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The Putnam-Goodman-Kripke Paradox

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Abstract

The extensions of Goodman’s ‘grue’ predicate and Kripke’s ‘quus’ are constructed from the extensions of more familiar terms via a reinterpretation that permutes assignments of reference. Since this manoeuvre is at the heart of Putnam’s model-theoretic and permutation arguments against metaphysical realism (‘Putnam’s Paradox’), both Goodman’s New Riddle of Induction and the paradox about meaning that Kripke attributes to Wittgenstein are instances of Putnam’s. Evidence cannot selectively confirm the green-hypothesis and disconfirm the grue-hypothesis, because the theory of which the green-hypothesis is a part has an unintended model in which the grue-hypothesis is equally confirmed; and there are no meaning-facts that determine reference, because the objects referred to by the referring terms of any language or set of intentional mental states are permutable in a way that is consistent with the truth-values of all other sentences in that language or beliefs in that set. The upshot is that the three paradoxes need to be solved in a unified way.

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Notes

  1. Putnam credits Catherine Elgin with having suggested the resemblance to him (Goodman ([1954] 1983), viii); earlier remarks on the affinity between Goodman and Wittgenstein can be found in Blackburn (1969) and Hacking (1975), 69.

  2. See Putnam ([1978] 2010a) and Putnam (1981), respectively.

  3. Kripke himself calls it ‘Wittgenstein’s sceptical problem’. As customary in most discussions of Kripke (1982), I bracket the interesting, but for present purposes irrelevant, question how much Wittgenstein there is in Kripke’s Wittgenstein. For important early criticisms of Kripke’s exegesis, see e.g. Baker and Hacker (1984), Blackburn (1984), McDowell (1984), Shanker (1987), Savigny (1988) and Cavell (1990).

  4. See e.g. McGinn (1984); Fodor (1990), chs. 3 and 4; Horwich (1998), chs. 4 and 10; Tennant (1997), ch. 4 and Soames (1997, 1998); amongst the defenders are Allen (1989), Wilson (1998), Kusch (2006) and Wright (2012). For a collection and overview and a recent discussion, see Miller and Wright (2002) and Hale (2017), respectively.

  5. Cf. Kripke (1982), 19; Stroud (2000), 129.

  6. See Barker and Achinstein (1960), 511. Israel (2004) is adamant that defining ‘grue’ in this way amounts to a serious misunderstanding of the New Riddle. But Goodman himself used Barker and Achinstein’s ‘grue’ (see e.g. Goodman (1960)), and there are reasons for thinking that it better captures the essence of the paradox (Kowalenko (2011)). Kripke (1982) uses this definition, in any event, and so does Putnam, see Goodman (1954, 1983), xi.

  7. In the context of Putnam’s permutation argument (Putnam (1981), ch. 2); see Hale and Wright (2017), 712, and infra.

  8. The grey rectangle in Fig. 1 represents the chromatic variation conventionally allowed by the ordinary language predicate ‘green’. There is no sharp demarcation between clear-cut instances of ‘green’ and ‘borderline’ cases, and clear-cut instances of ‘¬green’, but it suffices for present purposes that there are instances where application of the predicate is uncontroversial. Goodman himself discusses grue-like hypotheses in the context of curve-fitting and simplicity in Goodman (1972), 344–345.

  9. Note that Fig. 2 represents the grue colour-spectrum using what appear to be two separate spectra. The grue/bleen colour coordinate scale as a result seems strangely ‘gerrymandered’, but this is an artefact of any attempt to graphically represent grue using our own colours. For ‘grue’ and ‘bleen’ are not actually colours, but schmolours (Ullian (1961), 387); also Goodman (1960); see infra on the concept of ‘schmolour’.

  10. He cites Hesse (1969) who claimed that at least as far as the language of science is concerned, it is not. If Putnam’s arguments against metaphysical realism are sound, then that claim is incorrect (see infra).

