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Against logical generalism

  • S.I.: Pluralistic Perspectives on Logic
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Abstract

The orthodox view of logic takes for granted the central importance of logical principles. Logic, and thus logical reasoning, is to be understood as a system of rules or principles with universal application. Let us call this orthodox view logical generalism. In this paper we argue that logical generalism, whether monist or pluralist, is wrong. We then outline an account of logical consequence in the absence of general logical principles, which we call logical particularism.

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Notes

  1. e.g. McGee (1985) offers counter-examples to modus ponens, Yalcin (2012) offers counter-examples to modus tollens, and the well known debates between relevance, inuitionist, paraconsistentist, and classical logicians show the scope of disagreement over the putative laws of excluded middle, non-contradiction, and disjunctive syllogism (Priest et al. 1989).

  2. See Sect. 2 for details.

  3. We discuss this problem in more detail in Wyatt and Payette (2018).

  4. What we say here applies equally to the pluralist since the view of the pluralist isn’t that all logics are correct. Thus the pluralist must have some criteria for excluding logical systems. We expand on this point in Sect. 7.

  5. To verify these claims see Priest (2008) chapters six and eight, respectively.

  6. The examples here are informal analogues of the mathematical formulations found in Russell (2017) based on discussion in Russell (2015).

  7. Similar issues apply to the claim that Russell’s counter-examples are ‘far-fetched’. In order for this response to the nihilist’s argument for N2 to be satisfactory, there must be a principled and independent basis on which certain operators, or arguments, are classified as far-fetched, and so somehow beyond the scope of logic.

  8. Glanzberg is not particularly precise as to what formality amounts to, but his comments on it suggest that he is thinking in terms of a distinction between form and content.

  9. V is the number of vertices, F is the number of faces, and E is the number of edges of a 3-dimensional polyhedron.

  10. We discuss the role of this practice in logic extensively in Payette and Wyatt (2018a).

  11. Exceptionalists also usually take logic truths to be necessary and arrived at via a priori reasoning. This in and of itself doesn’t preclude exceptions—a logical truth \(\varphi \) could be necessarily true with respect to a given subject matter or discourse. But when combined with universality they reinforce the expectation of exceptionless laws.

  12. Some might prefer to describe logic as ‘formal’ rather than schematic. Given the diverse interpretations of ‘formal’ we prefer to be specific about its interpretation. For our view on logical form see Wyatt and Payette (2018), and see Dutilh (2011) for extensive discussion of ways in which logic has been thought of as formal. Finally, see Smiley (1998) for criticism of the central role sometimes given to the schematic in logic.

  13. We have also discussed this thesis at some length elsewhere (Payette and Wyatt 2018a).

  14. This example is borrowed from Lipton (2001).

  15. Others have advocated the view that logic is a form of modelling, for example Shapiro (2014), Cook (2014), however generally they take the view that models themselves are subject to standards of correctness. See Payette and Wyatt (2018a) for further discussion of the role of incorrect models in science and logic.

  16. Mizrahi (2012) is less radical in insisting that the laws must be what he calls ‘quasi-factive’.

  17. See Smiley (1982) on his ‘Schematic fallacy’ for further reasons why schematic validity is not the focus of logic.

  18. Dancy (2004) points this out in the moral context.

  19. See Jennings et al. (2009) for discussion of preservationism and its history.

  20. For a more complete description of the treatment see Payette and Schotch (2007).

  21. We are classifying Caret’s view as local pluralism: although it is not clear he would agree with our name, we hope he will agree with our characterization of his view.

  22. Shapiro (2014) defends a form of local pluralism that restricts the cannonical application of logic to mathematics—on Shapiro’s view different mathematical discourses require different logics, making him a discourse pluralist, but he expresses no view on the applicability of logic(s) to non-mathematical arguments.

  23. In this respect logical particularism bears some similarities to logical instrumentalism as described by Haack (1978, pp. 224–225). However Haack characterizes instrumentalists as either (a) denying that there is any extra-systematic idea of validity which could serve as a standard for correctness claims or (b) maintaining that logics are systems of rules or procedures rather than systems of statements for which questions of truth or falsity could arise. Neither of these claims are part of particularism.

  24. Global pluralism doesn’t suffer from this problem since according to the global pluralist the correct logics are all always in force.

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Acknowledgements

The authors are grateful for extensive feedback from referees for Synthese, as well as from audiences at the 2016 meeting of the Society for Exact Philosophy and the 2016 meeting of the Canadian Philosophical Association.

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Authors and Affiliations

  1. University of Calgary, Calgary, Canada

    Nicole Wyatt

  2. University of British Columbia, Vancouver, Canada

    Gillman Payette

  3. University of Lethbridge, Lethbridge, Canada

    Gillman Payette

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  1. Nicole Wyatt
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  2. Gillman Payette
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Correspondence to Nicole Wyatt.

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Gillman Payette would like to acknowledge the support of a Social Sciences and Humanities Council of Canada Banting Postdoctoral Fellowship from 2014 to 2016 which supported the work that led to this paper.

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Wyatt, N., Payette, G. Against logical generalism. Synthese 198 (Suppl 20), 4813–4830 (2021). https://doi.org/10.1007/s11229-018-02073-w

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