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This book is the English explanation of the main doctrine of Vienna Circle, an association of philosophers that applied verificationism on Wittgenstein's Tractatus Logico-Philosophicus which formed the basis for the group's philosophy. Ayer wrote: "Wittgenstein did not then figure in the Oxford curriculum, and I knew nothing about him at all until I started to read this book. Its effect on me was overwhelming ... This was exactly what I wanted, the very conclusions I had been groping towards on my own. All the difficulties that had perplexed me were instantly removed?"

The views which are put forward in this treatise derive from the doctrines of Bertrand Russell and Wittgenstein, which are themselves the logical outcome of the empiricism of Berkeley and David Hume.

Ayer starts by defining a few terms: A sentence is factually significant if, and only if, we know how to verify the proposition it purports to express that is, if we know what observations would lead us to accept the proposition as true or reject it as false. A proposition is analytic when its validity depends solely on the definitions of the symbols it contains, and synthetic when its validity is determined by the facts of experience. A proposition is verifiable in the strong sense if, and only if, its truth could be conclusively established by experience. But If we adopt conclusive verifiability as our criterion of significance, our argument will prove too much, for even general laws such as "all men are mortal" or "arsenic is poisonous" cannot be established with certainty by any finite number of observations. So we need a weak verification principle "if it is possible for experience to render it probable".

But the 'facts of experience' can never compel one to abandon a hypothesis. It just probability and this was the main defect in the verification principle that was rectified in the falsification principle that replaced it.

Applying this weak verification principle leads us to say Metaphysical sentences, ethics and atheistic are nonsensical; only tautologies (a priori truth) and empirical hypotheses are significant propositions.

For example, rationalists uphold, and empiricists reject, the idea that there is a supra-sensible world accessible to intuition and alone wholly real. We have already seen that it is senseless. And therefore we are entitled to deny the possibility of such a world and to dismiss as nonsensical the descriptions which have been given of it. Also We have no empirical grounds for believing that mind and matter are independent.

Also It is impossible to find a criterion for determining the validity of ethical judgements. When someone disagrees with us about moral value we do not attempt to show that he has wrong ethical feelings. We attempt to show that he is mistaken about the facts of the case, or we employ general arguments about which actions produce what effect. But if our opponent has had different moral conditioning from ourselves so that, even when he acknowledges all the facts he still disagrees, we say that it is impossible to argue with him because he has a distorted moral sense. On this view it is impossible to dispute questions of value, only questions of fact. Our judgement that it is so is itself a moral judgement, and so outside the scope of argument. Kant accused metaphysicians of ignoring the limits of understanding, we accuse them of disobeying the rules of significant language.

That's why Wittgenstein said: "If there is any value that does have value, it must lie outside the whole sphere of what happens and is the case". The value of ethics and the World lies outside of the world. And that is the importance of Religion, it the source of value

Also the view that philosophy is the business of building a system of first principles and to offer them and their consequences as a complete picture of reality is abondened. This is illustrated in the barrenness of Descartes system, where he attempts to base all our knowledge on the 'cogito' But according to Ayer, he was mistaken, for 'I exist' does not follow from 'there is a thought now'. The fact that a thought occurs at a given moment does not entail that any other thought has occurred at any other moment. As Hume showed, no one event intrinsically points to any other. We infer the existence of events which we are not actually observing, with the help of general principles. But these principles must be obtained inductively. By mere deduction from what is immediately given we cannot advance a single step beyond.

The most that philosophy can do is to show what are the criteria used to determine the truth or falsehood of any given proposition. And this applies equally to science as to common sense. The propositions of philosophy are not factual, we may say that philosophy is a branch of logic, concerned with the formal consequences of our definitions and not with questions of empirical fact. Philosophy is wholly critical, an activity of linguistic analysis. Philosophy is not concerned with meaning, but with definitions in use. We define a symbol in use, not by saying that it is synonymous with some other symbol, but by showing how the sentences in which it significantly occurs can be translated into equivalent sentences, which contain neither the definiendum itself, nor any of its synonyms. (Analyze the symbols). A complete philosophical elucidation of any language would consist in enumerating the types of sentence significant in that language, and then displaying the relations of equivalence that held between sentences of various types. This is made complicated in languages such as English by the prevalence of ambiguous symbols. If we were guided merely by the form of the sign, we should assume that the 'is' in the sentence 'He is the author of that book' was the same as that in 'A cat is a mammal'. 'is' is an ambiguous symbol for existence, class-membership, identity and entailment. Accordingly, one should avoid saying that philosophy is concerned with the meaning of symbols, because the ambiguity of their 'meaning' on different groups of people. Thus there arc many people for whom these sentences do, in this common sense of 'meaning', have different meanings.

