sexta-feira, 5 de maio de 2017

CRITICIZING THE NEW ORTHODOXY - Kripke, Putnam, Burge, Perry

Revised version of a draft of an appendix of the book PHILOSOPHICAL SEMANTICS. The final version will be published by CSP in 2017.

Appendix to Chapter II


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; they are rooted as deeply in us as the forms of our language, and their significance is as great as the importance of our language.]

Philosophy unties the knots in our thinking, which we have tangled up in an absurd way; but to do that, it must make movements that are just as complicated as the knots.

Although exceedingly original and thought-provoking, Saul Kripke’s philosophical application of modal logic to problems of reference seems burdened by a disturbing web of confusion. Since many would disagree, I will justify this conclusion with a critical discussion of his article ‘Identity and Necessity’ (Kripke 1971), which preceded the more developed views defended in his book Naming and Necessity (Kripke 1980), since takes the central ideas directly from the oven. The paragraphs below summarizing Kripke’s article are in italics, in order to distinguish them from paragraphs containing my own comments. After my comments on this article, I provide an Addendum containing a series of brief criticisms of positions taken by Kripke, Hilary Putnam, Gareth Evans, David Kaplan, Tyler Burge and John Perry, as part of my project of debunking the metaphysics of reference/meaning.

Kripke begins by considering the modal argument for the necessity of identity statements. This argument can be summarized as follows. Given the principle of indiscernibility of the identical, 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 necessarily to be applied to x, then y must also have this property. That is, 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 identities between proper names are necessary. We know this 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) Tulli’: they must necessarily be identical. 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 recognizes that identities between names and between theoretical identities have generally been considered contingent. There seem to be good reasons for this. 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 points out. 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 resulted from scientific discovery 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 contingent statement, since it clearly could be otherwise.
   Kripke’s thesis, however, is that contrary to appearances, all these identities, despite having been discovered a posteriori, are necessary, even if they do not seem to be: they are necessary a posteriori identities. 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 any possible world where this object exists or would exist, and the non-rigid or accidental designator, which can refer to different objects in distinct possible worlds (1971: 146). Proper names and terms of natural species are rigid designators designating the same object in different worlds. Most definite descriptions, by contrast, are accidental designators, designating different objects in different possible worlds. An example of an accidental designator would be the definite description ‘the inventor of bifocals,’ which in our world refers to Benjamin Franklin, but in some possible worlds could refer to any other person or even to no person. In contrast, the proper name ‘Benjamin Franklin’ always refers to the same person in any possible world where Benjamin Franklin exists. Thus, 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 these proper names, being rigid, must have the same bearers in any different possible worlds where their bearers exist.

It is 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 it really impossible for proper names to be other than rigid designators? If we want to show that sometimes they could be accidental designators, we can imagine the following. Suppose it were discovered that shortly after G. W. Bush’s childhood an extra-terrestrial being took possession of his body, assumed his identity and impersonated him from then on, subsequently being elected president of the United States and performing all the actions attributed to him. In this case, wouldn’t the proper name ‘G. W. Bush’ be used unknowingly to refer to this extra-terrestrial being instead of to the son of Barbara and George Bush, born on 6/7/1946, becoming in this way an accidental designator?
   Nevertheless, the idea that a proper name is a rigid designator could easily withstand such critical objections. According to Kripke, the reference of a proper name is due to an act of baptism. But this means that the true W. G. Bush, as the bearer of the rigid designator ‘W. G. Bush,’ would long since have ceased to exist. On the other hand, the embodied extra-terrestrial being, whose true name was, say, Gkw9, would have had its proper first baptism in some remote place and time. Hence, the name W. G. Bush (in fact here a mere alias of Gkw9) would apply to this same extra-terrestrial being in any possible world where he existed, satisfying the property of being a rigid designator. We simply have two different rigid designators with different bearers – two different proper names.
   Applying my own theory of proper names, as summarized in the appendix of chapter I, the results would be the same. According to this theory, the proper name’s bearer is the object that satisfies its identification rule. What this identification rule requires is that this object sufficiently and better than any other satisfies 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 earlier spatio-temporal career on another planet before his embodiment on Earth, and after this his performance as President Bush in Washington and his subsequent life. On the other hand, the characterizing description would include his main accomplishments, including his election as 43rd president of the USA, leading the country after 9/11, beginning wars in Iraq and Afghanistan, and also his life as the being who earlier on a distant planet had the career of Gkw9... In every possible world where the identification rule is satisfied, W. G. Bush (as Gkw9) would exist. Hence, the identification rule for the name is also a rigid designator. Something of the kind could also be easily established for the child really baptized W. G. Bush, born on the Earth on 6/7/1946… also making this name a rigid designator of another bearer by satisfying its own identification rule.
   In addition, Kripke believes he has warranted the necessity of the identity between proper names by having discovered some radical metaphysical difference between proper names, on the one hand, and definite descriptions, on the other. What his words suggest is that a proper name would attach to its reference without intermediaries by means of a direct (in my view purely magical) relation instituted by the act of baptism. For him, this act does not really depend on any property of the object, even if we are helped by their descriptions to identify it. Notwithstanding, this baptism allows the post-baptismal production of external causal-historical chains between speakers and hearers. These chains ultimately enable any speaker who utters the name as the last link of a chain to refer to the name’s bearer.[1] A definite description, in contrast, is only an accidental designator: it would refer to different objects in different possible worlds, presumably because it has a completely different reference mechanism, based on what John Stuart Mill called a ‘connotation.’ Mill defined this as ‘the description’s implication of an attribute that the object may have’ (1881, I, Ch. 2).
   In my view, Kripke’s explanation for this dichotomy, suggesting a categorical difference in the nature of each referring process, is as mysterious as dispensable. The only way to really explain the dichotomy is by appealing to the already discussed meta-descriptivist theory of proper names (Appendix of Chapter I, sec. 7, 8), which gives an adequate justification for the contrast between the rigidity of proper names and the accidental character of their associated definite descriptions. There I show that descriptions are rigid only insofar as we compare them to the reference of the proper names they are associated with, which means that definite descriptions lacking an associated proper name are rigid. After these explanations, the idea of a rigid designator, at first seemingly so original, turns out to be nothing but the technical expression of a more trivial idea. It is the idea that in all circumstances (possible worlds) a proper name must refer to its own bearer. No one would disagree with this.
   Furthermore, unlike Kripke’s view, the necessity of the rigid designator is the product of de dicto conventions. I say this because I agree with John Searle’s brilliant analysis (1983: 208-220). According to Searle, so-called de re beliefs are only a sub-class of de dicto beliefs, so that there is no irreducible de re belief as Kripke has supposed. Beliefs are de re only in the sense that they are intended to refer to real objects, not that they harpoon real objects. As he notes, 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 true difference between beliefs called de dicto and ones called de re turns out to be a mere difference between reports. In a de dicto belief like ‘Ralf believes that the man with the brown hat is a spy,’ we commit ourselves only to the report of Ralf’s belief. In a de re belief like ‘About the man with the brown hat, Ralf believes he is a spy,’ we also commit ourselves to the existence of the man with a brown hat. Hence, there is no reason why both should not at bottom be de dicto beliefs. Now, if we reject irreducible de re beliefs, we feel ourselves free to reject the kind of metaphysical de re necessity assumed by Kripke.
   The neo-descriptivism I have proposed makes a proper name a rigid designator because at least one combination of descriptions that allows its reference in accordance with its identifying rule must be satisfied in any possible world where the proper name has a bearer. However, the reason for this rigidity is not metaphysical. It is simply because the identifying rule defines what any bearer of the proper name can be. Now, considering identity between different proper names, here we may have two clearly different cases. The first is the following:

(a)   Two different proper names of the same object have different identifying rules that identify 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 if they are rigid designators, without additional information we cannot know that they refer to the same object in all possible worlds. It may be an empirical matter to decide if these two different rigid designators refer 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, since we still do not have this rule. Consequently, in a first moment an identity statement of the kind a = b would be contingent a posteriori. The modal form of this identity could only be formulated as ◊ (a = b). This was the case before astronomy showed that the morning star is the evening star, for instance, when for the first time someone observed the evening star in the sky the whole night long and noticed that it was the same as the morning star. (Venus disappears to earthly observers during part of the year, when it passes behind the Sun).

