Hume's Fork and Regularity Theory of Causation

1. Hume's Fork: The Two Branches of Human Inquiry

Hume begins his An Enquiry concerning Human Understanding by setting out a powerful distinction that sorts all possible objects of knowledge, or propositions, into two exclusive and exhaustive categories. This division is famously known as "Hume's Fork." Understanding this distinction is the key to unlocking his entire philosophy.

The two prongs of the fork are Relations of Ideas and Matters of Fact.

Relations of Ideas

• These are propositions whose truth can be determined by reason alone, without any reference to experience of the world.
• They are known a priori.
• Their denial results in a logical contradiction.
• Examples include the truths of mathematics, geometry, and logic. The statement "A triangle has three sides" is a relation of ideas; its truth is contained in the definitions of the terms. You don't need to go out and inspect triangles to verify it. To say "A triangle does not have three sides" is to contradict yourself.
• These truths are certain, but in a sense, they are tautological. They don't tell you anything new about what exists in the world; they only clarify the relationships between our concepts.

Matters of Fact

• These are propositions about the world, telling us about what exists and how it behaves.
• They can only be known through experience, or a posteriori.
• Their denial, however strange, is never a logical contradiction. It is always conceivable.
• The proposition "The Sun will rise tomorrow" is a matter of fact. We believe it with great confidence, but it's based on past experience, not logical necessity. The statement "The Sun will not rise tomorrow" is false, but it's not a logical contradiction. We can imagine a world where it is true without our concepts falling apart.

To begin exploring this critical distinction, please watch the following video.

The following reading from the Internet Encyclopedia of Philosophy provides a more formal summary and grounds the distinction in Hume's broader project.

As a physicist, you can see this fork clearly at play. The truths of pure mathematics ("$2+2=4$"), which you use constantly, belong to relations of ideas. The laws of physics, like Newton's law of universal gravitation, are matters of fact. They describe how the universe seems to work, but we can conceive of a universe with different laws without logical contradiction. Hume's central question is: what is the foundation for our belief in these matters of fact?

2. The Anatomy of Causation

Hume observes that all our reasoning about matters of fact—everything beyond the immediate evidence of our senses and memory—depends on the relation of cause and effect. How do you know your friend is in France? Because you received a letter (a present fact) that you believe was caused by your friend's being there (an absent fact). How do you know that dropping a pen will result in it falling? Because you believe the act of letting go will cause it to fall.

Given that causation is so fundamental, Hume subjects it to a rigorous empirical analysis. If causal knowledge is a matter of fact, it must be derived from experience. So, what do we actually experience when we observe what we call a "causal" event—say, one billiard ball striking another?

Hume identifies three observable elements:

1. Contiguity: The cause and effect are close to each other in space and time. (The balls touch).
2. Temporal Priority: The cause occurs before the effect. (The first ball moves before the second one does).
3. Constant Conjunction: We have observed this sequence of events—one ball striking another and the second moving—repeatedly in the past. Every time we've seen an event of type A, it has been followed by an event of type B.

But, Hume notes, our idea of causation includes something more: a sense of necessary connection. We don't just think that the second ball will move, but that it must move. We believe there is some power in the first ball to produce the motion in the second.

This is the crux of the problem. Look as closely as you can at the event. You can see the contiguity, the priority, and you can remember the constant conjunction. But you can never, ever perceive the necessity. You don't see a "force" or "power" passing from one ball to the other. That necessary connection is entirely unobservable.

So, if every idea must be a copy of some impression (Hume's Copy Principle), where does our idea of necessary connection come from? We have no external impression of it.

3. The Regularity Theory: Causation as a Habit of Mind

Hume's answer is a brilliant and radical turn inward. Since the idea of necessary connection does not come from an impression of the external world, it must arise from an internal impression—a feeling or a "determination of the mind."

Here is how it works:

1. We observe the constant conjunction of two events, A and B, over and over again.
2. This repetition creates a habit or custom in our minds.
3. Because of this habit, when we observe a new instance of event A, our mind is irresistibly led to form a lively idea of event B. We develop a strong feeling of expectation.
4. This internal feeling—this mental transition from A to B that our own imagination produces—is the impression from which our idea of necessary connection is copied.

This is the essence of Hume's regularity theory of causation. In the world itself, causation is nothing more than the regular, exceptionless succession of one event by another (constant conjunction). The "necessity" we attribute to this relationship is not a feature of reality, but a projection of our own minds. It's a psychological phenomenon, not a metaphysical one.

This leads Hume to his famous two definitions of a cause:

1. Objective Definition: "An object, followed by another, and where all the objects similar to the first are followed by objects similar to the second." (This just describes constant conjunction).
2. Subjective Definition: "An object followed by another, and whose appearance always conveys the thought to that other." (This describes the psychological habit).

To fully grasp the argument that leads to this conclusion, we'll examine one of the most famous arguments in philosophy: the problem of induction. Hume shows that our belief that the future will resemble the past—the very principle that underpins all causal reasoning—cannot be rationally justified.

The implication of this argument is staggering. All reasoning concerning matters of fact is founded on cause and effect. Our idea of cause and effect is founded on the assumption that the future will resemble the past (the principle of induction). But that assumption itself is just based on past experience—it's a habit of mind, not a principle of reason. Therefore, all our knowledge of the natural world, including the laws of science, rests not on a foundation of rational certainty, but on a psychological disposition. You cannot prove that dropping your pen will cause it to fall; you simply have a very, very strong, psychologically ingrained expectation that it will, based on what has been a completely uniform past experience.

Conclusion

In this lesson, we have seen how David Hume deployed his empiricist principles to challenge the very foundations of our knowledge of the world. He forces a stark choice upon us with his "fork" and then demonstrates that most of what we claim to know falls on the uncertain side.

Key Takeaways:

• Hume's Fork: All objects of human inquiry are either Relations of Ideas (known a priori and with certainty, like math) or Matters of Fact (known a posteriori and without certainty, like science).
• Causation is a Matter of Fact: Causal relationships are not discoverable by reason, only by experience.
• The Regularity Theory of Causation: Our experience of causation consists of contiguity, temporal priority, and constant conjunction. The crucial idea of necessary connection is not in the objects themselves.
• Psychological Origin of Necessity: The feeling of "necessity" is an internal impression, a determination of the mind created by custom or habit after observing a constant conjunction of events. Causation, as we think of it, is a projection of our own minds onto the world.

Preview of the Next Lesson:
Hume's analysis of causation gives birth to one of the most enduring problems in philosophy: the problem of induction. If our scientific laws and everyday predictions are based on inductive reasoning—generalizing from past experience to the future—and this form of reasoning has no rational justification, what becomes of scientific knowledge? In our next lesson, we will delve deeper into the structure of this problem and explore its profound significance for science and epistemology.