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A. J. Ayer (1910-1989) was an English Logical Positivist and Professor of Logic at Oxford. He developed the verification principle questioning the possibility of truth of a statement based on if it can be verified or is essentially unverifiable.
“Why should you mind being wrong if someone can show you that you are?”
“But it is not sensible to cry for what is logically impossible.”
“No moral system can rest solely on authority.”
“Even logical positivists are capable of love.”
“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.”
“The criterion which we use to test the genuineness of apparent statements of fact is the criterion of verifiability. We say that a sentence is factually significant to any given person, if, and only if, he knows how to verify the proposition which it purports to express — that is, if he knows what observations would lead him, under certain conditions, to accept the proposition as being true, or reject it as being false.”
“It is possible to be a meta-physician without believing in a transcendent reality; for we shall see that many metaphysical utterances are due to the commission of logical errors, rather than to a conscious desire on the part of their authors to go beyond the limits of experience.”
“The propositions of philosophy are not factual, but linguistic in character – that is, they do not describe the behavior of physical, or even mental, objects; they express definitions, or the formal consequences of definitions.”
“A point which is not sufficiently brought out by Russell, if indeed it is recognized by him at all, is that every logical proposition is valid in its own right.”
“In other words, the propositions of philosophy are not factual, but linguistic in character – that is, they do not describe the behavior 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 inquiry, is that it is concerned with the formal consequences of our definitions and not with questions of empirical fact.”
“A point which is not sufficiently brought out by Russell, if indeed it is recognized by him at all, is that every logical proposition is valid in its own right. Its validity does not depend upon its being incorporated in a system, and deduced from certain propositions which are taken as self-evident. The construction of systems of logic is useful as a means of discovering and certifying analytic propositions, but it is not in principle essential even for this purpose. For it is possible to conceive of a symbolism in which every analytic proposition could be seen to be analytic in virtue of its form alone. The fact that the validity of an analytic proposition in no way depends on its being deducible from other analytic propositions is our justification for disregarding the question whether the propositions of mathematics are reducible to propositions of formal logic, in the way that Russell supposed (1919, chap. 2). For even if it is the case that the definition of a cardinal number as a class of classes similar to a given class is circular, and it is not possible to reduce mathematical notions to purely logical notions, it will still remain true that the propositions of mathematics are analytic propositions. They will form a special class of analytic propositions, containing special terms, but they will be none the less analytic for that. For the criterion of an analytic proposition is that its validity should follow simply from the definition of the terms contained in it, and this condition is fulfilled by the propositions of pure mathematics.”
“The principles of logic and mathematics are true universally 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.”
Ayer asks for an impossible level of verification. Our human brains are made of layers of cells responding to other layers of cells which are responding to simple organizing principles based on the degree of energy received from connected cells. Only a tiny portion of this activity is ever available to our conscious observation, and yet we do have the capacity to direct its activity by where we choose to direct our attention. In such a loose system of cells there are no possibilities for absolute conditions of thought or of ideas; but our mind can point to things that are themselves absolutes. For example we can easily add 17 to 3,000 and get 3,017 and get an absolute number, but the absoluteness is in the number, not in our brain.
A. J. Ayer books at Amazon