alt=Four lines of text. The top two show Hume's fork, with analytic, a priori, and necessary in a line, followed by synthetic, a posteriori, and contingent. Below, Kant's trident, where synthetic statements may also be a priori.|thumb|Hume's fork contrasted with Kant's trident/pitchfork
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 or is . 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.—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.
Hume's fork is often stated in such a way that statements are divided up into two types:
- Statements about ideas. These are analytic, necessary, and knowable a priori.
- Statements about the world. These are synthetic, contingent, and knowable a posteriori.
In modern terminology, members of the first group are known as analytic propositions and members of the latter as synthetic propositions. This terminology comes from Kant (Introduction to Critique of Pure Reason, Section IV).
Into the first class fall statements such as "all bodies are extended", "all bachelors are unmarried", and ideas of mathematics and logic. Into the second class fall statements like "the sun rises in the morning", and "all bodies have mass".
Hume wants to prove that certainty does not exist in science. First, Hume notes that statements of the second type can never be entirely certain, due to the fallibility of our senses, the possibility of deception (see e.g. the modern brain in a vat theory) and other arguments made by philosophical skeptics. It is always possible that any given statement about the world is false.
Second, Hume claims that our belief in cause-and-effect relationships between events is not grounded on reason, but rather arises merely by habit or custom. Suppose one states: "Whenever someone on earth lets go of a stone it falls." While we can grant that in every instance thus far when a rock was dropped on Earth it went down, this does not make it logically necessary that in the future rocks will fall when in the same circumstances. Things of this nature rely upon the future conforming to the same principles which governed the past. But that isn't something that we can know based on past experience—all past experience could tell us is that in the past, the future has resembled the past.
Third, Hume notes that relations of ideas can be used only to prove other relations of ideas, and mean nothing outside of the context of how they relate to each other, and therefore tell us nothing about the world. Take the statement "An equilateral triangle has three sides of equal length." While some earlier philosophers (most notably Plato and Descartes) held that logical statements such as these contained the most formal reality, since they are always true and unchanging, Hume held that, while true, they contain no formal reality, because the truth of the statements rests on the definitions of the words involved, and not on actual things in the world, since there is no such thing as a true triangle or exact equality of length in the world. So for this reason, relations of ideas cannot be used to prove matters of fact.
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 accepted, Hume's fork makes it pointless to try to prove the existence of God (for example) as a matter of fact. If God is not literally made up of physical matter, and does not have an observable effect on the world [although virtually all theists believe that God has an observable effect on the world since they believe it is his creation], making a statement about God is not a matter of fact. Therefore, a statement about God must be a relation of ideas. In this case if we prove the statement "God exists," it doesn't really tell us anything about the world; it is just playing with words. It is easy to see how Hume's fork voids the causal argument and the ontological argument for the existence of a non-observable God. However, this does not mean that the validity of Hume's fork would imply that God definitely does not exist, only that it would imply that the existence of God cannot be proven as a matter of fact without worldly evidence.
Hume rejected the idea of any meaningful statement that did not fall into this schema, saying:
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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. — An Enquiry Concerning Human Understanding
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