# The Role of Logic in Argumentation

## Abstract

The main currently unsolved problem in the theory of argumentation concerns the function of logic in argumentation and reasoning. The traditional view simply identified logic with the theory of reasoning. This view is still being echoed in older textbooks of formal logic. In a different variant, the same view is even codified in the ordinary usage of words such as ‘logic’, ‘deduction’, ‘inference’, etc. For each actual occurrence of these terms in textbooks of formal logic, there are hundreds of uses of the same idioms to describe the feats of real or fictional detectives. I have called the idea reflected by this usage the “Sherlock Holmes conception of logic and deduction.” In the history of science, we find no less a thinker than Sir Isaac Newton describing his experimental method as one of analysis or resolution and claiming to have “deduced” at least some of his laws from the “phenomena.”^{1}

## Keywords

Deductive Reasoning Deductive Logic Definitory Rule Informal Logic Existential Sentence## Preview

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## Notes

- 1.For Newton, see Jaakko Hintikka and James Garrison, “Newton’s Methodology and the Interrogative Logic of Experimental Inquiry,” forthcoming in the proceedings of the Spring 1987 workshop on “300 Years of the
*Principia—*Realism Then and Now,” ed. by Zev Bechler*et al.*Google Scholar - 2.See Jaakko Hintikka,
*Logic, Language-Games and Information*, (Oxford: Clarendon Press, 1973). I have sometimes also used the terms “surface tautology” and “depth tautology” for the two parties of the distinction.Google Scholar - 3.See Jaakko Hintikka, “C. S. Peirce’s ‘First real Discovery’ and its Contemporary Significance,” in
*The Relevance of Charles Peirce*, (La Salle, IL: The Hegeler Institute, 1983), 107–18.Google Scholar - 4.For if there were a recursive function which would give an upper bound to the number of new individuals (existential instantiations) needed in the proof, we easily could construct a (finite) upper bound to the length of the prospective proofs which would lead from T to C. By constructing all the potential proofs of this length, we could decide effectively whether C follows logically from T. But such a decision method is known to be impossible.Google Scholar
- 5.See E. W. Beth, “Semantic Entailment and Formal Derivability,”
*Mededelingen van de Koninklijke Nederlandse Akademie van Wetenschappen*, Afd. Letterkunde, N.R. vol. 18, no. 13, (1955).Google Scholar - 6.But who among actual scientists ever carried out his or her experimental arguments as if they were logical proofs? An answer is easy: Isaac Newton, for one. His
*Optics is*constructed completely*à la*Euclid, with axioms, postulates, definitions, propositions, theorems, problems, and proofs. The only main difference as compared with Euclid is that Newton occasionally inserts into his exposition what he calls “a proof by experiment.” In other words, he describes an experiment and adds its result as a fresh premise. This is*mutatis mutandis*precisely what the interrogative model suggests.Google Scholar - 7.See, e.g., Jaakko Hintikka “What Is the Logic of Experimental Inquiry?”,
*Synthese vol.*74, no. 1 (1988): 173–90.CrossRefGoogle Scholar - 8.For a fine exposition of the “arbitrary objects” idea, see Kit Fine,
*Reasoning With Arbitrary Objects*(Oxford: Basil Blackwell, 1985). For some of the philosophical problems associated with the idea, see*op. cit.*, n2 above, pp. 109–14.Google Scholar - 9.See R. G. Collingwood,
*Essay on Metaphysics*(Oxford: Clarendon Press, 1940);Google Scholar - 9.Hans-Georg Gadamer,
*Truth and Method*(New York: Continuum, 1975), especially pp. 333–41.Google Scholar - 10.See here Jaakko Hintikka, “The Fallacy of Fallacies,”
*Argumentation*vol. 1 (1987), 211–38.CrossRefGoogle Scholar - 11.Cf. here Jaakko Hintikka, “Aristotle’s Incontinent Logician,”
*Ajatus*37 (1978), 48–65.Google Scholar - 12.Cf. Cf. here Jaakko Hintikka, “Aristotle’s Incontinent Logician,”
*Ajatus*37 (1978), n2 above, 201–05.Google Scholar - 13.
*The Critique of Pure Reason*, second ed., xii–xiii.Google Scholar - 14.See M. E. Szabo,
*The Collected Papers of Gerhard Gentzen*(Amsterdam: North-Holland, 1969).Google Scholar - 15.In “A Note on Anaphoric Pronouns and Information Processing by Humans,”
*Linguistic Inquiry*18 (1987), 111–19.Google Scholar - 16.See John von Neumann,
*The Computer and the Brain*(New Haven, CT: Yale University Press, 1958). The connection with my ideas is this: von Neumann considers the nesting of functions as the crucial obstacle to information-processing by humans. Now when existential quantifiers are replaced by what are known as Skolem functions, the kind of quantificational complexity I have in mind here simply becomes an instance of the von Neumann-type nesting of functions.Google Scholar - 17.Cf. See John von Neumann,
*The Computer and the Brain*(New Haven, CT: Yale University Press, 1958). The connection with my ideas is this: von Neumann considers the nesting of functions as the crucial obstacle to information-processing by humans. Now when existential quantifiers are replaced by what are known as Skolem functions, the kind of quantificational complexity I have in mind here simply becomes an instance of the von Neumann-type nesting of functions, n2 above, pp. 208–11.Google Scholar - 18.See See John von Neumann,
*The Computer and the Brain*(New Haven, CT: Yale University Press, 1958). The connection with my ideas is this: von Neumann considers the nesting of functions as the crucial obstacle to information-processing by humans. Now when existential quantifiers are replaced by what are known as Skolem functions, the kind of quantificational complexity I have in mind here simply becomes an instance of the von Neumann-type nesting of functions, n2 above, pp. 213–18.Google Scholar - 19.This extension of the interrogative model is introduced and briefly discussed in Jaakko Hintikka, “The Interrogative Approach to Inquiry and Probabilistic Inference,”
*Erkenntnis*26 (1987), 429–42.CrossRefGoogle Scholar