Kripke on the Inversion of Conditionals

We say of someone else that he follows a certain rule when his responses agree with our own and deny it when they do not . . . . When we pronounce that a child has mastered the rule of addition, we mean that we can entrust him to react as we do in interactions such as that . . . between [a] grocer and [a] customer. Our entire lives depend on countless such interactions, and on the 'game' of attributing to others the mastery of certain concepts or rules, thereby showing that we expect them to behave as we do.^{[1 ]} This expectation is not infallibly fulfilled. It places a substantive restriction on the behavior of each individual, and is not compatible with just any behavior he may choose. (Contrast this with the case where we considered one person alone.) ^[2]

Kripke goes on to say that "[w]e can restate this [i.e., the essence of the sceptical solution] in terms of a device that has been common in philosophy, inversion of a conditional." (K, p. 93; as we'll see below, what Kripke means by this is focusing on the contraposed form of a conditional rather than the conditional itself). Kripke goes on to say, in fn. 76, that conditional inversion (i.e., contraposition) "is a device for reversing priorities". (Just for the record, I am not, I repeat, I am not, making this up! Read pp. 93ff of Kripke's book for yourself). Further in this footnote, Kripke gives 5 slogans, presumably as illustrations of reversing priorities. The slogans include William James' claim that " . . . the . . . rational statement is that we feel sorry because we cry . . . not that we cry . . . because we are sorry . . . ", the unattributed, "We do not condemn certain acts because they are immoral; they are immoral because we condemn them", and a claim attributed to Hume, "Fire and heat are not constantly conjoined because fire causes heat; fire causes heat because they are constantly conjoined", and two others. Before looking at Kripke's inversion of a conditional in the case of KW, we should note that none of the claims in the footnote are CONDITIONALS. Every one of the claims is a "because" statement. Now, I am not going to claim that Kripke is unaware of the difference between, "If p then q" and, "p because q", but I do think it is clear that he neglects the difference here.

First, none of the 5 "because" statements can be restated as conditionals, preserving truth. Second, there is a considerable difference between the "because" statements and their "inversions". Third, and relatedly, inverting "because" statements doesn't reverse priorities, it gives us a very different statement. What we need to appreciate is that someone who advocates a switch from "p because q" to "q because p" is trying to correct a mistake, the more pervasive the mistake to be corrected, the better. And that is what each of Kripke's footnote examples try to do, viz., correct a pervasive misunderstanding. Most importantly, what Kripke means by inverting a conditional is not, and cannot be, going from a "If p then q" claim to a "If q then p" (which makes the examples of reversing the "because" statements even more bizarre and irrelevant). It's also clear that what Kripke means by inverting conditionals, viz., that we appeal to a conditional's contrapositive rather than the conditional itself, does not and cannot, correct a pervasive error. The obvious reason for this is that a conditional and its inversion, unlike a "because" statement and its "inversion", are logically equivalent. So if the original conditional expresses a mistake, so too does its inversion. The upshot here is that Kripke's appeal to "because" statements as a way of illustrating "inversion of a conditional" is thoroughly misleading. It is befuddling in the extreme to see Kripke offering up examples of going from "p because q" to "q because p" as being in any way similar to, or instructive of, the move from "If p then q" to "If not q then not p". The whole notion of "reversing priorities" is precisely what we don't get in either case. In the "because" case, we are presented with two statements making conflicting claims concerning causal direction whereas in the conditional case, there is no difference at all. But believe it or not, things get more bizarre further on in Kripke's text.

Kripke's first real case of an inverted conditional (i.e., a contraposition of a conditional) is a conditional purporting to express something important about our concept of causation:

If events of type A cause events of type B, and if an event e of type A occurs, then an event e' of type B must follow. (K, p. 93-4).

