Causation, Induction, and the Limits of Reason
Sections 4–5: Why we can’t rationally justify the things we most rely on.
This page covers five sections: Hume’s Fork, the problem of induction, the analysis of causation, Hume’s sceptical solution, and the is/ought distinction. Click any heading to open it.
Two kinds of knowledge, and nothing else
Section 4 opens with one of the most powerful moves in the history of philosophy. Hume divides all objects of human reason — everything we can possibly think or know — into exactly two classes. There is no third option.
Relations of ideas are propositions that are necessarily true or false in virtue of the meanings of the terms involved. Mathematics is the clearest example: “the interior angles of a triangle sum to 180 degrees” is true, and its truth can be established by pure reasoning, without going out and measuring any actual triangles. The contrary — that they sum to 200 degrees — is not just false but inconceivable. Logic works the same way: if all humans are mortal and Socrates is human, then Socrates is mortal is necessarily true. You cannot coherently deny it.
Matters of fact, by contrast, are propositions about how the world actually is. “The sun rises in the east” is a matter of fact. Its contrary — that it rises in the west — is not a logical contradiction. It is conceivable. It just happens to be false. All factual claims about the world, from the most mundane to the most scientific, fall into this category. And crucially: their truth cannot be established by reasoning alone. We have to go look.
| Relations of Ideas | Matters of Fact | |
|---|---|---|
| How established | By reasoning alone; no experience needed | By experience and observation |
| Contrary | Inconceivable / self-contradictory | Conceivable; could in principle be true |
| Examples | Mathematics, logic, definitions | Scientific laws, historical claims, causal claims |
| Certainty | Absolute; demonstrative | Probable; subject to revision by experience |
The Fork is called a “fork” because it is a two-pronged division that leaves no middle ground. Anything that is neither a relation of ideas nor a matter of fact — anything that claims certainty about the world without grounding in experience — is, Hume argues, “sophistry and illusion.”
← Looking back: Descartes
Recall Descartes’ project: using pure reason to establish the existence of God, the reality of the external world, and the reliability of clear and distinct perception — all without relying on the senses. For Hume, this is precisely what the Fork rules out. The existence of God and the external world are not relations of ideas (their contraries are conceivable) and not established by experience. They are, in Hume’s framework, neither demonstratively certain nor experimentally confirmed. The entire Cartesian enterprise lands in the category Hume will later call “sophistry and illusion.”
Why experience can’t justify itself
Consider what happens when you reason from experience. You have observed that fire is hot many times. You conclude that fire is always hot. You see a new flame and are confident it will burn you. This kind of inference — from observed cases to an unobserved conclusion — is called induction.
All scientific knowledge is built on inductive inference. We observe patterns and infer laws. We do experiments and generalize to conclusions about how nature works. Induction is so fundamental to how we understand the world that questioning it feels strange — even absurd. But Hume does exactly that.
His argument is precise. The belief that the future will resemble the past — which is what all inductive reasoning assumes — is not a relation of ideas. It is perfectly conceivable that the future will be wildly different from anything we have experienced. So if it is to be known at all, it must be established by experience. But how? Any attempt to use experience to justify induction goes in a circle: “Induction has worked in the past, therefore it will work in the future” is itself an inductive argument. It assumes the very principle it is supposed to justify.
Logic connection → Logic Reference
In the Logic Reference, inductive arguments are described as ones where true premises make the conclusion probable but not certain. Hume’s problem of induction goes one level deeper: he is not questioning whether any particular inductive argument is good, but whether induction as a method can be rationally justified at all. An inductively strong argument gives us good grounds for belief — but Hume is asking what grounds we have for trusting inductive strength in the first place.
The argument laid out formally:
Hume’s Induction Argument
P1: Our belief that the future will resemble the past cannot be a relation of ideas (its contrary is conceivable).
P2: If it is knowable at all, it must be established by experience (the only alternative, given the Fork).
P3: Any experiential justification takes the form: “It has worked before, so it will work again” — which is itself an inductive inference.
P4: Using induction to justify induction is circular.
C: Our belief that the future will resemble the past cannot be rationally justified.
This conclusion is not that induction is unreliable in practice — Hume has no intention of telling you to stop relying on past experience. It is that the rational justification for it does not exist. We use induction because we cannot help it. Not because we have a good argument for it.
That is a profoundly uncomfortable place to leave scientific knowledge. Section 5 is Hume’s attempt to explain how we manage, even without justification.
What do we actually see when we see a cause?
Imagine watching a billiard ball roll across a table and strike a second ball. The second ball immediately moves. You say, without hesitation: the first ball caused the second to move. But what exactly did you observe?
You observed the first ball moving. You observed contact. You observed the second ball moving. That is all. You did not observe any power, any force, any necessary connection passing from one ball to the other. The connection you feel so certain about is not in the scene you watched. It is something your mind added.
Hume breaks our idea of causation into three components: priority in time (the cause comes before the effect), contiguity in space (cause and effect are adjacent), and necessary connection. The first two are easy to account for: they trace back to our impressions of time and space. But the third — necessary connection, the sense that the cause had to produce the effect — is the problem. What impression does it come from?
