On basic logical knowlldgl

Philosophical Studies

Volumn 106, Issue 1-2, 2001, Pages 41-85

  Wright, Crispin ^a  

^a Och Spine at New York Presbyterian Hospitals   (United States)

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EID: 34247506097     PISSN: 00318116     EISSN: 15730883     Source Type: Journal    
DOI: 10.1023/a:1013100915387     Document Type: Article

References (19)

1. Paul Boghossian and I have discussed the present and related issues over a number of years, and it is a pleasure to have the opportunity to record something of the cross-flow of our ideas in print. My paper here is a development of comments made on Boghossian's presentation of the same title at the Pacific Divisional meetings of the American Philosophical Association held at Albuquerque in March 2000. That exchange grew out of an earlier one, on "Concepts and the A Priori", staged at the Epistemology and Naturalism Conference held at Stirling in May 1997 under the aegis of the Consciousness in a Natural World project. (A version of Boghossian's paper on that occasion has since been published as "Knowledge of Logic" in Paul Boghossian and Christopher Peacocke, eds., New Essays on the A Priori, Oxford: the Clarendon Press 2000, pp. 229-254.) For helpful criticisms and observations, I would like to record my thanks to participants in the discussions at Stirling and at Albuquerque, to Bob Hale who commented on an earlier draft of my present paper, and to Paul Boghossian.
2. Grundlagen §105.
3. This volume at pp. 1-40.
4. Remarks on the Foundations of Mathematics I, §156.
5. It may be countered that there is generality in the apprehension of logical form. In apprehending that a proposition is of a certain form, we do precisely apprehend a generality: one which quantifies over all tokens of the proposition in question. Generality of this kind, however, is not germane. If I perceive that the mug on my desk is blue, I likewise apprehend a generality: that all mugs like that are blue. But the generality apprehended in grasping the validity of a basic rule of inference is not ofthat (trivial) sort: if it were, one could not identify an instance of the rule except via a judgement about its validity (just as one could not verify that a mug was relevantly like that except via the judgement that it was blue). Whereas the whole point about knowledge of the validity of a rule of inference is that, in tandem with the identification of an instance, it grounds the judgement that the instance is valid.
6. - or even for agnosticism about it -
7. It is, for instance, arguable that no-one could coherently believe that they had a counterexample to modus ponens. For that would involve accepting instances both of P and of If P, then Q while, doubting the corresponding instance of Q, whereas it is plausibly constitutive of a grasp of the conditional - and hence a necessary condition of possession of any belief configuring it - that one precisely not be inclined to doubt what immediately follows by modus ponens from others of one's beliefs. Likewise, any demonstration that modus ponens was unsound when used in tandem with other rules would perforce depend on some sort of proof-theory in which to conduct it; and it seems hardly credible that such a proof-theory could avoid reliance on conditionals and their usual associated rules of inference. These thoughts are pursued by Bob Hale in forthcoming work.
8. This volume at pp. 1-40.
9. This is a close relative of the defensive thoughts outlined in footnote 7 as above and, as such, is not - it seems torn me - really to Boghossian's larger purpose. As soon as we try to harness it to that purpose - addressing the issue not of our commitment to modus ponens but of its objective validity - we confront a dilemma: is the intelligibility of the question whether modus ponens is valid taken to imply that it is valid, or not? If not, then to suppose that we could not so much as understand the question unless we had the prior practice of inference in accordance with modus ponens carries no implications of its actual validity. On the other hand, if the very intelligibility of the question is taken somehow to imply the validity of the rule, then the issue becomes with what right our practice in accordance with modus ponens (and other rules for the conditional) is assumed to constitute an intelligible meaning for that question. (As will become clear in the next paragraph, it seems that Boghossian was thinking of the situation in terms of the second alternative.)
10. A reader may wonder how this thought would play in relation to the rulecircular derivation of Denying the Antecedent given at the end of §5. Boghossian would claim presumably that, just as the tonk-niles fail to establish any meaning for 'tank', so Denying the Antecedent, taken as a conditional-elimination rule, fails, when teamed with Conditional Proof as the corresponding introduction rule, to establish any meaning for "If ..., then ... ". In that case, both derivations may be rejected on the ground that the Meaning Postulates they respectively use as premisses actually have no content and so may not be used to support any conclusion at all. But this could not be the objection to the derivation for Denying the Antecedent in the scenario where a meaning is independently established for "If ..., then ..." - for instance, by practice in accordance with modus ponens and Conditional Proof. Rather Boghossian's point would then be, I take it, that if a content is established for "If ..., then ..." independently of any practice in accordance with Denying the Antecedent, then the latter is not a meaningconstituting rule, and the use of it in the bogus derivation thus has to answer to the simple internalist account of the acquisition-condition, and so will confer warrant on the conclusion only if we are already justified in regarding Denying the Antecedent as a valid rule. I confess, though, to some uncertainty about this. 11 For an overview of the issues, see Bob Hale and Crispin Wright, The Reason 's Proper Study (Oxford: the Clarendon Press 2001).
11. This volume at pp. 1-40.
12. See chapter 3 of Robert Nozick Philosophical Explanations (Oxford: the Clarendon Press 1981).
13. If this line of thought is compelling, it scotches immediately all prospect of a thinker's coming to learn of necessities by reasoning from meaning postulates - for instance, in the fashion earlier illustrated in the template for tonk-Introduction and Denying the Antecedent. For given that it is contingent what any expression means, any model of that broad kind must proceed from contingent premisses (whether or not they are plausibly knowable a priori) and thus can ground no more than knowledge of the truth, contrast: the necessity, of the conclusion.
