Abstract
I consider Lewis’ appeal to naturalness to solve Kripke’s rule-following paradox. I then present a different interpretation of this paradox and offer reasons for thinking that this is what Kripke had in mind. I argue that Lewis’ proposal cannot provide a solution to this version of paradox.
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Notes
This is an argument that Kripke articulates and not one that he endorses. As Kripke puts it, in presenting this argument he is not speaking for himself. Rather, he presents it as an argument he found in Wittgenstein’s Philosophical Investigations.
In interpreting Kripke in this way, I am following Gómez-Torrente (2005).
Lewis (1983, pp. 375–376).
This minimum sense of determinacy is meant to be compatible with other forms of indeterminacy. There could be facts that determine that with my use of ‘+’ I mean addition and not quaddition even if there were no facts that determine that Joe, an unclear case of baldness, falls under the extension of ‘bald’ or not.
Lewis (1983, p. 346).
According to Lewis, an object has a property when it is a member of the class that that property is. Further, he takes relations to be classes of n-tuples (ordered pairs, triples, etc.). A relation among things would thus be “a property of ‘tuples’ of things”. (Lewis 1983, p. 344).
Cfr. Lewis (1983, p. 351 and p. 373). In referring to intentional states, Lewis writes: “[G]iven the functional roles of the states, the problem is to assign them content. Propositional content, some would say; but I would agree only if the propositions can be taken as egocentric ones, and I think an ‘egocentric proposition’ is simply a property.” [Lewis (1983), p. 373], my emphasis). See also (Lewis 1979).
Recall that according to Lewis, relations are properties. See footnote 6.
Cfr. Lewis (1983, p. 376).
Cfr. Lewis (1983, p. 345).
Lewis further claims that the natural/unnatural distinction can be drawn in different ways. For example, by adding universals, by taking the fact that some properties are perfectly natural as primitive and adding some principles to derive the less natural ones from these, or by taking as primitive an objective resemblance among certain things but not others.
Lewis takes eligible interpretations to be those interpretations of a subject’s intentional states constituted by the most natural properties (Lewis 1983, pp. 371–372). He writes (1983, pp. 376–377):
What is the status of the principles that constrain interpretation, in particular the charitable presumption in favour of eligible content? We must shun several misunderstandings. It is not to be said (1) that as a contingent psychological fact, the contents of our states turn out to be fairly eligible, we mostly believe and desire ourselves to have not-too-unnatural properties. Still less should it be said (2) that we should daringly presuppose this in our interpreting of one another, even if we haven’t a shred of evidence for it. Nor should it be said (3) that as a contingent psychological fact we turn out to have states whose content involves some properties rather than others, and that is what makes it so that the former properties are more natural. (This would be a psychologistic theory of naturalness).
Lewis claims: “Only if we have an independent, objective distinction among properties, and we impose the presumption in favour of eligible content a priori as a constitutive constraint, does the problem of interpretation have any solution at all” (Lewis 1983, p. 377).
As mentioned above (see footnote 14), Lewis takes eligible interpretations to be interpretations of a subject’s intentional state constituted by the most natural properties (Lewis 1983, pp. 371–372).
Lewis (1983, p. 371).
Kripke (1982, p. 17), Kripke’s emphasis.
The following are among the putative candidates to be meaning facts that Kripke considers and rejects: a mental image, an expression of the rule, a chain of mental expressions of the rule, the subject’s dispositions, a machine’s dispositions, an infinite object comprising all the instances of the concept or function in question, a primitive intentional fact, an idea that would serve to grasp a platonic object, a sensation. Cfr. Gómez-Torrente (2005).
Cfr. Kripke (1982, p. 10 and 15).
Kripke (1982, p. 24), his italics, my underlining. The following formulation of the paradox also makes this point clear:
Even now as I write, I feel confident that there is something in my mind—the meaning I attach to the ‘plus’ sign—that instructs me what I ought to do in all future cases. I do not predict what I will do […]—but instruct myself what I ought to do to conform to the meaning.[…]But when I concentrate on what is now in my mind, what instruction can be found there? How can I be said to be acting on the basis of these instructions when I act in the future? The infinitely many cases of the table are not in my mind for my future self to consult. To say that there is a general rule in my mind that tells me how to add in the future is only to throw the problem back on to other rules that also seem to be given only in terms of finitely many cases. What can there be in my mind that I make use of when I act in the future? It seems that the entire idea of meaning vanishes into thin air. (Kripke 1982, pp. 21–22, his italics, my underlining)
Consider also the following passage:
The idea that we lack ‘direct’ access to the facts whether we mean plus or quus is bizarre in any case. Do I not know, directly, and with a fair degree of certainty, that I mean plus? Recall that a fact as to what I mean now is supposed to justify my future actions, to make them inevitable if I wish to use words with the same meaning with which I used them before. This was our fundamental requirement on a fact as to what I meant…” (Kripke 1982, p. 40, his italics, my underlining).