  11. For a still useful if somewhat dated overview of the debate, see Stalker (1994); for more recent discussion, see e.g. McGowan (2003), Okasha (2007), Israel (2004), Fitelson (2008), Kowalenko (2011), Freitag (2016) and Skiles (2016). It is worthwhile to point out here, however, that just as many other proposed solutions of Goodman’s paradox, Shoemaker’s argument—the ‘incoherence dissolution’, as Stalker (1994), 2 calls it—is premised on de-emphasising the symmetry between green- and grue-like sets of predicates, languages and conceptual schemes that Goodman insisted upon. To the nominalist Goodman, nothing about the predicate ‘green’ is special, except that it is ours. If he is correct about that, then any philosophical argument expressed in a language L1 (our green-language) that purports to establish, on grounds of incoherence, that a rival set of grue-like predicates cannot be admitted into L1 or its inductive practices, could be expected to work equally well from within language L2 (the grue-language). There, this sort of argument would establish equally firmly that the predicates of L1 cannot, on grounds of incoherence, be admitted into L2 or its inductive practices, and so on. In other words, the incoherence dissolution argument is language-relative in itself, which suggests that Shoemaker’s agreement-after-t0 condition need not be satisfied: green- and grue-speakers after t0 will think, quite reasonably, that their respective inductions came out right. What they think, say or take themselves to observe is irrelevant, however, insofar as what matters is that green- and grue-speakers cannot both be right simultaneously; see Putnam (1981), 36, and infra.

  12. Goodman (1978), 3ff; cf. Putnam ([1978] 2010a), 137, also Hacking (1993), 271.

  13. For a simple illustration of permutation, take the theory (T) consisting of the three sentences ‘Joe is taller than Peter’, ‘Peter is taller than Carol’ and ‘Joe is taller than Carol’ (see McGowan (2002), 29; also Williams (2007), 369). Whether (T) is true depends on whether there are objects in the world that simultaneously satisfy all the sentences of (T), and that depends on how we interpret the referring terms in these sentences, in particular, on whether ‘Joe’, ‘Peter’ and ‘Carol’ refer to objects that do in actual fact stand in the relation of ‘is taller than’ to each other in the way (T) alleges (in which case (T) has a model and Joe, Peter, Carol and the taller-than relation are the domain of the model.) It is clear that (T) has more than just one model. For if ‘Joe’, ‘Peter’, ‘Carol’ and ‘is taller than’ were defined as referring to the mountains Sagarmāthā, Kilimanjaro, Mont Blanc and the higher-than relation, respectively, then these objects would also constitute a model, albeit unintended, for (T), as would the natural numbers 3, 2, 1 and the greater-than relation ( >), and so on. It is intuitive to think that if there are enough distinct objects and relations in the world, then (T) will have quite a large number of unintended models, and that the more things there are, the more there will be models of (T), and further, that if the actual world consisted of infinitely many objects and infinitely many relations between these objects—as metaphysical realists typically believe—that (T) would have infinitely many models, and, finally, that in such a world, every theory would have a model. The same would be true of languages, if we think of languages as sets of sentences.

  14. Hale and Wright extended Putnam’s method of proof to show the same for second-order and modal languages (op. cit., 723–725).

  15. Also Putnam (1981), 33–36, Putnam (1983a), Putnam ([1978] 2010a).

  16. The fact that if a first-order theory has a model, then it has a countably infinite model (the ‘Downward’ Löwenheim-Skolem), and that if a such a theory has a model of any infinite cardinality, then it has models of every infinite cardinality (the ‘Upward’ Löwenheim Skolem), see Skolem ([1920] 1967).

  17. For early criticisms and more recent contributions, see e.g. Lewis (1984); Devitt (1984), ch. 11; van Fraassen (1997); Douven (1999); Chambers (2000); Bays (2001); Weiss (2004); Taylor (2006); Williams (2007) and Button (2011, 2013); for an overview of the state of the debate, see Hale and Wright (2017).

  18. See Putnam (1980), 476ff; Putnam (1981), 45–46 and Putnam (1983b), 18, (1994a), 358ff. For a critical discussion of the ‘Just More Theory’ argument, in particular the charge that it begs the question against metaphysical realism, see e.g. Devitt (1984), ch. 11; Taylor (1991); Melia (1996) and Hale and Wright (2017), 714–716. For a defence, see e.g. Button (2013), ch. 4.2.

  19. See e.g. Miller (1997); Martin and Heil (1998) and Horwich (1998, 2005).

  20. ‘If meaning determines reference then reference is determinate’; ‘reference is not determinate’ (Putnam’s paradox); therefore, ‘meaning does not determine reference’. In fact, on a model-theoretic account of semantic facts, this inference is likely to hold quite independently of our preferred theory of meaning, causal or not (see Button (2013), p. 11ff; Sova (2017), 9). In any event, without the sort of understanding of the meaning of our terms that could help us disambiguate between referential permutations, we stumble directly into the Kripke-Wittgenstein paradox (see infra).

