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Extra resources for Advances in Computers, Vol. 24
Let us go a bit further in order to appreciate the importance of this approach to logic and reasoning. A well-known (by now) twelfth century example of a derivation by Petrus Abelardus in his Dialectica is recalled by W. Kneale and M. Kneale (Kneale and Kneale 1985, p. 217): the conclusion si Socrates est lapis, est asinus (“if Socrates is a stone, he is an ass”) as a consequence of the validity of the Disjunctive Syllogism ˛ _ ˇ; :˛ ` ˇ. Indeed, from the hypothesis Socrates est lapis one derives Socrates est lapis or Socrates est asinus.
1 It is believed that the “infidel mathematician” in question was either Edmond Halley or Isaac Newton himself. W. E. br K. Tanaka et al. 1007/978-94-007-4438-7__3, © Springer Science+Business Media Dordrecht 2013 27 28 W. E. Coniglio However, Berkeley’s criticisms did not have an effect on everyone. Leonard Euler, for instance, paid little attention to the invectives against the use of infinite series, and found an astonishing new proof of the fact, originally proved by Euclid, that there are infinitely many prime numbers.
Cambridge: Harvard University Press. Routley, R. K. 1972. The semantics of entailment – II. Journal of Philosophical Logic 1: 53–73. Routley, R. K. 1973. The semantics of entailment – I. In Truth, syntax and modality, ed. H. Leblanc, 199–243. Amsterdam: North-Holland. Routley, R. and Routley, V. 1972. The semantics of first degree entailment. Noûs 6: 335–359. Tanaka, K. 2000. The labyrinth of trees and the sound of silence: Topics in dialetheism. D. thesis, University of Queensland. Urquhart, A.
Advances in Computers, Vol. 24