Definitions of logic

Definitions of logic

Many treatises on logic begin with a discursion on the difficulty of defining the subject, many do not even attempt to provide a definition. Nevertheless, many definitions have been offered because it is felt to be necessary.

This article divides the definitions into two classes: first are the simple definitions, that consist of a pithy sentence characterising the topic; second are theoretical definitions, where the definition of logic turns on an analysis the definer provides.

Contents

Simple definitions of logic

Arranged in approximate chronological order.

  • The tool for distinguishing between the true and the false (Averroes).
  • The science of reasoning, teaching the way of investigating unknown truth in connection with a thesis (Robert Kilwardby).
  • The art whose function is to direct the reason lest it err in the manner of inferring or knowing (John Poinsot).
  • The art of conducting reason well in knowing things (Antoine Arnauld).
  • The right use of reason in the inquiry after truth (Isaac Watts).
  • The Science, as well as the Art, of reasoning (Richard Whately).
  • The science of the operations of the understanding which are subservient to the estimation of evidence (John Stuart Mill).
  • The science of the laws of discursive thought (James McCosh).
  • The science of the most general laws of truth (Gottlob Frege).
  • The science which directs the operations of the mind in the attainment of truth (George Hayward Joyce).
  • The branch of philosophy concerned with analysing the patterns of reasoning by which a conclusion is drawn from a set of premisses (Collins English Dictionary)
  • The formal systematic study of the principles of valid inference and correct reasoning (Penguin Encyclopedia).

Theoretical definitions of logic

Quine (1940, pp. 2–3) defines logic in terms of a logical vocabulary, which in turn is identified by an argument that the many particular vocabularies —Quine mentions geological vocabulary— are used in their particular discourses together with a common, topic-independent kernel of terms.[1] These terms, then, constitute the logical vocabulary, and the logical truths are those truths common to all particular topics.

Hofweber (2004) lists several definitions of logic, and goes on to claim that all definitions of logic are of one of four sorts. These are that logic is the study of: (i) artificial formal structures, (ii) sound inference (e.g., Poinsot), (iii) tautologies (e.g., Watts), or (iv) general features of thought (e.g., Frege). He argues then that these definitions are related to each other, but do not exhaust each other, and that an examination of formal ontology shows that these mismatches between rival definitions is due to tricky issues in ontology.

Notes

  1. ^ Cf. Ferreiros, 2001

References

  • Ferreiros, J. (2001). The road to modern logic: an interpretation. In Bulletin of Symbolic Logic 7(4):441-483.
  • Frege, G. (1897). Logic. transl. Long, P. & White, R., Posthumous Writings.
  • Hofweber, T. (2004). Logic and ontology. Stanford Encyclopedia of Philosophy.
  • Joyce, G.H. (1908). Principles of Logic. London.
  • Kilwardby, R. The Nature of Logic, from De Ortu Scientarum, transl. Kretzmann, in Kretzmann N. & Stump E., The Cambridge Translation of Medieval Philosophical Texts, Vol I. Cambridge 1988, pp. 262 ff.)
  • McCosh, J. (1870). The Laws of Discursive Thought. London.
  • Mill, J.S. (1904). A System of Logic. 8th edition. London.
  • Poinsot, J. (1637/1955). 'Outlines of Formal Logic'. In his Ars Logica, Lyons 1637, ed. and transl. F.C. Wade, 1955.
  • Quine, W.V.O. (1940/1981). Mathematical Logic. Third edition. Harvard University Press.
  • Watts, I. (1725). Logick.
  • Whateley, R.. Elements of Logic.

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