Philosophy and Phenomenological Research Vol. LXV, No. 1 , July 2002

Can Arboreal Knotwork Help Blackburn out of Frege’s Abyss?

BOB HALE

University of Glasgow

An early objection to Simon Blackburn’s first attempts to breathe new life into expressivism-by solving the Frege-Geach problem-was that whilst viewing compound sentences featuring moral components as expressive of (higher-order) attitudes towards combinations of (doxastic or normative) atti- tudes might enable one to make out that a thinker who, to take the usual example, asserts the premisses but will not accept the conclusion of a moral modus ponens is at fault because they are involved in a “clash of attitudes”, this does no justice to the data of the problem, since the failing here is logi- cal, not just moral or more generally practical. Blackburn claims to have an effective answer to this objection-a way to see how, as he now puts it,’ expressivism can after all “deliver the mighty ‘musts’ of logic”. I remain unconvinced.’

The general idea, as I understand it, is to explain the use of conditionals, disjunction, etc., not in the usual way, by giving their truth-conditions, but saying what kinds of complex commitment-to combinations of beliefs or other attitudes-a speaker incurs by asserting them, i.e. by giving what

’ Ruling Passions, p. 72. Some references to relevant work can be found in Blackburn’s footnote 15. See also Crispin Wright’s “Realism, Anti-Realism, Irrealism and Quasi- Realism” in P. French, T. Uehling, Jr., and H. Wettstein (eds.), Midwest Studies in Philosophy 12 and Max Ktilbel “Expressivism and the Syntactic Uniformity of Declarative Sentences”, Cri’ficu 29, pp. 3-51 and “Expressivism and the Geach Objec- tion”, in G. Meggle (ed.), Perspectives in Analytical Philosophy, Berlin: de Gruyter, 1997. Something somewhat like to the answer Blackbum now seems to favour was advanced in his “Attitudes and Contents”, Ethics 1988. I raised a number of difficulties for that earlier version in “Can there be a logic of attitudes?” in John Haldane & Crispin Wright, (eds.): Reufity, Representation C Projection, Oxford Oxford University F’ress 1993. Here I shall focus on what he says in his new book. The difficulties I shall raise are additional to and largely independent of those pressed in that paper. 1 gather from my colleague Jimmy Lenman that difficulties related to those I am going to press are pursued in Nicholas Unwin’s paper “Quasi-Realism, Negation and the Frege-Geach Problem” Philosophical Quarterly 49, 1999, and in an as yet unpublished paper by him on Allan Gibbard’s theory. I regret that Unwin’s work came to my notice too late for me to take account of it here.

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might be termed a commitment semantic^.^ The essential claims appear to be two. First, that while our commitments may be to holding beliefs (involving acceptance of ‘descriptive’ propositions having truth-conditions), they may equally well be to making favourable or unfavourable valuations (endorsing ‘ethical propositions’ which cannot be understood as “simply discussions of a way the world is” on pain of the open question4); and second that, irrespective of the specific kind of commitments involved, the validity of deductively valid patterns of inference such as modus ponens can then be seen as consist- ing in the fact that violating them requires incurring an impossible bundle of commitments-one that we can’t intelligibly maintain. He writes:

The key idea here is one of a functional structure of commitments ... isomorphic with ... the propositional structure that we use to express them. Thus someone may be what I called ‘tied to a tree’: in a state in which he or she can only endorse some combination of attitude and belief. Suppose I hold that either John is to blame, or he didn’t do the deed. Then I am in a state in which ifone side is closed off to me, I am to switch to the other-or withdraw the commit- ment. And this is what I express by saying ‘Either John is to blame, or he didn’t do the deed‘ ... By advancing disjunctions and COnditiOMlS we avow these more complex dispositional states.. . . By using the disjunction, I am presenting myself in a way that will deserve reproach and bewilderment if, without explanation, I go on to suppose both that John did the deed and is blameless. This makes no sense, unless I have changed my mind . . . ... To avow anything of the form ‘if p then 4’ is to commit oneself to the combination ‘Either not-p or 4’ and to be tied to that combination is to disavow the combination of p with not-q. Holding both together is therefore unintelligible. Logic is our way of codifying and keeping track of intelligible combinations of commitment.’

One cause for concern here is the equation of illogicality with unintelligi- bility. It is one thing to say that if X won’t agree with simple instances of, say, modus ponens or conjunction elimination, then-unless there is some saving explanation-we shall suspect that whatever, if anything, X means by ‘if and ‘and’, he doesn’t mean what we mean by them. It is quite another to suggest that whenever anyone makes a fallacious inference or declines a valid one, she lapses into unintelligibility or interpretational darkness. Blackburn’s claim that “Logic is our way of codifying and keeping track of intelligible combinations of commitment” seems at best an exaggeration, probably resulting from undue concentration upon principles of inference whose amp- tance is plausibly taken as constitutive of or criterial for understanding the logical connectives involved. But perhaps it is a stronger claim than he needs.

