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Dialetheism in Action: A New Strategy for Solving the Equal Validity Paradox?

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Dialetheism and its Applications

Part of the book series: Trends in Logic ((TREN,volume 52))

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Abstract

This paper starts from the Equal Validity Paradox, a paradoxical argument connected to the so-called phenomenon of faultless disagreement. It is argued that there are at least six strategies for solving the paradox. After presenting the first five strategies and their main problems, the paper focuses on the sixth strategy which rejects the assumption that every proposition cannot be both true and false. Dialetheism is the natural candidate for developing strategy six. After presenting strategy six in detail, we formulate a normative problem for the dialetheist and offer a tentative solution to it. We then elaborate further considerations connecting strategy six to pluralism about truth and logic. Even if strategy six is a hard path to take, its scrutiny highlights some important points on truth, logic and the norms for acceptance and rejection.

This paper has been developed along a considerable amount of time. The general strategy of considering the prospects of dialetheism for making sense of relativism was first sketched in [11]; Sects. 1–4.2 have been elaborated jointly, while part of Sects. 5 and 5.1–6 have been developed by Sebastiano Moruzzi.

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Notes

  1. 1.

    The expression “faultless disagreement” has been introduced in the literature by Kölbel [27]. See [18] for a useful normative analysis of the phenomenon.

  2. 2.

    We use italics for referring to propositions.

  3. 3.

    Grim [21] has in fact calculated that there at least 240 possible formulations of LNC!

  4. 4.

    See [10, pp. 166–69] for a discussion of the semantic formulation.

  5. 5.

    We use ‘<p>’ to name the proposition that p, and ‘circ(<s,c>)’ to name the circumstances of evaluation relative to the utterance of ‘s’ in context c.

  6. 6.

    We are appealing to contradiction because in the example in question are involved sentences of the from “p” and “not-p”. The more general relation should be the one of incompatibility which can involve also being contraries.

  7. 7.

    For a more detailed and slightly different reconstruction of the Equal Validity Paradox see [13].

  8. 8.

    See for example [24] for the thesis that there is no faultless disagreement.

  9. 9.

    Following [53], this solution is an “unhappy face” solution to the paradox.

  10. 10.

    See also [13].

  11. 11.

    For realism see [4, 52]; for assessment-sensitive relativism see [29, 30, 32], for non-indexical contextualism (aka truth relativism) see [28].

  12. 12.

    See [61].

  13. 13.

    The critical literature on MacFarlane’s relativism is huge. For some recent critical points see [19, 20, 34, 35, 49, 55, 58, 60].

  14. 14.

    The debate on the normativity of truth is wide and complex. We are here assuming a rather weak norm. See Ferrari 2016 and ms for an analysis on the different varieties of normativity that could exert on truth.

  15. 15.

    Ayer [2] is the first example of this strategy in relation to aesthetics and morality. For contemporary examples of this strategy see [22, 23, 50].

  16. 16.

    See [57].

  17. 17.

    See [17].

  18. 18.

    For the basic worry of the lost disagreement problem see [12]. For sophisticated forms of contextualism see [14, 56, 63].

  19. 19.

    Notice that in order to avoid violation of LNC, it should claimed that either (a) one proposition is true and the other is false; or (b) the propositions expressed are not contradictory; or (c) that <p> is untrue (but not false) and that <not-p> is false. As for option (a), it seems tantamount to realism, so option (a) collapses into strategy (ii). Analogously, option (b) seems just indexical contextualism, so we have a collapse into strategy (iv). Finally, option (c) requires to adopt some version of three-valued semantics with a value (call it “untruth only”) that is excluded by truth of a negation. This latter option seems the most promising option for avoiding the collapse into other strategies.

  20. 20.

    Assuming that propositions are objects of belief.

  21. 21.