  21. Where ‘x, y, x + y’ stands for the infinite set of ordered triples that constitutes the plus-function as defined over positive integers: {〈1, 1, 2〉, 〈2, 1, 3〉, ...  〈57, 68, 125〉 …}.

  22. Any two ordered triples 〈x, y, z〉, where x, y, z ∈ ℤ+, can be defined as having the same schmorm iffdf they have the same form for all x, y < 57, and have the form 〈x, y, 5〉 for all x, y ≥ 57.

  23. This is the assumption Putnam explicitly questioned in his internal realist phase, as well as after his ‘pragmatist turn’ (see e.g. Putnam (1994b, 2004) and Putnam and Putnam (2017)); we only need interpretations to attach words/thoughts to their referents/objects, if they would be unattached without them. A similar intuition is at work in Goodman’s and Kripke’s use-based solutions to their respective problems (cf. Wittgenstein ([1953] 2009), §198). Whether these moves are successful is beyond the scope of this paper.

  24. Cf. Sova (2017), 13–14 who agrees that permutation is the core idea of Putnam’s as well as Kripke-Wittgenstein’s paradox, and that the two pose the same dilemma for realism: either there are no facts about meaning/reference, or meaning-ascriptions have intrinsically unobservable and irreducible truth-conditions. Sova draws a different conclusion, however, and does not mention Goodman.

  25. See e.g. Putnam (1979) and Putnam (1982), 162. Putnam hints at a generalisation of Goodman’s New Riddle to explanation at Putnam (1982), 151; Goodman’s influence on Kripke is self-evident.

  26. See e.g. Goodman ([1954] 1983), 79 and Goodman (1966). Others in his wake re-deployed the argument, see e.g. Barker and Achinstein (1960), Davidson (1966), Schwartz, Scheffler et al. (1970), and many more.

  27. McGowan was the first to explicitly connect Putnam’s paradox with Goodman’s New Riddle in this manner, although she did so in the context of Russell’s theory of knowledge (McGowan (2002), 26–28) and passim, skipping over Kripke-Wittgenstein.

  28. ‘Intentionality won’t be reduced and won’t go away’ (Putnam (1988), 1).

References

  • Allen, B. (1989). Gruesome arithmetic: Kripke’s sceptic replies. Dialogue, 28(2), 257–264.

    Article  Google Scholar 

  • Baker, G. P., & Hacker, P. M. S. (1984). On misunderstanding Wittgenstein: Kripke’s private language argument. Synthese, 58, 407–450.

    Article  Google Scholar 

  • Barker, S. F., & Achinstein, P. (1960). On the new riddle of induction. Philosophical Review, 69, 511–522.

    Article  Google Scholar 

  • Bays, T. (2001). On Putnam and his models. The Journal of Philosophy, 98(7), 331–350.

    Article  Google Scholar 

  • Blackburn, S. (1969). ‘Goodman’s paradox’. Studies in the Philosophy of Science. N. Rescher. Oxford, Basil Blackwell., 3, 128–142.

    Google Scholar 

  • Blackburn, S. (1984). The individual strikes back. Synthese, 58, 281–302.

    Article  Google Scholar 

  • Boghossian, P. A. (1989). The rule-following considerations. Mind, 98, 507–549.

    Article  Google Scholar 

  • Button, T. (2011). The metamathematics of Putnam’s model-theoretic arguments. Erkenntnis, 74(3), 321–349.

    Article  Google Scholar 

  • Button, T. (2013). The limits of realism. Oxford University Press.

    Book  Google Scholar 

  • Carnap, R. (1947). On the application of inductive logic. Philosophy and Phenomenological Research, 8, 133–148.

    Article  Google Scholar 

  • Cavell, S. (1990). Conditions Handsome and Unhandsome. University of Chicago Press.

    Google Scholar 

  • Chambers, T. (2000). A quick reply to Putnam’s paradox. Mind, 109(434), 195–197.

    Article  Google Scholar 

  • Davidson, D. (1966). Emeroses by other names. Journal of Philosophy, 63, 778–780.

    Article  Google Scholar 

  • Devitt, M. (1984). Realism & truth. Princeton.

