Identity and Synonymy
It is commonly supposed that “water is H2O” is both known to be true and synthetic (hence a posteriori). I think this is not so. The reason is not difficult to see: if the sentence is known to be true, then speakers will associate the same descriptions with each term (following Leibniz’s law), so the sentence will be analytic for them. Consider a group of scientists working in the same lab and knowing the identity of water and H2O: when they speak to each other they use the two terms interchangeably, knowing that the denoted things are identical. For them, the terms are synonymous and the sentence “water is H2O” is analytic. It is always possible to substitute these terms in belief contexts, given that everyone knows the truth of the identity statement (and knows that others also know it). Nobody thinks there is any more to one of the denoted things than the other: there is complete ontological parity, utter indiscernibility. They might even use “hydrox” as a more vernacular term than “H2O”, so producing the identity statement “water is hydrox”, which is also analytic (everyone assents to this sentence). Before the discovery of the identity people would suppose the two terms had distinct references, but afterwards the difference of meaning disappears. It is the same with Hesperus and Phosphorous: once the identity is discovered and generally accepted “Hesperus is Phosphorous” is analytic, since whatever is believed true of one is believed true of the other. This means that being synthetic is not compatible with being known to be true: no identity statement can be both. Of course, a false identity statement can be synthetic, given that the two terms have distinct references. All this seems clear enough, but matters turn murkier when we come to statements like “pain is C-fiber firing”. Here we are encouraged to believe that the statement is both true and synthetic—informative, a posteriori. It could have those attributes and be false, but it is said to be both true and synthetic; it is “empirically true”. This combination is supposed to be exemplified in such statements as “water is H2O”, thus providing a precedent for the claim of identity between pain and C-fiber firing. But I just argued that the former case is not an example of a synthetic identity statement. So, if the latter case is synthetic, as it seems to be, then this can be so only because it is not true (and known to be true). The explanation of its appearing not to be analytic is simply that it is not true—the two terms refer to distinct properties. If it were known to be true, then speakers would associate the same descriptions with each term, thus rendering the statement analytic. This doesn’t happen because speakers can see that the two terms have different denotations, so the statement can’t be analytic. The case is essentially like “creature with a heart” and “creature with a kidney”: the two predicates are coextensive (the properties denoted are correlated), but the properties are numerically distinct. Similarly, “pain” and “C-fiber firing” are coextensive (the properties are correlated), but the properties themselves are numerically distinct. This is the reason the statement is not analytic: there is more to pain than C-fiber firing, as any competent person can see. That is, the identity theory is false. And its characteristic formulation has no precedent in the sciences—no identity statement can be both known to be true and synthetic. Therefore, we cannot be lulled into accepting the truth of “pain is C-fiber firing” by alleged cases of known synthetic identity in the (respectable) sciences. If that sentence were an accepted identity sentence, then it would have to be analytic; but it isn’t, so it must be false. The explanation of its apparent non-analytic status must be that the properties are distinct, recognizably so. In other words, the identity could only be known to be true by being a priori—as in the case of “water is H2O”. Once that statement is known (or believed) to be true it becomes analytic, as it is for my group of savvy scientists; but this can’t happen with “pain is C-fiber firing” for the simple reason that the alleged identity claim is patently untrue. Ifpeople came to accept it as true, then it would be analytic for them; but it clearly isn’t analytic for anybody, so it cannot be true. There is no obstacle to water being recognized as identical to H2O, since there is demonstrably nothing more to water than H2O; but there is an obstacle to recognizing that pain is identical to C-fiber firing, namely that there clearly is more to pain than C-fiber firing. If that were not so, then the identity statement could be happily analytic—but that it can never be. The sentence is robustly synthetic, permanently informative, indelibly a posteriori: but this is incompatible with the truth of the identity statement. For, if the statement were true, it would have the status I attributed to “water is H2O”—an analytic truth. The fact is that there is no meaningful analogy between “water is H2O” and “pain is C-fiber firing”. Accordingly, the only way to make good on materialism is to provide an a priori analysis of the concept of pain—just the kind of thing attempted by the analytical behaviorists and functionalists. The idea of an empirically true central state materialism is a chimera born of a faulty analysis of so-called theoretical identifications in science. The mind-body problem requires an a priori analysis of the mental. No adequate solution can take the form of an a posteriori synthetic reduction of the mental to the physical. None of the standard alleged analogues have the properties required: “heat is molecular motion”, “light is a stream of photons”, “genes are strands of DNA”, etc. These all involve post-discovery synonymy, produced by the operation of Leibniz’s law. Once you discover that Hesperus is Phosphorous the names “Hesperus” and “Phosphorous” become synonyms for you, intersubstitutable everywhere salva veritate. There is no such thing as a known synthetic identity.
 It might be said that this is too strong, because some identity statements contain definite descriptions that enable them to be both known and synthetic (“Benjamin Franklin was the inventor of bifocals”). But this is to overlook the point that such descriptions will typically contain terms that refer to distinct properties or objects. In cases in which this isn’t so we get full synonymy, as in “the bachelor at the back is identical to the unmarried man at the back”. It is really always reference that ultimately determines whether words are synonymous or not.