The second case is the following:

(b)  After many and varied empirical experiences we establish a convention – a rule according to which the different ways of presentation, the different identifying rules, are constituents of a single more complex identifying rule that includes both anterior rules, each of them emphasizing a different aspect or mode of presentation of the same object. In this case, however, what we ultimately have is a single rigid designator able to identify the same object in any possible world, even if under different guises. The identity resulting from the newly established convention will be necessary a priori. Its modal form will be □ (a = b). This is the case today when we identify the morning star with the evening star, having as a background our modern knowledge of astronomy. We see that at no moment of this process do we need to resort to a Kripkean necessary a posteriori identity, except if we confuse the a posteriority of (a) with the necessity of (b), as Kripke seems to do.

Just 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, even though examined from a different, complementary perspective, which gives these names different but complementary senses, guises or modes of presentation. However, someday explorers may ask themselves whether Afla is Ateb. At first, they see this identification as a contingent matter: possibly or probably ‘Afla = Ateb.’ After they reassure themselves that they do indeed refer to the same mountain, the more complete identity sentence will be considered to have the implicit form ‘Afla-[Ateb] = Ateb-[Afla].’ That is: Afla and Ateb express rules numerically identifying the same object, simply because they are in the end blended in the formation of one and the same rigid identifying rule, applicable to each side of the same mountain under a different semantic guise. In the first moment, ‘Afla’ and ‘Ateb’ are considered to be possibly or even probably de dicto rigid designators, and in the end they are assumed to be necessary de dicto rigid designators. Whether they are also metaphysically de re rigid designators is something only God has the power to know.

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

The claim that necessity is metaphysical while apriority is epistemological seems to me not fully mistaken, but rather requires better qualification. I reject this distinction as Kripke understands it. His understanding would be justified only if we were able to find out real metaphysical de re necessities, since a de dicto necessity would follow from a more trivial, conventionally established apriority, even if rooted in experience. Moreover, the existence of metaphysical de re necessities in the supposed sense is something that goes beyond our cognitive faculties, since our empirical knowledge is inherently fallible – a point that has been consistently emphasized by philosophers of science from C. S. Peirce (1991, Ch. 7) to Karl Popper (1989, Ch. 10). From this perspective, the most we can do is to postulate as natural laws those empirical regularities that are not only strongly inductively grounded, but also the most deeply entrenched ones[2] (Tugendhat 1983: 253; Mackie 1974). We cannot speak of a necessity of a natural law going beyond this well-grounded postulation, since to prove this metaphysical necessity we would need absolute knowledge – something our epistemic fallibility makes impossible. Therefore, the so-called necessity of natural laws and what follows from them are simply a result of a well-grounded decision to treat them as necessary, and since this conventional decision is well grounded, we have a right to expect (pace Armstrong[3]) that they will resist counterfactual situations. This is necessity in a weaker sense of the word, of course. However, once we postulate their necessity, we have a right to treat them as what we have made of them: rules of our own conceptual system. This seems to be why we constantly use derived statements of necessity like ‘It is necessary to have fire to light a candle.’ Such empirical necessities should be epistemically identified with practical certainties, once we see that they can be treated as certainties, because we can grant them a sufficiently high degree of probability.
   Finally, we must ask what remains of the empirical root, the seemingly unknowable real objective essence responsible for ‘metaphysical necessity’? In my view, it still has a function in the sense that remembers what Kant called an ideal of reason. We can have a normative concept (whose supposed reference is impossible to find), constructed only to offer a horizon able to measure and motivate our investigation. This normative concept of metaphysically de re necessities (corresponding to a real essence instead of merely a nominal essence in Lockean terms) can justify our approximations of absolute, unquestionable necessities. The normative concept can serve as an unreachable target for our comparison between these approximations, allowing us to establish comparative degrees of assurance between our judgments. In this context, ideas like that of a ‘real essence’ serve as heuristic tools, even if they cannot be true objects of reference. We proceed as if something were objectively necessary,[4] and the only justification we can give for such normative concepts resides in the pragmatic success of the procedures following from admitting them. Summarizing the profession of faith of the old empiricist that I am: I admit that necessity is a metaphysically loaded concept. However, it works for us as a conventional de dicto necessity which we can only believe to be rooted in a de re necessity, in a way similar to the way we can only believe that a nominal essence is rooted in a real essence. And this same necessity can be epistemologically spelled out in the form of a priori knowledge expressed by analytic statements.
   If this empiricist analysis of necessity is correct, as I believe, one could go ahead in suggesting a very broad distinction between two main kinds of necessity, both of them conventional and with essentially epistemic (and only ideally metaphysical) import:

(a)   Formal necessities. These are necessities that we find mainly in logic and mathematics and in definitional sentences (like ‘brother (Df.) = male person with the same parents as another person’), which often can easily be shown to express tautologies. Their statements are analytic and their negations are contradictory or inconsistent.
(b)  Empirical necessities. These are necessities arrived at a posteriori, which once obtained are simply assumed or postulated as necessities. This is a weaker but very common sense of the term that presupposes the truth of a theory and system of beliefs in which it is inserted (like the nomothetic necessity expressed in a statement such as ‘necessarily V = ∆P/∆t [assuming traditional kinematics]’). Under the presupposition of the theory and the system of beliefs in which they occur, empirical necessities can also be seen as analytic and their negation as contradictory or inconsistent relative to what they assume as true.

These two general kinds of necessity have a long tradition in philosophy that began with Aristotle: (a) was absolute necessity and (b) hypothetical necessity. For Aristotle, the first was necessity in the proper sense. The second, so-called hypothetical necessity, would be a necessity whose opposite implies a contradiction under a given condition, such as the assumed theory.[5] Wittgenstein would classify them as ‘grammatical rules’ – rules grounding a useful linguistic practice (1984a). Here is his suggestion, in which I read the word ‘rule’ as referring to necessary (a priori) propositions:

Every empirical proposition can serve as a rule if it is fixed as the immovable 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)

Since these are postulated empirical necessities, they do not have the same warrant of formal necessities. Moreover, (a) and (b) are conventionally established.[6]  Finally, one is entitled to doubt whether it is possible to establish a sharp demarcation between them. Anyway, I believe that this distinction may helps us to understand better the two proposed ways to read identity statements of the kind a = b.
   To begin with, consider the first of Kripke’s examples: (i) ‘Hesperus is Phosphorus.’ In accordance with the suggested analysis, it can be read as:

(a)  A contingent a posteriori statement, broadly understood in relation to our whole unstable overall system of beliefs. In this case, (i) means (i-a): ‘(Contingently, depending on what experience has shown) Hesperus = Phosphorus.’ Statement (i-a) isn’t yet seen as analytical, and its negation is regarded as possible.

Perhaps it was so when the Babylonians discovered that Hesperus is Phosphorus. They could track Venus’ trajectory during the night, they could notice that as a planet inside the earth’s orbit it is always near the sun, etc. However, at first they were not sure of this identity. It had the modal form of a possible and, additionally, a sufficiently probable identity. The modal form ◊ (a = b) is insufficient, since modal logic is too weak to display a possibility to which is added a sufficiently high probability to give us something close to practical certainty. Even today, we have some right to doubt when we oppose the statement ‘Hesperus is Phosphorus’ with our in principle ever changeable overall system of beliefs, since the original rules for the identification of Hesperus and Phosphorus were distinct.
   The second way of interpreting the identity is when we establish a conventional rule warranting to us that a and b, if they refer, refer to the same object in any possible world, that is, we assume or postulate that □ (a = b). In this case, (i) can be read as:
(b) A necessary a priori identity statement – as an element of the subsystem of beliefs that constitutes our astronomical knowledge, assuming the truth of this subsystem. In this case (i) means (i-b): ‘(Assuming our present astronomical knowledge) Hesperus-[Phosphorus] = Phosphorus-[Hesperus].’ The identification rules are now seen as blended in a single rule though in different guises. Statement (i-b) can also be seen as analytical and its negation as contradictory or inconsistent. Even so, what we have is empirical (hypothetical) necessity.

Consider now (ii) ‘Heat (in gases) is molecular kinetic energy.’ This identity can be read as:

(a)   A contingent a posteriori statement, since it is understood in relation to our unstable overall system of beliefs. In this case, (ii) means (ii-a): ‘(Contingently and in accordance with what experience has shown up until now) heat in gases = average molecular kinetic energy.’ The identity is believed, but it isn’t yet seen as conventional; (ii-b) isn’t yet seen as analytical, and its negation is still seen as possible.