    The idea of using dialetheism for accounting for the phenomenon of faultless disagreement is sketched in [7] where it is claimed that analetheism—which interprets gappy propositions as designated—is a better option. See [9] for a presentation of analetheism. Beall [7] prefers this strategy to dialetheism in relation to taste on the grounds that analetheism makes sense of the idea that there is no fact of the matter in matters of sense (taste propositions are neither true nor false). We agree with [1] in thinking that analetheism does not do justice to the truth-norm for the same problems we have raised before in relation to the indeterminist gappy theory (see supra Sect. 3.1). Insofar as truth is the norm for assertion, we do not think that this model of indeterminacy is sufficient for accounting for the rational sustainability of a dispute. We will thus focus on dialetheism.

  22. 22.

    Recall that we are using a semantic reading of LNC. In LP the formula \(\lnot (p \wedge \lnot p)\) is never false only since, when p is dialetheia, the formula itself is a dialetheia.

  23. 23.

    “I am frequently asked for a criterion as to when contradictions are acceptable and when they are not. It would be nice if there were a substantial answer to this question—or even if one could give a partial answer, in the form of some algorithm to demonstrate that an area of discourse is contradiction free. But I doubt that this is possible. Nor is this a matter for surprise. Few would now seriously suppose that one can give an algorithm—or any other informative criterion—to determine when it is rational to accept something. There is no reason why the fact that something has a certain syntactic form—be it \(p \wedge \lnot p\) or anything else—should change this. One can determine the acceptability of any given contradiction, as of anything else, only on its individual merits” [45, p. 423].

  24. 24.

    See [3, 11].

  25. 25.

    Aristotle (Metaphysics, \(\Gamma \) 4) famously held that LNC cannot admit exceptions. See [44] for a discussion of Aristotle on LNC.

  26. 26.

    This normative problem in relation to faultless disagreement is outlined in [11, pp. 151–152]. See also [59, p. 438].

  27. 27.

    The equivalence between acceptance of not-P and rejection (or denial) of P is known as “denial equivalence” in [51] and as “classical denial” in [36]. Also gappy theorists reject this equivalence—see [37].

  28. 28.

    We can interpret acceptance of p and rejection of p as “yes-or-no questions, respectively reading A? Yes! and A? No!” [36, \(\S 2\)].

  29. 29.

    See [10, 21]. Berto [10, pp. 174–178] states some worries regarding the idea that acceptance and rejection are primitively exclusive mental states. Berto argues that it is better to explain this incompatibility between attitudes through a notion of content exclusion. We agree with Berto’s point, however this issue will not be crucial for the following discussion.

  30. 30.

    In other words the exclusivity relation between acceptance and rejection involve that accepting p and rejecting p cannot be jointly correct attitudes. For the notion of joint correctness and its relation to disagreement see [32].

  31. 31.

    “If denial is to serve as a means to express disagreement, it must be rationally impermissible to both assert and deny A. Yet, in view of the Paradox of Deniability, no comprehensive set of norms for exclusive denial can be formulated in the glut-theorist’s language” [36]. See also [51] for similar worries.

  32. 32.

    This a modified version considered by Murzi and Carrara [36] under the label “Deny(U)*”.

  33. 33.

    It is also doubtful that in mathematics the evidence for an assertion must always be a proof.

  34. 34.

    The other option Carrara and Murzi consider is [6]’s proposal according to which we can add the so-called shriek-rules to express that a sentence is true-only. For each sentence A which is not glutty it is added a non-logical rule of the form: \(A, \lnot A \vdash \bot \), where ‘\(\bot \)’ is an operator that implies triviality. By means of the shriek-rules we can then express that a theory is consistent by stating shriek-rules for all the predicates—a shrieked theory. A shrieked-theory is thus either consistent or trivial. Notice, however, that this proposal will not work if the dialetheist position for the Equal Validity Paradox entails local triviality as argued below—see infra Sect. 6.

  35. 35.

    For issues related to domains of discourse see [62].

  36. 36.

    “LP has its so-called trivial model: if all atomic sentences of the relevant language are both true and false (or both true and false at the base world where truth is evaluated, if we have a worlds semantics for LP plus arrow), then all sentences are true and false.” [10, p. 170].

