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Full Idea
In Modus Ponens where the first premise is 'P' and the second 'P→Q', in the first premise P is asserted but in the second it is not. Yet it must mean the same in both premises, or it would be guilty of the fallacy of equivocation.
Gist of Idea
In logic a proposition means the same when it is and when it is not asserted
Source
David Bostock (Philosophy of Mathematics [2009], 7.2)
Book Ref
Bostock,David: 'Philosophy of Mathematics: An Introduction' [Wiley-Blackwell 2009], p.207
A Reaction
This is Geach's thought (leading to an objection to expressivism in ethics, that P means the same even if it is not expressed).
13951 | Assertions, unlike sentence meanings, can be accurate, probable, exaggerated, false.... [Cartwright,R] |
18052 | An assertion aims to add to the content of a context [Stalnaker, by Magidor] |
18121 | In logic a proposition means the same when it is and when it is not asserted [Bostock] |
18762 | A maxim claims that if we are allowed to assert a sentence, that means it must be true [McGee] |