    Google Scholar 

  • Douven, I. (1999). Putnam’s model-theoretic argument reconstructed. Journal of Philosophy, 96(9), 479–490.

    Article  Google Scholar 

  • Elgin, C. Z. (1995). Unnatural science. Journal of Philosophy, XCII(6), 289–302.

    Article  Google Scholar 

  • Fitelson, B. (2008). Goodman’s “New Riddle.” Journal of Philosophical Logic, 37, 613–643.

    Article  Google Scholar 

  • Fodor, J. A. (1990). A theory of content II. MIT Press.

    Google Scholar 

  • Freitag, W. (2016). The disjunctive riddle and the grue-paradox. Dialectica, 70(2), 185–200.

    Article  Google Scholar 

  • Goodman, N. (1946). A query on confirmation. Journal of Philosophy, 43, 383–385.

    Article  Google Scholar 

  • Goodman, N. (1947). On infirmities of confirmation-theory. Philosophy and Phenomenological Research, 8(1), 149–151.

    Article  Google Scholar 

  • Goodman, N. (1949). On likeness of meaning. Analysis, 10, 1–7.

    Article  Google Scholar 

  • Goodman, N. (1953). On some differences about meaning. Analysis, 13, 90–96.

    Article  Google Scholar 

  • Goodman, N., & (1954,. (1983). Fact, Fiction, and Forecast. Harvard University Press.

  • Goodman, N. (1960). Positionality and pictures. Philosophical Review, 69, 523–525.

    Article  Google Scholar 

  • Goodman, N. (1966). Comments. Journal of Philosophy, 68, 328–331.

    Article  Google Scholar 

  • Goodman, N. (1972). Problems and Projects. Bobbs Merrill.

  • Goodman, N. (1976). Languages of Art. An Approach to a Theory of Symbols. Hackett.

  • Goodman, N. (1978). Ways of Worldmaking. Hassocks, Harvester Pr.

  • Goodman, N., & ([1954],. (1983). Fact, Fiction, and Forecast. Harvard University Press.

  • Hacking, I. (1975). Why Does Language Matter to Philosophy? Cambridge University Press.

    Book  Google Scholar 

  • Hacking, I. (1993). On Kripke’s and Goodman’s uses of ‘grue.’ Philosophy, 68(265), 269–295.

    Article  Google Scholar 

  • Hacking, I. (1998). ‘Entrenchment.’ Grue! The New Riddle of Induction. D. Stalker. Chicago and La Salle, Illinois, Open Court: 193–224.

  • Hale, B. (2017). Rule-following, objectivity, and meaning. In B. Hale, C. Wright, & A. Miller (Eds.), A Companion to the philosophy of language (pp. 619–649). Wiley-Blackwell.

    Chapter  Google Scholar 

  • Hale, B., & Wright, C. (2017). Putnam’s model-theoretic argument against metaphysical realism. In B. Hale, C. Wright, & A. Miller (Eds.), A Companion to the Philosophy of Language. Wiley.

    Chapter  Google Scholar 

  • Hesse, M. (1969). Ramifications of ‘grue.’ British Journal for the Philosophy of Science, 20, 13–25.

    Article  Google Scholar 

  • Horwich, P. (1998). Meaning. Clarendon.

    Book  Google Scholar 

  • Horwich, P. (2005). Reflections on Meaning. Clarendon Press.

    Book  Google Scholar 

  • Hume, D. ([1777] 1975). Enquiries concerning human understanding and concerning the principles of morals. Reprinted from the posthumous edition of 1777 and edited with introduction, comparative table of contents, and analytical index by L.A. Selby-Bigge. Oxford.

  • Israel, R. (2004). Two interpretations of ‘grue’ - or How to misunderstand the new riddle of induction. Analysis, 64(4), 335–339.

    Article  Google Scholar 

  • Kowalenko, R. (2011). Reply to Israel on the new riddle of induction. Philosophia, 40(3), 549–552.

    Article  Google Scholar 

  • Kripke, S. A. (1982). Wittgenstein on rules and private language. Harvard University Press.

    Google Scholar 

  • Kusch, M (2006). A Sceptical Guide to Meaning and Rules: Defending Kripke's Wittgenstein. Acumen & McGill-Queen's University Press.

  • Lewis, D. (1983). New work for a theory of universals. Australasian Journal of Philosophy, 61, 343–377.

