On 10/19/2013 6:23 AM, Peter Percival wrote: > Nam Nguyen wrote: > >> What definition of "invalidity" were you referring to _here_ ? Mine? > > If you use the word "invalidity" is newsgroups called sci.logic and > sci.math then it should probably be with its usual technical meaning. If > you use it in another sense you should probably say what sense that is > right from the start. >
It does get confusing, doesn't it? Given that Nam's apparent views are epistemic and modal, his use of "validity" probably correspond with "necessity" in some system of frames. Generally, modal logic is based on classical logic and frame systems simply incorporate mathematical necessity into all worlds. But, since Nam is applying the modal reasoning to the reasoning of mathematics itself, truths on the basis of valid proofs are not necessary. And, if this can even be made to work at all in some system of frames, those truths would not be valid in the semantic sense as the notion would be conflated with necessity.