Kant's own framework permits synthetic a priori knowledge of structural features (causality, space, time) that are necessarily instantiated in any possible experience, grounding objective validity.
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A claim that depends on facts about the world rather than just the definitions of the words used—for example, 'water boils at 100°C' is synthetic because you have to test it, not just look up what 'water' means.
a posteriori(Used to classify the epistemic status of necessary statements post-Kripke)
Knowable, but not independently of empirical experience
a priori(Frege treats 'analytic' as entailing 'a priori' for arithmetic.)
Knowable independently of empirical experience; here treated as a consequence of analyticity.
framework(Carnap's philosophy of language and logic)
A structured system of rules or language that must be in place for rational discourse to be possible.
knowledge(Distinguished from mere true belief, which may be the product of indoctrination and need not exercise deliberative capacities.)
Justified true belief — true belief that has been arrived at through the exercise of deliberative capacities, including comparison of and deliberation among alternatives.
objective validity(Kant's epistemology; contrasted with merely subjective validity)
The property of a representation whereby it represents an objective feature of reality — a feature whose existence and nature is independent of how it is perceived.
synthetic a priori knowledge(Kant's epistemology; distinguished from analytic a priori (conceptual analysis) and empirical a posteriori (experience-dependent) knowledge)
Knowledge that goes beyond the mere analysis of concepts — doing more than unpacking explicit or tacit definitions — yet legitimately claims universal and necessary validity.