Russell’s Human Knowledge

B. Russell Human Knowledge: Its scope and limits, George Allen and Unwin, 1948.

Russell builds on Keynes’ work on probability to argue that Human Knowledge is empirical, but always depends on unjustifiable assumptions. He gives five postulates (Part VI, Ch. XI) under which inference is justified. These assume a remarkable degree of regularity. Otherwise conventional scientific inference and what he calls ‘mathematical’ (i.e., Bayesian) property are not justified and may be misleading.

Russell’s findings are broadly in line with Whitehead. (Russell and Keynes studied under Whitehead.)

In so far as he justifies ‘the scientific method’  Russell is clearly not intending to justify the view that the method, as it stands, is universally applicable.

Part V. Probability

This reviews the then mainstream probability material, and adapts Keynes’ theory. It is notoriously obscure, perhaps because most readers will have been conditioned to the view that statements like ‘P(A|B)=p’ always make sense, and so fail to see what the fuss is about.

Some highlights follow.


Russell notes that doubt is justified in ‘laws that we have to assume in order to predict the future’.

Ch. I  Kinds of Probability

  Attempts to establish a logic of probability have been numerous, but to most of them there have been fatal objections.  …

… There is … a fairly complete agreement as to everything that can be expressed in mathematical symbols, but an entire absence of agreement as to the interpretation of the mathematical formulae. …

… When we use probability as a guide to conduct, it is because our knowledge is inadequate ; we know that the event in question is one of a class B of events, and we may know what proportion of this class belongs to some class A in which we are interested. But the proportion will vary according to our choice of class B ; we shall thus obtain different probabilities, all equally valid from a mathematical standpoint. …

… The importance of probability in practice is due to its connection with credibility, but if we imagine this connection to be closer than it is, we bring confusion into the theory of probability.

Ch. II  Mathematical Probability

This deals with the case where probability can be represented by a number, not Keynes’ broader concept. Unfortunately for the modern reader it adopts Keynes’ obscure notation. Other reviews follow (Ch.s III, IV).

Ch. V  Keynes’ Theory of Probability

This is the core, which Russell slightly modifies and then applies.

Ch. VI  Degrees of credibility

The degree of credibility is the relative reliability of a statement. It is not the same as mathematical probability (above) and cannot always be represented and handled in a similar way. The notion of classification is critical.

A.  General Considerations

… the rational man … will be guided by the mathematical theory of probability when it is applicable.

B.  Credibility and Frequency

The familiar principle of indifference is developed and shown to rely on having identified the atomic factors, something which Whitehead, for example, regards as always doubtful.

D.  Degrees of Subjective Certainty

   … We assume in practice that a class of beliefs may be regarded as true if … (c) there is no known reason for supposing that mankind would believe them if they were untrue.

Perfect rationality consists, not in believing what is true, but in attaching to every proposition a degree of belief corresponding to its degree of credibility. …

E.  Probability and Conduct

Russell introduces a ‘practical man’, who seems similar to Keynes’, and hence may exclude those with long-run considerations. In essence, ‘the practical man’ ignores tghe long-run and any uncertainty beyond probability. This seems to justify Popper’s incrementalism and ‘no-strategy strategies’. It is stated without any supporting argumentation, and without addressing the proper scope and limitations of the ‘practical man’ .

Ch. VII  Probability and Induction

A.  Statement of the Problem

Naive induction has it that if something has always been so, then it will continue to be so.

B.  Induction by Simple Enumeration

Induction can only refer to classes that are define logically, not those defined in terms of explicit membership.

C.  Mathematical Treatment of Induction

  From the time of Laplace onward, various attempts have been made to show the probable truth of an inductive inference follows from the mathematical theory of probability. It is now generally agreed that these attempts were all unsuccessful, and if inductive arguments are valid it must be true of some extra-logical characteristic of the actual world … .

Keynes … has done the best that can be done for induction on purely mathematical lines. …

D. Reichenbach’s Theory

[Reichenbach’s] posit is this: … if … after a sufficient number of α’s have been examined, the proportion that are β’s is always roughly m/n, then this proportion will continue however many instances of α may be subsequently observed.

This is a kind of ‘small world’.

E.  Conclusions

  First: there is nothing in the mathematical theory … to justify us in regarding … induction as probable … .

Second: if no limitation is placed on the … definitions of the classes … the principle of induction can be shown to be … false.

… [thus] ..

Fifth: scientific inferences, if they are in general valid, must be by virtue of some law or laws of nature, stating a synthetic property of the world  … .


