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Alethic Pluralism, Logical Validity, and Natural Truth

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Abstract

Alethic pluralism holds that there are many ways of being true. The view has been accused of being unable to do justice to the traditional account of logical validity, understood as necessary truth preservation. In this paper I reformulate the debate in terms of the naturalness of generic truth, and discuss some notable consequences of this more careful reformulation. I show not only that some alleged solutions, like the resort to plural quantification, are ineffective, but also that the problem is not really posed by mixed inferences, as usually thought. Finally, I argue that the traditional account of logical validity does carry a commitment to generic truth, so that a strong version of alethic pluralism can hardly vindicate it.

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Notes

  1. See Wright (1992, 1999, 2013) and Lynch (2009).

  2. Alethic pluralism can also be formulated in terms of a plurality of truth concepts and truth predicates (see, e.g. Kölbel, 2008). In this paper, however, I focus on a metaphysical version of pluralism.

  3. Pedersen (2006).

  4. Williamson (1994), Tappolet (1997, 2000).

  5. This objection is particularly troublesome for strong forms of pluralism, since moderate pluralists may easily point out that, if there is a generic truth property had by all true propositions, then the truth property preserved in mixed valid inferences is exactly such a generic property. In the following I thus focus on strong pluralism and put moderate versions aside.

  6. Notice that the objection is not intended to show that strong pluralism cannot account for validity in any reasonable sense. The point is just that strong pluralism seems incompatible with a well established semantic analysis of validity, so that it is prone to a specific theoretical cost.

  7. Lewis (1983).

  8. Recently, some authors, such as Gamester (2018) and Lynch and Pedersen (2018) have argued that mixed inferences pose no serious problem to strong truth pluralism. Basically, the reason is that the idea of truth preservation should not be taken literally, since what is meant is just that the truth properties of the premises and the truth property of the conclusion (all possibly different) covary in the right way. Such a dissolution of the problem, however, is irrelevant for this paper, since the problem raised by logical validity is different and deeper, as I am going to argue.

  9. Beall (2000).

  10. Tappolet (2000).

  11. In this paper I do not discuss the possibility that designation might not represent truth. Apart from the desire of simplicity, this can be motivated in two ways. First of all, designation and generic truth have the same extension. Secondly, insofar as the pluralist sees validity as preservation of designation, she is forced to claim that designation is a kind of truth. Otherwise she would apparently fail to vindicate the classical account which requires truth be the property necessarily preserved.

  12. Pedersen (2006).

  13. See Cotnoir (2013).

  14. As in Urbaniak (2013).

  15. It should be noted, to be fair, that Pedersen is aware that the problem is genuinely metaphysical. He appeals to the sparse/abundant distinction to clarify the issue and does not rely merely on plural quantification.

  16. Lewis (1983), Edwards (2013a), and Asay (2014). Edwards (2018) provides an extensive discussion and systematic application of the distinction between the sparse/abundant distinction in the truth debate.

  17. In what follows I take 'sparse' (abundant) and 'natural' (non natural) basically as synonymous.

  18. Lewis' talk of properties is itself intended to be a neutral way of speaking of the phenomenon of attribute agreement, preferring the term 'universal' for the entity corresponding to a property in the realistic view. Lewis (1983).

  19. Edwards (2018).

  20. The application was originally put forward in Edwards (2013a) and Asay (2014) to make sense of the claim that deflationary truth is insubstantial. See also Edwards (2018).

  21. This is a further application of the approach defended in Edwards (2018), where he discusses the relationship between pluralism and the sparse/abundant distinction at length. For example, Edwards uses the sparse/abundant distinction to shed light on deflationism and on semantic differences of various kinds of discourse.

  22. This point is already quite known, and sometimes discussed in connection with the so-called instability challenge of alethic pluralism. See, in particular, Pedersen and Wright (2013).

  23. At this point, thus, I disagree with Pedersen and Wright (2013). I am inclined to think that once it is admitted that the alleged disjunctive property exhibits some qualitative core feature, then it should no longer be deemed as an authentic disjunctive property. Indeed, why should it be? I suspect, however, that Pedersen and Wright could simply turn their disjunctive proposal into a form of second order functionalism about truth. Indeed, they already seem to flirt with this option, given that they admit that the two approaches could be considered as mere notational variants.

  24. For instance, the property of being a (positive natural) number is extensionally equivalent to the property of being equal to 1, or being equal to 2, or being equal to 3, or being etc..

  25. See Edwards (2018, p. 150–151, where also Kris McDaniel discussing ontological pluralism is cited. McDaniel, for example, writes: “Being healthy is something like a mere disjunction whose disjuncts… But being healthy is not a mere disjunction: the various specifications of being healthy are related in such a way to ensure some kind of unity.” McDaniel (2010, pp. 695–6.). Some observations in a similar spirit can also be found in Lynch (2009, p. 126–127). See also Edwards (2012).

  26. See Lynch (2009), Pedersen and Wright (2013), Edwards (2012, 2018).

  27. This corresponds, respectively, to second order or functional pluralism (Lynch, 2001, 2004), manifestation pluralism (Lynch, 2009), and determination pluralism (Edwards, 2013b, 2018).

  28. One possibility might be that of denying that the obtained generic property itself would satisfy the truisms. See Lynch (2009, pp. 63–57) and Pedersen and Wright (2013, p.121).

  29. If a mere instrumental account were enough, then also strong pluralists could appeal to generic truth, since such an account would not force a commitment to the ontological reality of such a property. Thus, if we gathered the inferences in the subclass of the valid ones just in accordance with pragmatic motivations, then the problem of the nature of validity would disappear.

  30. This provides a reply to Wright (2013) who claims that the objection of mixed inferences only goes through if there are independent reasons to think that what is preserved must be a unique property. Indeed, the above discussion shows that such independent reasons do exist.

  31. One might find strange that validity is here considered sparse, given that the notion of naturalness finds its home in the context of objective resemblance and causality. Accordingly, logical properties might not seem good candidates for natural properties. I offer two quick reasons to put such worries aside. First, it is customary to consider also broad explanatory roles as marks of naturalness, and objective resemblance also holds for abstract entities (triangles versus circles, for instance). Secondly, the objection would extend also to other semantic properties such as truth. The application of the sparse/natural distinction in the case of truth, however, has been explicitly defended and is now rather customary. See Edwards (2013a, 2018) and Asay (2014).

  32. Edwards (2018, p. 95–96).

  33. Usually, Tarskian biconditionals are included among the truth platitudes or derived from them.

  34. See Gamester (2018).

  35. This goes in the direction of Asay (2016).

  36. Such as Shapiro (2011).

  37. For matter of space, an extensive discussion of the relation between the preservation problem of mixed inferences and the uniformity problem of valid inferences is left to a different work. (reference omitted)

  38. This blocks the strategy proposed in Gamester (2018).

  39. Alternatively, one might try to avoid generic truth by exploiting only one area specific truth property. As in Strollo (2018).

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  1. Department of Philosophy, Nanjing University, Nanjing, China

    Andrea Strollo

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Strollo, A. Alethic Pluralism, Logical Validity, and Natural Truth. Philosophia 50, 269–284 (2022). https://doi.org/10.1007/s11406-021-00383-x

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