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Thursday, July 8, 2010

Reading E-quanfified formulae

Now, we've seen the case clear enough with constant a.

What happens when a variable is used?

Here the pair is:

Ex4~2F1x3
Ex4~3F1x2

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The situation is analogous to the cases with constant alpha.

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Grice notes:

"The idea which lies behind the treatment of [E-] quantification
in [my natural deduction system] is that while only the former
represents 'There exists something which is not F'.

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The latter has other readings:

"There IS something which is not F"

or, in simpler terms,

'something is not F' --- and these readings are shared by the latter and the former formulae. But, again, it is only the former formula which should be read as the stronger locution, 'there EXISTS something which is not F'.

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