the Awesome Highlighter

m of induction arises from (1) Hume's discovery (so well expressed by Born) that it is impossible to justify a law by observation or experiment, since it 'transcends experience'; (2) the fact that science proposes and uses laws 'everywhere and all the time'. (Like Hume, Born is struck by the 'scanty material', i.e. the few observed instances upon which the law may be based.) To this we have to add (3) the principle of empiricism which asserts that in science only observation and experiment may decide upon the acceptance or rejection of scientific statements, including laws and theories.

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this the moment we realize that the acceptance by science of a law or of a theory is tentative only; which is to say that all laws and theories are conjectures, or tentative hypotheses (a position which I have sometimes called 'hypotheticism'); and that we may reject a law or theory on the basis of new evidence, without necessarily discarding the old evidence which originally led us to accept it. (I do not doubt that Born and many others would agree that theories are accepted only tentatively. But the widespread belief in induction shows that the far-reaching implications of this view are rarely seen.)

The principle of empiricism (3) can be fully preserved, since the fate of a the   remove

Only the falsity of the theory can be inferred from empirical evidence and this inference is a purely deductive one.   remove

I hold with Hume that there simply is no such logical entity as an inductive inference; or, that all so-called inductive inferences are logically invalid - and even inductively invalid, to put it more sharply [see the end of this selection].   remove

We have many examples of deductively valid inferences, and even some partial criteria of deductive validity; but no example of an inductively valid inference exists. 2   remove

Induction simply does not exist   remove

the whole apparatus of induction becomes unnecessary once we admit the general fallibility of human knowledge or, as I like to call it, the conjectural character of human knowledge.   remove

Take as an example classical Newtonian mechanics. There never was a more successful theory. If repeated observational success could establish a theory, it would have established Newton's theory. Yet Newton's theory was superseded in the field of astronomy by Einstein's theory, and in the atomic field by quantum theory. And almost all physicists think now that Newtonian classical mechanics is no more than a marvellous conjecture, a strangely successful hypothesis, and a staggeringly good approximation to the truth.   remove

there is no need any longer to ascribe to human knowledge a validity derived from repeated observations.   remove

Human knowledge possesses no such validity.   remove

Genuine knowledge consisted for both Berkeley and Hume essentially of belief, backed by sufficient reasons   remove

He believed that induction by repetition was logically untenable - that rationally, or logically, no amount of observed instances can have the slightest bearing upon unobserved instances. This is Hume's negative solution of the problem of induction, a solution which I fully endorse.   remove

According to Hume, all our knowledge, especially all our scientific knowledge, is just irrational habit or custom, and it is rationally totally indefensible.   remove

Hume himself thought of this a   remove

s a form of scepticism; but it was rather, as Bertrand Russell pointed out, an unintended surrender to irrationalism. It is an amazing fact that a peerless critical genius, one of the most rational minds of all ages, not only came to disbelieve in reason, but became a champion of unreason, of irrationalism.   remove

Thus we can say: Hume was right in his negative result that there can be no logically valid positive argument leading in the inductive direction. But there is a further negative result; there are logically valid negative arguments leading in the inductive direction: a counterinstance may disprove a law.   remove

Hume's negative result establishes for good that all our universal laws or theories remain for ever guesses, conjectures, hypotheses. But the second negative result concerning the force of counterinstances by no means rules out the possibility of a positive theory of how, by purely rational arguments, we can prefer some competing conjectures to others.   remove

n fact, we can erect a fairly elaborate logical theory of preference - preference from the point of view of the search for truth.   remove

It is therefore important to discover whether there is any answer to Hume within a philosophy that is wholly or mainly empirical. If not, there is no intellectual difference between sanity and insanity.   remove

But some conjectures are much better than others; and this is a sufficient answer to Russell, and it is sufficient to avoid radical scepticism.   remove

if a true theory should be among   remove

even if we shall never be able to make sure of any one that it is true.   remove

from a rational point of view, we should not 'rely' on any theory, for no theory has been shown to be true, or can be shown to be true (or 'reliable').   remove

If I ask why you believe any particular matter of fact . . ., you must tell me some reason; and this reason will be some other fact, connected with it. But as you cannot proceed after this manner, in infinitum, you must at last terminate in some fact, which is present to your memory or senses; or must allow that your belief is entirely without foundation.'   remove

This is why the programme of tracing back all knowledge to its ultimate source in observation is logically impossible to carry through: it leads to an infinite regress. (The doctrine that truth is manifest cuts off the regress. This is interesting because it may help to explain the attractiveness of that doctrine.)   remove

I wish to mention, in parentheses, that this argument is closely related to another - that all observation involves interpretation in the light of our theoretical knowledge, or that pure observational knowledge, unadulterated by theory, would, if at all possible, be utterly barren and futile.   remove

The answer, I think, is this: there are all kinds of sources of our knowledge; but none has authority.   remove