of Abel and Berta Lowenstein’, with concerns the question of parenthood, the conclusion may be more ambiguous.[10] One could use as criterion of parenthood those who have taken care of the child and nurtured him with love until the adulthood, and in this case the statement ‘Ismael is the son of Abel and Berta Lowenstein’ will be seen as true, even if he is originated from one spermatozoid of Mario and one ovulo of Amanda. Under this understanding the statement ‘Ismael is the son of Abel and Berta Lowenstein’ is contingent a posteriori. Contingent because it could be false that they have taken care and nurtured him. A posteriori because it depends on experience to be learned.
   However, it is easy to imagine a situation in which Kripke’s view would apply. Suppose that we were in the Nazi Germany and that Abel Lowenstein were Jewish. Suppose that the Nazis have catch him. It is clear that for them the criterion of parenthood was genetic. In this case, Ismael Lowenstein would be considered son of Mario and Amanda Belinzoni, while Carlos would be considered the son of Abel and Berta Lowenstein and sent to a concentration camp. Finally, it is even possible that the Nazis have established that the true name of a person must be related to her genetic origins, concluding that the person called Ismael Lowenstein is in fact Mario Belinzoni and that Mario Belinzoni is in fact the true Ismael Lowenstein. Anyway, even in this case the statement ‘Carlos Belinzoni is the son of Mario and Amanda Belinzoni’ would not be necessary a posteriori, even if in this case the parenthood turns to be part of the localizing description-rule, since the whole identifying rule involves much more than this. It would be rather seen by the Nazis as contingent a posteriori discover, as far as they still have achieved only an inductive certainty of its truth, even if they consider it a practical certainty.

2. Worst than the necessary a posteriori is a later invention of Kripke called contingent a priori. It is the case involving the platinum rode in Paris, which once defined the meter as the unity of length. According to him, analysis of meaning is something different from a definition; the first is necessary, the second not.  The definition of ‘one meter’ as ‘the length of S at to’ was a priori but contingent. Moreover, ‘one meter’ is a rigid designator while ‘the length of S at to,’ being a definite description, is an accidental designator, allowing the length to be possibly longer or shorter than one metter, for instance, by earlier heating or cooling. Therefore, the statement ‘Paris platinum rode is one meter long’, though established a priori, is contingent, for it could be different. (Kripke 1980: 56)
   A difficult it that Kripke gives no satisfactory reason for this conclusion. The definition of one meter as ‘the length of S at to’ is a stipulative definition establishing a new meaning. Beside this, why cannot ‘one meter’ be an abbreviation of ‘the length of S in ∆t[11], whoever this length is,’ as it seems? Assuming this, our intuitive reasoning would be to think that if the length changes the meter itself isn’t different, since the standard meter is defined as whatever length S has when used as a pattern. Being so it is recommendable to have the most unchangeable possible standard meter. For suppose that the standard meter were something elastic, always changing. It would remain the same standard meter, for sure, but it would be very unpractical. Using this standard according to the given definition, we could be forced to say of a woman who was 1:67 m high two hours ago that she is 2:24 m high right now, or that two object with very different sizes would have the same size only because they were measured in different times… Anyway, if you consider that the statement ‘One meter is the length of S in ∆t’ presents the definition of a standard meter – and it really does – this definition is necessary, since it is conventional and cannot be falsified in any possible world in which it holds. Moreover, this definition is a priori, for we don’t need to have any experience to know its truth (it exemplifies the law of identity). Consequently, the definition:

Paris platinum rode is one meter long in ∆t as a standard to be met in any circumstance.

is a necessary a priori truth, not a contingent a priori one.
   Now, if you decide to treat it differently, comparing different possible standard meters in different times or different counterfactual situations, then you are reading the statement ‘Paris platinum rode is one meter long’ as something like ‘The standard meter in w1 has the same length as the standard meter in w2 (or in a counterfactual situation)’. In this case it means more precisely:

Paris platinum rode is one meter long during ∆t only if compared with others standard meters that could be used as standards in different times or in any counterfactual circumstances.

This, of course, is impossible. Now, because Kripke sees that the standard meter cannot perform this function he comes to the conclusion that it must be contingent. But this function was never required. Consequently, the standard meter isn’t contingent: it is, as Wittgenstein correctly saw, a necessary a priori stipulation.