The obvious question is, why the 'must'? No post-Quinean, indeed, no post-Humean, would accept this conditional. Drop the 'must' in favor of 'will' or dare I say, 'should', and all would be better, maybe even well.
Kripke remarks, quite rightly, that the conditional above "commits us to a belief in a [necessary] nexus" (K, p. 94). He also notes, quite rightly, that Humeans would balk at the conditional. However, he is wrong or slippery to suggest that Humeans, since they deny the existence of necessary connections, "concentrate on the assertability conditions of a contrapositive form of the conditional." (K, p. 94). They do nothing of the sort. Instead, they reject the conditional as it stands and accept one which would substitute 'always follows' for 'must follow'. Contra Kripke, it is misleading in the extreme to paint Humeans as objecting to seeing "causal connections" as primary (whatever that means; see K, p. 94), nor do they object to taking regularities as "flowing" from causal connections (again, whatever that means, see K, p. 94). What Humeans object to is taking causal connections to be necessary connections, taking causal connections as necessitating an effect. Most importantly perhaps, there is simply no need at all for Humeans (or anyone else) to "look at the matter contrapositively". For it is clear that nothing at all is gained by doing so. Contra Kripke, we should appreciate that "withdrawing a causal hypothesis when the corresponding regularity has a definite counter-instance" does not require appeal to the contraposition of the conditional. In either form, the conditional warrants withdrawing a causal hypothesis in the face of a definite counter-instance. I'm leery of saying this but it seems warranted: Kripke's "inversion of the conditional" and its alleged attendant, "reversal of priorities", is significant only if one supposes that given a specific counter-instance to a conditional, i.e., given something that falsifies the conditional's consequent, we must use a contraposed form of the conditional in order to affirm the denial of the original antecedent. Yes, Virginia, that means Kripke is saying that we must contrapose rather than use modus tollens to deny the antecedents of conditionals. "Bizarre" doesn't do justice to this part of Kripke's story.

ENDNOTES

¹ For the uninitiated, it should be pointed out that Kripke is here trying, among other things, to make a case for "the utility" of our practice of asserting or making meaning attributions, i.e., the utility of ascribing meaning or rule following, to others. I think it's clear that not only does he fail, in a big way, to do this, but it's also clear that the felt need to account for the utility of our meaning attribution practice is misguided. On the failure side, it's clear that Kripke confuses the utility of the practice of counting or adding (of which there is no doubt) with the utility of attributing meaning addition to someone else. I see nothing in his story about the grocer to show that pronouncing that a child or a grocer has mastered the notion of addition is utilitous. As for the misguided character of trying to show that our game of meaning attributions is utilitous, see Goldfarb's essay, "Kripke on Wittgenstein on Rules", and Winch's essay, "Facts and Superfacts". As Goldfarb rightly notes, "It is hard to see any content in a general notion of "role and utility in our lives"; what does it rule out?" Although I believe that Goldfarb is correct to note that the boundaries on utility are vague at best (e.g., does printing our meaning attributions on wallpaper give them a role and utility in our lives?!), I would still insist that Kripke has ignored the problem of showing how and why meaning attributions are utilitous and has shown only that using addition is utilitous.


² This last claim makes it clear that Kripke is confused or guilty of overstating KW's case, for there simply is no contrast to be had. Kripke's suggestion to contrast the case of the ICI with the "substantive restriction on behavior" which is allegedly made possible once we ""widen our gaze from consideration of the [ICI] to consider him as interacting with a wider community". (K, p. 89), shows that he believes,
(i) meaning attributions (or the expectations that come alone with their assertions) place substantive restrictions on the behavior of individuals, and
(ii) no "substantive restrictions on the behavior" of an ICI are possible. The truth is however that (i) is either false (leaving ICIs in the same spot as community members), or, (i) is true only if (ii) is false, for the simple reason that nothing prevents us from making meaning attributions about ICIs. And if meaning attributions are what give rise to substantive restrictions on behavior, then the behavior of ICIs can be, contra KW, substantively restricted. (See appendix for argument).

Be this last point as it may, I believe that KW is wrong to hold that meaning attributions place substantive restrictions on the behavior of individuals. If I attribute meaning addition to Jones, this does nothing to restrict Jones' behavior. Jones may still say anything he likes, including, of course, 68 + 57 = 5. While it might fairly be said that Jones' meaning addition by '+' places a substantive restriction on the behavior of Jones, it is abundantly clear that my attributing meaning addition by '+' to Jones does nothing of the sort. The chief reason for this is simple, viz., the meaning attribution may be false. Let's agree that no false meaning attribution ought to be allowed to restrict Jones from saying what he means. If I attribute meaning addition to Jones when he in fact means quaddition, he surely is free to say, indeed, ought to say, 68 + 57 = 5 rather than 68 + 57 = 125.
Of course, Kripke is correct to say that asserting of Jones that he means addition, along with the expectation that goes along with it, "is not compatible with just any behavior [Jones] may choose." But surely we ought not milk this incompatibility into the claim that a meaning attribution about Jones puts a substantive restriction on Jones' behavior. A meaning attribution about Jones does not, and ought not, restrict his behavior since, as noted above, the meaning attribution may be false. At best, it turns out that Jones cannot behave in certain ways, i.e., can't say certain things, and still be considered (within reason) an adder. (Recall Putnam's claim that meaning attributions admit of empirical refutation). By my lights, the safest thing to say is that if anyone's behavior is substantively restricted by a meaning attribution it is that of the asserter, not the subject, of the meaning attribution. For the behavior of the subject of the meaning attribution (which may, for all the meaning attribution tells us, be anything at all) can force a retraction by the asserter.

