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Logic for Alethic, Logical, and Ontological Pluralists

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Pluralisms in Truth and Logic

Part of the book series: Palgrave Innovations in Philosophy ((PIIP))

Abstract

There have been few attempts to answer the challenges for alethic pluralists to maintain standard accounts of the logical operators and of logical consequence in a sufficiently systematic and precise way. This chapter presents a pluralist account of logic and semantics that answers these challenges. The chapter also shows how to accommodate logical pluralism and ontological pluralism within an extension of the framework.

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Notes

  1. 1.

    Sometimes, it is added that a truth property is whatever satisfies certain truth-characterizing principles. However, this possibly extra feature does not concern me here, so I omit mention of it for simplicity.

  2. 2.

    See Yu (2017).

  3. 3.

    This challenge is discussed in Lynch (2005b), Sher (2005, 2013), Wyatt (2013), Pedersen and Wright (2013b).

  4. 4.

    This challenge is discussed in Lynch (2009), Shapiro (2009, 2011), Cotnoir (2013), Pedersen and Wright (2013b).

  5. 5.

    See Tappolet (2000), Edwards (2008, 2009, 2012), Cotnoir (2009, 2013), Pedersen (2006, 2010, 2012), Pedersen and Wright (2013a), Wright (2012) on the extent to which pluralists should grant a generic truth property theoretical significance.

  6. 6.

    This challenge is discussed in Williamson (1994), Tappolet (2000), Lynch (2001, 2004, 2005b, 2008, 2009, 2013), Edwards (2008, 2009), Cotnoir (2009), Pedersen and Wright (2013b), Wright (2013).

  7. 7.

    Where there is little risk of confusion, I am somewhat loose with the distinction between truth properties themselves and truth values that formally represent them. For example, I may write of T as either being a truth property or representing a truth property. When discussing alethic pluralism informally, it is more natural to talk about truth properties, but when discussing the provision of a formal semantics, it is more natural to talk about truth values.

  8. 8.

    This challenge is discussed in Sainsbury (1996), Tappolet (1997), Beall (2000), Lynch (2000, 2004, 2005a, 2008, 2009), Pedersen (2006), Cotnoir (2013), Wright (2013).

  9. 9.

    See Yu (2017).

  10. 10.

    See Pedersen (2014), Cotnoir and Edwards (2015).

  11. 11.

    See Pedersen (2014) for the suggested combination of all three pluralisms.

  12. 12.

    See Beall and Restall (2006), Shapiro (2014) on logical pluralism more generally. The versions they discuss are not all domain-specific versions of logical pluralism.

  13. 13.

    Wright (1992, 44) seems to suggest this combination of alethic pluralism with logical pluralism . Lynch (2008, 2009) and Pedersen (2014) both suggest the combination.

  14. 14.

    See McDaniel (2009, 2010a, b, 2017), Turner (2010, 2012) on ontological pluralism.

  15. 15.

    In the scientific case, I assume for the sake of illustration that mathematics—or at least commitment to the existence of abstract mathematical objects—is dispensable; see Field (1980) for a defense of this view. In the ethical case, the relevant entities might be mind-dependent overall but have some basis in mind-independent entities as well. For example, perhaps the fact that an action constitutes murder is mind-dependent but has basis in the mind-independent fact that death is brought about.

  16. 16.

    Pedersen (2014), Cotnoir and Edwards (2015) suggest this combination of alethic pluralism with ontological pluralism.

  17. 17.

    See Pedersen (2014), Cotnoir and Edwards (2015).

  18. 18.

    We might restrict sentences associated with realist domains to only domain-specific truth values that represent either domain-specific truth or domain-specific falsity.

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Authors and Affiliations

  1. Faculty of Law, University of Toronto, Toronto, ON, Canada

    Andy D. Yu

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  1. Andy D. Yu
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Editors and Affiliations

  1. Underwood International College, Yonsei University, Incheon, Korea (Republic of)

    Jeremy Wyatt

  2. Underwood International College, Yonsei University, Incheon, Korea (Republic of)

    Nikolaj J. L. L. Pedersen

  3. University of Connecticut, Storrs, CT, USA

    Nathan Kellen

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Yu, A.D. (2018). Logic for Alethic, Logical, and Ontological Pluralists. In: Wyatt, J., Pedersen, N., Kellen, N. (eds) Pluralisms in Truth and Logic. Palgrave Innovations in Philosophy. Palgrave Macmillan, Cham. https://doi.org/10.1007/978-3-319-98346-2_17

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