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This is a bit subtle. I'm guessing "case of knowledge justified through reason alone" is pointing to the Kantian conception of mathematics as synthetic a priori knowledge. Frege really wanted to be a Kantian and expressed great admiration for Kant, whom had come up with the distinction between synthetic a priori and analytic a priori knowledge. But ...


3

Logical positivism may not be the perfect label, actually according to Hempel who's one of its major figures during its heyday in last century, it should be more properly called logical empiricism as described here: Hempel never embraced the term "logical positivism" as an accurate description of the Vienna Circle and Berlin Group, preferring to ...


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The split between Rationalism and Empiricism (note the capital letters) goes back to the 17th century. Basically, it is a dispute about the proper foundation of knowledge: Rationalism holds that knowledge is (in one of several ways) founded in our mind and in the human capacity to use reason. Empiricism holds that knowledge must (in one form or another) be ...


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