  37. 37.

    Together with all the other propositions targeted by the dialetheist such as the liar, Russell’s paradox, sentences expressing change etc.

  38. 38.

    For domain-based logical pluralism see [31, Chap. 5], [39, 40].

  39. 39.

    For alethic pluralism see [31] and the collection [41].

References

  1. Armour-Garb, B., & Priest, G. (2005). Analetheism: A pyrrhic victory. Analysis, 65(286), 167–173.

    Article  Google Scholar 

  2. Ayer, A. J. (1936). Language, truth and logic, London: V. Gollancz.

    Google Scholar 

  3. Baghramian, M., & Coliva, A. (forthcoming). Relativism. London: Routledge.

    Google Scholar 

  4. Baker, C., & Robson, J. (2017). An absolutist theory of faultless disagreement in aesthetics. Pacific Philosophical Quarterly, 98(3).

    Google Scholar 

  5. Batens, D. (1990). Against global paraconsistency. Studies in East European Thought, 39(3–4), 209–229.

    Article  Google Scholar 

  6. Beall, J. (2013). A simple approach towards recapturing consistent theories in paraconsistent settings. Review of Symbolic Logic, 6(4), 755–764.

    Article  Google Scholar 

  7. Beall, J. C. (2006). Modelling the ‘ordinary view’. In P. Greenough & M. Lynch (Eds.), Truth and relativism (pp. 61–76). Clarendon Press.

    Google Scholar 

  8. Beall, J. C. (2009). Spandrels of truth. Oxford, UK: Oxford University Press.

    Book  Google Scholar 

  9. Beall, J., & Ripley, D. (2004). Analetheism and dialetheism. Analysis, 64(281), 30–35.

    Article  Google Scholar 

  10. Berto, F. (2008). Adynaton and material exclusion. Australasian Journal of Philosophy, 86(2), 165–190.

    Article  Google Scholar 

  11. Coliva, A. (2009). I modi del relativismo. Roma-Bari: Laterza.

    Google Scholar 

  12. Coliva, A., & Moruzzi, S. (2014). Basic disagreement, basic contextualism and basic relativism. Iride, 27(2), 537–554.

    Google Scholar 

  13. Coliva, A., & Moruzzi, S. (2014). Faultless disagreement and the equal validity paradox. In S. Caputo, F. Bacchini, & M. Dell’Utri (Eds.), New frontiers in truth. Newcastle upon Tyne: Cambridge Scholars Publishing.

    Google Scholar 

  14. de Sa, D. L. (2015). Expressing disagreement: A presuppositional indexical contextualist relativist account. Erkenntnis, 80(1), 153–165.

    Google Scholar 

  15. Dummett, M. (1959). Truth. Proceedings of the Aristotelian Society, 59. Reprinted with a post-scriptum in Dummett (pp. 1–24) (1978).

    Google Scholar 

  16. Dummett, M. (1978). Truth and others enigmas. Duckworth.

    Google Scholar 

  17. Eklund, M. (2010). Vagueness and second-level indeterminacy. In R. Dietz & S. Moruzzi (Eds.), Cuts and clouds: Vaguenesss, its nature and its logic. Oxford University Press.

    Google Scholar 

  18. Ferrari, F. (2016). Disagreement about taste and alethic suberogation. The Philosophical Quarterly, 66(264), 516–535. http://pq.oxfordjournals.org/content/66/264/516.abstract.

    Article  Google Scholar 

  19. Ferrari, F. (2016). Relativism, faultlessness and parity: Why we should be pluralists about truths normative function. Argumenta, 2(1), 77–94.

    Google Scholar 

  20. Ferrari, F., & Wright, C. (2017). Talking with vultures, Mind 126(503), 911–936. http://dx.doi.org/10.1093/mind/fzw066.

  21. Grim, P. (2004). What is a contradiction? In G. Priest, J. Beall, & B. P. Armour-Garb (Eds.), The law of non-contradiction: New philosophical essays (pp. 49–72). Oxford University Press.