    Article  Google Scholar 

  • Lewis, D. (1984). Putnam’s paradox. Australasian Journal of Philosophy, 62, 221–236.

    Article  Google Scholar 

  • Martin, C. B., & Heil, J. (1998). Rules and powers. Language, Mind, and Ontology, 12, 283–311.

    Google Scholar 

  • McDowell, J. (1984). Wittgenstein on following a rule. Synthèse, 58, 326–363.

    Article  Google Scholar 

  • McGinn, C. (1984). Wittgenstein on meaning. Blackwell.

    Google Scholar 

  • McGowan, M. K. (2002). Gruesome connections. The Philosophical Quarterly, 52(206), 21–33.

    Article  Google Scholar 

  • McGowan, M. K. (2003). Realism, reference and grue (why metaphysical realism cannot solve the grue paradox). American Philosophical Quarterly, 40(1), 47–57.

    Google Scholar 

  • Melia, J. (1996). Against Taylor’s Putnam. Australasian Journal of Philosophy, 74(1), 171–174.

    Article  Google Scholar 

  • Merrill, G. H. (1980). The model-theoretic argument against realism. Philosophy of Science, 47(1), 69–81.

    Article  Google Scholar 

  • Miller, A. (1997). Boghossian on reductive dispositionalism about content: The case strengthened. Mind and Language, 12, 1–10.

    Article  Google Scholar 

  • Miller, A., & Wright, C. (Eds.). (2002). Rule-following and meaning. Chesham.

    Google Scholar 

  • Millikan, R. G. (1990). Truth rules, hoverflies, and the Kripke-Wittgenstein paradox. Philosophical Review, 99(3), 323–353.

    Article  Google Scholar 

  • Okasha, S. (2007). What does Goodman’s ‘grue’ Problem really show? Philosophical Papers, 36(3), 483–502.

    Article  Google Scholar 

  • Putnam, H. (1981). Reason. Cambridge University Press.

    Google Scholar 

  • Putnam, H., & ([1978],. (2010a). Realism and reason (pp. 123–141). Routledge.

  • Putnam, H. (1979). Reflections in Goodman’s ways of world making. Journal of Philosophy, 76(11), 603–618.

    Article  Google Scholar 

  • Putnam, H. (1980). Models and reality. Journal of Symbolic Logic, 45, 464–482.

    Article  Google Scholar 

  • Putnam, H. (1982). Why there isn’t a ready-made world. Synthese, 51, 141–167.

    Article  Google Scholar 

  • Putnam, H. (1983a). Models and reality. In H. Putnam (Ed.), Realism and Reason. Philosophical Papers (Vol. 3, pp. 1–26). Cambridge University Press.

    Chapter  Google Scholar 

  • Putnam, H. (1983b). Realism and Reason. Philosophical Papers (Vol. 3). Cambridge University Press.

    Book  Google Scholar 

  • Putnam, H. (1988). Representation and Reality. MIT Press.

    Google Scholar 

  • Putnam, H. (1990). Realism with a Human Face. Edited by James Conant. Harvard University Press.

    Google Scholar 

  • Putnam, H. (1994a). ‘Model theory and the “Factuality” of semantics.’ Words and Life, edited by James Conant. J. Conant: 351–375.

  • Putnam, H. (1994b). Words and Life, edited by James Conant. Harvard University Press.

  • Putnam, H. (2004). Ethics without Ontology. Harvard University Press.

    Google Scholar 

  • Putnam, H., & ([1978],. (2010b). Meaning and the Moral Sciences. Routledge.

  • Putnam, Hilary and Ruth Anna Putnam (2017). Pragmatism as a Way of Life. The Lasting Legacy of William James and John Dewey. Ed. by D. Macarthur. Harvard University Press.

  • Quine, W. V. O. (1968). Ontological relativity. Journal of Philosophy, 65(7), 185–212.

    Article  Google Scholar 

  • Quine, Willard van Orman (1969). ‘Natural kinds.’ Essays in Honor of Carl G. Hempel. N. RescherSpringer.

  • Savigny, Eike V. (1988). Wittgensteins “Philosophische Untersuchungen”: Ein Kommentar für Leser (Band 1). Klostermann.

  • Schwartz, R., Scheffler, I., & Goodman, N. (1970). An improvement in the theory of projectibility. Journal of Philosophy, 67(18), 605–608.