3. Another attempt to exemplify the contingent a priori could come from Gareth Evans’ example with the name ‘Julius’, which is artificially stipulated as ‘the inventor of the zip’ (Evans 1982: 31). According to some, the statement (i) ‘Julius was the inventor of the zip’ is contingent a priori. It is a priori because we don’t need the experience to know this. But it is also contingent since it is possible that he dropped on his head when little, growing up too stupid to invent the zip (Papineau 2012: 61).
   Here we have in fact a contingent a posteriori statement. It is a posteriori because its truth depends on experience to be learned. It is contingent because in a counterfactual situation the zip wasn’t invented or was invented by several persons. Of course, assuming to be true that someone invented the zip, we could paraphrase ‘Julius invented the zip’ as (ii) ‘If someone invented the zip we decide that we will call this person Julius’. However, this paraphrase of (i) is not contingent a priori, but necessary a priori. It is necessary because it is a stipulation and it is a priori because it is independent of experience.

4. A related funny example is the following utterance: ‘I am here now.’ According to David Kaplan, this is also a kind of contingent a priori truth. It is a priori because since each one of its terms refers directly respectively to the agent, the place and the time of a given context of utterance, the possibility of its falsity is excluded. But since we can imagine counterfactual circumstances in which I would not be here, its utterance is only contingently true (Kaplan 1989: 509).
   This example is also delusive. For ‘I am here now’ can be false in the actual world too. I remember a case related by Dr. Oliver Sacks of a patient who had a seriously deranged perception of the continuity of time. Because of this, her daily life was made of time lapses: she could think ‘I am here now’ as if she were still in the sleeping room, when in fact she had already moved to the kitchen. So, in this case ‘I am here now’ is empirically false. The statement is contingent and also a posteriori, since dependent on the context of the experience.

5. I also do not agree with Hilary Putnam’s view that the meaning of the word ‘water’ must be (essentially) external to our heads. This is perhaps the most influential argument for semantic externalism. According to Putnam’s thought-experiment, in 1750 Oscar-1 in the Earth and Oscar-2 in the Twin-Earth – both nearly identical planets with the same history – seeing that it rains, could have only the same idea of a watery liquid (an under normal temperatures transparent, inodorous, tasteless… liquid) within their heads. However, without their knowledge, they were referring to very different composites, the first H2O and the second XYZ, since the water in the Twin-Earth has a very different chemical composition, summarized by Putnam as XYZ, though with the same appearance and effects. For Putnam this proves that the meaning of water – which for him concerns essentially amounts of atoms with the same microstructure H2O – wasn’t in the heads of the Oscars, since in their heads they had the same state, namely, the idea of a watery liquid. Consequently, the meaning isn’t in the head. As he in a central passage wrote:

Oscar-1 and Oscar-2 understood the term ‘water’ differently in 1750, although they had the same psychological state, and though, given the state of development of Science in their epoch, the scientific community would need to take circa 50 years to Discovery that they understood the term ‘water’ differently. Hence, the extension of the term ‘water’ (and, in fact, its meaning in the pre-analytic intuitive use of the term isn’t function of the psychological state of the speaker. (My italics)[12]

