Elementary Logic: Revised Edition by W. V. Quine

Author:W. V. Quine
Language: eng
Format: epub
Published: 2011-09-20T05:36:00+00:00

Successive transformations by §21(13) turn it into:

(with tacit cancellation of '--'). Transformations by §21(10)distributions-turn this result successively into:

which is an alternational normal schema. Two of the last three transformations turned on a switched version of §21(10), but the switch was just a matter of tacit § 16(1).

The notations '-p' and 'p . q' are not the only notations for denial and conjunction that are current in the literature of logic. For denial some authors use 'p', some 'p^, some '-.p'. For conjunction some use 'pq', some 'p & q', some 'p A q'. With the ascendancy of alternational normal schemata it is indeed convenient to turn to two of these variant notations part of the time: to the bar as in 'p' whenever only a single letter is denied, and to juxtaposition as in 'pq' whenever only literals are conjoined. Thus (3) becomes:

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