[FOM] A question on Core Logic--reply to Eric Astor

[Tennant, Neil]

Eric Astor wrote

____________

... (possibly Classical) Core Logic DOES allow us to derive (P -> Q) from (P -> #), yes? ...
If so, then since Core Logic does not prove EFQ, then it seems that at least one of the following derivations must be impossible in Core Logic:
1) Derive Q from (T -> Q),
2) Derive (T -> Q) from Q,
as otherwise, I think we can construct a naïve derivation of EFQ... unless I'm missing something that renders another step invalid.

I'm certain at least one of the above things is invalid in Core Logic. However, as I'm not experienced with it... which one?


____________

Thanks for your question, Eric. Here are all the answers you may need.

Core Logic allows us to conclude P->Q when we have derived # from the assumption P, and we are entitled to discharge the assumption P in doing so.

[Assuming T means the True?...] Since we can derive Q from T->Q plus whatever premises we may use to derive T (in the so-called 'minor' proof for ->E), we can derive Q from T->Q:

                  [ ] - emptyset of premises
                   :      __(1)
      T->Q     T      Q
     _______________(1)
                  Q

We can derive P->Q from Q, regardless of what P may be. So, in particular, we can derive T->Q from Q.

I would be interested to see the naive derivation of EFQ that you have in mind here.

Neil Tennant

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