By James Edwin Creighton
This Elibron Classics version is a facsimile reprint of a 1905 version through the Macmillan corporation, manhattan.
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Extra resources for An Introductory Logic
16 we can prove [p ::> [q ::> [r ::> sJJ] on the hypothesis [[p & q & r] ::> s]. An analogous result can be THE :\IETHOD OF SUBORDINATE PROOFS Ch. 2) 35 obtained for [p :::> [q :::> [r :::> [s :::> t]]]J and [[p & q & r & s] :::> t], and so on. 18. 19. The rule for conjunction introduction, we know, asserts that the proposition [p & q] is a direct consequence of the pair of propositions, p and q. In case p and q are the same proposition, the rule for conjunction introduction is to be understood as asserting that [p & p] is a direct consequence of the proposition p ..
Many well-known systems of logic have never been shown to be consistent. The system being presented here, however, can be proved to be free from contradiction. 3. Three rules for negation will now be presented. These three rules are concerned only with negation. Subsequently some further rules will be added, relating negation to conjunction and disjunction. 4. Rule of negation elimination ("neg elim"). lp, Thus from a pair of contradictory propositions every proposition may be regarded as following.
21. 22. It is often convenient to be able to repeat some item of a proof as a later item of the same proof. This is always permissible, since if a proposition occurs as an item of a proof and also as a later item of the same proof, we can give the same "reason" for it in its later occurrence as in its earlier occurrence. We can merely write "rep" after the second occurrence, together with a numerical reference to the first occurrence, and this will be taken to mean that the reason for the second occurrence is the same as for the first occurrence.
An Introductory Logic by James Edwin Creighton