Maybe there are two kinds of positions we can call empiricism. First, radical empiricism: there are no propositions justifiable a priori, but only a posteriori. Second, moderate empiricism: there are propositions justifiable a priori, but they are all analytically true. I am interested in arguing against the second of those by tackling the concept of analyticity.
Point 1: Claiming we are justified in believing P because it is analytic requires claiming we can recognize P is analytic. Too strong a conception of analyticity and it becomes as mysterious (i) how we can recognize analyticity as (ii) how we could have the sort of rational insight rationalists claim we do.
Point 2: There is neither an analytic nor an a posteriori way from (1) our justified beliefs of particular propositions about our experience to (2) our justified beliefs of general propositions about the world — perhaps unless one is willing to be a phenomenalist about the external world, for instance: the world is a logical construction out of sense-data.
Extra point: Phenomenal conservatism seems literally irrefutable, and it yields a massive amount of a priori justification of non-analytic propositions — but without the claim that there is some rational insight involved. See this essay for a defense of this point.
I will first proceed to a defense of point one. Let us examine various concepts of analyticity to see if my contention is true.
I. P is analytic if P is logically true. Therefore, we must be able to recognize logical truth. I would state it thus: we must know that a certain argument-schema preserves the truth of its premises into its conclusion. For instance, we must be able to recognize “P & P→Q” implies “Q”. For longer logical formulae, their truth is not immediate, and we must be able to apply logical operations to decompose them into simpler logical formulae we can see are jointly true. However, what is the account of the empiricist of how we grasp such logical truths?
I.A. Logical truths are linguistic stipulations. We can see they are true because we stipulated them to be true. This response prevents us from understanding how logic applies to the real world. See section II.
I.B. We do not grasp logical truths. Our brains were designed by evolution so that we naturally believed them. I think this is the response the empiricist will give if it wants to avoid postulating any ability to mentally understand something (substantial) is true, without appeal to experience. It will include logic alongside anything else of substance. It implies that our justification for believing in logic stems from our knowledge of evolution. However, it seems that our knowledge of evolution depends on logical statements — a basic of the internalistic foundationalist credo, which I believe in. Therefore, our justification to believe evolution stems from logic. This is circular, and the empiricist is thrown into skepticism about any substantial claim, since it can never erect anything to justify their belief in logic.
II. P is analytic if P is a linguistic stipulation. Note to myself: Grice, Haack, and others have written on the relation between logical connectives (and other logical paraphernalia) and their ‘counterparts’ in natural language. Anyhow, let’s take a clear example a linguistic stipulation: logical truths. See the truth table we defined for ‘→’:One can readily see from this definition of T, F, and →, that every time P is attributed T and P→Q is attributed T, we have that Q happens to be attributed T too. Modus ponens is equivalent with this. Let ‘v(P) = T’ mean P is attributed T, and ‘v(P) = F’ mean P is attributed F. Then, we have that: v(P) = T and v(P→Q) = T imply, by definition, v(Q) = T.
What sense are we to make of the symbols ‘T’ and ‘F’, though? We can just define T to mean ‘truth’ and F to mean ‘false’. Are we left with the same meaning for the word ‘truth’ as we had before our stipulations? We would have that ‘v(P) = T’ means P corresponds with the world. Now we have that, by definition, when P corresponds with the world and when P→Q corresponds with the world, Q corresponds with the world too.
Wow! We just got substantial knowledge of the world from three pieces: the definition, the knowledge that v(P) = T, and the knowledge that v(P→Q) = T. Now, what does it mean to say that P→Q corresponds to the world? Whatever it means, it must be bounded by our definitions. So we have that P→Q corresponds with the world in two situations: (s-1) when P does not correspond with the world, and (s-2) when Q corresponds with the world. So to know that v(P) = T and v(P→Q) = T, we must already know v(Q) = T. Therefore, there is no way to ever use modus ponens. A dire consequence!
We can see the same pattern with all other basic logical truths. With modus tollens, we have that v(P→Q) = T and v(not-Q) = T implies, by definition, v(P) = F. — (Note that v(not-Q) = T implies, by definition, v(Q) = F. We have as well that v(not-Q) = F implies, by definition, v(Q) = T. This is all the meaning of ‘not’, these two definitions.) — But you can only know that v(P→Q) = T if you know that v(P) = F or if you know that v(Q) = T. Once more, we have a basic logical tautology that is never applicable to gain knowledge in any situation. (That is what you get for making molecular sentences strictly truth-functional — that is, strictly stipulated. They have no meaning outside their truth-functionality.)
Check out the principle of excluded middle: P or not-P. Here is a low-definition definition for ‘or’:
We have defined that v(P) = T iff v(not-P) = F. Therefore, we cannot have that v(P) = T and v(not-P) = T. Neither can we have that v(P) = F and v(not-P) = F — by definition. So the principle of excluded middle becomes a logical truth. However, we know it to be false about future contingents, and about vague statements, and about statements about incomplete fictional entities. Therefore, our definition has lost connection with reality. We can no longer consistently hold that ‘T’ means the same as the ordinary word ‘truth’, because it says either P corresponds with the world, or not-P corresponds with the world, thus saying that v(P or not-P) = T in all interpretations of P and not-P — and this we know is not a truth in the ordinary meaning of ‘truth’.
The empiricist sure wants to have a logic that yields T to true statements. Finding out what this logic is — that’s not a matter of linguistic stipulation. As we have seen, not all stipulations will make “T-statements” true statements. Specifically, we saw that the stipulation for ‘not’ above either (i) blows up the stipulated logic by making a false statement true, viz. the principle of excluded middle, or (ii) does not correspond to what ‘not’ means in common parlance, viz. ‘is false’ — it could mean ‘false or undetermined’ instead, for example. Now “F-statements” are not false statements, but false or undetermined statements. It seems I have rediscovered the problem of interpreting logical connectives and logical truth. Here are the moves the empiricist can make in response:
II. A. Bite the bullet: our interpretation of the formalism should be based on the workings of phenomena we want to explain, and this will be only doable a posteriori. We interpret it so that it comes out true. Consider what S. Haacks says in the preface of Philosophy of Logics: “In view of the existence of alternative logics, prudence demands a reasonably radical stance on the question of the epistemological status of logic.”
But this means logic is utterly uninformative until we verify how the world works — until then, we’ll have no justification in believing our logic preserves truth. (For instance, James Ladyman has for decades examined whether the recent developments of physics shed any light on the truth of the principle of identity of indiscernibles.) However, how could we find out the workings of the world without applying logic in the first place? How could we do science without any logic? (See my defense of point two below for this.)
Here is another problem: it seems we can verify a priori the ‘workings’ of fictional statements, or vague statements, or statements about future contingents. This means that the empiricists should rather. . .
II. B. Concede defeat: finding out the true logic, or the true logic when it comes to a certain range of phenomena, is at least once doable a priori. This response is no fun, because it is easy on me. But it seems forced once we consider fictional, vague, and future-contingent statements. However, fictional statements seem to be merely linguistic, as well as vague statements. But statements about future contingents do not. Perhaps reality is deterministic, or perhaps the future exists in the same sense the present exists (except that it doesn’t exist now), but this does not mean that if the future were contingent, then statements about it would be indeterminate. Does this follow logically from the definition of ‘future’ and ‘contingency’? It does not seem so.
Anyhow, some logic must be discoverable a priori if we want to have some rational inquiry of the world. Which leads me to the next point.
I will now defend point two.