Blackbum never, I think, explicitly says that he is proposing an alternative explanation of the meanings of the connectives, preferring to speak rather of “what is going on” when we assert logical compounds-but I cannot see what he is saying if this is not what he means. Cf. p. 70 on “the reason expressivism in ethics has to be correct”. ’ 4.71-72.

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Assuming that he has access to a suitable notion of consistency,6 why shouldn’t Blackburn’s expressivist say instead that logic codifies and keeps track of consistent combinations of commitment?

To assess the prospects for a commitment-theoretic defence of expressiv- ism, we need to look more closely at the details of the theory. I shall take it that what, in Blackburn’s view, we are committed to are beliefs or other atti- tudes or combinations of such-so that when I assert ‘Either John is to blame, or he didn’t do it’, the disjunctive commitment I incur is to either holding John to be blameworthy or believing that he didn’t do the dastardly deed. That is, I shall assume that when he appears to speak (as he does, for example, in the passage quoted) of sentences as objects of commitment, what is strictly meant is that one is committed to the (combination of) beliefs or other attitudes which might be expressed by uttering those sentences? Thus on what appears to be Blackburn’s p r e f d ‘tree tied‘ account of the conditional, someone who asserts ‘If John did it, he is to blame’ is committed to endorsing the disapproving attitude expressible by direct assertion of the consequent, if she believes the antecedent, or equiva- lently, to either not believing that John did it, or disapproving, etc. To formulate the commitment condition in full generality-allowing, as Blackburn requires, for each of the antedent and consequent to be either evaluative or non-evaluative sentences-it is convenient to employ a term, such as ‘accept’, that is neutral as between different types of commitment (such as belief or other favourable or unfavourable attitude). We may then say that to assert ‘if p then q’ is to commit oneself to either not accepting that p or accepting that q.* It is then straightforward to verify that this commitment

The requirements for a combination of beliefs and (other) attitudes to be consistent include, but must extend beyond, being consistently describable. Beliefs should rank as inconsistent if they cannot be true together, for all that there need be no inconsistency in attributing them to a single thinker at a single time. As Blackbum appreciates, something analogous will be required for evaluative attitudes, if a ‘logic’ is to be possible. His idea is, roughly, that attitudes will be consistent only if they admit of simultaneous realisation, so that-taking an extreme case-approving of its being the case that p and also of its being the case that -p will be inconsistent. This idea is not free of difficulty. In particu- lar. even if we assume that all the relevant attitudes can be treated as attitudes towards propositions, and further assume that there is something wrong in holding one and the same attitude towards one and the same proposition and its negation, it is not clear that it is always illogical or irrational to do so. For argument’s sake, I shall assume here that some such notion is available to the expressivist. It’s unclear what could be meant by commitment to a sentence other than this. Blackburn also speaks of ‘beliefs in the ethical proposition’, but it seems to me that in so far as this is explained, the explanation depends upon giving prior content to conditionals, disjunctions, etc., involving ethical (or more generally, evaluative) sentences as components in terms of the idea that they are used to register complex commitments, so that there could be no question of ‘proposition’ being our primary means of specifying the objects of commit- ment-no suitably neutral notion of proposition having yet been made available. Note that the commitment is not distributed across the disjunction-that is, the thinker is not committed to not accepting that p or committed to accepting that q.

*

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condition for the conditional validates modus ponens, whether its ingredient clauses are descriptive propositions (e.g. that Cain slew Abel) or moral ones (e.g. that Cain did wrong). Endorsing the premisses but refusing to endorse the conclusion involves accepting that p , either not accepting that p or accepting that q, and not accepting that q. and so must involve either accept- ing and not accepting that p or accepting and not accepting that q.

So far, so good. For an expressivist who goes this way, however, the hope must be that a suitable commitment semantics will, like the more usual truth-conditional semantics, validate all our standardly accepted logical princi- ples, whilst at the same time, and in contrast with the usual semantics, allowing the commitments whose combinations are regulated by those principles to be to (non-doxastic) attitudes, or valuations, as well as to (non- evaluative) beliefs. The prospects+r so it seems to me-are less than rosy. Since a full survey is obviously beyond the scope of this brief discussion, consider what would seem to be a crucial case: modus tollens. If the commitment-theoretic approach is good, asserting p+q and l q but declining to accept 1 p should involve inconsistent commitments. If we take it-as seems most plausible-that asserting 7 q commits one to rejecting q (i.e. accepting l q , as opposed to merely not accepting q) , then one who asserts the premisses but declines to accept the conclusion is committed to: accept- ing l q , either not accepting p or accepting q, but not committed to accepting 1 p . Is this combination inconsistent? Since the ingredient conditional commitment generates a branch, it will be so only if both branches issue in inconsistent combinations. One branch-the one which requires accepting l q , accepting q, but not accepting I p d o e s so.’ But the other requires only accepting l q and not accepting p , coupled with non-acceptance of 1 p . This does not appear inconsistent, and it surely ought not to be. On the contrary, declining to accept p or to accept its negation is surely the right response, if the available evidence leaves it unclear whether p or not. Of course, if we have, independently, grounds to accept that p+q and that -q. then we ought to accept that l p , since it follows by modus tollens. But we can scarcely appeal to that consideration here, since what is in question is precisely whether the commitment-theoretic account does validate that principle. Its apparent failure to do so tells, on the face of it, against that account’s claim to yield a more general conception of logical validity which conserves stan- dard principles of inference whilst allowing them to apply in contexts where ingredient sentences are not assumed to be truth-valued.

