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Tuesday, January 15, 2019

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>> A proposition p presupposes a proposition q just in case both p and its negation ~p entail q.

Narrow or wide scope negation? If the former, what you say is trivial. If the latter, false.

Thanks Bill.

A proposition p presupposes a proposition q just in case: (i) p entails q, and (ii) ~p entails q.

Why false? It's a definition. You need to do better.

>>A proposition p presupposes a proposition q just in case: (i) p entails q, and (ii) ~p entails q.

Why false? It's a definition. You need to do better.
<<

The terms of the definition need to be clear. You now have a ~ instead of the word 'negation'. Is ~ wide or narrow scope?

Conventionally it is wide scope. Thus q is a necessary, if p presupposes it, as defined.

And just to be crystal clear, by 'false', I mean the suggestion that 'Tom has lied to his wife' is necessary.

p = Tom regrets lying to his wife
q = Tom has lied to his wife

If p presupposes q in the sense you define, and if the ~ is wide scope, then it is necessary that Tom has lied to his wife.

If by contrast ~ is narrow scope, p presupposes q trivially.

So your definition needs to be clearer.

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