This was the case in the last half of the 19th century, when chemists were unsure about the real cause of heat in gases. The identity had the logical form +◊ (a = b), if we may add the modifier ‘+’ to indicate a sufficiently high probability linked to the possibility – a probability sufficiently high to give us practical certainty and allow us to judge. The remote possibility that heat in gases isn’t the kinetic energy of their molecules can never be completely ruled out. Anyway, we can assume or postulate the truth of the kinetic theory of gases and in this way come to the modal form □ (a = b), so that (ii) will be read as:

(b)  A necessary a priori (analytic) statement – if read as a constituent of the subsystem of beliefs that forms the kinetic theory of gases, assuming the truth of this subsystem. In this case, (ii) means (ii-b): ‘(Assuming the truth of the kinetic theory of gases) heat in gases = average molecular kinetic energy.’ Here the ascription rules for the terms flanking the identity sign are blended into a single rule that points to an identity under different semantic guises. (One could say with Wittgenstein that the statement is here hardened, becoming an immovable part of a mechanism.) Its negation is also contradictory under the assumptions of the kinetic theory of gases, though what we have in this case is empirical, hypothetical necessity.

In this case, heat (as temperature) is understood, based on general acceptance of the kinetic theory of gases, as a kind of abbreviation for ‘molecular mass-motion,’ which once accepted does not require experience to be seen as true. The rule is a blended one, with two different guises, one emphazising ‘heat in gases’ and the other emphazising ‘average molecular kinetic energy.’ (See Ch. IV, sec. 23-26)
   In my view, Kripke unduly conflates the a posteriori character of the first readings of these statements with the necessity of their second readings, arriving at an illusory necessary a posteriori.

   As for Goldbach’s conjecture, the fact that it may be a necessary truth without our being aware of it does not mean that in this case the suggestion that any natural number is the sum of two primes is not an a priori truth, since it can also be an a priori truth without our being aware of it. It can be necessary but unknown insofar as it is a priori but unknown. Moreover, if it happens that we never discover its truth a priori, we will also never discover its necessity. And it is not impossible that someone will find a proof of this conjecture, finally giving it the cognitive status of a theorem with a priori necessity. Indeed, it is because mathematicians (pace Gödel’s theorem) maintain as an heuristic rule that it is possible to reach such an a priori necessity that they will still insist on searching for proof.

The most striking and revealing example of a necessary a posteriori statement introduced by Kripke is that of the wooden lectern in front of him. It starts with the question: could this lectern 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 lectern, if it exists, cannot be made of ice,’ is a necessary truth known a posteriori. Lecterns are usually not made of ice. This lectern 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 lectern 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. More precisely: being P = ‘This lectern is not made of ice,’ and considering that we know both, the a priori truth that ‘If P then P’ and, from empirical research, that P is true... Kripke constructs the following argument, applying a modus ponens:

     1  P □P

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

Unfortunately, there is a well-hidden mistake in Kripke’s argument. It concerns the epistemological status of P in the second premise. In this premise, the truth of P is affirmed in complete disregard for the fact (earlier confusingly introduced by him) that P, like any empirical statement, can only be known to be true by inevitably fallible epistemic subjects. However, if this is so, P can in principle be false. In order to show my point clearly, I first need to define a statement as practically certain if it is sufficiently likely to be true that the probability of its being false may be ignored. This is usually the case when we can assign to the statement a probability of being true very close to 1.[7] On the other hand, I define a statement as absolutely certain if it simply cannot be false, having a probability 1 of being true, which makes it obviously necessary.[8] Considering this, we can instead say that statement P of the second premise should more precisely be written as (2’): ‘It is practically certain (or, it has a probability very near 1 of being true) that P (that this lectern is not made of ice).’ Indeed, (2’) must be true, because we know this. However, only God – the infallible and omniscient epistemic subject – could know with absolute certainty the truth of statement P (that is, God would be able to assign it the probability 1). Only God, the infallible knower, could know for sure the factual existence of P. He would in this way give the state of affairs described by P a truly metaphysically de re necessity. Unfortunately, we cannot appeal to God in this matter… All we can know is that P is practically certain in the already stated sense that assuming all available information it is sufficiently likely to be accepted as true. This must be so, if we accept the fallibility of our empirical knowledge, its lack of absoluteness.[9] (Never impossible is a radically skeptical scenario in which Kripke believes he is standing before a hard wooden lectern, as indicated by all available testimony and after doing all possible empirical tests, even though the lectern is really made of ice[10]).
   Assuming this, consider Kripke’s premises again. First, it is fully acceptable that given the fact that P, P follows by necessity. What P → P says is ‘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 of P → P requires is that P implies □P only if P is really the case, what means that P must be absolutely certain, with probability 1 and not just an assertion that a fallible knower ‘holds to be true’ (das Fürwahrhalten). Only when P has a probability 1 of being true it turns to be a necessary truth.
   In other words, only an absolutely certain truth would warrant the necessity of the consequent, what would require as its knower an unfallible being. Hence, the most complete analysis of premise (1) must 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 analyzed as (1’’) ‘If it is practically certain that P is the case (that is, if P has a probability close to 1), then P is necessary,’ since the mere probability of P, no matter how high, as it is less than 1, would not warrant the necessity of P. Once we admit the change of premises (1) to (1’) and (2) to (2’), Kripke’s argument can be made completely explicit as saying:

1’ If it is absolutely certain (with probability 1) that P, then it is necessary that P.
2’  It is practically certain (with a probability close to 1) that P.
3’  It is necessary that P.

Obviously, argument (B) is not valid, since the modus ponens cannot be applied to (1’) and (2’) to give us (3’). The reason is that the antecedent of (1’) does not mean precisely the same thing as (2’), which makes the argument equivocal, hence fallacious. We conclude that under more careful scrutiny Kripke’s argument is clearly flawed and consequently insufficient to convince us that the utterance ‘This lectern is not made of ice’ is a metaphysically necessary a posteriori truth.
   Now we can easily see the reason for Kripke’s misleading claim that the conclusion of his argument must be necessary a posteriori. He ignores the fine semantic differences made explicit in version (B) of his argument, and by doing so he jumps to a conclusion that unduly joins the necessity of his argument’s first premise with the aposteriority of its second premise, producing what he calls a necessary a posteriori truth in the conclusion (3).

Kripke then goes on to the analysis of identities between proper names such as ‘Hesperus is Phosphorus’ and ‘Cicero is Tulli.’ These empirical identities were traditionally seen as contingent. However, for Kripke they are identities between rigid designators, which makes them necessary, since in the most diverse possible worlds these names will refer to the same object, which would not be possible if Hesperus weren’t Phosphorus or if Cicero weren’t Tulli. 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 lived on Earth and had identified Hesperus with Venus and Phosphorus with Mars... The same is true for the identity ‘Cicero is Tulli.’ 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 rigid designators.

In order to demonstrate that the statement ‘Hesperus is (the same as) Phosphorus’ cannot be necessary a posteriori, here we can produce an argument parallel to the argument applied by Kripke to the indexical predicative case of the wooden lectern. Calling Hesperus h and Phosphorus p, we can construct the following Kripkean modus ponens:

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

The Kripkean conclusion of this argument is that ‘Hesperus is Phosphorus’ would be a necessary identity that has been reached a posteriori.
   Nonetheless, here as well the modus ponens does not apply because although the first premise is true, the second premise would only conjoin with the first one to reach the conclusion ‘(h = p)’ if it were able to give us an absolute assurance that ‘h = p.’ However, this is not the case. In order to get the absolute assurance (probability 1) that ‘h = p,’ which enables us to reach the conclusion of the conditional, this truth must be discovered, not by inevitably fallible human epistemic subjects only capable of practical certainty, but again only by God, the omniscient and infallible epistemic subject.[11]  Because of this, ‘h = p’ can be seen here as merely an empirically reached fallible conclusion, stating that it is practically certain (sufficiently probable) that ‘h = p,’ which is still far from absolute certainty or probability 1. The following reformulation demonstrates the argument’s hidden flaw:

