In philosophy, Hume's fork (also called Hume's dictum) is a distinction, due to David Hume, 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:
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, pp. 48).
Into the first class fall statements such as "2 + 2 = 4", "all bachelors are unmarried", and truths of mathematics and logic. Into the second class fall statements like "the sun rises in the morning", "the Earth has precisely one moon", and "water freezes at 32 degrees Fahrenheit".
Hume essentially proved that no certainty exists 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 logically possible that any given statement about the world is false. (note that statements like "either the Earth has precisely one moon, or not" are really truths of logic, and say nothing about the world).
Second, Hume claims that the cause-and-effect relationship of events is not certain like it may seem, just something people judge out of habit, and so it is impossible to state definite truths about the world or make definite predictions. Suppose one states this as a "truth" of the world: "When a rock is dropped while on Earth, it goes down." While we can predict with probability that when you drop a rock it will go down, since in every instance thus far when a rock was dropped on Earth it went down, we technically cannot prove that it always will. The next time we drop a rock, it might abruptly be subject to a previously unseen upward force. In the same way, it is not possible to prove a mathematical fact by stating examples, no matter how many you state. So for this reason, matters of fact cannot be used to prove relations of ideas.
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). Since God is not literally made up of physical matter in the world, making a statement about God is not a matter of fact. Therefore, a statement about God must be a relation of ideas. So 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 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.
Hume famously rejected the idea of any meaningful statement that did not fall into this schema, saying:
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
This same idea has perdured in relatively contemporary schools of philosophy, such as logical positivism. This general attitude is strikingly present in Alfred Ayer's logical empiricist work Language, Truth and Logic.
Not everyone, however, has agreed with Hume's fork. Kant, for example, famously defended the idea of synthetic a priori propositions. W.V.O. Quine also argued against the well-defined distinction between analytic and synthetic propositions required by Hume's fork in his landmark paper Two Dogmas of Empiricism.