This shocking conclusion was later radicalized by John McDowell, who concluded that even the mind is external to the heads because it is the locus of our manipulation of meanings (1992: 36).
   My neodescriptivist answer is that Putnan’s result comes from the overseen of the fact that the word ‘water’ has in fact two descriptive nuclei of meaning: a popular and a scientific one.[13]  First there is an old popular nucleus of meaning of the word ‘water’, which is phenomenal or dispositional and can be summarized in the expression ‘watery liquid’ (the under normal temperatures transparent, inodorous liquid, that quenches the thirst, serves to wash, extinguish fire, falls as rain, fulfils rivers, lakes and oceans, when made cold turns into ice, when warmed into steam, has high superficial tension, etc.). This was the only meaning in the market until the end of the XVIII century. Then a new meaning was increasingly added: the scientific nucleus of meaning, which can be summarized as ‘quantities of H2O’ (which results from 2H2 + O2 = 2H2O, can be subjected to electrolysis, forms intermolecular hydrogen bounds responsible for its high superficial tension, etc.). Both nuclei of meaning are obviously descriptive (since the domain of what can be described is much wider then a merely phenomenal domain) and can be found today in any good dictionary.[14] Furthermore, it is easy to see that in consonance with the variability of the context, one of these meanings comes often to the fore.
   This summary already allows a convincing internalist explanation to the Twin-Earth fantasy. In 1750 the two Oscars had only the meaning ‘watery liquid’ in their heads, so that the extension of the word water were the same for them. But when Putnam considers what is going on, he is unconsciously projecting the scientific meanings of the word water in the utterances of the two Oscars. What he does is to treat them as indexical devices for the projection of the new nucleus of meaning, whose true locus is in fact our own heads (i.e., those of Putnam and his readers), since we know that Oscar-1 is pointing to H2O while Oscar-2 is pointing to XYZ. Consequently, the different scientific meanings of the word ‘water’ are not in the world and out of our heads, as Putnam believes, but in Putnam’s head when he thinks his thought-experiment and in our heads when we read him, since we all today know the scientific core of meaning. And since Putnam and his readers have different scientific meaning-descriptions in their heads when unconsciously projecting them to Oscar-1 and Oscar-2 by using them as indexical devices, these different meanings remain, as they should, internal properties of minds.
   This idea is reinforced within the neodescriptivist view that I suggest by the consideration that the meaning of ‘water’ varies with the context of interest in which the word is used. In a scientific context of interest (e.g., in a laboratory of chemistry) the scientific nucleus of meaning is emphasized. Here ‘Water is H2O’ means (a) ‘Hydroxide of oxygen = H2O’: a tautological analytic statement. In this context even if water were not a watery liquid, but something like coal, it could still be called water, as far as it preserves the right microstructure.
   Now, in a popular context of interest (e.g., of fishermen wishing to use water for drinking and washing) ‘Water is H2O’ the sense of water that is emphasized is that of a watery liquid. In this case `Water is H20` means (b) `Watery liquid = liquid composed of H2O`. This is an a posteriori contingent statement, not only because it isn`t known without experience but because at least in principle (though very improbably) it could be false.
   Conclusion: Putnam’s and Kripke’s classification of the statement ‘Water is H2O’ as a necessary a posteriori statement is only a confusion between the necessity of the statement (a) and the a posteriori nature of the similar statement (b). A confusion resulting from lack of attention to the pragmatic of natural language. We already spoke about these kinds of confusion as we examined Wittgenstein’s account of the transgressions of the internal limits of language.
   The point can be easily generalized. Consider the statement (i) ‘Hydrogen is a gas containing atoms with one proton and one electron.’ One could say: though necessary, it was discovered a posteriori. But in fact it has at least two contextualized senses: First, if you think of the transparent inflammable gas discovered by Cavendish in 1766, called by him ‘inflammable air’, which was later analysed as constituted by atoms with one electron and one proton. In this case statement (i) is read as contingent a posteriori; this gas could have a different atomic structure and one could spell the same statement as (i-a) ‘Inflammable air is constituted by atoms containing one proton and one electron.’ On the other hand, after we conventionally established the meaning of hydrogen as a gas containing atoms with one electron and one proton (as we do definitionally in science today), (i) can be read as (i-b) ‘Hydrogen (Df) = the gas constituted by atoms containing one proton and one electron’, as far as we emphasize the sense that the word ‘hydrogen’ has gained in the modern chemistry. In this case (i) will be read as a tautological, necessary a priori statement. (We will come back to this point in the chapter 4, sec. 25).