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

Since we do not have the absolute certainty required by the identity of the antecedent of the first premise with the second premise, the equivocal character of the argument becomes clear. We cannot use the modus ponens to derive the a posteriori necessity of h = p. In this inter­pretation the statement ‘Hesperus is Phosphorus’ is contingent a posteriori. It cannot be metaphysically necessary, because since this identity is only highly probable, it will always be possible that Hesperus is not Phosphorus. For instance, although extremely unlikely, it is logically possible that the gods have until now maintained an incredibly complex illusion of knowledge in 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, when seen by the naked eye Hesperus would have a different location than Phosphorus, but it would appear identical to Phosphorus when viewed through a telescope – not because it is the same planet or even a planet at all, but as a result of an illusion.
   Kripke’s second example is very different, and one should not confuse it with the first one. It concerns the utterance ‘Cicero is Tulli.’ Assuming the neo-descriptivist theory of proper names proposed in the appendix of chapter I, the localizing description for his identification is (concisely) ‘the person born in Greece on 3.1.106 BC and deceased in Rome on 7.12.43 BC,’ while the characterizing description is (concisely) ‘the most famous Roman orator, also a statesman, jurist and philosopher.’ His whole name was ‘Marcus Tullius Cicero.’ Since the proper name is not a fundamental description, but rather an auxiliary one (he could easily be given another name in a different possible world), Kripke is only relying on the fact that not all speakers know that Cicero and Tullius are parts of the same proper name, as a convention in our actual world. The statement informs the hearer that the bearer of the fundamental descriptions implied by each term flanking the identity sign is referred to by only part of the whole name of the same person.
   The result is that the statement’s aim turns out to be a trivial one, namely, to communicate to the hearer a convention regarding the auxiliary description ‘the person whose name was “Marcus Tullius Cicero”.’ Hence, the right answer is that ‘Cicero is Tullius’ only communicates part of a necessary a priori linguistic convention, since the convention that the whole name is ‘Marcus Tullius Cicero’ is decided a priori, just as is the convention that a triangle is a trilateral figure. Moreover, to say that the statement ‘Cicero is Tullius’ 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 been given in different counterfactual situations. Indeed, it is possible that Cicero could have been given the name ‘Marcus Titus Cicero’ in a different possible world, making the identity ‘Cicero is Tullius’ false. However, this is as trivial as to say that in a very different language (or world) people use a different name for ‘triangle,’ for instance, ‘colmio.’[12] Consider the statement found in a bi-lingual dictionary, ‘triangle means colmio.’ It is not necessary a posteriori. It is the obvious expression of a necessary a priori identity regarding conventions.

The next of Kripke’s examples concerns the identity between kinds of things, as in the already discussed statement Heat is molecular motion. Many think that this identity, being the result of empirical research, expresses an a posteriori truth. However, for Kripke this is a necessary a posteriori identity because the heat (in a gas) cannot be anything other than molecular kinetic energy, since the terms ‘heat’ and ‘molecular motion’ are rigid designators. It may be, he says, that the Earth could at some time have been inhabited by beings who feel cold where we feel hot 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.

The fact that the terms of an identity are rigid designators does not warrant that they are rigid designators of the same bearer, picking up the same object in the same possible worlds, since any identity can be false. Thus, this fact alone warrants absolutely nothing.
   Anyway, as noted in the Appendix to Chapter I, since we have ways to translate rigidity in descriptive terms for 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 for heat in gas and kinetic molecular energy to create a unified ascription rule that has two different guises – two different but interchangeable main designative criteria, producing a necessary a priori identity.
   Since I have already said something about this, what I will do now is only to employ the same strategy used above in order to discredit the thesis that we may have a case of a necessary a posteriori. Thus, considering heat in gas and kinetic molecular energy as rigid designators that necessarily designate an essence, we could construct the following Kripkean argument calling heat in gas H and kinetic molecular energy M:

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

Clearly, the same problem reappears. The first premise says only that if the identity (x) (Hx = Mx) is really the case, then it is necessarily the case that all heat is molecular motion. Or, in epistemic parlance, if it is absolutely certain that all heat in gas is kinetic molecular energy, then it is necessary that all heat in gas is kinetic molecular energy. However, since the identity affirmed in the second premise, being empirical, is inevitably fallible, 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 a probability close to 1) that (Hx = Mx).
    (x) (Hx = Mx)

Here again the more explicit formulation shows an equivocal and consequently fallacious argument for the same reason given in the above arguments. It is thus clear that we cannot in this way conclude that the statement ‘Heat (in gas) is the same as molecular motion’ is a Kripkean necessary a posteriori truth. Thought of in this way it is a contingent a posteriori truth.

The last of Kripke’s examples should be the most important one. It is intended as a refutation of identity theories 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 that has not been made. But, as Kripke writes, ‘pain’ and ‘such and such a brain state’ are rigid designators here, for they refer to essential properties. However, if this is the case, the identity theorist is in trouble, because this identity should be necessary, which frontally clashes with the fact that whenever you feel pain you do have pain, while no one is denying that it is possible to conceive that we have pain without having the corresponding brain states. For a theistic philosopher like Kripke this makes identity theory implausible.
I find this argument puzzling. First, as a matter of fact, one can feel pain without there being an identifiable organic cause, for instance, in the case of hypnotized people who feel imaginary pains. However, even if we ignore this, assuming that we cannot feel legitimate physical pain without having some qualitative subjective state of pain, the fact that we can conceive of pain without the corresponding brain states isn’t enough to prove anything, as much as the fact that Descartes could imagine his mind existing without his body would not suffice to prove that the mind can exist without the body.[13] Why does this force us to think that a future neuroscience might not be able to show us that by speaking of such and such a brain state we make a rigid reference to exactly the same thing we experience as a state of pain, so that this identity would be necessary, as in the case of heat? It is true that feeling pain isn’t the same as detecting heat outside us by feeling hot inside. The first is subjective and immediate. But in the same way that a Martian might feel cold when we feel hot, a Martian might feel a tingling sensation when we feel pain. And we can similarly imagine that feelings of pain, like those of heat, can be identified using different procedures or criteria. Hence, the only real difference that remains between the two cases is that kinetic molecular energy in gas is located externally, outside a person’s head, while such and such a brain state is located internally, within a person’s head. But why should this be relevant for the point in question? Kripke concludes his argument by saying: ‘heat is picked out by the contingent property of being felt in a certain way; pain, on the other hand, is picked out by an essential property’ (1971, note 18). However, even in the case of pain there is no warrant that the feeling of pain, as long as put in words, picks out the real essence instead of a nominal essence, in the same way as there is no grant that a discovered general neuronal pattern of pain picks out the essence of pain instead of an only nominal essence. Both can be stated as real only from a hypothetical perspective. (Imagine a world where most people’s pains are imaginary and it extremely easy to mistake imaginary from real physical pains; worst than this, imagine a tribe of people whose pains are always imaginary but so well justified that we mistakenly believe their pains to be real.)
   As I see it, 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 that belongs to a different interpretation of an identity, which makes it a necessary a priori truth. This leads him to believe in a supra-epistemic de re metaphysical necessity, which is discovered a posteriori. In doing so, he assigns to ontologically unknowable identities the same status of epistemo­logically assumed identities. He proceeds as if we could assert ontological (metaphysical) truths without considering our epistemic capabilities and their intrinsic fallibility. He refuses to accept that we can never completely separate the epistemic from the ontic; and in so doing he denies an insight accepted by modern philosophers since Descartes, namely, that we lack access to supra-epistemic truths.

Addendum: disposing of externalism
There are a great variety of arguments by Kripke and other externalist philosophers that deserve closer examination. In what follows, I will limit myself to a few comments, since a more detailed analysis would far exceed the scope of this book.

1. There are a variety of supposed examples of necessary a posteriori truths that were later proposed 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 of a cat that is not an animal; but it is also a posteriori, since it was discovered a posteriori. Therefore, it is a necessary a posteriori truth.
   For us (i) can be given a double interpretation, depending on the context. Here it is:

(a)   Contingent a posteriori: a primitive tribe that sees a cat for the first time might easily suppose, based on its aspect and behavior, that it is an animal like others. The tribe arrives at this knowledge a posteriori, because it is based on experience, and contingently, because it is liable to revision (it could well be that in this case the cat is a forest spirit assuming the appearance of an animal).
(b)  Necessary a priori: a zoologist, assuming the truth of our contemporary taxonomy, according to which the cat is classified as an organism belonging to the Animalia kingdom, would see statement (i) as necessary a priori. It is an a priori analytic statement, since (i) abbreviates the tautology (ii) ‘Animals called cats are animals.’ No sign of a necessary a posteriori.
Again, we can only arrive at the necessary a posteriori by confusing the necessity of interpretation (b) with the a posteriori character of interpretation (a).