Wittgenstein said "The correct method in philosophy would really be the following: to say nothing except what can be said, i.e. propositions of natural science—i.e. something that has nothing to do with philosophy—and then, whenever someone else wanted to say something metaphysical, to demonstrate to him that he had failed to give a meaning to certain signs in his propositions".

The principles of logic and mathematics are true universally and the reason for this is that we cannot abandon them without contradicting ourselves so they are analytic propositions or tautologies. They lack factual content. One might pardonably suppose the propositions of geometry to by synthetic. For it is natural for us to think, as Kant thought, that geometry is the study of the properties of physical space. We conclude, then, that the: propositions of pure geometry are analytic. And this leads us to reject Kant's hypothesis that geometry deals with the form of intuition of our outer sense. His own Theory is that the sense of invention and discovery in mathematics belongs to it in virtue of mathematical induction, the principle that what is true for the number 1, and true for n + 1 when it is true for n, u is true for all numbers. And he claims that this is a as 'true for a when it is true for n+ I', synthetic a priori principle. It is, in fact, a priori, but it is not synthetic. It is a defining principle of the natural numbers. As Poincaré says: 'If all the assertions which mathematics puts forward can be derived from one another by formal logic, mathematics cannot account to anything more than an immense tautology'. A being whose intellect was infinitely powerful would take no interest in logic and mathematics. For he would see at a glance everything that his definitions implied. But our intellects are not of this order. Even so simple a tautology as 91x79=7189 is beyond the scope of our immediate apprehension and requires us to resort to calculation, which is simply a process of tautological transformation.

Wittgenstein says: "The propositions of logic are tautologies.  The propositions of logic therefore say nothing. (They are the analytical propositions.) And, that the propositions of mathematics can be proved means nothing else than that their correctness can be seen without our having to compare what they express with the facts as regards correctness.  The essential of mathematical method is working with equations. On this method depends the fact that every proposition of mathematics must be self-evident."

This brings us to God. The existence of regularity in nature does not prove "God exists", unless by that you just mean "there is regularity in nature". Unlike atheists (who say god does not exist) or agnostics (who say god might exist), we hold that no statement about god can possess any literal significance. And our view that all utterances about the nature of God are nonsensical. For if the assertion that there is a god is non-sensical then the atheist's assertion that there is no god is equally nonsensical. As for the agnostic, although he refrains from saying either that there is or that there is not a god, he does not deny that the question whether a transcendent god exists is a genuine question. He docs not deny that the two sentences 'There is a transcendent god' and 'There is no transcendent god' express propositions one of which is actually true and the other false. All he says is that we have no means of telling which of them is true. Thus we offer the theist the same comfort we gave to the moralist. His assertions Cannot possibly be valid, but they cannot be invalid either. As he says nothing at all about the world, he cannot justly be accused of saying anything false, or anything for which he has insufficient grounds. It is only when the theist claims that in asserting the existence of a transcendent god he is expressing a genuine proposition that we are entitled to disagree with him. Where deities are identified with natural objects I may conclude that the words "Jehovah is angry" mean exactly the same thing as, for instance, "it is thundering". But sophisticated religions foster the illusion that god is real by giving the concept a noun. In fact our views accord with theists, to whom God is a mystery which transcends human understanding, and therefore cannot significantly be described. An interesting feature of this conclusion is that it accords with what many theists are accustomed to say themselves. For we are often told that the nature of God is a mystery which transcends the human understanding. But to say that something transcends the human understanding is to say that it is unintelligible. And what is unintelligible cannot significantly be described. Again, we are told that God is not an object of reason but an object of faith, since it cannot be proved. If a mystic admits that the object of his vision is something which cannot be described, then he must also admit that he is bound to talk nonsense when he describes it.