So-called mathematical probability assigns numbers to propositions consistent with some firmly established ‘laws’. Keynes’ theory is more general, so that probability is explicitly dependent on what is ‘known’. In particular, the principle of indifference may not always be applicable.

Despite Russell’s objections, we can perhaps use probabilistic notions as long as we recognize that they only apply to ‘the current epoch’ (in Whitehead’s terms) where one has an adequate understanding; that is, that they are conditional on Reichenbach’s posit, and as long as we guard against wishful thinking and group-think.

Part VI. Postulates of Scientific Inference

This reasons from considerations of probability to inference, identifying some key postulates.

Ch. I  Kinds of Knowledge

Russell discusses classification and expectation as heuristics rather than logical constructs.

Ch. II  The Role of Induction

… I hold that the work of Keynes … suggests a change of emphasis, making induction no longer a premiss, but an application of mathematical probability to premisses arrived at independently of induction. …

… To justify induction as such is impossible, since it can be shown to lead to falsehood as to truth. Nevertheless it remains important as a means of increasing the probability of generalization in suitable cases. …

As regards, the scientific use of induction, I accept the results reached by Keynes … .

Our problem … is to find principles which will make suitable generalizations probable in advance of evidence.

Russell seems to side with those who interpret the Ellsberg paradox as showing that people are irrational. But in the long run the two types of probability are very different.

Ch. III  The Postulate of Natural Kinds, or of Limited Variety

Russell discusses Keynes’ notion of limited variety (as corrected by Nicod). It excludes any innovation or surprise.

Russell’s view of classes as having logical definitions means that, they resemble biological species, only representing ‘typical’ members.

   Such considerations suggest … a transformation of Keynes’ postulate into something more flexible and less reminiscent of a logical text-book than the principle that he enunciates. … This process leads to functional laws of correlation as probably more fundamental than natural kinds.

This is in line with Whitehead.

  I conclude that the doctrine of natural kinds, though useful in establishing such pre-scientific inductions as “dogs bark” and “cats mew”, is only an approximate and transitional assumption on the road towards fundamental laws of a different kind. …

Ch. IV  Knowledge Transcending Experience

Some modern [1940s] empiricists – in particular, the majority of logical positivists – have, in my opinion, misconceived the relation of knowledge to experience. …

A.  Meaning and Verification

  There is a theory that the meaning of a proposition consists in its method of verification. …  I reject [this], and I do not think that those who advocate them have fully realized [its]implications.

B.  Inferential Existence-Propositions

  I incline to think that valid inductions, and generally, inferences going beyond my personal past and present experience, always depend on causation, sometimes supplemented by analogy. …

Ch. V Causal Lines

   The concept of “cause”, as it occurs in the works of most philosophers, is one which is apparently not used in any advanced science. But … the primitive concept, as I try to show, still has importance as the source of approximate generalizations and pre-scientific inductions, and as a concept which is valid when suitably limited.

… [W]e have seen that induction cannot prove causation unless causation is antecedently probable. …

Whether from pure prejudice, or from the influence of tradition, or for some other reason, it is easier to believe that there is a law of nature to the effect that causes are always followed by their effects than to imagine that this usually happens. …

Belief in causation, whether valid or not, is deeply embedded in language. …

This is reminiscent of Whitehead.

… On statistical regularity it is not necessary to say much, since it appears to be an inference, not a postulate. …

Moreover the substitution of statistical for individual regularities has only been necessary in regard to atomic phenomena, all of which are inferred. All the phenomena that can be observed are macroscopic, and the problem of making such phenomena amenable to science remains what it was.

Thus science is quite different from economics, where in ‘the Great Moderation’ regularity was a postulate about compound macro phenomena.

Ch. VI Structure and Causal Laws

… What I am suggesting is that we are not merely to seek simple laws such as A causes B, but are to enumerate a principle of the following sort: given two identical structures, it is probable that that have a causal connection of one of two kinds.
The first kind consists of having a common causal ancestor … .
The second kind arises where two structures are composed of similar ingredients and there exists a causal law leading such ingredients to arrange themselves in a certain pattern. …

On the whole it may be said that the similarity of structure is taken as showing causal ancestry whenever the structure is very complex. …

Sometimes the change of structure is much more complete … . To such changes our principle of constancy of structure is inapplicable.

Structures generally persist, but can change.

Ch.  Interaction

  It will be observed that I have not introduced a postulate to the effect that there are natural laws. My reason for not doing so is that, in any verifiable form, such a postulate would be would be either false or a tautology. …

Russell considers typical inferences, such as to the motion of the planets.