Constant conjunction
Hume’s investigation reveals that we never observe necessary connection directly. What we observe is constant conjunction: events of type A are always (in our experience) followed by events of type B. Fire is always followed by heat. The first billiard ball’s motion is always followed by the second ball’s motion. The conjunction is constant, but we never see the necessity.
After repeated conjunctions, the mind develops a habit: upon observing A, it automatically expects B. That expectation — that internal feeling of being drawn from one idea to another — is the impression from which our idea of necessary connection is actually copied. Necessary connection is not a feature of the external world that we observe. It is a feature of our minds that we project onto the world.
What this means
When scientists say that smoking causes cancer, they are not describing something they directly observed in the world. They are describing a constant conjunction (smokers get cancer at much higher rates than non-smokers) and expressing the mind’s habituated expectation that the pattern will continue. This is not a critique of science — constant conjunction is real evidence, and Hume is not a fool. It is a correction to our metaphysical picture of what causation actually is.
← Looking back: Descartes on causation
Descartes used a causal argument in Meditation III: the idea of an infinitely perfect being must have an equally perfect cause, which must be God. For Hume, this entire argument rests on a misconstrual of causation. If necessary connection is not a feature of the external world but a habit of the mind, then the principle that “every idea must have a cause at least as great as its content” is not a necessary truth. It is, at best, a regularity we have observed — and even that regularity does not extend to ideas in the way Descartes needs.
Custom and habit: the real foundation
So: we can’t justify induction by reason, we can’t justify it by experience without circularity, and causation turns out to be a projection of the mind rather than a feature of the world. How do we function at all?
Hume’s answer is disarmingly simple: custom and habit. After repeated experiences of A followed by B, the mind develops an expectation — an automatic, non-rational tendency to expect B whenever A appears. This expectation is not the product of reasoning; it is a natural operation of the mind. We are built this way. We could not avoid forming these expectations even if we wanted to.
And that, Hume says, is enough. The basis of our confidence in the future is not a rational justification but a natural instinct. Custom is “the great guide of human life.” It is what makes our past experience useful — it allows us to act as though the future will resemble the past, even though we cannot prove it will. The lack of rational justification does not mean we are wrong to rely on experience. It means we were wrong to think reason was what we were relying on.
Hume on belief
Hume’s Section 5 also offers an account of what a belief actually is. A belief, he says, is not merely an idea — it is an idea held with a certain vivacity and force. When I believe that the sun will rise tomorrow, I don’t just have the idea of the sun rising; I hold that idea with a kind of urgency and conviction that mere imagination lacks. That difference in vivacity is what distinguishes belief from mere conception. And that vivacity is produced — by custom, by repeated experience, not by rational argument.
This is Hume’s naturalism: rather than explaining human knowledge by appeal to reason or God, he explains it by appeal to how human beings actually work — the psychological mechanisms that govern thought and expectation. It is a modest conclusion, but Hume thinks it is the honest one.
You can’t get ought from is
Hume’s most influential contribution to ethics comes not from the Enquiry but from the Treatise — but it follows directly from the same empiricist principles. It is short, and it is devastating.
Hume notices that in most moral arguments, a writer begins by making factual claims — statements about what is the case — and then, at some point, makes a subtle transition to claims about what ought to be done. The shift often happens without explanation, as though it were obvious. But Hume argues that the shift is never obvious: there is a logical gap between descriptive claims and normative ones, and it requires an explicit argument to cross it.
Logic concept: Is/Ought Distinction → Logic Reference
The is/ought distinction (sometimes called Hume’s Guillotine) is the claim that you cannot validly derive a normative conclusion (“one ought to do X”) from purely descriptive premises (“X is the case”) without some additional normative premise bridging the gap.
Examples of the fallacy:
— “Humans have always gone to war. Therefore war is natural and permissible.”
(Moves from “always done” to “therefore acceptable” — missing normative premise)
— “God created this social hierarchy. Therefore it ought to be preserved.”
(Moves from “is created by God” to “ought to be preserved” — requires the added premise “what God creates ought to be preserved”)
— “Evolution selected for aggression. Therefore aggression is natural and we should not suppress it.”
(Moves from biological fact to ethical conclusion — the missing premise: “we ought to act on whatever evolution selected”)
The distinction matters far beyond ethics. It applies to any argument that tries to derive what should be the case from what is the case — arguments from nature, from God, from history, from economics. All of these face Hume’s challenge: show me the normative premise that bridges the gap.
Looking ahead →
As you move through the remaining units, apply Hume’s distinction to each philosopher’s moral or political arguments. Hegel will argue that Reason unfolds through History — does that give us an “ought”? Marx will argue that capitalism contradicts human nature and historical development — does that tell us what we should do? Sartre will deny any natural or historical essence to ground values — is that an answer to Hume, or does it make his problem worse? Hume’s Guillotine keeps falling.