I apologize for my lack of clarity. I may be poor writer but it is never my intention to be unclear.Perhaps you can clarify what it is that you are saying. For a start it's not clear what statement 'the statement' refers to in 1, 2 and 3. — andrewk
Thoughts? — Purple Pond
It's just something that I hear a lot. A proposition's truth is analytic if and only if the negation of that proposition implies a contradiction. To quote the Encyclopedia Britannica:"Some philosophers prefer to define as analytic all statements whose denial would be self-contradictory, and to define the term synthetic as meaning “not analytic.” ". Here's a link.The key point of interest is your suggestion that if S is true by virtue of 1 then the negation of S must be self-contradictory. — andrewk
This bachelor is married' would not be self-contradictory, even though the statement 'No bachelor is married' is used as a canonical example of an analytic truth. — andrewk
A contradiction can be deduced from the statement together with additional axioms. But a contradiction cannot be deduced from the statement on its own, so it is not self-contradictory.Saying the bachelor is married contradicts the definition. — Marchesk
Say not 'the language has defeated me' but rather 'the language and I failed to reach an agreement'. Personally, I blame the language. :wink:I have nothing more to say other than language has defeated me once again. — Purple Pond
Mathematical conjectures are not known a priori, nor a posterori, but they're are guessed. The same is true for some physical predictions. Furthermore, it's possible for mathematical conjectures and physics predictions to turn out to be false, and knowledge includes only true propositions.The synthetic a priori fits for example to mathematical conjectures and physics predictions. — Belter
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