  Mathematical probability does not play any part in the above inferences.

The conclusion … is that the fundamental postulate is that of “causal lines”. This postulate enables us to infer, from any given event, something (thought not much) as to what is probable at all neighbouring times and some neighbouring places. So long as a causal line is not entangled with another, a good deal can be inferred … . [When entangled and] quantitative measurement is possible, the measurably different possibilities after an interaction are finite in number, and therefore observation plus induction can make a general law highly probable. In this kind of way, step by step, it would seem that scientific generalizations can be justified.

Ch. VIII  Analogy

This chapter is more tentative – and questionable. It develops a postulate which would justify us in supposing that people who seem to be human, are.

Ch. IX  Summary of postulates

… The five postulates to which previous analyses have led may be called:

I.     The postulate of quasi-permance.
II.   The postulate of separable causal lines.
III. The postulate of spatio-temporal continuity in casual lines.
IV.  The … structural postulate.
V.    The postulate of analogy.

Each of these postulates asserts that something happens often, but not necessarily always … . Each has an objective and a subjective aspect: objectively, it asserts that something happens in most cases of a certain sort; subjectively,  it asserts that, in certain circumstances, an expectation falling short of certainty … has rational credibility. The postulates collectively are intended to provide the antecedent probabilities required to justify inductions.

It is not so much ‘If postulates then induction’, since we can never know the postulates for sure. It is more that ‘If the result of induction is falsified then some postulate must be false’.

It should also be born in mind that Russell is considering the short-run. In the long-run the postulates fail, so one can only use induction in so far as the postulates do hold.

Ch. X  The Limits of Empiricism

   Empiricism may be defined as the assertion “all synthetic knowledge is based on experience”. …

… [W]e have to consider when … an inference makes its conclusion a piece of “knowledge”, granted that we know the premises.
This … question has sometimes a precise answer. …
But such precision is seldom possible. We do not usually know any mathematical measure of the probability conferred by a non-demonstrative inference, and we hardly ever know the degree of doubtfulness of our premisses. …

[T]o the principle that words which I can understand derive their meaning from my experience there is no need to admit any exceptions whatever. This part of empiricist theory appears to be true without any qualification.

This has implications for the relationship between decision-makers and expert advisers, below.

   Induction, we have seen, is not quite the universal proposition that we need to justify scientific inference. But most certainly we do need some universal proposition or propositions, whether the five canons suggested [above] or something different. … they certainly cannot be logically deduced from facts of experience. …

[T]he doctrine that all our synthetic knowledge is based on experience … if true, cannot be known, since it is a universal proposition of just the sort that experience that experience alone cannot prove.  …

[I]nferences from facts to other facts can only be valid if the world has certain characteristics which are not necessary. Are these characteristics known to us by experience? It would seem not.
Our knowledge of these principles … exists at first solely in the form of propensity to inferences of the kind that they justify. It is by reflecting upon such inferences that we make the principles explicit. And when they have been explicit, we can use logical technique to improve the form in which they are stated, and remove unnecessary accretions.

The approach of experience, reflect, refine could, perhaps, be applied more widely.


Russell is helpful in uncovering what might otherwise be hidden assumptions, whether we agree with Russell’s judgment on them or not.

In addressing himself mainly to ‘scientific’ inferences Russell focusses on cases where such inferences are appropriate. But we may take his assumptions, such as of the ‘practical man’,  and use Russell’s detailed arguments to see how Keynes’ theory could be used more generally for inferencing, within a reformed concept of pragmatism.

It follows from his view on empiricism that where an expert is advising a decision-maker, there is inevitably limited mutual understanding, and their cooperation is problematic. For example, they may have different views on what sorts of reasonings and behaviours are ‘pragmatic’. If the expert’s knowledge is largely technical or formal (and hence formally teachable) then it may be that a clever decision-maker can come to understand the expert, but if the decision-maker’s competence has inevitably been gained through rare experience (as in art, politics or warfare) then it is hard to see how the expert could come adequately to understand the decision maker. There may be a further problem in that if the expert’s domain is technical or formal then they may be incapable of dealing with uncertainties beyond mere probabilities: the expert’s version of pragmatism may ignore long-run issues and lead to crises in the long-run, if left unchecked by informed wisdom. The approach in Human Knowledge, of using logic to critique, refine and formalise views developed through experience may be applicable here: instead of the expert trying to convert the decision maker to a narrow scientism, they should work with them to refine and supplement their understanding, mutually.

Dave Marsay

4 Responses to Russell’s Human Knowledge

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