If synthetic a priori knowledge is possible, then the failure to reducepremises to self-evident principles does not automatically render an argument merely dialectical rather than demonstrative.
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premises(as used in logic and philosophical arguments)
Starting statements or assumptions that are used to support a conclusion—like the opening claims in an argument that lead to a final point.
self-evident principles(logic and argumentation)
Basic truths that are so obvious they don't need proof or explanation—everyone can see they're true just by understanding what the words mean.
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.
synthetic knowledge(Kant's epistemological framework; contrasted with analytic knowledge)
Knowledge that is not tautological in character — the predicate adds something beyond what is contained in the subject concept