2. Another form of necessary a posteriori later suggested by Kripke concerns origins. For him, rigidity makes true parenthood necessary. He considers the case of Queen Elizabeth II (1980: 112 f.). Although he does not say, it is well-known that she was at birth the daughter of Albert, Duke of York, and his wife, Lady Elizabeth Bowes-Lyon. Note that this is a suggestive, but biased example, since in the case of a queen the ovum origin acquires maximal importance, which we would easily analyze as a case of contamination of the characterizing description-rule of its identifying rule by descriptions of origins (cf. Appendix to Ch. I, sec. 9 (v)). Suggestiveness and biased concrete examples work here as a way to confuse things and mimic a wrong kind of relevance.
   By contrast, consider the statement (i) ‘Ishmael Lowenstein is the son of Abel and Berta Lowenstein.’ According to a Kripkean philosopher, this statement should be necessary a posteriori because even if it is known a posteriori, an adult with different parents stemming from a different ovum and a different sperm cell would not be Ishmael Lowenstein.
   However, suppose that the adult Ishmael makes the shocking discovery that his parents are not his biological parents. There was a mix-up of infants in the hospital where he was born, and a subsequent DNA analysis showed that he was actually the son of Amanda and Mario Belinzoni, who was baptized with the name Carlos. Of course, this is no reason to think that Ishmael thereby ceases to be Ishmael. This name is even given on his birth certificate and drivers license. If asked, he could insist on answering that his name is Ishmael Lowenstein, probably with the agreement of others. This is consistent with our identification rule, since Ishmael still satisfies the localizing and characterizing conditions sufficiently and more than any other person.
   In any case, our conclusion may be less straightforward regarding the main point, namely, the complete statement (i) ‘Ishmael is the son of Abel and Berta Lowenstein,’ which addresses the question of parenthood.[14] One could use as a criterion of parenthood those who cared for the child and raised him with loving care until adulthood. In this case the statement ‘Ishmael is the son of Abel and Berta Lowenstein’ will be regarded as true, even if he was conceived from Mario’s sperm cell and Amanda’s ovum. So understood, the statement ‘Ishmael is the son of Abel and Berta Lowenstein’ is contingent a posteriori. Contingent because it could be false that they cared for and nurtured him; a posteriori because knowledge of this kind is acquired through experience.
   However, it is easy to imagine a situation in which Kripke’s view would apply. Suppose we were in Nazi Germany and the Lowensteins were Jewish. Suppose the Nazis had arrested the family. For the Nazis the criterion of parenthood was clearly biological. In this case, if the Nazis were informed about the mix-up of babies, Ishmael Lowenstein would be considered the son of Mario and Amanda Belinzoni, while Carlos would be considered the son of Abel and Berta Lowenstein, and as such would be arrested and sent to a concentration camp. With regard to the proper name the matter isn’t so simple. However, it could even be possible that the Nazis had a rule according to which a person’s true and legal name must be the name linked to his biological origin, so that they would replace the name of Ishmael Lowenstein with Mario Belinzoni, and the unfortunate Mario Belinzoni would become Ishmael Lowenstein.
   Anyway, even in this case a statement like (ii) ‘Carlos Belinzoni (Ishmael Lowenstein) is the son of Mario and Amanda Belinzoni’ would not be a necessary a posteriori truth. In this case, parenthood and even naming turn out to be part of the characterizing description-rule. This could lead to a dual interpretation of the statement:

(a)    It could be seen as an uncertain contingent a posteriori discovery, insofar as one emphasizes the fact that the name Carlos Belinzoni (= Ishmael Lowenstein) now should mean the same thing as the son of Mario and Amanda as an (a posteriori) discovered truth and a (contingent) conclusion reached inductively.
(b)    If one emphasizes a stipulated decision to treat ‘Carlos Belinzoni’ (= Ishmael) as an abbreviation of ‘the son of Mario and Amanda Belinzoni,’ making this an essential part of his identification rule, we have a blending identification rule, and statement (ii) could be seen as necessary a priori.

Of course, Kripke could answer by noting that what we discover about parents doesn’t matter. What matters is that if one were born to parents x and y, one could not have been born to different parents (1980: 113). But so expressed this is a trivial statement like ‘If a woman is using a hat she has something on her head.’ The problem is that any attempt to give a concrete example will lose its character of necessity, since it will demand be based on empirical experience, being therefore in principle fallible. Indeed, there is only one way in which for our cases a given origin would generate a necessary a posteriori, namely, when viewed by an infallible knower. He would discern that Ishmael is definitely the son of Mario and Amanda Belinzoni, giving this the probability 1 (necessity), and he would know it as a de re metaphysical necessity. He knows this because he is able to achieve some kind of supra-epistemic knowledge. We, as fallible knowers, do not possess this gift. By using concrete examples, Kripke gives the impression of having made a metaphysical discovery about the world when he is really only saying something that is either trivial or contains an elusive anticipation of the meta-descriptivist theory of proper names proposed in the present book.

3. Worse than the necessary a posteriori is Kripke’s later invention, the contingent a priori (Kripke 1980: 54-56). It uses a case involving the platinum rod stored in Paris, once designated as the standard metric unit of length. According to Kripke, analysis of meaning is something different from definition; the first is necessary, the second is not (although he gives no satisfactory justification for this). Then he claims that the definition of ‘one meter’ as ‘the length of S at to’ is not necessary a priori, but contingent a priori! The reason is that the term ‘one meter’ is a rigid designator, while ‘the length of S at to,’ being a definite description, is an accidental designator, only helping to fix the reference. Since the accidental designator may change, in different possible worlds the length of S at to could be longer or shorter than a meter on Earth, for instance, due to heating or cooling. Thus, in a different possible world one meter could be a length different from ‘the length of S at to.’ Therefore, the statement ‘the Paris platinum rod is one meter long (has the length S),’ although established a priori, is contingent.
   This argument could be strong enough if we accept the existence of some metaphysical reason for the distinction between names as rigid designators and descriptions as accidental designators. But the real reasons for the distinction are non-metaphysical, as I make clear in the appendix of chapter I (sec. 7-8): definite descriptions are only accidental when dependent on proper names but not when they make proper names depend on them, as in the present case. Consequently, Kripke’s affirmation turns out to be highly questionable that after being established definitions are neither meaning-giving nor necessary. For it seems clear that the definition of a meter as ‘the length of S during ∆t[15]’ is a stipulative definition made to establish the proper meaning of one meter. Thus, why cannot ‘one meter’ have been chosen as a mere abbreviation of ‘the length of S during ∆t,’ whatever this length is? Why cannot ‘the length of S during ∆t’ be a rigid designator, no less than ‘the average kinetic molecular energy’? Assuming this, our intuitive reasoning would be to think that whether the length of the standard meter changes or not, the meter in its function as a standard of measure remains the same, since the standard meter is defined as whatever length S has in the ∆t in which it is used as a standard. This means that in any possible world where the standard meter exists, the length of this meter will continue to be the same, no matter what its trans-world comparative length may be.
   Only for practical reasons is it better to use the most rigid, unchangeable possible standard meter, if we wish to preserve the comparative function of measuring length. For suppose that the standard meter were a kind of very elastic rubber rod, continually changing its length. It would remain the same standard meter, of course, but it would be quite impractical. Using this standard in accordance with the given definition, we could be led to agree that a woman who two hours ago was 1.67 m tall is right now 2.24 m tall; or that objects with very different sizes could be the same size if we measured them at different times…
   The point is that if you accept that the statement ‘A meter is the length of S during ∆t, whatever length it has when measured’ is the actual definition of a standard meter – and it really is – this definition isn’t contingent, but necessary, since it is a convention that cannot be falsified in any possible world where it holds. Moreover, this definition is a priori, for we do not need to have any experience to know its truth. Consequently, the following identity is the right definition of a meter:

One meter (Df.) = the length of the standard rod S during any moment of ∆t, disregarding the possible world (circumstance) in which its length is considered.

Here the definiendum is nothing but an abbreviation of the definiens. This identity is necessary and a priori; and its necessity is supplementary evidence that stipulative definite definitions are rigid. They are rigid because we have established them as the proper definiens of a name, as in the present case.

