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12. Knowledge Sources / A. A Priori Knowledge / 4. A Priori as Necessities

[a priori knowledge is an insight into necessary truths]

18 ideas
A triangle has a separate non-invented nature, shown by my ability to prove facts about it [Descartes]
What experience could prove 'If a=c and b=c then a=b'? [Descartes]
'Nothing comes from nothing' is an eternal truth found within the mind [Descartes]
Mathematical analysis ends in primitive principles, which cannot be and need not be demonstrated [Leibniz]
An a priori proof is independent of experience [Leibniz]
Two plus two objects make four objects even if experience is impossible, so Kant is wrong [Russell on Kant]
Propositions involving necessity are a priori, and pure a priori if they only derive from other necessities [Kant]
The apriori is independent of its sources, and marked by necessity and generality [Burge on Kant]
A priori knowledge is indispensable for the possibility and certainty of experience [Kant]
An a priori truth is one derived from general laws which do not require proof [Frege]
A truth is a priori if it can be proved entirely from general unproven laws [Frege]
An apriori truth is grounded in generality, which is universal quantification [Burge on Frege]
The rationalists were right, because we know logical principles without experience [Russell]
We could verify 'a thing can't be in two places at once' by destroying one of the things [Ierubino on Ayer]
Why should necessities only be knowable a priori? That Hesperus is Phosporus is known empirically. [Devitt]
How could the mind have a link to the necessary character of reality? [Devitt]
A sentence is a priori if no possible way the world might actually be could make it false [Chalmers]
'Snow is white or it isn't' is just true, not made true by stipulation [Boghossian]