In epistemology, Hume's fork is a tenet elaborating upon British empiricist philosopher David Hume's emphatic division between "relations of ideas" and "matters of fact." (Alternatively, Hume's fork may refer to what is otherwise termed Hume's law, a tenet of ethics.) As phrased in Immanuel Kant's characterization of Hume's thesis, and furthered in the 1930s by the logical empiricists, Hume's fork asserts that all statements are exclusively either "analytic a priori" or "synthetic a posteriori," which, respectively, are universally true by mere definition or, however apparently probable, are unknowable without exact experience. By Hume's fork, a statement's meaning either is analytic or is synthetic, the statement's truth—its agreement with the real world—either is necessary or is contingent, and the statement's purported knowledge either is a priori or is a posteriori. An analytic statement is true via its terms' meanings alone, hence true by definition, like Bachelors are unmarried, whereas a synthetic statement, concerning external states of affairs, may be false, like Bachelors age badly. By mere logical validity, the necessary is true in all possible worlds, whereas the contingent hinges on the world's state, a metaphysical basis. And the a priori is knowable without, whereas the a posteriori is knowable only upon, experience in the area of interest. By Hume's fork, sheer conceptual derivations (ostensibly, logic and mathematics), being analytic, are necessary and a priori, whereas assertions of "real existence" and traits, being synthetic, are contingent and a posteriori. Hume's own, simpler, distinction concerned the problem of induction—that no amount of examination of cases will logically entail the conformity of unexamined cases—and supported Hume's aim to position humanism on par with empirical science while combatting allegedly rampant "sophistry and illusion" by philosophers and religionists. Being a transcendental idealist, Kant asserted both the hope of a true metaphysics, and a literal view of Newton's law of universal gravitation by defying Hume's fork to declare the "synthetic a priori." In the 1930s, the logical empiricists staked Hume's fork. Yet in the 1950s, W. V. O Quine undermined its analytic/synthetic distinction. And in the 1970s, Saul Kripke established the necessary a posteriori. Still, Hume's fork is a useful starting point to anchor philosophical scrutiny.
Hume's theory and Kant's response Hume's strong empiricism, as in Hume's fork as well as Hume's problem of induction, was taken as a threat to Newton's theory of motion. Immanuel Kant responded with his Transcendental Idealism in his 1781 Critique of Pure Reason, where Kant attributed to the mind a causal role in sensory experience by the mind's aligning the environmental input by arranging those sense data into the experience of space and time. Kant thus reasoned existence of the synthetic a priori—combining meanings of terms with states of facts, yet known true without experience of the particular instance—replacing the two prongs of Hume's fork with a three-pronged-fork thesis (Kant's pitchfork) and thus saving Newton's law of universal gravitation. In 1919, Newton's theory fell to Einstein's general theory of relativity. In the late 1920s, the logical positivists rejected Kant's synthetic a priori and asserted Hume's fork, so called, while hinging it at language—the analytic/synthetic division—while presuming that by holding to analyticity, they could develop a logical syntax entailing both necessity and aprioricity via logic on one side and, on the other side, demand empirical verification, altogether restricting philosophical discourse to claims verifiable as either false or true. In the early 1950s, Willard Van Orman Quine undermined the analytic/synthetic division by explicating ontological relativity, as every term in any statement has its meaning contingent on a vast network of knowledge and belief, the speaker's conception of the entire world. By the early 1970s, Saul Kripke established the necessary a posteriori, since if the Morning Star and the Evening Star are the same star, they are the same star by necessity, but this is known true by a human only through relevant experience. Hume's fork remains basic in Anglo-American philosophy. Many deceptions and confusions are foisted by surreptitious or unwitting conversion of a synthetic claim to an analytic claim, rendered true by necessity but merely a tautology, for instance the No true Scotsman move. Simply put, Hume's fork has limitations. Related concerns are Hume's distinction of demonstrative versus probable reasoning and Hume's law. Hume makes other, important two-category distinctions, such as beliefs versus desires and as impressions versus ideas.
Relations of ideas and matters of fact The first distinction is between two different areas of human study:
All the objects of human reason or enquiry may naturally be divided into two kinds, to wit, relations of ideas, and matters of fact. Of the first kind are the sciences of Geometry, Algebra, and Arithmetic ... [which are] discoverable by the mere operation of thought ... Matters of fact, which are the second object of human reason, are not ascertained in the same manner; nor is our evidence of their truth, however great, of a like nature with the foregoing. — An Enquiry Concerning Human Understanding Hume's fork is often stated in such a way that statements are divided up into two types:
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