Finally, a question must be raised about about the legitimacy of KW's claims here as a "solution" to the alleged sceptical problem of meaning and rule following. Once all the dust settles, KW's sceptical solution says that our ability to assert meaning attributions of others gives us something we can't have in the case of the ICI, viz., the ability to say more of someone than "s/he can "apply the rule in the way it strikes [him/her]". (K, p. 88). For KW, the last claim is all we can say about an ICI. It should be clear from the above, that KW is correct about this just in case we cannot assert meaning attributions about ICIs. For if we could assert a meaning attribution of an ICI then it is clear that the attribution would not be compatible with just any behavior the ICI may choose. As such, KW is clearly committed to saying that we cannot ascribe meaning to ICIs. However, no where in the text does KW succeed in showing that we are unable to assert meaning attributions of ICIs. This is not surprising, for it cannot be done, except by completely trivializing the claim by way of making the notion of an ICI well-nigh useless.
Kripke himself comes close to recognizing that nothing prevents us from affirming meaning attributions of ICIs when he notes, quite rightly, that nothing his Wittgenstein says rules out the possibility of our ascribing rule following to a Crusoe figure (assuming he behaves as a rule follower should). To use Kripke's terminology, his Wittgenstein's case against private rule following "need not mean that a physically isolated individual cannot be said to follow rules . . . ." (K, p. 110). At this point, legitimate questions arise concerning the possibility of distinguishing a "physically isolated individual", or PII, from an ICI. I contend that it's impossible to do so without making an ICI a thoroughly useless notion.
For starters, a PII is not to be distinguished from an ICI on the basis of physical isolation. For we can certainly conceive of an ICI being physically isolated from others. The key difference, for KW, is that that PIIs can be thought of as rule followers whereas ICIs cannot. And the reason he gives for this difference is as follows: Once WE think of an isolated individual as a rule follower (or not, as the case may be; I assume that we could do this either as the result of a thought experiment or as a result of secretly observing some heretofore isolated individual. N.B. In both cases, it's clear that the community is allowed to act at a distance, i.e., there need be no teaching of the individual by members of a community in order for that community to be able to designate him/her a rule follower) we have undermined his/her status as an ICI because we have thereby taken him/her into our community. Presumably, no one who has been "taken into a community" can be an ICI, and no ICI, qua ICI, can be taken into a community.
A bit of reflection on this idea ought to bring pause. In particular, if we accept KW's distinction then it follows that we cannot say anything at all about an ICI. For once we say so much as that an ICI sleeps, walks, talks, etc., we have taken him/her into our community and so undermined his/her status as an ICI. For in order to say something of someone requires us to make use of our language, our concepts, our logic, etc. And this is, it seems, what is involved in "taking someone into our community". But if it is not, KW owes us some reason to think that talk of someone following a rule requires taking someone into our community in a way that is not required of our talk of someone doing other mundane activities like sleeping, eating, running, creating, etc. I am dubious of there being any such reason. But I am certain that Kripke no where provides such a reason in his text.
For the record, I am not denying that KW can understand an ICI to be someone of whom we can say nothing at all (on the grounds that once we would do so we would thereby undermine his/her status as an ICI). My complaint is twofold. First, without such a notion of an ICI, KW's distinction between a PII and ICI falls apart. And since KW allows that PIIs can be said to be rule followers, the collapse of the PII/ICI distinction leaves KW no basis for saying that ICIs cannot be rule followers. Second, given KW's notion of an ICI, his claim that an ICI cannot be said to be a rule follower is a triviality at best. For given that an ICI can't be said to do anything at all (for talking about an ICI undermines his/her status as an ICI), KW's claim ends up telling us nothing at all about rule following.

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