    Google Scholar 

  22. Huvenes, T. T. (2012). Varieties of disagreement and predicates of taste. Australasian Journal of Philosophy, 90(1), 167–181.

    Article  Google Scholar 

  23. Huvenes, T. T. (2014). Disagreement without error. Erkenntnis, 79(1), 143–154.

    Article  Google Scholar 

  24. Iacona, A. (2007). Faultless or disagreement. In M. Kölbel & M. García-Carpintero (Eds.), Relative truth. Oxford University Press.

    Google Scholar 

  25. Kabay, P. (2010). On the plenitude of truth: A defense of trivialism. Saarbrücken: Lambert Academic Publishing.

    Google Scholar 

  26. Kelly, T. (2005). The epistemic significance of disagreement. In J. Hawthorne & T. Gendler (Eds.), Oxford studies in epistemology (Vol. 1, pp. 167–196). Oxford University Press.

    Google Scholar 

  27. Kölbel, M. (2003). Faultless Disagreement. Proceedings of the Aristotelian Society, 54(1), 53–73.

    Article  Google Scholar 

  28. Kölbel, M. (2004). Indexical relativism versus genuine relativism. International Journal of Philosophical Studies, 297–313.

    Article  Google Scholar 

  29. Lasersohn, P. (2005). Context dependence. Disagreement, and Predicates of Personal Taste, Linguisticis and Philosophy, 28(6), 643–686.

    Article  Google Scholar 

  30. Lasersohn, P. (2013). Non-world indices and assessment-sensitivity, Inquiry: An Interdisciplinary. Journal of Philosophy, 56(2–3), 122–148.

    Google Scholar 

  31. Lynch, M. P. (2009). Truth as one and many. Oxford University Press.

    Google Scholar 

  32. MacFarlane, J. (2014). Assessment sensitivity: Relative truth and its applications. Oxford: Oxford University Press.

    Book  Google Scholar 

  33. Mares, E. D. (2004). Semantic dialetheism. In G. Priest, J. C. Beall, & B. Armour-Garb (Eds.), The law of non-contradiction. Clarendon Press.

    Google Scholar 

  34. Marques, T. (2014). Relative correctness. Philosophical Studies, 167(2), 361–373. http://dx.doi.org/10.1007/s11098-013-0100-3.

    Article  Google Scholar 

  35. Moruzzi, S. (2008). Assertion, belief and disagreement: A problem for truth-relativism. In M. Kölbel & M. García-Carpintero (Eds.), Relative truth. Oxford University Press. In corso di pubblicazione.

    Google Scholar 

  36. Murzi, J., & Carrara, M. (2014). Denial and disagreement. Topoi, 34(1), 109–119.

    Article  Google Scholar 

  37. Parsons, T. (1984). Assertion, denial, and the liar paradox. Journal of Philosophical Logic, 13(2), 137–152.

    Article  Google Scholar 

  38. Parsons, T. (1990). True contradictions. Canadian Journal of Philosophy, 20(3), 335–353.

    Article  Google Scholar 

  39. Pedersen, N. (n.d.). On moderate pluralism about truth and logic: Truth and logic as one, quasi-truth and quasi-logic as many.

    Google Scholar 

  40. Pedersen, N. J. L. L. (2014). Pluralism x 3: Truth, logic, metaphysics. Erkenntnis, 79(2), 259–277.

    Article  Google Scholar 

  41. Pedersen, N. J. L. L., & Wright, C. D. (2013). Truth and pluralism: Current debates. Oxford University Press.

    Google Scholar 

  42. Plebani, M. (2015). Could everything be true? Probably not. Philosophia, 43(2), 499–504.

    Article  Google Scholar 

  43. Priest, G. (1989). Reductio ad absurdum et modus tollendo ponens. In G. Priest, R. Routley, & J. Norman (Eds.), Paraconsistent logic. Essays on the inconsistent (pp. 613–626). Philosophia Verlag, München.

