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Published online by Cambridge University Press: 25 November 2010
ABSTRACT: I argue that mathematical norms are real. Semantic norms, including mathematical norms for adding, are governed by social practices of undertaking and attributing meaning, and this fact has obscured the objectivity of norms from view. However, a conception of human normativity that takes as its starting point that humans are part of the world undercuts the misconception that our practices are not sufficient to ground real meaning.
RÉSUMÉ : J’affirme que les normes sémantiques, y compris les normes mathématiques pour l’addition, sont réelles. Ces normes sont régies par des pratiques sociales d’attribuer aux autres et d’entreprendre soi-même la signification, et cet aspect sociale obscurci l’objectivité des normes. L’attribution par Kripke d’un paradoxe sceptique, quant à la possibilité de suivre une règle, relève d’une conception de la normativité selon laquelle les pratiques sociales sont insuffisantes pour autoriser les normes sémantiques. Or, une conception de la normativité qui prend comme point de départ que les êtres humains font partie du monde, détrône cette idée fausse ainsi que le scepticisme sémantique qu’elle soutien.
I wish to thank Professor Richmond Campbell and Professor Michael Hymers for their helpful comments, and steadfast support.
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2 Here Kripke quotes Wittgenstein’s Philosophical Investigations §201. See Wittgenstein, Ludwig, Philosophical Investigations, trans. Anscombe, G. E. M., 3rd ed. (Oxford: Blackwell, 1953).Google Scholar
3 Brandom, Robert, Making It Explicit: Reasoning, Representing, and Discursive Commitment (Cambridge: Harvard University Press, 1994).Google Scholar
4 See Wittgenstein’s Philosophical Investigations, §§256–271.
5 Soames, Scott, “Facts, Truths, and the Skeptical Solution to the Rule-Following Paradox,” in Philosophical Perspectives 12, Language, Mind and Ontology, ed. Tomberlin, James (Atascadero: Ridgeview, 1998), 313–48.Google Scholar
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8 Ebbs, Gary, Rule-Following and Realism (Cambridge: Harvard University Press, 1997).Google Scholar
9 Brandom, Robert, Making It Explicit: Reasoning, Representing, and Discursive Commitment (Cambridge: Harvard University Press, 1994).Google Scholar
10 R. M. Hare, “Philosophical Discoveries” (1967), reprinted in Richard Rorty (ed.) The Linguistic Turn: Recent Essays in Philosophical Method (Chicago: University of Chicago Press, 1988).
11 See Rule-Following and Realism, chapter 3, especially p.65, and chapters 8, 9 and 10.
12 Hymers, Michael, Philosophy and Its Epistemic Neuroses (Boulder: Westview, 2000).Google Scholar
13 Hymers, Michael, “Ebbs’ Participant Perspective on Self-Knowledge,” Dialogue 41 (2002): 10–1.CrossRefGoogle Scholar
14 In his discussion of internal and external sanctions, Brandom notes that the complexes of intentional internal sanctions may arise out of other internal sanctions or out of non-intentional (but still normative) external sanctions. However, both varieties of sanction depend fundamentally upon the attitudes of individuals, and societies, who take particular behaviours to be deserving of sanctions.
15 This contrasts Kripke’s reliance on a correspondence theory of truth with Ebbs and Brandom’s rejection of correspondence theories of truth. Below, I review Paul Boghossian’s contention that Kripke’s reliance on the correspondence theory of truth to foment meaning scepticism betrays an overly philosophical conception of facts. My thanks to an anonymous referee for drawing my attention to this facet of the dispute.
16 Putnam, Hilary, “Meaning and Reference,” in Martinich, A. P. (ed.) The Philosophy of Language (Oxford: Oxford University Press, 1973), 284–91.Google Scholar
17 Brandom outlines his prosentential theory of truth in chapter 5 of Making It Explicit. The prosentential theory of truth seeks to amend certain inadequacies of the disquotational truth schema such as its inability to account for the truth of “a quantified sentence nominalization” (300).
18 Quoted in Rosen, Gideon, “Who Makes the Rules Around Here?” Philosophy and Phenomenological Research 57 (1997): 163–71.CrossRefGoogle Scholar
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20 The foregoing exegesis is meant to lend some plausibility to the intuition that there is a non-trivial similarity between Brandom’s and Ebbs’s straight solutions and Kripke’s skeptical solution. For reasons of perspicuity the analysis omits the finer details of Ebbs’s and Brandom’s views.
21 Ebbs’s conception of “us” comprises a spatially and temporally extended community of language users whose insights into their environment includes actual and possible discoveries.
22 Wilson, George, “Semantic Realism and Kripke’s Wittgenstein,” Philosophy and Phenomenological Research 58 (1998): 99–122.CrossRefGoogle Scholar
23 By contrast, the strong truth-conditional conception of meaning claims that “if x means something by a (general) term Φ, then x does so because there is a set of properties P1-Pn, of which x has a prior grasp, and x has the intention … that Φ is to apply to an object o if o has P1-Pn” (Soames, 332). Kripke’s argument does not obviously invoke the strong truth-conditional interpretation of meaningfulness.
24 Kripke reads Wittgenstein’s claim “To obey a rule, to make a report, to give an order to play a game of chess, are customs (uses, institutions)” (PI: §199), as endorsing a communitarian conception of rule-following. Although “practice,” “custom,” “institution,” and even “usage” often pick out group activities, what makes an act conform to or defy a rule does not simply redound to whether that move is accepted by other participants.
25 Byrne, Alex, “On Misinterpreting Kripke’s Wittgenstein,” Philosophy and Phenomenological Research 51 (1996): 339–43.CrossRefGoogle Scholar
26 In particular, Boghossian charges Kripke with an excessively philosophical correspondence theory of truth.
27 Boghossian, Paul, “The Rule Following Considerations,” Mind 98 (1989): 507–49.CrossRefGoogle Scholar
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29 Wright, Crispin, “Kripke’s Account of the Argument Against Private Language,” The Journal of Philosophy 81 (1984): 754–78.CrossRefGoogle Scholar
30 McDowell, John, “Wittgenstein on Following a Rule,” in Mind Value and Reality (Cambridge: Harvard University Press, 1998).Google Scholar
31 The practice of adding cannot be justified from within that practice, any more than logic can be justified from within logic. See Gödel, Kurt, On Formally Undecidable Propositions of Principia Mathematica and Related Systems, trans. Meltzer, B. (New York: Dover, 1962).Google Scholar
32 In conversation, Brandom has admitted that there is some promise to the view that implicit know-how is located at the intersection of non-normative bedrock and the normative sphere that lies above bedrock. This view finds support from Ruth Millikan’s conception of motivational/representational states which “mediate the production of certain variation in the environment, thus directly translating the shape of the environment to the shape of a certain kind of conforming action” (145). See her 1995 “Pushmi-Pullyu Representations” in Philosophical Perspectives 9: AI, Connectionism, and Philosophical Psychology, ed. Tomberlin, James (Atascadero: Ridgeview, 1995), 185–200.Google Scholar
33 See Kant, Immanuel, Critique of Pure Reason, trans. Guyer, Paul and Wood, Allen W. (1781; rep. Cambridge: Cambridge University Press, 1998), A 547Google Scholar.
34 This way of putting the point is Michael Hymers’s (personal communication).
35 Ebbs’s commitment to anti-individualism (chapters 7 and 8 of Rule-Following and Realism) shows that his position is congenial to the broader notion of “participation” that I advocate.