6. There are two others examples of Putnam aiming to show that the meaning is not only in the external physical world, but also in the society. In the first one, Putnam assumes that aluminium and molybdenum are only distinguishable by metalworkers and that the Twin-Earth is full of molybdenum used to build pots and pans. In addition, he imagines that the inhabitants of the Twin-Earth call molybdenum ‘aluminium’. In this case, he writes, the word ‘aluminium’ said by Oscar-1 will have an extension different than the word ‘aluminium’ said by Oscar-2, so that they mean different things with the word. However, as they are not Steelworkers, they have the same psychological states. Hence, the real meaning of these words is external to what happens in their heads, depending on the society.
  Our answer is as follows. If we consider the words ‘aluminium’ and ‘molybdenum’ in the way they were used by Oscar-1 and Oscar-2, the Oscars are unable to really decide if what they have is aluminium or molybdenum. They are not experts and what they have in their minds is indeed the same, as much as the extension that they can give to their concept of aluminium. For the metalworkers of Earth and Twin-Earth, on the other hand, the aluminium and molybdenum have very different constitutive properties, what means that they would have something different in their heads. The Oscar’s, on their hand, may confuse both things, but only because they do not know really what these things are: they are using the words in a subsidiary sense. However, we can consider the aluminium and the molybdenum observed by Oscar-1 and Oscar-2 and take both persons as referential devices, so that we would say that Oscar-2 is pointing at what his linguistic community calls aluminium, but which is what we in our linguistic community call molybdenum. That people should use the words in accordance with the conventions of their own linguistic community does not make the meaning external, only dependent of the explicit or implicit agreements under the members of their communities.
   In the second example, Putnam considers the difference between elms and beeches. Most of us do not know how to distinguish elms from beeches in a forest. However, we are able to assume that these words have different extensions. Thus, what we mean with these words are different, though we do not have different concepts and the difference is not in our heads... Consequently, their meanings are external: the physical world and the society with its specialists are those who have the ability to fix the referential meaning of these words.
   The important point to be noticed here is that we in fact do have an insufficient knowledge of the meaning of the words ‘elm’ and ‘beech’. But we already know something very generic about them: we surely know that they are trees and we guess as very probable that these two names refer to distinct kinds of trees. With help of these convergent descriptions (see appendix of chapter 1, sec 4) we are able to insert these words into the discourse, often waiting for the distinguishing information given by specialists, privileged speakers who have the sufficient knowledge of the meaning of these words, which enables them to identify the different kinds. But the meaning – sufficient or not – is always in the heads of the speakers.[15]
   In these two cases, Putnam appeals to a division of linguistic labour in order to explain different dimensions of meaning that may be considered by different speakers. This is an important suggestion. However, this is not a suggestion that confirms an externalist conception of meaning. It is rather neutral, for the idea of a division of labour of the language was already suggested by internalist philosophers, from John Locke to C. S. Peirce (Smith 2005: 70-73). In effect, this idea is perfectly compatible with the difference in the fact that, even if being socially shared, the meaning remains in the heads of the speakers, specialists or not, in different dimensions and degrees. In none of the cases above the meaning needs to be outside the heads.
   Finally, to be fair, Putnam expresses himself much more carefully in a later writing (Putnam, 1988, Ch. 2), e.g., by saying that the meaning is determined by the external world. However, either we understand this in the sense that it is the external world that ultimately produces referential meanings in our minds, what is an obvious truism that as a weak internalist I have no desire to deny, or what he means with the word ‘determination’ remains a too subtle metaphor to find any intelligible rescue.

7. Now I wish to reinforce my anti-externalist arguments discussing Tyler Burge’s social externalism of thought concerning the concept of arthritis, which is complementary to Putnam’s argument. What Burge intended was, apart from Putnam, to show that not only the meaning is outside the head, but the beliefs’ extension, i.e., the proper content of thought (Burge 1979).
   I will first summarize the argument of Burge and then show that it is easy to find a much more plausible weak internalist explanation for what happens, simply by developing an objection already made by John Searle (2004: 284-6). In order to make it clearer, instead of following Burge’s counterfactual mental experiment, I will first suppose that a person with the name Oscar feels pain in the thigh and see a doctor saying:

(i) I think I have arthritis in the thigh.

Since arthritis is characterized as a painful inflammation of the joints, the doctor sees that his belief is false, for one cannot have arthritis in the thigh. Imagine now Oscar-2 in the Twin-Earth visits a doctor for the same reason. But although in the Twin-Earth all things occur nearly as in the Earth, the people use the word ‘arthritis’ in a much broader sense, referring to any kind of inflammation. Suppose that in this second linguistic community Oscar-2 says to the doctor (i) ‘I think I have arthritis in the thigh’, having in mind exactly the same as in his first utterance. In this place, as one would expect, the doctor will confirm the suspicion, agreeing that this is an unquestionably true belief.
   Based on this example, Burge’s reasoning goes as follows. Without doubt, the psychological States of Oscar-1 and Oscar-2, when they said to have arthritis in the thigh are exactly the same, as well as their behaviour. But the contents of thought expressed in the two utterances must be different, since the thought expressed by the first utterance is false, while the thought expressed by the second is true, and the same thought cannot be false and true. We can even mark the second meaning of the word ‘arthritis’ on the utterance of Oscar-2 with a new word: ‘tharthritis’. Burge’s conclusion is that the contents of thoughts cannot be merely psychological.[16] These contents must belong also to the outside world, to the social communities involving the speakers.
   Against this conclusion it isn’t difficult to find a commonsensical internalist-descriptivist explanation for what happens. For this healthy internalism (which admits that our mental subjectivity unavoidably depends on external inputs), in the Twin-Earth the concept-word ‘arthritis’ is the expression of an ascription rule constitutive of its meaning, which is more general, designating any kind of inflammation. According to this rule, ‘an inflammation that occurs in the thigh’ serves as a criterial condition and belongs to the sense of the word in the linguistic community of the twin-Earth, though not in the linguistic community of our Earth. Thus, although the thought expressed in the sentence ‘I think I have arthritis in the thigh’ said by the Oscars in the two linguistic communities are exactly the same, there is a fundamental difference that was rightly recalled by John Searle in the following words:

