"Hume's fork is an explanation, developed by later philosophers, of David Hume's aggressive, 1730s division of "relations of ideas" from "matters of fact and real existence".[1] On the necessary versus contingent (concerning reality), the a priori versus a posteriori (concerning knowledge), and the analytic versus synthetic (concerning language), truths relating ideas (abstract) all align on one side (necessary, a priori, analytic), whereas truths on actualities (concrete) always align on the other side (contingent, a posteriori, synthetic).[1] "
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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.
- Statements about ideas. These are analytic, necessary statements that are knowable a priori.
- Statements about the world. These are synthetic, contingent, and knowable a posteriori.
The results claimed by Hume as consequences of his fork are drastic. According to him, relations of ideas can be proved with certainty (by using other relations of ideas), however, they don't really mean anything about the world. Since they don't mean anything about the world, relations of ideas cannot be used to prove matters of fact. Because of this, matters of fact have no certainty and therefore cannot be used to prove anything. Only certain things can be used to prove other things for certain, but only things about the world can be used to prove other things about the world. But since we can't cross the fork, nothing is both certain and about the world, only one or the other, and so it is impossible to prove something about the world with certainty.
If we take in our hand any volume; of divinity or school metaphysics, for instance; let us ask, Does it contain any abstract reasoning concerning quantity or number? No. Does it contain any experimental reasoning concerning matter of fact and existence? No. Commit it then to the flames: for it can contain nothing but sophistry and illusion.[8] - An Enquiry Concerning Human Understanding
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