4. Another attempt to exemplify the contingent a priori could come from Gareth Evans’ example with the name ‘Julius,’ which he artificially stipulates as naming ‘the inventor of the zipper’ (Evans 1982: 31). According to some, the statement (i) ‘Julius was the inventor of the zipper’ is contingent a priori. It is a priori because we do not need experience to know this; but it is also contingent, since it is possible that ‘Julius’ was dropped on his head when little and grew up too stupid to invent the zipper (Papineau 2012: 61).
   Concerning statement (i) we again find a dual reading:

(a)   On the one hand, it is contingent a posteriori. It is contingent because in a counterfactual situation it could be that the zipper was not invented by anyone or that it was invented by several persons… but it is also a posteriori because its truth depends on experience to be discovered.
(b)   On the other hand, assuming it to be true that someone invented the zipper, we could paraphrase ‘Julius invented the zipper’ as (ii) ‘Assuming that someone invented the zipper, we have decided to 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 harmless stipulation, and it is a priori because established independently of experience. In any case, we do not have a contingent a priori.

5. A curious attempt is the following utterance: ‘I am here now,’ proposed by David Kaplan (1989: 509). This would also be a contingent a priori truth. It is a priori because, since each of its terms directly refers respectively to the agent, the place and the time of a given context of utterance, this excludes the possibility of its falsity. However, since we can imagine counterfactual circumstances in which I would not be here, this utterance is only contingently true.
This example is also deceptive. Even ‘I am here now’ can be a false statement in the real world! I remember a case related by Dr. Oliver Sacks of a patient who had a seriously deranged perception of temporal continuity. Because of this, her daily life was a succession of time-lapses: she could think ‘I am here now’ as if she were still in her bedroom, when in fact she was already in her kitchen. Thus, in this case, ‘I am here now’ was empirically false! This shows that the statement ‘I am here now’ is in fact contingent a posteriori, since it is falsifiable and dependent on the context of the experience to be learned about.

6. I also disagree with Hilary Putnam’s view, according to which the meaning of the word ‘water’ must essentially be external to our heads.[16] This is perhaps the most influential argument for semantic externalism. According to Putnam’s Twin-Earth fantasy, in 1750 Oscar-1 on the Earth and his Doppelgänger Oscar-2 on Twin-Earth – two nearly identical planets with the same history – both simultaneously see that it was raining. Since the chemical structure of water wasn’t yet known in 1750, all that Oscar-1 and Oscar-2 could have in their heads would be the same idea of a watery fluid (a fluid that at room temperature is transparent, odorless, tasteless…). However, unknown to them, they were referring to very different compounds, Oscar-1 to H2O, while Oscar-2 was referring to XYZ. Water on Twin-Earth (believe or not) has a very different chemical composition, summarized by Putnam as XYZ, even though it has the same appearance and behavior as water on our Earth. For Putnam this proves that the meaning of water – which for him essentially concerns quantities of molecules with the same micro-structure of H2O – could not be in the heads of the Oscars, since in their heads they had the same state of mind, namely, the idea of a watery fluid and nothing more. Putnam’s conclusion is the most famous statement of externalism: ‘Meaning just ain’t in the head.’(1975: 227) As he summarizes in a central passage:

Oscar-1 and Oscar-2 understood the term ‘water’ differently in 1750, although they had the same psychological state, and although, given the state of development of Science in their epoch, the scientific community would need to take circa 50 years to discover 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 a function of the speaker’s psychological state) (my italics). (1975: 224)

This is a shocking conclusion, later radicalized by John McDowell’s inference that even the mind must be external to the head, because it is the locus of our manipulation of meanings (McDowell 1992: 36).
   My neo-descriptivist answer is that Putnam’s result is due to his over­looking the fact that ‘water’ has two descriptive nuclei of meaning: a popular and a scientific one.[17] First, there is an old popular nucleus of meaning of the word ‘water.’ This nucleus is phenomenal and also dispositional and can be summarized by the expression ‘watery fluid’. It is a fluid that at normal temperatures is transparent, odorless, quenches thirst, can be used to wash things, is a universal solvent, extinguishes many kinds of fire, falls from the sky as rain, forms rivers, lakes and oceans, freezes when cooled below 0 degrees C, evaporates when heated above 100 degrees C, has high surface tension, etc. This was the usual meaning until the end of the eighteenth century. Then a great semantic upheaval occurred. A new dimension of meaning was increasingly added: the scientific nucleus, which can be summarized as ‘quantities of H2O.’ It is a substance that results from combining hydrogen and oxygen, as summarized in the formula 2H2 + O2 = 2H2O, which can be shown by burning hydrogen mixed with oxygen and by electrolysis, forms intermolecular hydrogen bonds responsible for its high surface tension, etc. Both nuclei of meaning are not only intrinsically inferential. They are also obviously objects of descriptions (since in opposition to Putnam’s apparent bias, the domain of what can be described is much wider than a merely perceptual domain, containing descriptions of dispositions, micro-structures, etc.), what can be assured today by any good dictionary.[18] We use the word ‘water’ on an everyday basis in accordance with what we know from the inferential semantic rules of these two nuclei.[19] Furthermore, it is easy to see that in consonance with contextual variations, one of these clusters of meaning tends to come to the fore.
   This summary already allows a convincing internalist explanation of the Twin-Earth fantasy. First, in 1750 the two Oscars had in their heads only the nucleus of meaning expressed by ‘watery fluid’, so that the extension and meaning of the word water was the same for both Oscars. However, when Putnam considers what is happening, he is overvaluing and unconsciously projecting the scientific nucleus of meaning of the word ‘water’ into the two Oscars’ utterances, as if it were the only truly relevant one. What he does then is to treat the two Oscars as mere indexical devices for the projection of the new scientific 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 outside of our heads, as Putnam believes. They are in Putnam’s head when he thinks his thought-experiment and in our heads when we read him. Today we all know some basic things about the scientific nucleus of meaning (H2O) and may guess that a different scientific nucleus with similar effects (XYZ) would perhaps not be impossible. Finally, since Putnam and his readers have different scientific meaning-descriptions in their heads when unconsciously projecting them onto Oscar-1 and Oscar-2 by using them as indexical devices, these different meanings remain, as they should, internal properties of minds. This also explains why we give them (by means of our instrumental referential devices called ‘Oscars’) different extensions.
   The neo-descriptivist view suggested above by the consideration that the meaning of ‘water’ leads to variations of emphasis according with what we could call the context of interest in which a word is used, that is, the context of its circumstantial utility. In this case there is a popular and a scientific context of interest leading to different interpretations as follows:

(a)   In a popular context of interest (e.g., of fishermen who use water for cooking, drinking and washing) the sense that is emphasized in the statement ‘Water is H2O’ is that of a watery fluid. In this case, ‘Water is H2O’ means above all (i) ‘Watery fluid = fluid composed of H2O.’ Taken at face value, this is a contingent a posteriori statement. Contingent because, at least in principle (though very improbably), it could be proved false; a posteriori because it was learned from experience. Its modal form, modified by the addition of a high level of probability, is +◊ (a = b).
(b)  In a scientific context of interest (e.g., in a chemist’s laboratory) the scientific nucleus of meaning is emphasized. Here ‘Water is H2O’ means above all (ii) ‘Hydroxide of oxygen = H2O.’ As expected, (ii) is a necessary a priori statement with the modal form □ (a = b). In this context even if water were not a watery fluid, but rather something like a black oil, it could still be called ‘water,’ insofar as it has the right micro-structure.

Conclusion: the Kripkean classification of the statement ‘Water is H2O’ as a necessary a posteriori statement results from a confusion between the a posteriori nature of statement (a) and the necessity of the similar statement (b). Since both senses are components of the whole meaning of ‘water’ and may alternatively come to the fore, it is easy to fall into a confusion resulting from lack of attention to the pragmatics of natural language, as Putnam and Kripke overvalue the scientific nucleus. We already dealt with these kinds of confusion when we examined Wittgenstein’s account of transgressing the internal limits of language. In this case, the confusion is a matter of equivocity resulting from the unsatisfactory attempt to import the scientific into the popular usage (cf. Ch. III, sec. 11).

