How A Priori Knowledge Is Possible

Immanuel Kant is generally regarded as the greatest of the modern philosophers.

He lived through the Seven Years War and the French Revolution. But he never interrupted his teaching of philosophy at Königsberg in East Prussia.

His most distinctive contribution was the invention of what he called the ‘critical’ philosophy, which, assuming as a datum that there is knowledge of various kinds, inquired how such knowledge comes to be possible, and deduced, from the answer to this inquiry, many metaphysical results as to the nature of the world.

Whether these results were valid may well be doubted. But Kant undoubtedly deserves credit for two things: first, for having perceived that we have a priori knowledge which is not purely ‘analytic’, i.e. such that the opposite would be self-contradictory, and secondly, for having made evident the philosophical importance of the theory of knowledge.

Before Kant’s time, people believed that whatever a priori knowledge was ‘analytic’.

Examples of purely analytic judgements are:

• ‘A bald man is a man’
• ‘A plane figure is a shape’
• ‘A bad poet is a poet’

The subject is given having at least 2 properties. One is singled out to be asserted of it.

Such propositions are trivial, and would never be enunciated in real life except by an orator preparing the way for a piece of sophistry.

They are called ‘analytic’ because the predicate is obtained by merely analysing the subject*.

Before Kant’s time, people thought that all judgements of which we could be certain a priori were analytic*. In all of them there was a predicate which was only part of the subject of which it was asserted. If this were so, we should be involved in a definite contradiction if we attempted to deny anything that could be known a priori.

‘A bald man is not bald’ would assert and deny baldness of the same man, and would therefore contradict itself*.

The law of contradiction asserts that nothing can at the same time have and not have a certain property.

Thus, according to the philosophers before Kant, the law of contradiction sufficed to establish the truth of all a priori knowledge*.

Hume (1711-76) preceded Kant. He accepted the usual view as to what makes knowledge a priori. He discovered that, in many cases which had previously been supposed analytic, and notably in the case of cause and effect, the connection was really synthetic.

Before Hume, rationalists thought that the effect could be logically deduced from the cause, if only we had sufficient knowledge.

Hume argued correctly that this could not be done.

Hence, he inferred the far more doubtful proposition that nothing could be known a priori about the connection of cause and effect.

Kant had been educated in the rationalist tradition. He was much perturbed by Hume’s scepticism. He endeavoured to find an answer to it.

He perceived that the connection of cause and effect and all the propositions of arithmetic and geometry are ‘synthetic’ and not analytic.

In all these propositions, no analysis of the subject will reveal the predicate. His stock instance was the proposition 7 + 5 = 12.

He pointed out that 7 and 5 have to be put together to give 12. The idea of 12 is not contained in them, nor even in the idea of adding them together.

Thus, he concluded that all pure mathematics is a priori but is synthetic. This conclusion raised a new problem:‘How is pure mathematics possible?’

This is an interesting and difficult one, to which every philosophy which is not purely sceptical must find some answer.

Pure empiricists answer that our mathematical knowledge is derived by induction from particular instances. I think this is inadequate for 2 reasons:

1. The validity of the inductive principle itself cannot be proved by induction

2. The general propositions of mathematics, such as ‘2 and 2 always makes 4’, can obviously be known with certainty by consideration of a single instance, and gain nothing by enumeration of other cases in which they have been found to be true.

Thus our knowledge of the general propositions of mathematics (and the same applies to logic) must be accounted for otherwise than our (merely probable) knowledge of empirical generalizations such as ‘all men are mortal’.

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.

We do not know who will be the inhabitants of London a hundred years hence; but we know that any two of them and any other two of them will make four of them.

This apparent power of anticipating facts about things of which we have no experience is certainly surprising. Kant’s solution of the problem, though not valid in my opinion, is interesting.

It is, however, very difficult, and is differently understood by different philosophers.

We can, therefore, only give the merest outline of it, and even that will be thought misleading by many exponents of Kant’s system.