It might be replied that the difficulty results from adopting the wrong commitment condition for the conditional-that the disjunctive commitment Blackbum takes to be incurred by asserting ‘p+q’ is not to: either not accepting that p or accepting that q , but to: either accepting that 1 p or

See note 6 above.

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accepting that q. Someone who flouts modus tollens will then be committed to: accepting that l q and either accepting that - ~ p or accepting that q, but not committed to accepting that 1 p . These do indeed yield inconsistent branches4n the one side, we have: accepting that l q , accepting that l p , and not accepting that 1p, and on the other: accepting that lq, accepting that q, and not accepting that l p . This conditional commitment condition does, therefore, validate modus tollens; and it is easily verified that it also validates modus ponens. But the price of taking this way out appears unacceptable. On any account, we should surely accept all instances of the law of identity p+p. That does not, as far as I can see, raise any special problem for the earlier and weaker account of the commitment incurred by asserting a condi- tional, which requires, in the present case, only a commitment to either not accepting p or accepting p. But on the stronger account now proposed, a stronger and substantial commitment is incurred. It is required that, for each choice of p, one has the commitment: either accept that 1 p or accept that p. However, in states of information neutral with respect to a given proposition p , we should neither accept that -p nor accept that p. That is, adopting the stronger commitment condition for conditionals appears improperly to fore- close on the possibility of neutral states of information-unless, implausi- bly, one denies the general logical law of identity that for all p, p+p.I0

It might, alternatively, be suggested that the difficulty can be avoided by adopting a different account of negation from the one I have been assuming the commitment theorist will give. If the commitment incurred by asserting 1 p is taken to be to not accepting that p , rather than to accepting that l p , then one who flouts modus tollens will be committed to not accepting that q and to either not accepting that p or accepting that q. but not committed to not accepting that p-which involves an inconsistency whichever way the disjunctive commitment is resolved. But is this a defensible account of nega- tion? It might be urged in its support that while there is clearly a gap between not accepting that p and accepting that l p , being committed to not accepting p goes beyond merely not accepting p-roughly, one might say that the latter just consists in lacking a commitment to accepting that p, whereas someone committed to not accepting that p has, so to speak, set her face (or mind) against accepting that p . Because not accepting that p falls short of being committed to not accepting that p, one cannot directly infer, from the consistency of not accepting that p with not accepting that l p , that being committed to not accepting that p cannot be the commitment incurred by asserting that l p . But it seems to me that there remains a crippling flaw in the idea that that is the commitment incurred when one asserts that l p . If

lo Essentially the same difficulty arises over the Law of Excluded Middle, if the commit- ment incurred by asserting a disjunction pvq is taken to be a commitment to accepting p or accepting q.

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we come to know that we shall never be in possession of evidence sufficient to warrant belief that p , then we should be committed to not accepting that p. But we should not, on the strength of that alone, be willing to assert that

In sum, it appears that the commitment theorist is spiked on one or other horn of a simple dilemma: if he adopts the weaker commitment condition for the conditional, the possibility of neutral information states ensures that his account fails to validate modus tollens, whereas if he opts for the stronger conditional commitment condition, he can secure that principle only at the unacceptable cost of foreclosing on the possibility of such neutral states. It is tempting to think that the difficulty is symptomatic of a deeper-and more clearly decisive-flaw which must afflict any attempt to explain the condi- tional (or more generally, any binary sentential operator which generates unasserted contexts of its operands) in terms of a disjunctive or conditional commitment along the lines Blackburn appears to envisage. Just as we must distinguish between a conditional bet and a bet on a conditional, so, more generally, we must distinguish between a conditional commitment and commitment to a conditional. And just as we cannot explain what it is to bet on a conditional in terms of betting on the consequent conditionally upon fulfillment of the antecedent, so we cannot explain what it is to assert a conditional in terms of conditional assertion. The commitment one incurs by asserting a conditional does not, and cannot, reduce to any combination of conditional commitments to its constituents.'*

7p ."

The situation may-perhaps most likely would-be one in which I know that the only evidence which would settle the question whether or not p has been irrecoverably lost; in that case, I should neither assert that p nor assert its negation. It is conceivable that the possibility of our coming to possess decisive negative evidence should remain open even though the possibility of OUT ever getting positive evidence has been closed off, and that is enough for my point. I should like to thank John Benson, Jimmy Lenman, Adam Rieger and Crispin Wright for extremely helpful discussion of earlier drafts of this paper.

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