In an earlier post, I provided a rough characterization of eliminative materialism (EM). Here is a more technical exposition for the stout of heart. If EM is true, then there are no beliefs. But what about the belief that EM is true, a belief that one would expect eliminative materialists to hold? If we exfoliate this question will we find an objection to EM? Let's see.
If it is true that there are no beliefs, then there is no belief the content of which is the proposition expressed by 'There are no beliefs.' So far, no problem. But if 'There are no beliefs' is true, then no one believes it. But also: no one doubts it, rejects it, entertains it, or practices epoché with respect to it. For none of these propositional attitudes can stand if belief falls. In other words, if 'folk psychology' is a false theory, and 'belief' is vacuous, then the same goes for 'doubt' and other mental terms. One could then neither accept nor reject a proposition. One could not even 'entertain' a proposition, i.e., just consider it without either affirming it or denying it. Nor could one withdraw one's intellectual assent from a proposition that one had previously affirmed. Furthermore, no one could seek reasons for its truth, nor deduce consequences of its being true. To deduce a consequence is to enact an inference. But if there are no beliefs, then there are no inferences either. Inference is a mental process. It is not to be confused with implication which is a relation that can subsist independently of minds.
Now if you have any common sense, that there are no beliefs, inferences, and the like should smack of lunacy, of a "lunatic philosophy of mind" in Arthur Collins' phrase quoted in an earlier installment. (How could there be no inferences? We draw inferences day and night: I hear the sound of the garage door opener, and I infer that wifey is back from the store.) But philosophy does not genuflect before anything, not even common sense, so let's proceed in our search for an argument against EM. In other words, one cannot refute a philosophical thesis merely by appeal to common sense since if we relied entirely on common sense there would be no philosophy in the first place. (In the days of Aristotle it was common sense that some humans are naturally slaves and therefore justifiably enslaved.)
2. The proposition expressed by 'There are no beliefs' is supposed to be true. But what are propositions? Could one have the concept of a proposition without the concept of a propositional attitude such as belief? I don't think so. Fregean propositions — the senses of sentences in the indicative mood from which all indexical elemnts have been expunged – just are the accusatives of the propositional attitudes: thus a proposition is the content of a believing or a desiring or a wishing or a willing, etc. Now if EM is true, then there are no propositional attitudes. It follows that there are no contents of such attitudes and no propositions. And if there are no propositions, then there is no proposition expressed by 'There are no beliefs.' If so, then 'There are no beliefs' is neither true nor false. For propositions are the vehicles of the truth-values.
We appear to be approaching a knock-down refutation: if 'There are no beliefs' is true, then nothing is either true or false; hence 'There are no beliefs' is neither true nor false.
3. But there is trouble even if we don't identify propositions with the contents of the propositional attitudes. Suppose we just say that propositions are the vehicles or bearers of the truth-values, and we leave propositional attitudes out of it. Propositions, then, are the entities that are appropriately characterizable as either true or false. Among these propositions is the one expressed by 'There are no beliefs.'
Now could truth be out of all relation to belief and knowledge? Truth is a property of (some) propositions. If there are no beliefs, then no proposition is believable (able to be believed), and no true proposition is knowable. For one cannot know what one cannot believe. Knowledge entails belief, though not vice versa. So I argue as follows:
A. If a proposition is true, then it is possibly such that it is believed by someone.
B. If EM is true, then there are no beliefs and no proposition is possibly such that it is believed by someone.
C. EM is true. (Assumption for reductio ad absurdum) Therefore
D. There are no beliefs and no proposition is possibly such that it is believed by someone. (From B and C by Modus Ponens)
E. No proposition is possibly such that it is believed by someone. (From D by Simplification)
F. Some proposition is possibly such that it is believed by someone. (From A and C by Universal Instantiation and Modus Ponens)
Therefore
G. It is not the case that EM is true. (From E and F by reductio ad absurdum: the conjunction of E and F is a contradiction)
The crucial premise in this reductio is (A). What it says in effect is that the concept of truth is the concept of something that cannot be coherently conceived except in relation to the concepts of belief and knowledge. Whether or not you agree that this is self-evident, it is surely more evident than the well-nigh crazy view that there are no beliefs. Since EM entails that there are no beliefs, the rational course is to reject EM.