Millican’s Hume, Induction and Probability

Peter J.R. Millican Hume, Induction, and Probability The University of Leeds, Department of Philosophy (Thesis, 1995)

An argument of David Hume’s against probable reasoning is summarised as:

  • Probable arguments presuppose the Uniformity Principle.
  • The Uniformity Principle has no foundation in reason.


  • Probable arguments are not founded on reason or any process of the understanding.


  • No probable argument (moral argument, reasoning concerning matter of fact) is rationally justified, and hence it is not reason [but instead custom or habit, a nonrational instinct] which engages us to make probable inferences.

This would be unfortunate, since nothing could be justified without some form of argument, and deductive arguments can never take us very far.

It is now time to begin our discussion by sketching the three main non-probabilistic approaches to the justification of induction that have dominated the contemporary debate:  the “inductive”, the “analytic”, and the “pragmatic”.

Against the inductive justification we can invoke … another Humean notion, that of “presuppositional circularity”.

In so far as the analytic justification has any merit, then, Hume can comfortably go along with it, for he himself takes induction to be paradigmatically reasonable in his intermediate, “empirical” sense.  But as a would-be rebuttal of Hume, the analytic justification is utterly ineffective.

Finally, we come to the pragmatic justification, which on its own admission seems to pose little threat to the Humean position. … We are indeed thus committed … ,:  we do in fact believe firmly in uniformity, at least from day to day even if not in the infinite Reichenbachian “long run”.  Moreover we cannot stop believing this and judging accordingly, however hard we try – even the impact of one of the most powerful philosophical arguments ever devised has absolutely no effect on our animal tendency to believe and to infer.


the only kind of strategy which stands much prospect of defeating Hume’s argument is one based on a priori probabilistic reasoning.

But this approach fails, and so the thesis concludes:

On the whole … if I had to bet, I would bet on Hume. It seems to me that the results of this thesis have given excellent inductive grounds for confidence that he will ultimately emerge victorious against every attempt to refute him. And just as Hume did, I trust induction.

His gives his reasons as:

First, I continue to find it extremely implausible that substantial epistemological conclusions such as this should be drawn by pure reason.

Secondly … I continue to feel very uneasy about the use of improper prior distributions except as a convenient approximation to proper priors. Without considerably more investigation and understanding of the implications of their use, I cannot express any confidence that the results they yield are fully meaningful and coherent.

Thirdly, I believe that there are strong theoretical grounds …  for refusing to accept that knowledge and ignorance can adequately be modelled by conventional probability distribution functions. In most cases, perhaps, they perform reasonably well, but when extreme situations of absolute ignorance are in question, the cracks begin to show. Interval-valued probabilities and other richer and more flexible models seem in such cases better motivated, but these provide an unlikely basis for a defence of induction, precisely because they put fewer constraints on coherent degrees of belief, ignorance and indecision.

He refers to and commends Keynes’ Treatise, e.g.:

Chapter IV of Keynes’ Treatise on Probability is still one of the very best discussions of the principle [of indifference] with many telling examples both of “discrete” and of “geometrical” paradoxes.

(In a footnote:) A personal hunch here is that the development and incorporation into probability theory of Keynes’ concept of “weight” (1921, chapter VI) might help to explain in a well-motivated manner why conventional probability models break down in situations of extreme ignorance (somewhat as arithmetical division breaks down when the denominator is zero).


Weak induction

I find Millican’s thesis more accessible than his more popular works derived from it, and suppose that these are still his ideas. [Please let me know if I am wrong.] Technically, I find Keynes’ Treatise better, albeit less readable.

As stated by Millican, the Uniformity Principle is that:

instances, of which we have had no experience, must resemble those, of which we have had experience, and that the course of nature continues always uniformly the same.

My own experience is that for any claim to bound possible experience, there is always a counter-example. For example, when an academic subject (such as veterinary science or economics) becomes relevant to some political situation, experts often lack suitable experience to enable them to collaborate effectively.

We might use the term ‘ordinary’ as follows:

Instances, of which we have had no experience, ordinarily resemble those, of which we have had experience, and that the course of nature ordinarily continues [approximately] the same.

Thus when a group of people with different domains of experience collaborate, we might anticipate (and even hope for) something out of the ordinary., beyond anyone’s experience.

Now in any situation that conventional induction would suggest that something will or will probably occur, a weaker form is to simply claim that that something will ordinarily occur, or alternatively that conventional indication is ordinarily reliable.

Keynes can be read as describing some situations that are not ordinary, and as showing that we can never be certain that a given situation is ordinary. But the greater the ‘weight of evidence’ that a situation is ordinary the more we might rely on the result of conventional induction, if never absolutely.


If induction is just an ingrained habit without genuine justification, then science and rationality are just habit, only ever justified in the context of some unjustifiable culture, and there can be no reason to prefer one culture to another, except by some ‘pragmatic’ test. Thus, for example, American ideas must be regarded as better than the Chinese unless and until the Chinese overtake the Americans economically.

But if we prefix statements that rely on induction with ‘ordinarily …’ without claiming that what is ordinary is necessary or probable, then we have something that is more credible, and perhaps even tautological. It also seems reasonable to act on what would be ordinary when there is a great weight of evidence that the situation is ordinary. But more reasonably, we might recognize the inevitable residual uncertainty and act accordingly. To Bowdlerize Ronald Regan:

Trust [induction] but verify [as far as is practical].

To edit Millican:

[We may mostly]  believe firmly in uniformity, at least from day to day even if not in the infinite Reichenbachian “long run”. [But we should not be so firm.]

[One] of the most powerful philosophical arguments ever devised has [had] absolutely no effect on our animal tendency to believe and to infer. [We need to do better. Beliefs and inferences should never be absolute, but only relative to the evidence for them.]

This begs the question of what would be a ‘healthy’ relationship between experience and habits, and whether our views of such a relationship are necessarily conditioned by culture or could be more ‘objective’. Contrary to what most readers may take from Millican, I think the question is left wide open, at least until one reads Whitehead/Keynes/Russell. (And I dont find them particularly clear.)

Dave Marsay




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