The Problems of Philosophy: Brief and Accessible Guide to the Problems of Philosophy - Bertrand Russell's Philosophical Exploration: Navigating the Problems of Philosophy

by Bertrand Russell

If this were not known to us, we could never extend our knowledge beyond the sphere of our private experience; and this sphere, as we have seen, is exceedingly limited.

The principle we are examining may be called the principle of induction, and its two parts may be stated as follows: (a) When a thing of a certain sort A has been found to be associated with

for they show that we may have indubitable knowledge which is in no way derived from objects of sense.

for what is important is not the fact that we think in accordance with these laws, but the fact that things behave in accordance with them;

One of the great historic controversies in philosophy is the controversy between the two schools called respectively ‘empiricists’ and ‘rationalists'. The empiricists—who are best represented by the British philosophers, Locke, Berkeley, and Hume—maintained that all our knowledge is derived from experience; the rationalists—who are represented by the Continental philosophers of the seventeenth century, especially Descartes and Leibniz—maintained that, in addition to what we know by experience, there are certain ‘innate ideas’ and ‘innate principles', which we know independently of experience.

the rationalists—who are represented by the Continental philosophers of the seventeenth century, especially Descartes and Leibniz—maintained that, in addition to what we know by experience, there are certain ‘innate ideas’ and ‘innate principles', which we know independently of experience.

The fact is that, in simple mathematical judgements such as ‘two and two are four', and also in many judgements of logic, we can know the general proposition without inferring it from instances, although some instance is usually necessary to make clear to us what the general proposition means. This is why there is real utility in the process of deduction, which goes from the general to the general, or from the general to the particular, as well as in the process of induction, which goes from the particular to the particular, or from the particular to the general. It is an old debate among philosophers whether deduction ever gives new knowledge. We can now see that in certain cases, at least, it does do so.

This illustrates the difference between general propositions known a priori such as ‘two and two are four', and empirical generalizations such as ‘all men are mortal'. In regard to the former, deduction is the right mode of argument, whereas in regard to the latter, induction is always theoretically preferable, and warrants a greater confidence in the truth of our conclusion, because all empirical generalizations are more uncertain than the instances of them.

The problem arises through the fact that such knowledge is general, whereas all experience is particular. It seems strange that we should apparently be able to know some truths in advance about particular things of which we have as yet no experience; but it cannot easily be doubted that logic and arithmetic will apply to such things.

What Kant maintained was that in all our experience there are two elements to be distinguished, the one due to the object (i.e. to what we have called the ‘physical object'), the other due to our own nature.

He considers that the crude material given in sensation—the colour, hardness, etc.—is due to the object, and that what we supply is the arrangement in space and time, and all the relations between sense – data which result from comparison or from considering one as the cause of the other or in any other way.

Apart from minor grounds on which Kant’s philosophy may be criticized, there is one main objection which seems fatal to any attempt to deal with the problem of a priori knowledge by his method. The thing to be accounted for is our certainty that the facts must always conform to logic and arithmetic. To say that logic and arithmetic are contributed by us does not account for this. Our nature is as much a fact of the existing world as anything, and there can be no certainty that it will remain constant. It might happen, if Kant is right, that to – morrow our nature would so change as to make two and two become five. This possibility seems never to have occurred to him, yet it is one which utterly destroys the certainty and universality which he is anxious to vindicate for arithmetical propositions.

Thus the law of contradiction is about things, and not merely about thoughts; and although belief in the law of contradiction is a thought, the law of contradiction itself is not a thought, but a fact concerning the things in the world.

Thus our a priori knowledge, if it is not erroneous, is not merely knowledge about the constitution of our minds, but is applicable to whatever the world may contain, both what is mental and what is non – mental.

Many philosophers, following Kant, have maintained that relations are the work of the mind, that things in themselves have no relations, but that the mind brings them together in one act of thought and thus produces the relations which it judges them to have.

Thus relations, as we shall see more fully in the next chapter, must be placed in a world which is neither mental nor physical. This world is of great importance to philosophy, and in particular to the problems of a priori knowledge. In the next chapter we shall proceed to develop its nature and its bearing upon the questions with which we have been dealing.

This conclusion, however, is met by the difficulty that the relation ‘north of’ does not seem to exist in the same sense in which Edinburgh and London exist. If we ask ‘Where and when does this relation exist?’ the answer must be ‘Nowhere and nowhen'. There is no place or time where we can find the relation ‘north of'. It does not exist in Edinburgh any more than in London, for it relates the two and is neutral as between them. Nor can we say that it exists at any particular time. Now everything that can be apprehended by the senses or by introspection exists at some particular time. Hence the relation ‘north of’ is radically different from such things. It is neither in space nor in time, neither material nor mental; yet it is something. It is largely the very peculiar kind of being that belongs to universals which has led many people to suppose that they are really mental.

Thus universals are not thoughts, though when known they are the objects of thoughts.

All a priori knowledge deals exclusively with the relations of universals.

Hence, although our general proposition is a priori, all its applications to actual particulars involve experience and therefore contain an empirical element.

Thus the difference between an a priori general proposition and an empirical generalization does not come in the meaning of the proposition; it comes in the nature of the evidence for it.

The progress of science is constantly producing such subsumptions, and therefore giving a constantly wider inductive basis for scientific generalizations. But although this gives a greater degreeof certainty, it does not give a different kind: the ultimate ground remains inductive, i.e. derived from instances, and not an a priori connexion of universals such as we have in logic and arithmetic.