Knowledge

I have always said that a belief was knowledge if it was (i) true, (ii) certain, (iii) obtained by a reliable process. But the word 'process' is very unsatisfactory; we can call inference a process, but even then unreliable seems to refer only to a fallacious method not to a false premiss as it is supposed to do. Can we say that a memory is obtained by a reliable process? I think perhaps we can if we mean the causal process connecting what happens with my remembering it. We might then say, a belief obtained by a reliable process must be caused by what are not beliefs in a way or with accompaniments that can be more or less relied on to give true beliefs, and if in this train of causation occur other intermediary beliefs these must all be true ones.

E.g. 'Is telepathy knowledge?' may mean: (a) Taking it there is such a process, can it be relied on to create true beliefs in the telepathee (within some limits, e.g. when what is believed is about the telepathee's thoughts)? or (b) Supposing we are agnostic, does the feeling of being telepathed to guarantee truth? Ditto for female intuition, impressions of character, etc. Perhaps we should say not (iii) obtained by a reliable process but (iii) formed in a reliable way.

We say 'I know', however, whenever we are certain, without reflecting on reliability. But if we did reflect then we should remain certain if, and only if, we thought our way reliable. (Supposing us to know it; if not, taking it merely as described it would be the same, e.g. God put it into my mind: a supposedly reliable process.) For to think the way reliable is simply to formulate in a variable hypothetical the habit of following the way.

One more thing. Russell says in his Problems of Philosophy that there is no doubt that we are sometimes mistaken, so that all our knowledge is infected with some degree of doubt. Moore used to deny this, saying of course it was self-contradictory, which is mere pedantry and ignoration of the kind of knowledge meant.

But substantially the point is this: we cannot without self-contradiction say p and q and r and . . . and one of p, q, r . . . is false. (N.B.— We know what we know, otherwise there would not be a contradiction). But we can be nearly certain that one is false and yet nearly certain of each; but p, q, r are then infected with doubt. But Moore is right in saying that not necessarily all are so infected; but if we exempt some, we shall probably become fairly clear that one of the exempted is probably wrong, and so on.
(Foundations of Mathematics and Other Logical Essays , 1931), Last Papers, D. Knowledge, p.258-9)

Reasonable Degree of Belief

When we pass beyond reasonable = my, or = scientific, to define it precisely is quite impossible. Following Peirce we predicate it of a habit not of an individual judgment. Roughly, reasonable degree of belief = proportion of cases in which habit leads to truth. But in trying to be more exact we encounter the following difficulties :—

(1) We cannot always take the actual habit: this may be correctly derived from some previous accidentally misleading experience. We then look to wider habit of forming such a habit.

(2) We cannot take proportion of actual cases; e.g. in a card game very rarely played, so that of the particular combination in question there are very few actual instances.

(3) We sometimes really assume a theory of the world with laws and chances, and mean not the proportion of actual cases but what is chance on our theory.

(4) But it might be argued that this complication was not necessary on account of (1) by which we only consider very general habits of which there are so many instances that, if chance on our theory differed from the actual proportion, our theory would have to be wrong.

(5) Also in an ultimate case like induction, there could be no chance for it: it is not the sort of thing that has a chance.

Fortunately there is no point in fixing on a precise sense of 'reasonable'; this could only be required for one of two reasons: either because the reasonable was the subject matter of a science (which is not the case); or because it helped us to be reasonable to know what reasonableness is (which it does not, though some false notions might hinder us). To make clear that it is not needed for either of these purposes we must consider (1) the content of logic

and (2) the utility of logic.

THE CONTENT OF LOGIC

(1) Preliminary philosophico-psychological investigation into nature of thought, truth and reasonableness.

(2) Formulae for formal inference = mathematics.

(3) Hints for avoiding confusion (belongs to medical psychology).

(4) Outline of most general propositions known or used as habits of inference from an abstract point of view; either crudely inductive, as 'Mathematical method has solved all these other problems, therefore...' or else systematic, when it is called metaphysics. All this might anyhow be called metaphysics; but it is regarded as logic when adduced as bearing on an unsolved problem, not simply as information interesting for its own sake.

The only one of these which is a distinct science is evidently (2).