    Google Scholar 

  44. Priest, G. (1998). To be and not to be-that is the answer. On Aristotle on the law of non-contradiction. Logical Analysis and History of Philosophy, 1.

    Google Scholar 

  45. Priest, G. (1998). What is so bad about contradictions? Journal of Philosophy, 95(8), 410–426.

    Article  Google Scholar 

  46. Priest, G. (2000). Could everything be true? Australasian Journal of Philosophy, 78(2), 189–195.

    Article  Google Scholar 

  47. Priest, G. (2005). Doubt truth to be a liar. Oxford University Press.

    Google Scholar 

  48. Priest, G. (2006). In contradiction: a study of the transconsistent. Oxford University Press.

    Google Scholar 

  49. Raffman, D. (2016). Relativism, retraction, and evidence. Philosophy and Phenomenological Research, 92(1), 171–178.

    Article  Google Scholar 

  50. Richard, M. (2008). When truth gives out. Oxford University Press, UK.

    Google Scholar 

  51. Ripley, D. (2015). Embedding denial. In C. Caret & O. Hjortland (Eds.), Foundations of logical consequence (pp. 289–309). Oxford University Press.

    Google Scholar 

  52. Schafer, K. (2011). Faultless disagreement and aesthetic realism. Philosophy and Phenomenological Research, 82(2), 265–286.

    Article  Google Scholar 

  53. Schiffer, S. (2003). The things we mean. Oxford: Oxford University Press.

    Book  Google Scholar 

  54. Schroeder, M. A. (2008). Being for: Evaluating the semantic program of expressivism. Oxford University Press.

    Google Scholar 

  55. Stanley, J. (2016). On a case for truthrelativism. Philosophy and Phenomenological Research, 92(1), 179–188.

    Article  Google Scholar 

  56. Sundell, T. (2011). Disagreements about taste. Philosophical Studies, 155(2), 267–288.

    Article  Google Scholar 

  57. Woods, J. (forthcoming). The frege-geach problem. In D. Plunkett & T. McPherson (Eds.), The Routledge handbook of metaethics. Routledge.

    Google Scholar 

  58. Wright, C. (2007). Relativism about Truth Itself: Further thoughts about the Very Idea. In M. Kölbel & M. García-Carpintero (Eds.), Relative truth. Oxford University Press.

    Google Scholar 

  59. Wright, C. (2012). Mind, meaning and knowledge: Themes from the Philosophy of Crispin Wright. In Replies part III: Truth, objectivity, realism and relativism (pp. 418–450). Oxford University Press, Oxford.

    Chapter  Google Scholar 

  60. Wright, C. (2016). Assessment sensitivity: The manifestation challenge. Philosophy and Phenomenological Research, 92(1), 189–196.

    Article  Google Scholar 

  61. Wright, C. J. G. (2001). On being in a quandary. Relativism vagueness logical revisionism. Mind, 110(437), 45–97.

    Article  Google Scholar 

  62. Wyatt, J. (2013). Domains, plural truth, and mixed atomic propositions. Philosophical Studies, 166(1), 225–236.

    Article  Google Scholar 

  63. Wyatt, J. (forthcoming). Absolutely tasty: An examination of predicates of personal taste and faultless disagreement. Inquiry.

    Google Scholar 

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Authors and Affiliations

  1. Department of Philosophy and Communication Studies, University of Bologna, Bologna, Italy

    Sebastiano Moruzzi

  2. University of California, Irvine, CA, USA

    Annalisa Coliva

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  1. Sebastiano Moruzzi
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Correspondence to Sebastiano Moruzzi .

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  1. University of Glasgow, Glasgow, UK

    Adam Rieger

  2. University of Glasgow, Glasgow, UK

    Gareth Young

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Moruzzi, S., Coliva, A. (2019). Dialetheism in Action: A New Strategy for Solving the Equal Validity Paradox?. In: Rieger, A., Young, G. (eds) Dialetheism and its Applications. Trends in Logic, vol 52. Springer, Cham. https://doi.org/10.1007/978-3-030-30221-4_4

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