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Recently retired from Cambridge Philosophy Faculty, interested in logic and philosophy of maths.

I waste time on twitter @PeterSmith (http://twitter.com/PeterSmith/)

For more about me, see http://www.logicmatters.net/about/


5h
revised Proofs for Relational Predicate Logic --Difficult Question!
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5h
revised Proofs for Relational Predicate Logic --Difficult Question!
added 19 characters in body
5h
answered Proofs for Relational Predicate Logic --Difficult Question!
6h
comment “Logically equivalent formulae express the same _______.” <- What word do logicians use for the blank?
@Denis Talk of semantics, yes, of course. "The semantic of $\varphi$", no. It isn't either ordinary English or technical logicians' English.
11h
comment “Logically equivalent formulae express the same _______.” <- What word do logicians use for the blank?
@Hal The logical tradition would say that the extension of a sentential wff is its truth-value.
11h
comment “Logically equivalent formulae express the same _______.” <- What word do logicians use for the blank?
@Denis The Wikipedia page you link to of course does talks about semantics, as logicians do, not about "the semantic of $\varphi$" (a phrase seemingly of your own invention).
14h
comment “Logically equivalent formulae express the same _______.” <- What word do logicians use for the blank?
"Logicians use the word semantic to refer to the "meaning" of a formula. It is the interpretation of the formula in a given structure." Eh? I have never, ever, come across this usage. Which logicians use this terminology and in which books?
1d
comment Is Douglas Hofstadter's version of Godel's proof utter nonsense?
Here is a book which, for all its quirkiness and digressions, has been regarded by logicians as fine as far as the technical Gödelian details are concerned. Which is really more likely, do you think? That in a crucial way, it involves "utter nonsense", that no one else has spotted for 35 years? Or that you've misunderstood something?
1d
comment Boolean Expression simplification help
Don't lose sight of what expressions mean! Informally what does the given one mean? "Either A and B are both true or they're both false". And that can't always take the value 'true" can it?
1d
revised Give L structures A and B such that the following formula is true in A but not true in B.
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1d
revised Give L structures A and B such that the following formula is true in A but not true in B.
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1d
answered Give L structures A and B such that the following formula is true in A but not true in B.
2d
comment Show that $((\phi → \psi)→((\psi→\chi)→(\phi→\chi)))$ is a Theorem of L.
The mixed system allows the temporary introduction of new assumptions; a Frege-Hilbert system doesn't, by definition.
2d
comment Show that $((\phi → \psi)→((\psi→\chi)→(\phi→\chi)))$ is a Theorem of L.
It is rather more delicate an issue than that. What is true is that you can conservatively extended a Hilbert system into a mixed system which allow the making and discharge of temporary assumptions. But that's to introduce a proof-system of a new character, and we are no longer inside e.g. The Mendelson system I guess the OP is using.
2d
comment Show that $((\phi → \psi)→((\psi→\chi)→(\phi→\chi)))$ is a Theorem of L.
This looks dangerously close to confusing the Deduction Theorem, a meta-level theorem about a Hilbert-style proofs system, with Conditional Proof as a rule inside a natural deduction system allowing the making and discharge of temporary assumptions.
2d
revised Show that $((\phi → \psi)→((\psi→\chi)→(\phi→\chi)))$ is a Theorem of L.
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2d
comment Show that $((\phi → \psi)→((\psi→\chi)→(\phi→\chi)))$ is a Theorem of L.
That's just a list of three premises, separated by commas. But your even asking that suggests you need to do some serious homework, with a textbook or three in the library!
2d
answered Show that $((\phi → \psi)→((\psi→\chi)→(\phi→\chi)))$ is a Theorem of L.
2d
comment Show that the set {¬, v} is adequate.
Go the library. Look at a couple of good intro logic texts. There should be dozens to choose from!
Apr
21
revised Question about definition of binary relation
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