Hume's Fork, which divides knowledge into 'relations of ideas' and 'matters of fact' has had an incredible influence on philosophy ever since its conception (though it is sometimes claimed that others before Hume, such as Leibniz, anticipated a version of the thesis). So influential is the thesis that it seems to have been a rather potent presumption in the minds of modern philosophers throughout time.

For example, Hume's criticism of induction and the wedge he placed between what experience offers us and what we conclude about said experience was incorporated by Kant, who was a critic of Hume in many senses of the word. That same wedge could be argued to be a driving presumption in Kant's understandings of the terms apriori, aposteriori, analytic, and synthetic (even if Kant's famous synthetic apriori was a response to Hume's seeming attack upon the possibility of science).

In more contemporary philosophy, such as in the works of Carnap, it is held that statements are either true by virtue of their form alone or are empirical statements.

To what degree is Hume's Fork, in some sort of manifestation or another, present in philosophy in the analytical community (especially in the works of Wittgenstein, Ayer, Carnap and Quine)?

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    I'm not really following your claim in the first paragraph in all honesty. Also, could you rewrite this to be less umm.. grandiose in style? – virmaior Apr 1 '16 at 2:28
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    I wouldn't call Carnap contemporary. – Alexander S King Apr 1 '16 at 2:34
  • What you call "Hume's fork" came to be known as the analytic/synthetic distinction after Kant. Even Carnap only retained it in relativized and externalized form of "linguistic frameworks" adopted "by convention". Quine in Two Dogmas of Empiricism rejected it completely as a useless contrivance with misleading consequences, although he softened his stance a bit in later years. Today it survives only in deflated form of a practicality coming in vague degrees, not reducible to any explicit conventions. As a cornerstone of epistemology, that it was for Kant and less so Carnap, it is long discarded – Conifold Apr 1 '16 at 16:08
  • @Conifold As I understood it, Hume's Fork has been implicit in modern philosophy's assumptions regarding the possibility of metaphysics. Quine is held to have dismissed 'metaphysics' because metaphysics is equated with Kant's synthetic apriori, which is truly only one understanding of the nature of metaphysics (and Kant in turn churned out his synthetic apriori only because he accepted Hume's criticism of induction, which goes hand in hand with Hume's Fork). So the point is not so much whether the fork endures in philosophy, but rather the effect it still has by its dictation of responses. – Ovid Apr 2 '16 at 3:09
  • Neither Kant nor Quine dismissed metaphysics, even in Two Dogmas he credits it as a hypotheses generator for science, they only dismissed its pretenses to accessing extra-empirical truths. But the source of it I think is not Hume's fork, but rejection of innate ideas, intellectual intuition, phenomenological reduction, and other such inventions designed to secure an independent justificational warrant. This rejection certainly endures, analytic philosophers are content to confine philosophy to conceptual analysis of practice, which in a way derives from Kant's transcendental analyses. – Conifold Apr 2 '16 at 21:37

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