I can't say these statements are meaningless, as Wittgenstein said: "There is indeed the inexpressible. This shows itself; it is the mystical".

Assertions that an object exists are always synthetic propositions; and it has been shown that no synthetic proposition is logically sacrosanct. It is only tautologies which are certain. So it seems advisable to speak of the 'occurrence' of sense-contents and experience not objects. For realists and also Berkeley 'x is real' or 'x exists' is equivalent to 'x is perceived'. This is a mistake on their part because we have seen that sense-contents are not in any way parts of the material things which they constitute, thus it is possible for a material thing to exist without being perceived. Like a chair in the dark for example.  Just as I must define material things and my own self in terms of their empirical manifestations, so I must define other people in terms of their empirical manifestations- that is, in terms of the behaviour of their bodies. Thus I have as good a reason to believe in the existence of other people as I have to believe in the existence of material things.

The existence of a 'substantive ego' is completely unverifiable. If it is not revealed in self-consciousness, then it is not revealed anywhere. It is clearly no more significant to assert that an 'unobservable somewhat' underlies the 'self' than it is to assert that an 'unobserved somewhat' underlies material things. Hume, rejected the notion of a substantive ego on the ground that no such entity was observable. For, he said, whenever he entered most intimately into what he called himself, he always stumbled on some particular perception or other — of heat or cold, light or shade, love or hatred, pain or pleasure, He never could catch himself at any time without a perception, and never could observe anything but the perception. And this led him to assert that a self was 'nothing but a bundle or collection of different perceptions'. We accord with Hume in accepting that memory does not produce personal identity, but we solve his problem of personal identity in terms of bodily  identity and bodily identity is to be defined in terms of the resemblance and continuity of sense-contents. And this procedure is justified by the fact that whereas it is permissible, in our language, to speak of a man as surviving a complete loss of memory, or a complete change of character, it is self-contradictory to speak of a man as surviving the annihilation of his body.' For that which is supposed to survive by those who look forward to a 'life after death' is not the empirical self, but a metaphysical entity - the soul. And this metaphysical entity, concerning which no genuine hypothesis can be formulated, has no logical connexion whatsoever with the self.

Wittgenstein says:"The subject does not belong to the world: rather, it is a limit of the world. You will say that this is exactly like the case of the eye and the visual field. But really you do not see the eye. And nothing in the visual field allows you to infer that it is seen by an eye. Thus there really is a sense in which philosophy can talk about the self in a non-psychological way.  What brings the self into philosophy is the fact that ‘the world is my world’.  The philosophical self is not the human being, not the human body, or the human soul, with which psychology deals, but rather the metaphysical subject, the limit of the world—not a part of it."

We do not hold, as be apparently did, that every general hypothesis is, in fact, a generalization from a number of observed instances, We agree with the rationalists that the process by which scientific theories come into being is often deductive rather than inductive. The scientist does not formulate his laws only as the result of seeing them exemplified in particular cases. Sometimes he considers the possibility of the law before he is in possession of the evidence which justifies it. It 'occurs' to him that a certain hypothesis or set of hypotheses may be true. He employs deductive reasoning to discover what he ought to experience in a given situation if the hypothesis is true; and if he makes the required observations, or has reason to believe that he could make them, he accepts the hypothesis. He does not, as Hume implied, passively wait for nature to instruct him; rather, as Kant saw, does he force nature to answer the questions which he puts to her, So that there is a sense in which the rationalists are right in asserting that the mind is active in knowledge. But it is true that the activity of theorizing is, in its subjective aspect, a creative activity, and that the psychological theories of empiricists concerning 'the origins of our knowledge' are vitiated by their failure to take this Into account. But while it must be recognized that scientific laws are often discovered through a process of intuition, this does not mean that they can be intuitively validated.

Regardless of the problems in the verification principle, saying that senseless propositions are meaningless is wrong. saying that the inexpressible is meaningless is wrong. Ayer later admitted that "the outlook of the Tractatus was misunderstood by the members of the Vienna Circle and the young English philosophers, including myself, who were strongly influenced by it". As Wittgenstein summrised "There is indeed the inexpressible. This shows itself; it is the mystical" and "What can be shown cannot be said".