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Pluralisms in Truth and Logic pp 301–329Cite as

Palgrave Macmillan

Logical Nihilism

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Abstract

Much of the discussion in the philosophy of logic over the last decade has been devoted to the debate between logical monism and logical pluralism. But logical nihilism hasn’t been given nearly as much attention, even though the view has historical roots and is philosophically defensible. I present and defend a number of arguments in favor of logical nihilism. These arguments are grouped into two main families: arguments from diversity (§2) and arguments from expressive limitations (§3). These arguments are often simple syllogisms pointing to fundamental differences between natural languages and formal consequence relations. Many of the arguments involve familiar problems in the philosophy of logic. The arguments, taken individually, are interesting in their own right; they each highlight an important way in which the formal methods of logic can be seen to be inadequate to modeling natural language inference. But the arguments taken jointly are more significant; by presenting all the arguments together, we can build something of a cumulative case for logical nihilism. Of course, if any of these arguments are sound, then logical nihilism is correct. But the arguments reinforce one another, such that logical nihilism presents us with a unified view across a broad range of issues in philosophy of logic. I conclude (§4) by considering related philosophical issues and sketching a general outlook on logic and formal methods that is nihilist-friendly.

Ordinary language has no exact logic.

Strawson (1950)

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Notes

  1. 1.

    Of course, there are many ways one might think about truth; one needn’t think of truth in terms of correct representation. But it is a reasonable way of thinking about the issue, and I think it is what the intuitive slogan ‘One True Logic’ is getting at.

  2. 2.

    This quote strongly suggests that Beall and Restall would not disagree with the characterization of logics as being in the business of correct representation of natural language inferential practice.

  3. 3.

    Compare recent authors like Bueno and Colyvan (2004), “The aim of logic is taken to be to provide an account of logical consequence that captures the intuitive notion of consequence found in natural language” (p. 168). Or Resnik (2004), “As practitioners of inference we make specific inferences […] As logicians we try to formulate a systematic account of this practice by producing various rules of inference and laws of logic by which we presume the practice to proceed. This aspect of our work as logicians is like the work of grammarians” (p. 179). Or consider Cook (2010) “[A] logic is ‘correct’, or ‘acceptable’, etc., if and only if it is a correct (or acceptable, etc.) codification of logical consequence. The idea that the philosophically primary (but obviously not only) goal of logical theorizing is to provide a formal codification of logical consequence in natural language traces back (at least) to the work of Alfred Tarski” (p. 195).

  4. 4.

    Cook (2010, p. 495f) gives a detailed account of what it means to say a logical consequence relation is adequate to natural language inference. I am assuming something like his definition is suitable for this purpose.

  5. 5.

    Another way of reading Mortensen is as arguing that real broad possibility outstrips pure logical possibility. In this case, then, there may be logically impossible scenarios that are not, broadly speaking, impossible. Mortensen would then not count as a logical nihilist in the sense above.

  6. 6.

    Parallel disputes over the metaphysics of composition. Here universalism states that composition always occurs, whereas nihilism claims that the composition relation is basically empty. ‘Emptyism’ just doesn’t have the same ring to it. And unfortunately, ‘Noneism’—the most natural name for the view defended in this chapter—is already taken.

  7. 7.

    There is also Eklund’s (2012) Carnapian language-relative approach; Shapiro’s (2011, 2014) contextual approach, and Cook’s (2010) logic-as-modeling approach. Later I’ll touch on some issues that directly relate to their motivations.

  8. 8.

    Similar arguments have been made by Read (2006, p. 208f) and Priest (2006, Chap. 12).

  9. 9.

    In Cotnoir (2013), I outline general approach to validity motivated by this idea. See also Pedersen (2014) for more motivations.

  10. 10.

    This was Tarski’s (1936) early view.

    But I also consider it to be quite possible that investigations will bring no positive results in this direction, so that we shall be compelled to regard such concepts as logical consequence as relative concepts. The fluctuation in the common usage of the concept of consequence would in part at least be quite naturally reflected in such a compulsory situation [of a relatively-defined concept of consequence]. (p. 420)

    See also Etchemendy (1990) and Dutilh-Novaes (2012).

  11. 11.

    Glanzberg’s (2015) rich and carefully argued paper is concerned with rejecting the view that natural language (a structure with a syntax and a semantics) determines a logical consequence relation. His position is very similar to logical nihilism of the sort I’m defending here, and he is probably one of the view’s closest allies. But strictly speaking Glanzberg’s view is compatible with logical monism and logical pluralism, since there could be one (or more) correct theory of natural language inference, even if it isn’t possible to simply read such a thing off from natural language itself.

