A priori justification ain't what it used to be. There was a time when philosophers and mathematicians perhaps thought that when we engaged in deductive, a priori constructions of proofs for claims from propositions that we know to be true a priori, then those conclusions are as justified as anything can be. That is, when we reason deductively and without error from truths that we know without any appeal to the empirical world, then we acquire new knowledge of a broader world.
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