Introduction to Logical Theory (Routledge Revivals) by Strawson P. F

Author:Strawson, P. F.
Language: eng
Format: epub
Publisher: Taylor & Francis (CAM)

These definitions1 are exactly parallel to the rules for ‘α = 1’ and ‘— α = 1’; for the two defining expressions are respectively the paraphrases of ‘— α = 0’ and ‘α = 0’. Just as we are tempted to read ‘α = 1’ as ‘Everything is a member of the class of α’, so we are tempted, and sometimes encouraged, to read ‘(x)(fx)’ as ‘Everything f’ or ‘For every x, fx’; and this is often convenient. But when we have questions of interpretation in mind, it is safer, as we shall see, to read it in terms of its definiens.

These two definitions yield, of course, the two equivalences

(1) (x)(fx) ≡

∼(∃x)(∼fx)

(2) (x)(∼fx) ≡

∼(∃x)(fx)

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