Friday, March 25, 2005

Nominalistic Validity?

Hilary Putnam is among the many helpful philosophers who have been informing my thought as of late. His wonderfully and compactly written Philosophy of Logic has been very helpful. Putnam begins his small book by stating some of the generally accepted principles of logic. He includes the principle of validity in the following familiar inference:

All S are M
All M are P
(Therefore) All S are P

He also includes the usual round of suspects: the laws of identity, contradiction, and excluded middle. Putnam notes that each of these general principles have been disputed by more than one contemporary philosopher. Note that this book was written in 1971; but I would imagine that this statement still holds true.

It is obvious from the first pages that Putnam wishes to show that the nominalistic view of the general rules of logic is much mistaken. In reference to the principle of valid inference he states that most logicians are likely to say:

(A) "For all classes S, M, P: if all S are M and all M are P, then all S are P."

A nominalist though is more likely to write:

(B) "The following turns into a true sentence no matter what words or phrases of the appropriate kind one may substitute for the letters S, M, P: 'if all S are M and all M are P, then all S are P'."

For the nominalist, the idea of "sentences" and "words" are much more "concrete" than the entities of "classes". So, based upon (B) we can see that a schema (or wff) is valid for the nominalist "just in case all substitution-instances of S in some particular formalized language L are true." Putnam believes that the logician wants to say more than this though. Validity should "mean that it is correct no matter what class-names may be substituted."

Putnam's desire to adopt (A) becomes more attractive when we see that the nominalist suggestion for validity (B) turns out to have a problem which mushrooms quickly. For if we adopt (B) we will not have one notion of validity but an infinite series of notions: validity in L1, validity in L2, validity in L3, etc. Since validity only relates to a particular formalized language L for the nominalist we must have different notions of validity for every type of language L used in logic. A most unwanted consequence.

We could avoid this maybe by stating "a schema is valid just in case all of its substitution-instances in every language L are true." But, as Putnam notes, it is highly questionable whether the notion of all possible formalized languages is any more "concrete" than the notion of "classes".

Is anybody else familiar with the nominalism-realism debate surrounding logical or mathematical entities? I would appreciate any helpful direction.

Tuesday, March 01, 2005

The Consequences of Eliminativism

Eliminative materialists like Stephen Stich and Paul Churchland have proposed a theory of "mind" (mind is in scare quotes because they eliminate its existence; strictly speaking they only have a theory of the brain) that is fascinating, creative, amenable to science, and that challenges the traditional conceptions about the mind. Most significantly, eliminativism proclaims that neuroscience is sufficient to explain the mental life, which has traditionally been understood using folk psychological terms like belief, desire, and intention. While rejecting folk psychology may be most consistent with a physicalistic/scientistic ontology, this rejection of folk psychology has some very strange results.

First, consider the enormous burden of proof that is required to deny that anyone has had a belief, desire, or intention. Lynne Rudder Baker has captured this point soundly in her criticism of physicalism Saving Belief (Princeton, NJ: Princeton UP, 1987):
If no one has ever had a belief or intention, it is unclear how to interpret any inscription to be a claim that such-and-such and, in particular, how to construe as meaningful a claim advancing the view that no one has ever had a belief. In the absence of some indication of how meaning would be possible without beliefs or intentions, one who denies that common-sense conception of the mental is akin to a logician who takes the moral of the semantic and logical paradoxes to be that all logic is wrong and just leaves it at that. Or, to use another of David Austin's suggestive analogies, it is as if someone were to write on a blackboard, "The following sentences have no meaning or interpretation," and then, three or four sentences down, repeat that same sentence. We would be entitled to puzzlement. We can hardly assess a claim that takes away everything we possess to understand it. (page 114)
When one considers that it follows from eliminativism that no one believes in eliminativism and there are no beliefs that confirm or deny eliminativism, this consequence of eliminativism can be downright baffling.

The aforementioned consequence of eliminativism is well known. But what other consequences follow from eliminativism? Consider what Stich himself suggests [From Folk Psychology to Cognitive Science (Cambridge, MA: MIT, 1983), 242], "Might it be the case that ordinary folk psychological ascriptions will turn out, quite generally, not to be true? The answer I have been urging is that this is a serious possibility.... If we had to renounce folk psychology, we should probably have to renounce the notions of personhood and agency as well." Baker draws thirteen consequences that follow if eliminativism is true (Saving Belief, 130-32). (1) The ability to predict others' behavior would become inexplicable. Suppose I call you on the phone and invite you to dinner at 7:00 on Saturday--without any beliefs, intentions, or desires, it would be amazing if I actually prepared dinner for you and you showed up. (2) Commonplace interaction among people and what is said about such interactions would become mysterious. (3) Behavior could never go wrong. Without folk psychological concepts like intention, one could never be said to have done something unintentionally or by accident or by mistake. Without any distinction between intentional and unintentional actions, justifying and excusing behavior cannot be sensibly maintained. (4) Almost every explanation that anyone has ever given would be false. (5) There would be no distinction between what we call lying and an honest mistake. (6) Every moral judgment would be false or senseless. (7) Nothing would ever have mattered to anybody. (8) It would be a total mystery why we say the things we do (though not why we emit the noises we emit) and why we give the explanations of our actions that we do. (9) It would be a miracle that we are able systematically to utter truths. (10) Reports of deliberation and decision would be false. (11) What one does would be totally unrelated to what one reports that she thinks she is doing. (12) Most of applied psychology, from market research to the various psychotherapies, would be bogus. (13) The explananda of psychology would become problematic.

Now this, so far, has not been an argument against eliminativism. Thus far, I have only shown that "if elimantivism is true, then these consequences follow." But I think we can turn this into an argument against eliminativism. Since eliminativism entails the denial of numerous facts most people find more plausible than eliminativism itself, we could employ modus tollens on the eliminativist. In other words, eliminativists want to argue that since eliminativism is true, we must reject folk psychology and accept the 13 consequences noted above. I, on the other hand, want to argue that since we cannot accept the 13 consequences noted above, eliminativism must be false.