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how to prove ‘¬∃xP(x)→(P(a)→Q(a))’ from no premises? fitch

Philosophy Asked by cluelesschloe on December 6, 2021

I am totally lost on how to do this… can anyone help?

What does it mean? I tried to understand what it means before proof but am totally clueless

2 Answers

@GrahamKemp is correct. The statement says that if P(x) holds for no member of the universe of discourse, then P(a)->Q(a).

Recall that the truth table for the material conditional informs us that a material conditional statement is true when the antecedent is false.

So the proof is relatively easy: enter image description here

Answered by Rob on December 6, 2021

¬∃xP(x)→(P(a)→Q(a))

What does it mean? I tried to understand what it means before proof but am totally clueless

It says: P(a)→Q(a) is true, if P(x) holds for no x.

So why would P(a)→Q(a) be true when that is assumed?

Answered by Graham Kemp on December 6, 2021

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