    Article  Google Scholar 

  • Shanker, S. (1987). Wittgenstein and the Turning-Point in the Philosophy of Mathematics. Croom Helm.

    Google Scholar 

  • Shoemaker, S. (1975). On projecting the unprojectible. Philosophical Review, 84, 178–219.

    Article  Google Scholar 

  • Sider, T. (2011). Writing the Book of the World. Oxford University Press.

    Book  Google Scholar 

  • Skiles, A. (2016). ‘In defense of the disjunctive.’ Inquiry: An Interdisciplinary Journal of Philosophy, 59(5), 471–487.

  • Skolem, T. ([1920] 1967). ‘Logico-combinatorial investigations in the satisfiability or provability of mathematical propositions: A simplified proof of a theorem by L. Löwenheim and generalizations of the theorem.’ From Frege to Gödel: A Source Book in Mathematical Logic, 1879–1931. J. v. Heijenoort. Harvard University Press, p 252–264.

  • Soames, S. (1997). ‘Skepticism about meaning: Indeterminacy, normativity, and the rule-following paradox.’ The Canadian Journal of Philosophy.

  • Soames, S. (1998). Facts, truth conditions, and the skeptical solution to the rule-following paradox. Philosophical Perspectives, 12, 313–348.

    Google Scholar 

  • Sova, H. (2017). The dilemma imposed on the realist by Putnam’s and the Kripkensteinian argument. Studia Philosophica Estonica, 10(1), 1–21.

    Google Scholar 

  • Stalker, D. (Ed.). (1994). Grue! The New Riddle of Induction. Chicago and La Salle.

    Google Scholar 

  • Stroud, B. (2000). Meaning, understanding, and practice. Oxford University Press.

    Google Scholar 

  • Taylor, B. (1991). ‘Just more theory’: A manoeuvre in Putnam’s model-theoretic argument for antirealism. Australasian Journal of Philosophy, 69(2), 152–166.

    Article  Google Scholar 

  • Taylor, B. (2006). Models, truth, and realism. Oxford University Press.

    Book  Google Scholar 

  • Tennant, N. (1997). The Taming of the True. Clarendon Press.

    Google Scholar 

  • Ullian, J. S. (1961). More on “grue” and grue. Philosophical Review, 70, 386–389.

    Article  Google Scholar 

  • van Fraassen, B. C. (1997). Putnam’s paradox: Metaphysical realism revamped and evaded. Philosophical Perspectives, 11, 17–42.

    Google Scholar 

  • van Inwagen, P. (1992). There is no such thing as addition. Midwest Studies in Philosophy, 17, 138–159.

    Article  Google Scholar 

  • Weiss, B. (2004). The place of semantic theory. Pacific Philosophical Quarterly, 85, 454–469.

    Article  Google Scholar 

  • Williams, J. R. G. (2007). Eligibility and inscrutability. Philosophical Review, 116(3), 361–399.

    Article  Google Scholar 

  • Wilson, G. M. (1998). Semantic realism and Kripke’s Wittgenstein. Philosophy and Phenomenological Research, 58(1), 99–122.

    Article  Google Scholar 

  • Wittgenstein, L. (1929). Some remarks on logical form. Proceedings of the Aristotelian Society, Supplementary Volumes, 9, 162–171.

    Article  Google Scholar 

  • Wittgenstein, L. (1975). Philosophical Remarks, edited by Rush Rhees and translated by Hargreaves and White. Blackwell.

    Google Scholar 

  • Wittgenstein, L. ([1953] 2009). Philosophische Untersuchungen. Philosophical Investigations. Translated by G. E. M. Anscombe, P. M. S. Hacker and Joachim Schulte (Rev. 4th ed.). Wiley-Blackwell.

  • Wright, C. (1980). Wittgenstein on the foundations of mathematics. Harvard University Press.

    Google Scholar 

  • Wright, C. (2001). Rails to infinity. Harvard University Press.

    Google Scholar 

  • Wright, J. N. (2012). In defence of Kripkenstein: On Lewis’ Proposed solution to the sceptical argument. International Journal of Philosophical Studies, 20(5), 603–621.

    Article  Google Scholar 

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Kowalenko, R. The Putnam-Goodman-Kripke Paradox. Acta Anal 37, 575–594 (2022). https://doi.org/10.1007/s12136-022-00507-2

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