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IT'S IMMATERIAL (A REPLY TOSINNOTT-ARMSTRONG)William G. Lycan aa University of North Carolina ,Published online: 21 Jan 2010.

To cite this article: William G. Lycan (1998) IT'S IMMATERIAL (A REPLY TO SINNOTT-ARMSTRONG), Philosophical Papers, 27:3, 203-206, DOI: 10.1080/05568649809506587

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Philosophical Papers Vol. XXVII (1998), No. 3

IT'S IMMATERIAL (A REPLY TO SI"0TT-ARMSTRONG)

William G. Lycan University of North Carolina

Walter Sinnott-Armstrong argues that my three alleged counter-examples to Modus Ponens are specious. His main argument is disarmingly simple. It is just that if the conditionals that figure in my examples are interpreted as material conditionals, then they can hardly afford counterexamples to Modus Ponens. (He adds that the appearances of invalidity can be explained away in terms of epistemic assertibility, since any of the arguments' conclusions can be unassertible even when the argument's premises are assertible.)

Well, of course: If my conditionals are interpreted as material conditionals, then they cannot be counterexamples to Modus Ponens. (Nor could there be any other counterexamples to Modus Ponens. That is tautologous, since the truth-table definition of the horseshoe in effect stipulates the validity of Modus Ponens.) I could hardly have offered putative counterexamples if I had thought that the conditionals were material conditionals. Indeed - as Sinnott-Armstrong fails to note - I explicitly rejected that thesis (1993, p. 4281119).

But the crux is that Sinnott-Armstrong thinks I am not entitled to that rejection:

Lycan never refutes that material interpretation of ... [the relevant] conditionals. So Lycan fails to show that modus ponens is invalid. (p. xx4xx)

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204 WILLIAM G LYCAN

And, Sinnott-Armstrong says, the “extreme usefulness” of “a dear old friend” like Modus Ponens (p. xx7xx) is an additional reason to be leery of the counterexamples.

I am unsure of my dialectical rights here, but contra Sinnott- Armstrong, I believe I am entitled to reject the material interpretation even though I did not digress to refute it in my paper. In any case, I have two worthwhile fallbacks. First, I merely conditionalize: So long as one accepts the mainstream view that English conditionals are not truth- functional, Modus Ponens is invalid. That thesis is striking enough to earn me some money, and Sinnott-Armstrong has offered no explicit resistance to it.

Second, notice that Sinnott-Armstrong firmly agrees with me on a further strong claim: that if Modus Ponens can be rescued from counterexample, then so can every other pattern of conditional inference rejected by Stalnaker (1968), Lewis (1973), and their followers such as Pollock (1 976): notably Antecedent-Strengthening, Contraposition, and Transitivity. For each of those too is valid on the material interpretation. It was a main purpose of my original article to prosecute the ad hominem charge that if one rejected each of those inferences for whatever reason, a parallel reason would impugn Modus Ponens.

I said that Sinnott-Armstrong has offered no explicit resistance to the conditional thesis that Modus Ponens is invalid unless the Horseshoe theory is correct. But his article does less emphatically sketch an argument against me that succeeds, or not, independently of the material interpretation:

Suppose both Albert and Betty come to the party, and it is great. Then (B)(l) [,‘If Albert comes to the party, it will be great”] is true but (B)(2) [,‘E Albert and Betty come to the party, it will be awful”] is false. Suppose both Albert and Betty come to the party, and it is awful. Then (B)(2) is true but (B)(l) is false. (p. xx3xx)

- the upshot being that if as my argument supposes Albert and Betty both come, then (B)(I) and (B)(2) cannot as my argument also supposes both be true. And that claim is entailed, not just by the material interpretation, but by mainstream theories like Stalnaker’s and Lewis’ as well.

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ON MORALITY’S DETHRONEMENT 205

Actually I had anticipated that objection in my original article (p. 419: “[Ilt may be complained that ... the first member of our sequence just is false, if the second member is true and Albert and Betty both do come to the party ... . The claim would be that Stalnaker and Lewis are intuitively right, not just technically able to save Modus Ponens because they want to”). I made two replies: The first was that (as in the case of Sinnott- Armstrong’s appeal to the Horseshoe theory) similar reasoning would reinstate Antcedent Strengthening, Transitivity et al., contra Stalnaker and Lewis. That point stands.

My second reply was the passage quoted by Sinnott-Armstrong on p. X X ~ X X , alleging that the objection ends in a standoff. Sinnott-Armstrong rejects that reply:

[Tlhere is nothing odd at all about the claim that propositions that are highly likely to be true still might turn out to be false. Every party, no matter how well planned, might go astray if someone like Betty shows up. (pp. A7m)

I agree that what I originally said is not compelling, and I did not put it well. The point was not supposed to be to find it odd that highly probable propositions might still turn out to be false; as Sinnott-Armstrong says, there is nothing at all odd about that. Rather the idea was supposed to be that most people at least feel the pull of epistemic theories of indicatives. What is odd or at least tendentious would be for someone to insist on radically nonepistemic truth-conditions for indicatives. (Often people suggest that the indicative/subjunctive distinction lines up well with the epistemic/metaphysical distinction.) And I see little difference between insisting on radically nonepistemic truth-conditions and just announcing that if a conditional in fact has a true antecedent and a false consequent, whatever the speaker’s epistemic circumstances, it is false - which would beg the question.

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206

NOTES

WILLIAM G LYCAN

1. The material interpretation is notoriously counterintuitive, what with the paradoxes of material implication, and ordinary informants unanimously reject it. Granted, (2) it has several reputable defenders, notably Grice (1967/1989) and Jackson (1987), who have hied to explain away the appearances; Lewis (1976) and Bennett (1988) sympathize. On the other hand, (3)few practitioners have been convinced; the majority opinion in print is still that ordinary English conditionals are not truth-functional. Also, (4) elsewhere I have myself argued against the material interpretation, and I did not want to repeat myself (Lycan (in preparation); see also Appiah (1985)). One quick but I think powerful argument is that nowhere (to my knowledge) has any Horseshoe theorist tackled the worst material-implication paradox of all, viz., “*(If A, B) / :.A Kt -B.” And fmally, (5 ) my counterexamples to Modus Ponens are as intuitive as they are in English independently of interpretation, so to that extent they themselves count against the Horseshoe theory. On balance, I think (l) , (3), (4) and (5) together entitle me to my original assumption.

For the record, I did not claim categorically to have refuted Modus Ponens. I surveyed several moves that might be made to explain away the apparent counterexamples, and granted that each is entirely tenable. The trouble was that each would also work against the standard counterexamples to the other inference patterns as well; one would thereby end up reinstating those inferences as valid. And that (for good or ill) would be to regress to the early 1960s and in effect to insist that if conditionals are stronger than material, they are full-bore nomologicals, period. I believe the work of Stalnaker and Lewis was more valuable than that.

Acknowledgement Thanks to the Editor and to an anonymous referee for critical remarks on a previous draft.

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