7. There are two other examples of Putnam trying to show that meaning is not only in the external physical world, but also in society. In the first one, he assumes that aluminum and molybdenum are only distinguishable by metalworkers and that Twin-Earth is rich in molybdenum, used to manufacture pots and pans. In addition, he imagines that the inhabitants of Twin-Earth call molybdenum ‘aluminum’ and aluminum ‘molybdenum.’ In this case, he writes, the word ‘aluminum’ said by Oscar-1 will have an extension different from that of the word ‘aluminum’ said by Oscar-2, so that they mean different things with the word. However, as they are not metalworkers, they have the same psychological states. Hence, the meaning of these words is external to what happens in their heads, depending on their societies.
   My answer is the following. If we consider how the words ‘aluminum’ and ‘molybdenum’ are used by Oscar-1 and Oscar-2, since they are not metalworkers, what they have in their minds is indeed the same thing. It is as much so as the extension that they are able to give to their concepts of aluminum and molybdenum, which in the example includes both. For the metalworkers of Earth and Twin-Earth, on the other hand, the aluminum of the Earth and the molybdenum of Twin-Earth (called by their inhabitants ‘aluminum’) have very different constituent properties, which means that metalworkers would have something very different in their heads. The Oscars may confuse both things, but only because they do not really know the intrinsic properties of these things when they use the words in a subsidiary sense. However, since we are informed about the differences between the amounts of these metals on both planets, we can consider the aluminum and the molybdenum respectively observed by Oscar-1 and Oscar-2 and unconsciously take both persons as referential devices for the different meanings we have in our heads. In this case, we would say that Oscar-2 is referring to what his linguistic community calls aluminum, but which in our linguistic community is called molybdenum, while Oscar-1 is indeed referring to what we call aluminum.
   That people should use the words in accordance with the conventions of their linguistic community does not make the meaning external. It only makes it dependent on the explicit or implicit agreement of members of their communities. In the two Oscars example, this agreement concerns only superficial properties. In the metalworkers example, this agreement also concerns intrinsic properties. These agreements are always located in individual heads, even if differently distributed in a social network.
   In the second example, Putnam considers differences between elm and beech trees. Most of us do not know how to distinguish between the two. However, we are able to guess correctly that these words are not synonymous, having different extensions, even without knowing the meanings of the two words. Hence, according to him the difference in meaning is not in our heads, but in society.
   In response to Putnam, the important point to be noted is that most of us really do lack sufficient knowledge of the meanings of the words ‘elm’ and ‘beech.’ However, we already know something very generic about them: we surely know that they are trees, and we consider it very probable (though not certain) that these two names refer to distinct kinds of trees.[20] With the help of these convergent descriptions (cf. Appendix to Chapter I, sec. 4), we are able to insert these words into a sufficiently vague discourse. Moreover, we often do this while waiting for the distinguishing information to be offered by specialists – those privileged speakers with sufficient knowledge of the meanings of these words. They are persons really able to identify examples of these different kinds of trees, so that without them these words would have no specific usage. The point is that meaning – sufficient or not – is always in the heads of speakers, even if (as I also agree) this meaning is located within many heads that make up the communicative network of a socio-linguistic community.[21]
   In these two cases, Putnam appeals to a division of linguistic labor in order to account for the variety of meaning dimensions that may be possessed by different speakers. As he writes:

We may summarize this discussion by pointing out that there are two sorts of tools in the world: there are tools like a hammer or a screwdriver, which can be used by one person; and there are tools like a steamship, which require the cooperative activity of a number of persons to use. Words have been thought of too much on the model of the first sort of tool. (Putnam 1975, p. 229)

This is an important suggestion. However, it does not confirm an externalist conception of meaning. It is rather neutral. After all, the idea of a division of labor in language has already been suggested by internalist philosophers, from John Locke to C. S. Peirce (Smith 2005: 70-73). The former championed a theory of meaning as something constructed from internal psychological ideas. In effect, the division of labor is perfectly compatible with the fact that, even if socially shared, meaning remains in the heads of speakers, specialists or not, in different dimensions and degrees. In none of the above cases does meaning need to be located outside of heads.
   Finally, to be fair, Putnam expresses himself much more precisely in a later text (Putnam 1988, Ch. 2), e.g., by suggesting that ‘reference [as meaning] is fixed by the environment itself,’ calling it ‘the contribution of the environment’ (1988: 32). However, we can understand the word ‘fixed’ in two ways. In the first, we understand ‘fixed’ in the sense in which the external physical and social world is what ultimately produces referential meanings in our minds-heads. This is an obvious truism – something that a weak internalist (= a very weak externalist) like myself would have no desire to deny. In the second way, which Putnam has in mind, what he means with the word ‘fixed’ remains a too subtle metaphor to find an intelligible rescue except by confessing that he is speaking about reference, which no one would claim to be internal, since it is indiscutable that external things are external references of their names.

8. Now, I wish to reinforce my anti-externalist arguments discussing Tyler Burge’s social externalism of thought, which in some ways complements Putnam’s argument (Burge 1979). What Burge’s text at least implicitly suggests is that the proper content of thought or belief and propositional attitudes are external.
   I will first summarize Burge’s argument and then show that it is easy to find a much more plausible weak internalist explanation for what happens, simply by elaborating an objection already made by John Searle (2004: 284-6). In order to make it as clear as possible, instead of following Burge’s counterfactual mental experiment, I will follow Searle’s version. Suppose that a man named Oscar, residing in region A, feels pain in his thigh and therefore goes to see a certain Dr. Fugly, whom he tells:

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

Since arthritis is characterized as a painful inflammation of the joints, the doctor regards this belief as obviously false, since one cannot have arthritis in the thigh. Suppose that Oscar next travels to the very remote region B of his country and visits a certain Doctor Enoc for the same reason. But although in region A arthritis has its usual conventional meaning, in the remote region B people use the word ‘arthritis’ in a much broader sense, as referring to any kind of inflammation. Suppose that having forgotten his visit to the first doctor, Oscar once more complains to this new doctor that he has arthritis in his thigh, having in mind exactly the same thing as previously. Now, in region B, as expected, the new doctor will confirm his suspicion, agreeing with Oscar’s unquestionably true belief.
   Based on such an example, Burge’s reasoning goes as follows. Without doubt, when he claims he has arthritis in his thigh in both the first and second regions, Oscar’s psychological states are exactly the same, as is his behavior. But the thought-contents expressed in the two utterances must be different, since thoughts are truth-bearers, and the thought expressed in the first utterance is false, while the thought expressed in the second is true, although the same thought cannot be both true and false! We can even mark the second meaning of the word ‘arthritis’ with a new word: ‘tharthritis.’ Burge’s conclusion is that the contents of the thoughts cannot be merely psychological. These contents must also belong to the outside world, to the social communities where the speakers live. (Burge 1976: 106)
   Against this conclusion, it is not hard to find a commonsensical internalist-descriptivist explanation for what happens. For a healthy weak internalism (which admits that our mental subjectivity unavoidably depends on external inputs), in region B the concept-word ‘arthritis’ is the expression of an ascription rule constitutive of a meaning that 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 region B, though not in the linguistic community of region A. Thus, although the thoughts expressed in the sentence ‘I think I have arthritis in my thigh’ spoken by Oscar in the two linguistic communities are exactly the same, there is a fundamental difference that was rightly identified by Searle in the following passage:

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; my italics)

That is, when Oscar says to Doctor Fugly, ‘I believe I have arthritis in my thigh,’ he must assume that his generalized ascription rule for the predicate ‘arthritis’ belongs to the language that other competent speakers of the language conventionally apply. The whole of what Oscar has in his mind (not only actually, but also dispositionally) in his utterance in the linguistic community of region A is:

(a)  I have arthritis in my thigh… [and I am assuming that pain and inflammation in my thigh are accepted as a usual symptom of arthritis by the linguistic community of region A, to which my present interlocutor, Dr. Fugly, belongs].

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

(b) I have arthritis in my thigh… [and I am assuming that pain and inflammation in my thigh are accepted as a usual symptom of arthritis by the linguistic community of region B, to which my present interlocutor, Dr. Enoc, belongs].

Now statement (b) is true. Although the statement ‘I have arthritis in my thigh’ says the same thing, it has a hidden indexical content that differs from (a) to (b). However, this hidden indexical meaning still belongs to Oscar’s mind. Thus, it is true that if we confine ourselves to the content expressed by Oscar’s thoughts when making the same utterance in both places, we see the statements as identical. However, there is an overall difference in what the hearers have in their minds (that is, in their heads) when hearing each utterance. It is different because Oscar wrongly assumed he was following conventions accepted by Doctor Fugly in the first linguistic community, while he later correctly assumes he is following conventions accepted by Doctor Enoc in the second linguistic community.
   When he speaks with the doctor from community A, Oscar infringes on the principle that in order to achieve truth, verifiability rules constituting the content of thoughts should correctly assume the conventions of the linguistic community where the thoughts are expressed. But the correlative assumption isn’t infringed on in community B, when Oscar speaks with Doctor Enoc. The conventional truth-makers given to members of the two social communities of speakers are different, although semantic assumptions related to them remain the same.
   To be fair to Burge, we need to remember that he called attention to something important: the truth or falsehood of utterances depends on their conformity with linguistic conventions adopted by the speaker’s community. This is already a relevant point, although it does not touch the claim that anything involved in thought-contents or beliefs is outside the internal psychological realm, in some way dispersed throughout the external socio-physical environment, as a strong externalist would like us to believe.
   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 externalist point of view, narrow content is what is in the speaker’s mind, while wide content is in some way external. The healthy internalist analysis of Burge’s example allows us to propose that the narrow content of a thought restricts itself to the semantic-cognitive verifiability rule that constitutes it. This rule is expressed by the statement ‘I think I have arthritis in my thigh.’ On the other hand, the wide content of a thought is what is assumed in the speaker’s mind as the social convention that he expects to be satisfied by the narrow content.