Our use of language is presumed to conform to the other members of our community, otherwise we could not intend to communicate with them by using a common language. (Searle 2004, 184-5)

That is, when Oscar-1 says to the doctor of the Earth ‘I believe I have arthritis in the thigh,’ he must be dispositional assuming that his generalised ascription rule for the predicate ‘arthritis’ belongs to the language that the other competent speakers of the language conventionally apply. The whole of what Oscar-1 has in mind (not only actually but also dispositional) in his utterance in the Earth’s linguistic community is:

(a)  I have arthritis in the thigh… [and I am assuming that the generalised criterial condition for the ascription of the predicate ‘arthritis’ is accepted as correct by the linguistic community speakers to which belongs my present interlocutor D1].

This is false because the second sentence of the conjunction is false. Let’s now see what is (actually and dispositional) meant when Oscar says he has arthritis in the thigh to the second doctor:

(b) I have arthritis in the thigh… [and I am assuming that the generalised criterial condition for the ascription of the predicate ‘arthritis’ is accepted as correct by the community of speakers to which belongs my present interlocutor D2].

Now the statement (b) is true. Although the statement ‘I have arthritis in the tight’ says the same, it has a hidden indexical meaning that differs from (a) to (b). And this hidden indexical content is in the minds of the Oscars. So, it may be true that if we confine ourselves to the content expressed in the thoughts of the Oscars in making the same utterance in both places we see them as identical. But the whole of what they have mind (that is, in their heads) with each utterance are different because in the first Oscar-1 knows that he is speaking with doctor D1 belonging to the linguistic community of the Earth, while in the second he is aware that he is speaking with doctor D2 at a linguistic community of the Twin-Earth.
   This assumption that the verifiability rules constituting the content of thought should be in accordance with the conventions of the community of language in which it is expressed in order to achieve truth is infringed by Oscar when he speaks with the doctor the community belonging to the earth, but it isn’t infringed when Oscar speaks with the doctor of the community belonging to the Twin-Earth.
   Nonetheless, Burge has called us attention to one important thing: that the truth or falsehood of utterances depends on the linguistic conventions adopted by the community involving the speaker. This is an already relevant point, though it does not reach the claim that anything of a thought-content or belief is outside the internal psychological realm, in some way dispersed in the external social-physical environment.
   Finally, the given explanation allows us to make a healthy internalist paraphrase of the well-known distinction between narrow content and wide content. For the unmasked externalist point of view, the narrow content is one that is in the mind of the speaker, while the wide content is external: it is out there in the world or in the society. The healthy internalist analysis of Burge’s example allows us to propose that the narrow content of thought is the semantic-cognitive verifiability rule that constitutes it (expressed by the statement ‘I think that I have arthritis in the thigh’), while the wide content of thought is what is assumed in the speaker’s mind as a provision whose expected existence will be arguably accepted.

8. Finally, one word about John Perry’s argument for the essential indexical (1979). I will be extremely short, since I am repeating an argument presented in details in another place (Costa 2014c). His view is that senses of indexicals are inevitably tied with the external circumstances of utterance, what can be proved by the fact that one cannot translate them into eternal sentences without loss. Consequently, externalism is correct.
   In Perry’s main example he is in a supermarket and discovers that there is a trail of sugar on the floor. He begins to search for the author of the trail only to discover that the person who is spilling sugar out of the car is he himself, what leads him to say: (i) ‘I am making a mess’, what immediately changes his behaviour. Suppose, says Perry, that he translate this statement in the non-indexical statement (ii) ‘Perry is making a mess’. It is not the same, since he could, for instance, be suffering from Alzheimer, having forgotten that his name is Perry…
   However, I think that there is indeed a way to preserve the sense of the indexical detaching it from the context. It is a technique that I call transplantation: if you need to change the place of a plant, you usually don’t take the plant alone, but the plant with the earth in which it is rooted, often together with a cover. Applying a analogue technique, here is how Perry’s example appears after transplantation:

(iii) At 10:20 a.m. on March 26, 1968 in the confectionary supplies of the Fleuty Supermarket in the city of Berkeley, CA, after noticing a sugar trail stretching away from his shopping cart, Perry says to himself that he is making a mess.

