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Concerning the Laws of Contradiction and Excluded Middle

Published online by Cambridge University Press:  14 March 2022

V. J. McGill
V. J. McGill*
Affiliation:
Hunter College, New York
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Extract

Tradition usually assigns greater importance to the so-called laws of thought than to other logical principles. Since these laws could apparently not be deduced from the other principles without circularity and all deductions appeared to make use of them, their priority was considered well established. Generally, it was held that the laws of thought have no proof and need none, that as universal constitutive or transcendental principles they are self-evident.

Type
Research Article
Information
Philosophy of Science , Volume 6 , Issue 2 , April 1939 , pp. 196 - 211
Copyright
Copyright © The Philosophy of Science Association

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References

Notes

1 Categoriae 10, 13a, 37.

2 “Philosophische Bemerkungen zu mehrwertigen Systemen des Aussagenkalküls” in Comptes Rendus des Séances de la Société des Sciences et des Lettres Varsovie, Classe III, Vol. xxiii, 1930. Fascicule 1-3, pp. 51-77.

3 See “On Mr. Broad's Theory of Time” by R. M. Blake, Mind (1925) for a discussion of Broad's view, and “Are Some Propositions Neither True Nor False?” by Charles A. Baylis Philosophy of Science (April, 1936) for a criticism of Lukasiewicz.

4 A. Heyting, “Die formalen Regeln der intuitionistischen Logik,” Sitzungsberichte der Preussischen Akademie der Wissenschaften, Physikalish-mathematische Klasse, 1930, pp. 47-58.

Also see Orrin Frink's interesting discussion, “New Algebras of Logic,” American Mathematical Monthly, Vol. XLV, No. 4, April, 1938.