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Logic as a methodological discipline

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Abstract

This essay offers a conception of logic by which logic may be considered to be exceptional among the sciences on the backdrop of a naturalistic outlook. The conception of logic focused on emphasises the traditional role of logic as a methodology for the sciences, which distinguishes it from other sciences that are not methodological. On the proposed conception, the methodological aims of logic drive its definitions and principles, rather than the description of scientific phenomena. The notion of a methodological discipline is explained as a relation between disciplines or practices. Logic serves as a methodological discipline with respect to any theoretical practice, and this generality, as well as logic’s reflexive nature, distinguish it from other methodological disciplines. Finally, the evolution of model theory is taken as a case study, with a focus on its methodological role. Following recent work by John Baldwin and Juliette Kennedy, we look at model theory from its inception in the mid-twentieth century as a foundational endeavour until developments at the end of the century, where the classification of theories has taken centre-stage.

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Notes

  1. Though we might consider here a broad conception of science, as any organised area of inquiry or body of truths [this, arguably, is Frege’s use of the term “science”, see Frege (1979, p. 168) and Rossberg and Shapiro 2021].

  2. This is not to say that none of the views of logic expressed by Frege are accepted by anti-exceptionalists, e.g., that the generality of logic is its defining feature is accepted by Williamson. See also Rossberg and Shapiro (2021) for anti-exceptionalist proclamations made by Frege.

  3. The same may be true about the apriority and analyticity of logic, but I leave that issue aside.

  4. Recall that “science” here and for Frege is used with the broadest meaning, see f.n. 1.

  5. For example, see Carnap’s description of the aims of The Logical Syntax of Language (Carnap 1934/1937) as instrumental:

    The aim of logical syntax is to provide a system of concepts, a language, by the help of which the results of logical analysis will be exactly formuable... the logic of science is nothing other than the logical syntax of the language of science (p. xiii)

    The logic of science (logical methodology) is nothing else than the syntax of the logic of science. (p. 7)

  6. A notable example is Gila Sher, who offers the following thesis in her recent book:

    Thesis 1: Function (Task) of Logic

    Logic’s task is to develop a method of inference which is both highly general and has an especially strong modal force. More specifically, its task is to develop a method for constructing inferences that transmit truth from sentences to sentences with an especially strong modal force and regardless of field of knowledge. ((Sher 2016, p. 255), boldface added).

    Sher is a proponent of foundational holism, by which knowledge is grounded in reality, but there need not be a strict ordering for grounding. So logic’s methodological role is separated from traditional foundationalism, an approach shared by contemporary model-theorists, as we’ll see in Sect. 4.

  7. For example, while Carnap and Tarski define logical properties and relations with respect to linguistic expressions, for Frege, and these days, Williamson, Sher and Maddy, logic is not primarily metalinguistic. But the disputes on whether logic operates on the level of linguistic expression or of mental content is an ancient one, see for example Adamson and Key (2015).

  8. See also Rossberg and Shapiro (2021), who contrast Priest’s methods with those of contemporary linguistics.

  9. Hjortland and Martin write that according to their account, “logical theories are ultimately chosen for their ability to make successful predictions. Such predictions include claims about which informal proofs mathematicians will find acceptable, and which arguments certain “reliable reasoners” will judge acceptable.” (Martin and Hjortland 2020).

    Later on they note that “in suggesting that logical theories appeal to judgements regarding arguments, the current proposal opens up the possibility that a priori evidence does indeed play a role within logical theory choice” (ibid). Now one might question whether a theory based on the collection of judgments elicited from selected subjects, using whatever method of survey available (as opposed to an armchair activity), might thus be a priori. Compare soliciting judgments from mathematicians on the truth of mathematical theorems: while this may be a reliable procedure for determining theoremhood, the type of justification that would base the apriority of mathematics would be the proofs of these theorems themselves. (See Malmgren 2006, who argues against the claim that there is a priori knowledge by testimony, and whose arguments apply to the present case as well.)

  10. Priest is an exception in basing logic on norms for correct reasoning, see also Sect. 3.

  11. In this way anti-exceptionalists rule out customary locutions in logical theories such as “from... infer...” or “from... one may infer...”. I thank Ran Lanzet for this comment.

  12. This issue was recently discussed by Sebastian Lutz, according to whom: “Since the sciences rely on language conventions whenever they go beyond observational claims, most entities and properties referred to by scientific theories (for instance momentum) are introduced rather than discovered” (Lutz 2020).

  13. For a rigorous presentation on the application of logical systems, see Avron (1994).

  14. Carnap (1962) distinguishes between the task of the logician (in that case, the inductive logician)—to calculate the value of a confirmation function, and the methodologist is in charge of applications of inductive logic. Here I take a wider view of the methodologist’s role: it includes both the logician’s theoretical work and its application (in this I follow Nola and Sankey 2014, pp. 30f).

  15. While at the first level we may have non-methodological disciplines, the methodological disciplines may not be neatly divided into levels higher up.

  16. Here I should emphasise that I am setting foundational issues aside, so that by logic applying to itself we do not commit to a vicious regress. The blacksmith’s first production might be manufactured using unforged steel or a steel-free device, and tools made out of forged steel can be manufactured and put into use at some point nonetheless. We don’t have the artifactual tools from the start, but this doesn’t mean that they appear ex nihilo–we use more rudimentary tools to forge the first instances (for details and discussion see Peregrin and Svoboda 2017). Notwithstanding, for the limitations of logic applying to itself in theoretical decisions such as choice of logic, see Woods (2019).

  17. Model-theoretic semantics is used in abundance in the Montagovian tradition in formal semantics (Montague 1974; Westerståhl 1989; Chierchia and McConnell-Ginet 1990; Heim and Kratzer 1998). For an overview of model theory in computer science, see Makowsky (1995). For an overview of the applications of model theory in philosophy, see Button and Walsh (2018).

  18. Tarski juxtaposes logical and geometrical notions already in Lindenbaum and Tarski (1935), but there syntactic aspects are prominent.

  19. Baldwin discusses the nature of classification and definition in Baldwin (2018, ch. 13). For a brief discussion on the philosophical aspects of classification, see also Button and Walsh (2018).

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  1. Philosophy Department, University of Haifa, 199 Aba Khoushy Ave. Mt. Carmal, 3498838, Haifa, Israel

    Gil Sagi

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This article belongs to the topical collection “Anti-Exceptionalism about Logic”, edited by Ben Martin, Maria Paola Sforza Fogliani, and Filippo Ferrari.

This paper was presented to the London Group for Formal Philosophy and the Jerusalem Working Group in Logic. I’d like to thank the members of both groups for a useful discussion. I’d also like to thank the following for helpful comments: Tim Button, Rea Golan, Balthasar Grabmayr, Catherine Herfeld, David Kashtan, Juliette Kennedy, Arnon Keren, Aviv Keren, Ran Lanzet, Talia Leven, Carlo Nicolai, Filippos Papagiannopoulos, Lavinia Picollo, Carl Posy, Daniel Statman and Florian Steinberger.

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Sagi, G. Logic as a methodological discipline. Synthese 199, 9725–9749 (2021). https://doi.org/10.1007/s11229-021-03223-3

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