  12. 12.

    Compare Zardini (2010, 2014) who argues that mid-argument context shifts invalidate standard inferences (e.g. “I am sitting” can fail to entail itself).

  13. 13.

    See also Bacon (2015) who argues that there can be no ‘linguistic’ theories of paradox based in a classical language due to revenge problems.

  14. 14.

    Thanks to Cory Wright for suggesting this way of framing the issue.

  15. 15.

    Related arguments first appeared in Whiǣle (2004), and Shapiro (2011). See also Murzi (2014). For dissenting voices see Cook (2014), Wansing and Priest (2015).

  16. 16.

    See e.g. Zardini (2013), Weber (2014).

  17. 17.

    For good introductory discussions of these issues see Florio (2014) and Rayo and Uzquiano (2006, p. 1). The following discussion is indebted to them in various ways.

  18. 18.

    See Lewis (1991) and Williamson (2003).

  19. 19.

    Priest himself rejects ‘No Universe’ for his preferred set theory; for discussion see below.

  20. 20.

    See Uzquiano (2009), Rayo (2002).

  21. 21.

    For example, Jané (1993), Resnik (1988), and more recently Linnebo (2003).

  22. 22.

    For example, one might utilize hyperplural quantification (Rayo 2006), which under certain assumptions, isomorphic to the type hierarchy (Linnebo and Rayo 2012). There are also modal approaches (Linnebo 2010 and Studd 2013) which allow set-theoretic domains to be indefinitely extensible.

  23. 23.

    For some defenders of this view, see Lavine (2006), McGee (2006), and Williamson (2006).

  24. 24.

    This problem is discussed, and some possible lines of response explored in Beall et al. (2006).

  25. 25.

    See also Weir (2006).

  26. 26.

    See Cook (2002) for discussion.

  27. 27.

    Wright (2010) contends that higher-order vagueness worries are pseudo-problems; it is a revenge problem that only arises for views which misunderstand first-order vagueness. The logical nihilist can afford sympathy to such claims.

  28. 28.

    Field takes this to be an argument for pluralism (because of an underlying antirealist pluralism about epistemic norms), one might well think such considerations provide better reasons to be nihilist about logic.

  29. 29.

    The comparison with morality is instructive: consider the relevance of anti-theory views in ethics (e.g. Clarke 1987) to logical nihilism, or even the similarities between particularism (e.g. Dancy 1983) and Hofweber’s (2007) view that we should give up the ideal of deductive inference as exceptionless and monotonic. Natural language inferences need not be exceptionless or monotonic, and often are not. But they might still be generically valid, in the sense that generics like “Humans are bipeds” are true.

  30. 30.

    E.g. Chihara (1979), Eklund (2002), and Ludwig (2002).

  31. 31.

    E.g. Scharp (2013) who thinks defective concepts like ‘truth’ need to be replaced, or Patterson (2009) who argues that we understand natural language using a false semantic theory, such that strictly speaking natural language sentences have no meanings.

  32. 32.

    See especially Glanzberg (2015, §IV), but also Cook (2002, 2010), Shapiro (2006), and Scharp’s (2013) metrological naturalism.

  33. 33.

    This point is made clearly and forcefully in Beall (2007) with respect to the semantic paradoxes. Cook (2002) argues for a similar perspective with respect to vagueness.

  34. 34.

    I’d like to thank audiences at the Truth Pluralism and Logical Pluralism Conference at the University of Connecticut, the Swiss Society for Logic and Philosophy of Science at the University of Neuchâtel, the Northern Institute of Philosophy 2011 Reading Party, the University of St Andrews Philosophy Society, and the students in my 2014 and 2017 Philosophy of Logic seminars. Their comments and questions led to many improvements and developments in the paper. Special thanks to Colin Caret, Roy Cook, Matti Eklund, Ole Hjortland, Michael Lynch, Julien Murzi, Stephen Read, Gillian Russell, Gil Sagi, Kevin Scharp, Stewart Shapiro, Keith Simmons, Crispin Wright, and Elia Zardini for discussions on these topics over a number of years. Thanks also to an anonymous referee for helpful comments on a previous version of the paper. The biggest debt of gratitude is owed to my PhD supervisor Jc Beall, who disagrees with many of the ideas in this paper. A reaction against one’s academic upbringing can be a sign of deep respect; and I hope this paper is taken in that spirit.

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  1. Department of Philosophy, University of St Andrews, St Andrews, UK

    Aaron J. Cotnoir

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  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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Cotnoir, A.J. (2018). Logical Nihilism. 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_13

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