As Kripke further claims, even if I could have a table with the infinite triples that are instances of addition in my mind, how could I go about using it without a rule? (Cfr. Kripke 1982, p. 52 ft.34).
Kripke (1982, p. vii), my emphasis.
Kripke (1982, p. 2, fn 1).
Kripke writes: “Such a state [the state of ‘meaning addition by “plus”’] would have to be a finite object, contained in our finite minds. It does not consist in my explicitly thinking of each case of the addition table, nor even of my encoding each separate case in the brain: we lack the capacity for that. Yet (§195) “in a queer way” each such case already is “in some sense present” […] What can that sense be? Can we conceive of a finite state which could not be interpreted in a quus-like way?” (Kripke 1982, p. 52).
Kripke (1982, p. 54) (his italics, my underlining).
Again, it is assumed here that the subject makes no computational mistakes. An acceptable solution to the paradox, however, needs to account for the possibility of making a metalinguistic mistake—a mistake in what function the word or sign means. A proposal according to which, for instance, an intention to mean addition by ‘+’ is constituted by whatever caused the actual responses given by the subject could not account for this normative aspect the problem. For if this were so it would not be possible for the subject to respond in ways that do not accord with her intention.
Kripke (1982, p. 40).
Based on Kripke’s discussion of an appeal to simplicity considerations to solve the paradox, one might think that an even stronger argument could be offered against Lewis. This argument would aim at establishing that Lewis’ proposal is not even a solution to his own formulation of the paradox. That is, it would aim to show that, even without appealing to the guidance constraint, Lewis’ solution would fail. The argument would proceed in analogy to an objection Kripke raised against a different appeal to simplicity to solve the paradox. It would go as follows.
Against the claim that one could solve the paradox by pointing out that the hypothesis that the subject means addition is simpler than the hypothesis that the subject means quaddition, Kripke argued that this would be to beg the question. For in order for simplicity considerations to distinguish between these hypotheses and, by so doing, provide us with meaning facts, one first needs to presuppose that the two competing hypotheses state matters of fact. But to presuppose that claims like
- (*):
-
The subject intends addition by ‘+’.
- (**):
-
The subject intends quaddition by ‘+’.
are factual is to presuppose that there are meaning facts.
One might interpret Lewis’ appeal to naturalness in a way that is prey to the same objection. For to argue that the subject means addition and not quaddition because the facts stated by (*) are more natural than the facts stated by (**) would be to beg the question. That is, to take these hypotheses as stating matters of fact would be to assume—not to show—that there are meaning facts.
I don’t think, however, that this is the most charitable way of interpreting Lewis. Instead, we can understand him as taking the content of an intentional state as the property that, from those that are fitting, is the most natural. In this way, while naturalness would indeed serve to distinguish between different properties, it would not be brought in to distinguish between different meaning facts. In this way, his appeal to naturalness would not beg the question—quotes like those included in footnotes 12 and 13 above suggest just this. (For this reason, I think Lewis is best understood as offering a response analogous to the appeal to simplicity that Kripke considers in the footnote to his discussion of simplicity, and not as analogous to the appeal to simplicity that Kripke discusses in the main text). Cfr. (Kripke 1982, pp. 39–40).
Note that adding an ontological measure of the naturalness of a sense analogous to the one Lewis proposed for properties would not help the Platonist meet the guidance constraint more than it helped the Lewisian. Under this interpretation, the guidance constraint would also be Kripke’s main reason for rejecting dispositionalist accounts.
Lewis (1983, p. 375), my emphasis.
References
Gómez-Torrente, M. (2005). El Wittgenstein de Kripke y la analogía entre reglas y fundamentos. Diánoia, 50(55), 55–94.
Kripke, S. (1982). Wittgenstein on rules and private language. Cambridge, MA: Harvard University Press.
Lewis, D. (1979). Attitudes De Dicto and De Se. Philosophical Review, 88, 513–543.
Lewis, D. (1983). New work for a theory of universals. The Australasian Journal of Philosophy, 61(4), 343–377.
Acknowledgments
Special thanks to Bas van Fraassen, Mark Johnston, Sarah-Jane Leslie, and Barry Maguire. For helpful comments and conversations, thanks also to Samuel Baker, John Burgess, Adam Elga, Bas van Fraassen, Frank Jackson, Mark Johnston, Sarah-Jane Leslie, Barry Maguire, Kristin Primus, Agustín Rayo, Gideon Rosen, Michael Smith, Michael Strevens, Jack Woods and the audiences of the First Meeting of the American Association for Mexican Philosophers held at MIT, Princeton Dissertation Seminar (2009), Princeton’s Metaphysics Graduate Seminar (Spring 2010), and Arizona State University Colloquium Series (Fall 2014).
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Merino-Rajme, C. Why Lewis’ appeal to natural properties fails to Kripke’s rule-following paradox. Philos Stud 172, 163–175 (2015). https://doi.org/10.1007/s11098-014-0282-3
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DOI: https://doi.org/10.1007/s11098-014-0282-3