Here what counts is the truth of the eternal sentence into which the indexical sentence is included. Although containing an indexical (he, himself), the statement (iii) is not referring to the real context, but referring indirectly to the Fregean thought expressed within the subordinate sentence after the that-clause. Thus, protected by its surrounding description (the covering of the eternal sentence) the sense of ‘I am making a mess’ is here integrally transplanted without loss into the non-indexical context that would be called by Frege indirect reference.[17] What this argument shows is that essential indexicals are not essential, once the external components can be internalized.

[1]  Rejecting the view of a particular as a bundle of abstract properties, he concludes: ‘What I do deny is that a particular is nothing but a ‘bundle of qualities’, whatever that may mean’. (1980: 52).
[2] According to Searle, although there is a class of beliefs whose explanation depends on contextual characteristics, one should not equivocally conclude that such characteristics cannot be entirely represented as part of the intentional (mental) content. The difference between beliefs called de dicto and de re is a difference between reports. In a de re belief like ‘About the man with the brown hat, Ralf believes he is a spy’, we commit ourselves with the existence of the man with brown hat. In a de dicto belief like ‘Ralf believes that the man in the brown hat is a spy’, we commit ourselves only with the report of Ralf’s belief. (Searle 1983: 208-220).
[3] It seems that the real reason why we distinguish the regularities that are natural laws from those that are merely coincidental is that the first are well-entrenched, that is, are strongly inferentially bounded with our scientific system of beliefs. This is what gives them the impression of logical necessity. It is true that we have in the present discussion several alternative approaches to this classic Humean regularity view. But first, the regularity view seems to be the most plausible approach, regarding the assumption of fallibility; second, the fact that something is presently very much on the stage is within the intrinsically changeable landscape of philosophy no value judgment.
[4] See also Wittgenstein 1984a sec. 96.
[5] Some say ‘almost never’, a point that is open to scrutiny, also because the extension of our empirical knowledge is still an open question.
[6] See my evaluation of the ‘brain in a vat’ argument in Costa 2014: 135-6.
[7] Anyway, see the section 5 of the Addendum to this Appendix, where the rules of application for the concept-word ‘water’ are analysed.
[8] According to Kant there is priori knowledge that isn’t pure, taking long exercise to be separated from the knowledge adquired by means of sensory experience (Kant 1787: Introduction, I).
[9] Kripke speaks of Elisabeth II, the Queen of England. But this is a biased example, since in the case of a queen the ovulo origin acquires maximal importance, contaminating the characterizing description of its identifying rule.
[10] There are today several competing theories of parenthood (genetic, labour-based, intentional, causal and pluralistic accounts) and there is no consensus on the right cluster of criteria (see Brake & Millum 2016, sec. 4).
[11] The symbol ‘∆t’ is more correct because the road served a standard not only in to but during all the time in which it was conventionally designed to this function.
[12] Hilary Putnam: “The Meaning of ‘Meaning’” (1995: 224).
[13] I am strongly summarizing here. For the full argument, which is preceded by a more careful neodescriptivist analysis of the meanings of the word ‘water’, see Costa 2014b.
[14] For instance, the main definition in the Merrian Webster dictionary contains elements of both, popular and scientific nuclei of meaning: ‘water = the liquid that descends from the clouds as rain, form streams, lakes, and seas, and is a major constituent of all living matter and that when pure is an odourless, tasteless, very slightlty compressible liquid oxide of hydrogen H2O which appears bluish in thic layers, freezes at 0°C freezes and boils at 100°C, has a maximum density at 4°C and a high specific heat, is feebly ionized to hydrogen and hydroxy ions, and is a poor cinductor of electricity and a good solvent.’ (See also Stroll 1996, Ch. 2)
[15] For interesting answers to some others externalist arguments see Searle 2004.
[16] As he wrote: ‘The upshot of these reflections is that the patient’s mental contents differ while his entire physical and non-intentional mental histories, considered in isolation from their social context, remain the same.’ (Burge 1976: 106, my italics)

[17] See appendix of chapter 4, sec. 5 (iv).