THE UTILITY OF LOGIC

That of (1) above and of (3) are evident: the interesting ones are (2) and (4). (2) = mathematics is indispensable for manipulating and systematizing our knowledge. Besides this (2) and (4) help us in some way in coming to conclusions in judgment.

LOGIC AS SELF-CONTROL (Cf. Peirce)

Self-control in general means either

(1) not acting on the temporarily uppermost desire, but stopping to think it out; i.e. pay regard to all desires and see which is really stronger; its value is to eliminate inconsistency in action;

or (2) forming as a result of a decision habits of acting not in response to temporary desire or stimulus but in a definite way adjusted to permanent desire.

The difference is that in (1) we stop to think it out but in (2) we've thought it out before and only stop to do what we had previously decided to do.

So also logic enables us

(1) Not to form a judgment on the evidence immediately before us, but to stop and think of all else that we know in any way relevant. It enables us not to be inconsistent, and also to pay regard to very general facts, e.g. all crows I've seen are black, so this one will be — No; colour is in such and such other species a variable quality. Also e.g. not merely to argue from φa . φb . . . to (x).φx probable, but to consider the bearing of a, b . . are the class I've seen (and visible ones are specially likely or unlikely to be φ). This difference between biassed and random selection. (Vide infra 'Chance'.)

(2) To form certain fixed habits of procedure or interpretation only revised at intervals when we think things out. In this it is the same as any general judgment; we should only regard the process as 'logic' when it is very general, not e.g. to expect a woman to be unfaithful, but e.g. to disregard correlation coefficients with a probable error greater than themselves.

With regard to forming a judgment or a partial judgment (which is a decision to have a belief of such a degree, i.e. to act in a certain way) we must note :-

(a) What we ask is p? not 'Would it be true to think p?' nor 'Would it be reasonable to think p?' (But these might be useful first steps.)

but (b) 'Would it be true to think p? ' can never be settled without settling p to which it is equivalent.

(c) 'Would it be reasonable to think p?' means simply 'Is p what usually happens in such a case?' and is as vague as 'usually'. To put this question may help us, but it will often seem no easier to answer than p itself.

(d) Nor can the precise sense in which 'reasonable' or 'usually' can usefully be taken be laid down, nor weight assigned on any principle to different considerations of such a sort. E.g. the death-rate for men of 60 is 1/10, but all the 20 red-haired 60-year-old men I've known have lived till 70, What should I expect of a new red-haired man of 60? I can but put the evidence before me, and let it act on my mind, There is a conflict of two 'usually's' which must work itself out in my mind ; one is not the really reasonable, the other the really unreasonable.

(e) When, however, the evidence is very complicated, statistics are introduced to simplify it. They are to be chosen in such a way as to influence me as nearly as possible in the same way as would the whole facts they represent if I could apprehend them clearly. But this cannot altogether be reduced to a formula; the rest of my knowledge may affect the matter, thus p may be equivalent in influence to q, but not ph to qh.

(f) There are exceptional cases in which 'It would reasonable to think p' absolutely settles the matter. Thus if we are told that one of these people's names begins with A and that there are 8 of them, it is reasonable to believe to degree 1/8th that any particular one's name begins with A, and this is what we should all do (unless we felt there was something else relevant).

(g) Nevertheless, to introduce the idea of 'reasonable ' is really a mistake; it is better to say 'usually', which wakes clear the vagueness of the range: what is reasonable depends on what is taken as relevant; if we take enough as relevant, whether it is reasonable to think p becomes at least as difficult a question as p. If we take everything as relevant, they are the same.

(h) What ought we to take as relevant? Those sorts of things which it is useful to take as relevant; if we could rely on being reasonable in regard to what we do take as relevant, this would mean everything. Otherwise it is impossible to say ; but the question is one asked by a spectator not by the thinker himself: if the thinker feels a thing relevant he can't dismiss it ; and if he feels it irrelevant he can't use it.

(i) Only then if we in fact feel very little to be relevant, do or can we answer the question by an appeal to what is reasonable, this being then equivalent to what we know ad consider relevant.

(j) What are or are not taken as relevant are not only propositions but formal facts, e.g. a = a: we may react differently to φa than to any other φx not because of anything we know about a but e.g. for emotional reasons.