14. Chrysippus' Dog provides another.
15. Mind 4 (1895), pp. 278-280.
16. Here is Boghossian's original expression of the argument: According to [simple internalism], one can only be justified in inferring a given conclusion from a given premise according to a given rule R, if one knows, or justifiably believes, that R has a particular logical property, say that it is truth-preserving. Unless you know that R is valid, you cannot use R to derive justified conclusions. So, for example, no-one simply reasoning from the particular proposition p and the particular proposition 'if p then q' to the proposition q could ever be justified in drawing the conclusion q. In addition, the thinker would have to know that his premises logically entail his conclusion. Clearly, however, the intention cannot be that a thinker know this separately for every inference that his is tempted to draw. That would require a thinker to know an impossible number of things. Rather, the idea is that the thinker has the general knowledge that the rule implicated in his reasoning is valid, that any inference of the form MPP is truth-preserving. Let's assume, then, for the purposes of argument that our thinker S has this knowledge: he knows that any argument of the form MPP is truthpreserving. How does this help him to be justified in justifiably [sic] inferring the particular proposition q from the particular premises p and 'if p then q'? The answer might seem quite simple. The general knowledge about modus ponens allows him to appreciate that the particular inference he is drawing is itself truth-preserving and so justified. But how does this general knowledge help him to appreciate this? Is there any alternative but to picture our thinker as reasoning, however tacitly, as follows: (a) any inference of the form MPP is truth-preserving. (b) this inference is of the form MPP. (c) therefore this inference is truth-preserving. Any such reasoning, however, would itself involve a step using modus ponens. Here, however, we are on the verge of launching an unstoppable regress. If the unsupported modus ponens inference could not generate justified belief all by itself, how will backing it up with general knowledge of the validity of modus ponens help? Bringing any such knowledge to bear on the justifiability of the inference would itself require justified use of the very same sort of inference whose justifiability the general knowledge was supposed to secure. What this Lewis Carroll-inspired argument shows, it seems to me, is that at some point it must be possible to use a rule in reasoning in order to arrive at a justified conclusion, without this use needing to be supported by some knowledge about the rules that one is relying on. It must be possible simply to move between thoughts in a way that generates justified belief, without this move being grounded in the thinker's justified belief about the rule used in the reasoning.
17. This volume, pp. 1-40.
18. The regressive thought is that if the information (3) is needed to justify the original inference at all, then - since that justification itself proceeds by inference - more information, so the simple internalist must concede, will be needed to underwrite the inference involved in the justification; and since that underwriting in turn will be inferential, yet more information will be needed to justify it... and so there is no end to the collateral information necessary to justify any inference. One doubt whether the regress is vicious turns on the reflection that all the successive items of information involved in any particular case are consequences of the first. In the above example, for instance, the successively required items of collateral information, represented as conditionals, look like this: (3) P-4 ((P → Q) → Q) (4) P-4 ((P → Q) → ((P → ((P → Q) → Q)) → Q)) (5) P → ((P → Q) → ((P → ((P →Q) → Q)) → ((P → ((P → Q) → ((P → ((P → Q) → Q)) → Q))) → Q))) and so on. Since each nth one of these differs from its predecessor merely by substitution for the latter's right-most occurrence of 'Q' of a formula of the form, 'n - 1 → Q' - it may seem that Hero doesn't need to be a terribly long-sighted logician to conclude that he can obtain - and therefore, in effect, already has - all these items of information just provided he has the first, and that he is therefore in position to justify each of the inferences involved in the regress. Which is accordingly harmless. It my be countered that, in order to claim the successive items of information of this kind, Hero will once again have to be in position to justify inferences to those items of information as conclusions. That will once again call for items of warranting collateral information, this time concerning entailments between earlier and later items in the above series of conditionals. But Hero can reply again that his knowledge of each of the relevant entailments - (3) ⇒ (4), (4) ⇒ (5), etc., - may be obtained by inference from the general reflection about the structure of their antecedents and consequents just outlined; and the obtainability of this knowledge is something he can foresee in advance. Of course, it takes inference to move from that general reflection to particular cases. And the internalist will have to regard the warrant for such inferences as once again depending on collateral information that those inferences are valid. But the reply will be that the requisite items of collateral information - each to the effect that a statement of one the above entailments, (n) ⇒ (n + 1), is itself entailed by an appropriate statement of the general reflection - can be recursively corralled by a single act of intellectual insight. In short, the merchant of regress charges that the simple internalism cannot explain how any of the relevant inferences in one of these series are justified since no end of collateral information is presupposed in every case; and the internalist responds that Hero can access the needed information without limit - not indeed by successive plodding inferences but by a single insight that each of them goes through; that he can know that he can do so; and hence that he is fully entitled to make each of the inferences concerned. This situation obviously needs further attention if it is to be clear if there is a winner.
19. Preface to the Critique of Pure Reason, 2nd. Edition, B xxxix, Kemp Smith tr. p. 34.