A.J. Ayer

The principles of logic and mathematics are true simply because we never allow them to be anything else. And the reason for this is that we cannot abandon them without contradicting ourselves, without sinning against the rules which govern the use of language, and so making our utterances self-stultifying. In other words, the truths of logic and mathematics are analytic propositions or tautologies.

In other words, the propositions of philosophy are not factual, but linguistic in character – that is, they do not describe the behaviour of physical, or even mental, objects; they express definitions, or the formal consequences of definitions. Accordingly we may say that philosophy is a department of logic. For we will see that the characteristic mark of a purely logical enquiry, is that it is concerned with the formal consequences of our definitions and not with questions of empirical fact.

The misfortunes which God is represented in the book of Job as allowing Satan to inflict on Job, merely to test his faith, are indications, if not of positive malevolence, at least of a suspicious and ruthless insecurity, which is characteristic more of a tyrant than of a wholly powerful and benevolent deity.

The traditional disputes of philosophers are, for the most part, as unwarranted as they are unfruitful. The surest way to end them is to establish beyond question what should be the purpose and method of a philosophical enquiry. And this is by no means so difficult a task as the history of philosophy would lead one to suppose. For if there are any questions which science leaves it to philosophy to answer, a straightforward process of elimination must lead to their discovery.

If one takes full account of the persecution of heretics, the frequency and savagery of the religious wars which Christianity had endangered, the harm caused, especially to children, by the pernicious doctrine of original sin, a case could be made for saying that the world would have been better off without Christianity.

A prevalent fallacy is the assumption that a proof of an afterlife would also be a proof of the existence of a deity. This is far from being the case. If, as I hold, there is no good reason to believe that a god either created or presides over this world, there is equally no good reason to believe that a god created or presides over the next world, on the unlikely supposition that such a thing exists.

It is time, therefore, to abandon the superstition that natural science cannot be regarded as logically respectable until philosophers have solved the problem of induction. The problem of induction is, roughly speaking, the problem of finding a way to prove that certain empirical generalizations which are derived from past experience will hold good also in the future.

To make our position clearer, we may formulate it in another way. Let us call a proposition which records an actual or possible observation an experiential proposition. Then we may say that it is the mark of a genuine factual proposition, not that it should be equivalent to an experiential proposition, or any finite number of experiential propositions, but simply that some experiential propositions can be deduced from it in conjunction with certain other premises without being deducible from those other premises alone.