8. Finally, one word about John Perry’s argument for the essential indexical (1979). I will be brief, since I am repeating an argument I presented in detail in another text (Costa 2014, Ch. 4). Against Frege, Perry’s view is that the senses of indexicals are inevitably tied with the external circumstances of utterances, which can be proved by the fact that one cannot translate them into eternal sentences without loss. The upshot is that, regarding indexicals, externalism of meaning is unavoidable.
   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 source of the mess only to discover that he himself is the one who is spilling sugar on the floor, and this leads him to say: (i) ‘I am making a mess,’ which changes his behavior. Now, suppose we translate his statement into a non-indexical statement like (ii) ‘Perry is making a mess.’ This (nearly) non-indexical statement cannot preserve exactly the same meaning. He could, for instance, be suffering from Alzheimer’s disease so that he has forgotten his name is Perry. In this case he would know the truth of (i), but not the truth of (ii). The conclusion is externalist: no non-indexical statement is able to rescue the whole content of an indexical utterance. Some semantic content must unavoidably belong to the world.
   However, I think there is in fact a way to preserve the whole content of the indexical, detaching it from its indexical context. It is a technique that I call transplanting: if you need to change the location of a plant, you almost never take the plant alone, but the plant together with the earth in which it is rooted… Applying an analogous technique, here is how Perry’s example appears after transplanting:

(iii) At 10:23 a.m. on March 26, 1968 in the confectionary supplies section of Fleuty Supermarket in the city of Berkeley, CA, after noticing a sugar trail leading away from his shopping cart, Perry says that he is making a mess (or: ‘I am making a mess’).

What counts now is the truth of this eternal sentence[22] (iii) in which the indexical subordinate sentence is presented after a that-clause. Although containing indexicals (‘he’ plus present tense), statement (iii) in no way refers to the indexical context, since the indexical subordinate sentence refers indirectly. It refers to what Frege called the thought (the belief-content) expressed by Perry in the subordinate sentence that follows the that-clause. Thus, protected by its surrounding description (the ‘volume of earth’ offered by the eternal sentence), the sense of ‘I am making a mess’ is here integrally transplanted without loss into the non-indexical context of a wider referring thought-content.[23] What this argument shows is that the so-called essential indexical is not essential, since we can explicitly internalize all its apparently external components.

[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). At the time, he was certainly unaware of the then recently born trope theory.
[2] It seems the real reason we distinguish between regularities that are natural laws and those that are merely coincidental is that the former are not so much relevant because they are strongly inductively grounded or resistant to refutation. Rather, they are relevant more because they are also well entrenched, that is, strongly inferentially integrated with our most plausible scientific system of beliefs. This creates the impression that our knowledge of natural laws is of something that exists by logical necessity.
[3] D. M. Armstrong defended the view that scientific laws are necessary because they are relations between universals, which explains their resistance to counterfactual examples (2010, Ch. 5). However, the price to be paid for defending this view seems too high.
[4] In a similar way we proceed as if we knew the ultimate truth and as if we had the ultimate knowledge until we discover that we were deluded.
[5] From Aristotle this distinction passed to Aquinas, Leibniz, Wolff and Kant in distinct formulations. See ‘necessità’ in Abbagnano (1968).
[6] I think this insight motivated Allan Sidelle’s view of the necessary a posteriori as the analytical result of convention (1989: Ch. 2, 4).
[7] The concept is important, since when we say that our (empirical) knowledge is justified true belief, we need to have practical certainty regarding the condition of truth. Thus, empirical knowledge is based on practical certainty (cf. Costa 2014, Ch. 5).
[8] I assume that ‘P is necessary’ means the same as ‘P has probability 1.’ Seen as a probability, the idea of a necessity without any epistemic import appears to be what it really is: nothing but an empty fetishism of necessity.
[9] As Popper clearly saw, even if we could someday find the absolute truth, we would still not be able to recognize it as absolute truth. Moreover, there are further questions, like the supposed exception of the Cartesian cogito and the question about the extension of our empirical knowledge, which I cannot address here.
[10] Hilary Putnam rejects the skeptical possibility that one could be a brain in a vat, hallucinating an unreal virtual reality produced by a supercomputer on the planet Omega or so (1981, Ch. 1), but his objection is controversial, to say the least. According to Putnam’s externalist point of view, if I am a brain in a vat, in order to have thoughts like those of brain, vat, water, etc., I need to be in causal contact with these things; hence, once I have these thoughts, I cannot be a brain in a vat. The problem with Putnam’s argument is that it ignores the flexibility of language. There is no reason to believe that electrical patterns in the brain cannot misleadingly appear to us as brains, vats, water, etc., being falsely represented and intended as such, insofar as we admit that outside factors (like the supercomputer on the planet Omega or anything belonging to a real external world) could systematically produce these patterns.
[11] God would be the only being able to know created things in their metaphysical necessities de re, since he knows them by sustaining them in their existence.
[12] ‘Colmio’ means triangle in Finnish.
[13] In the last case because imagine, like doubt, are verbs of propositional attitudes, what do not allow extensional inferences.
[14] Today there are several competing theories of parenthood (genetic, labor-based, intentional, causal and pluralistic ones), and there is no consensus on the right cluster of criteria (cf. Brake & Millum 2016, sec. 4).
[15] The symbol ‘∆t’ is more correct. The rod served as a standard not only at to, but during all the time in which it was conventionally designated to have its function.
[16] I say ‘essentially’ because Putnam admits that surface descriptions (stereotypes) and classifications (semantic markers) are internal secondary mental features of meaning (1975: 269).
[17] For a more detailed argument, including a more careful neo-descriptivist analysis of the meanings of ‘water’, see Costa 2014, Ch. 3.
[18] For instance, the main definition in a Merriam Webster dictionary contains elements of both popular and scientific nuclei of meaning. It is the following: ‘water = the liquid that descends from the clouds as rain, forms streams, lakes, and seas, and is a major constituent of all living matter and that when pure is an odorless, tasteless, very slightly compressible liquid oxide of hydrogen H2O which appears bluish in thick layers, freezes at 0°C and boils at 100°C, has a maximum density at 4°C and a high specific heat, is feebly ionized to hydrogen and hydroxyl ions, and is a poor conductor of electricity and a good solvent.’ (The descriptive relevance of the dispositional and scientific properties of water and their presentation in dictionaries was already noticed by Avrum Stroll, 1996: 71).
[19] We need to know only the most common descriptions, and this is enough to our use of the word adequately in more or less vague contexts. We do not need to know all the descriptions of water; even chemists do not know all of them. Did you know, for instance, that when water is cooled to near absolute zero (-273.15° C.), it assumes a liquid  state?
[20] In a later text (1988: 29), Putnam notes that if I know that a beech isn’t an elm, I also know that an elm isn’t a beech tree, which means that my knowledge is symmetrical, so that the representations are the same; furthermore, the words ‘beech’ and ‘elm’ are only phonetic shapes without meaning (1988: 27). But the semantic element here is just that we know that with these two names we mean different kinds of trees, for the description ‘A beech tree is a tree different from an elm tree’ is sufficient to allow us to insert these words in discourse as referring to different kinds of trees that can be in an asymmetrical way correctly classified by others.
[21] We can also find the right information in books, in the internet, etc., but in order to be there it must first in some way or measure be located in human heads.
[22] This is not a perfect eternal sentence, but it is questionable if a statement without any kind of indirect indexical aspects is possible. If I say, The Earth is round,’ I am already localizing the subject in our solar system.
[23] Phenomenal elements are obviously lost, but they do not belong to the conventional meaning. For a reconstruction of Frege’s indirect reference in subordinate sentences, see the Appendix of Chapter IV, sec. 5 (iv).

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