Causation, induction, probability: is causation regular succession (Humean), and is induction justified through probability rather than necessary connection?

A.J. Ayer, answered from the texts and cited to the page.

The position in brief

Causation is regular succession, not necessary connection. Hume was right: when we observe that one event regularly follows another, we are entitled to expect the second on future occasions of the first, but the "must" in "A must cause B" adds nothing factual to the regularity — it expresses our expectation, formed by habit, not a necessary connection in nature.¹

Inductive reasoning is justified pragmatically through probability calculus, not metaphysically through necessary connection or law-like structure.² The probability calculus, applied to evidence and hypothesis, gives us the rational basis for inductive conclusions; no stronger foundation is available, and none is needed. Ayer's Hume monograph (1980) defends this Humean position systematically; Probability and Evidence (1972 Dewey Lectures) develops the technical apparatus.

Free will is similarly Humean: freedom is opposed to constraint, not to causal determination; determinism is compatible with the freedom required for moral responsibility. The compatibilist line ('Freedom and Necessity' in Philosophical Essays 1954) follows Hume directly. The necessitarian alternative (Honderich's Hahn essay; the broader necessitarian tradition) posits necessary connections that nothing in observation supports; it is metaphysical residue the verificationist analysis would eliminate.³⁴

Sources

1. All that we have to go on is our past experience of regularity in nature; indeed there is nothing more there to be discovered. We become habituated to expecting that this regularity will be maintained.

   Hume, pp. 83–84

2. He puts this rather misleadingly by saying that 'all reasonings concerning matters of fact seem to be founded on the relation of cause and effect'.! He then raises the question whether our belief in the existence of these lawlike connections can ever be rationally justified, and he offers a proof that it cannot.

   Probability and Evidence, pp. 4–5

3. But the primary events, in terms of which alone the explanations can be cashed, stand in none but spatio-temporal or merely temporal relations to each other. I have developed this point because I think that it is of interest, but its validity is not essential to the main argument.

   Probability and Evidence, pp. 14–15

4. From the fact, if it be a fact, that a faithful description of some particular action of mine implies, either overtly or covertly, that I have undergone such an experience, it in no way follows that when I set myself to repeat the action, I shall have the same experience or indeed achieve the same result.

   Hume, pp. 80–81

Where the argument is made

• Probability and Evidence (Macmillan 1972, the Dewey Lectures)
• The Central Questions of Philosophy (1973) Chapter 8 on causation
• Hume (Past Masters Oxford 1980) for the systematic engagement with Hume
• 'What is a Law of Nature?' (Concept of a Person 1963)
• the reply to Ted Honderich on 'Causation: One Thing Just Happens After Another' (Hahn volume)
• Language, Truth and Logic (1936) Chapter 5 on probability

How the argument was received

The Humean treatment of causation, induction, and free will is the empiricist orthodoxy; Ayer's defense in Probability and Evidence (1972), the Hume monograph (1980), and Philosophical Essays' 'Freedom and Necessity' (1954) is the major twentieth-century British statement of the position. Honderich's necessitarian alternative (in his Hahn essay and in A Theory of Determinism 1988) is the major opposition. Mackie's INUS conditions, Lewis's counterfactual analysis, and the contemporary Bayesian tradition are descendants and refinements; the Humean core remains a live position.