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Ayer - Language, Truth and Logic
Bacon - Advancement of Learning
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Kant - Critiques of Reason
Kant - Metaphysics of Morals
Kierkegaard - Either Or
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Locke - Human Understanding
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Marcus Aurelius - Meditations
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Mill - System of Logic
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Paine - Rights of Man
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Popper - Scientific Discovery
Rand - Selfishness
Rousseau - Confessions
Rousseau - Social Contract
Sade - Philosophy in the Boudoir
Sartre - Existentialism is a Humanism
Schopenhauer - World as Will and Idea
Smith - Wealth of Nations
Spinoza - Ethics
The Ancient Greeks
The Aphorisms of the Philosophers
Thoreau - Walden
Tocqueville - America
Turing - Computing Machinery
Wittgenstein - Tractatus
Wollstonecraft - Rights of Woman


AJ 'Freddie' Ayer
Language, Truth and Logic
...
Squashed down to read in about 50 minutes
"The principles of logic and mathematics are true
simply because we never allow them to be anything else."



Wikipedia - Full Text - Print Edition: ISBN 0486200108
© This page does not contain Language, Truth and Logic, but a short abridgement for private study and research only. Copyright may exist on the original work.

INTRODUCTION TO Language, Truth and Logic

Round about 1920 a gang of philosophers including Rudolph Carnap and Kurt Godel started meeting in Vienna. This so-called 'Vienna Circle' dedicated themselves to reconciling philosophy with the new sciences and so determined to take it upon themselves to evaluate truth solely in terms of the empirical verifiability or logic of language. This was the school of 'Logical Positivism', and it was AJ Ayer who is chiefly remembered for popularising it in England.

His Language, Truth and Logic, first published in 1936 presents a modified version of logical positivism which he called 'logical empiricism'. This made rather radical charges against philosophy itself, such as asserting that metaphysics was simply nonsense, that questions of value were nonexistent and that philosophers should concern themselves almost solely with language.

All very interesting, and presented by Ayer in such a confident manner that it is easy to miss the fact that it might not actually be reasonable. On the one hand his dismissal of metaphysics doesn't mean that other philosophers are prevented from metaphysical enquiry, and on the other hand by raising language to the status of a sort of knowledge above and beyond that which is experienced he could be accused of treating it as a form of metaphysics.

In fairness, as he explains in his introduction to the 1946 edition (included here) Ayer himself realised many of the shortcomings of Language Truth and Logic. Then again, to declare oneself an out-and-out supporter of Ayer is to be left with such a simplified version of 'philosophy' that it shouldn't be too difficult to become an expert in it.

ABOUT THIS SQUASHED EDITION

AJ Ayer publicly declared that he was a very good writer, though anyone trying to read Language Truth and Logic may be willing to dispute this. We have retained much of his odd punctuation and grammar, but, by simplifying his horribly convoluted sentences and cutting out much of the repetition the book has been squashed to about 1/11th of its original size.

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Have a look how Karl Popper denounces Ayer's principles, or at a competing linguistic philosophy from Ludwig Wittgenstein.
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No Time? Read THE VERY, VERY SQUASHED VERSION...

AJ 'Freddie' Ayer, 1936
Language, Truth and Logic
"The principles of logic and mathematics are true
simply because we never allow them to be anything else."


We reject metaphysics and knowledge of a transcendent reality.
Kant accused metaphysicians of ignoring the limits of understanding, we accuse them of disobeying the rules of significant language.
For a statement of fact to be genuine it must be possible to verify it through experience.
Philosophy is wholly critical, an activity of linguistic analysis.
Philosophy is not concerned with meaning, but with definitions in use.
As empiricists, we deny that matters of fact can be known to be certainly valid.
Analytic propositions (tautologies), such as logic and mathematics, are true and can give us new knowledge by bringing to light our linguistic usages.
The words 'true' and 'false' are simply signs of negation or assertion.
The 'problem of truth' is the problem of how propositions are validated.
Observation can discredit not just a hypothesis, but a whole system of hypotheses.
But the 'facts of experience' can never compel one to abandon a hypothesis.
Assertions of value are not scientific but 'emotive', thus neither true not false. They express feelings or commands.
On this view it is impossible to dispute questions of value, only questions of fact.
Ethics and aesthetics are to be comprehended in the social sciences.
That a transcendent god or an immortal soul exist are metaphysical assertions of no literal significance.
This view is, in fact, supported by theists.
A sense-experience cannot belong to the sense-history of more than one self.
The ego is fictitious.
We know of other minds in the same way we know of our own, by inference from the body.
What exists need not necessarily be thought of.
Philosophy is the logic of science.


The Squashed Philosophers Edition of...

Language, Truth and Logic
AJ 'Freddie' Ayer
1936
Squashed version edited by Glyn Hughes © 2011


INTRODUCTION TO THE 1946 EDITION
In the ten years since Language Truth and Logic was first published I have come to see that a number of points require further explanation.
To begin with, I distinguished between 'strong' verification, where a truth could conclusively be established by experience, and 'weak' verification where it was merely probable. What I overlooked was that, since no evidence can ever reach a point at which experience might not go against it, 'strong' verification has no application, in which case there is no need to qualify the other sense of verifiability as 'weak'.
However, I do not draw this conclusion because I have come to think that 'basic propositions' which refer solely to the content of a single experience can be verified conclusively. Accordingly, I put forward a second version of my principle; a statement is verifiable, and consequently meaningful, if some observation-statement can be deduced from it in conjunction with certain other premises, without being deducible from those other premises alone.
I am inclined to maintain the 'behaviouristic' interpretation of the experiences of other persons given in this book. But I own that it has an air of paradox which prevents me from being wholly confident that it is true.
The emotive theory of values in chapter six is presented in a very summary way. I own that it is possible to influence other people by careful use of emotive language, but maintain that a value judgement is not a proposition and therefore neither true nor false.
In citing Russell's 'The author of Waverley was Scotch' as a specimen of analysis I unfortunately made a mistake. Professor Stebbing pointed out that 'if the word "that" is used referentially, then "that person was Scotch" is equivalent to the whole of the original.
For the rest I can find no better way of explaining my conception of philosophy than by referring to the argument of this book.

AJ AYER
Wadham College, Oxford
January 1946


CHAPTER 1
THE ELIMINATION OF METAPHYSICS


THE traditional disputes of philosophers are as unwarranted as they are unfruitful. The surest way to end them is to establish beyond question the purpose and method of philosophical enquiry. This is not necessarily a difficult task.

We begin by criticising the metaphysician who claims knowledge of transcendent reality by enquiring from what premises his propositions were deduced. Must he not begin, as other men do, with the evidence of his senses? He would say that he knew through intuition. Consequently one cannot overthrow transcendent metaphysics by criticizing how it arises, but by criticism of the actual statements which comprise it.

Kant said that human understanding became lost in contradiction when it ventured beyond experience. We ask how, if it is possible to know only what lies within sense-experience, it can be asserted that things lie beyond. As Wittgenstein says, "in order to draw a limit to thinking, we should have to think both sides of this limit", a truth which Bradley ingeniously twists in maintaining that anyone ready to prove metaphysics impossible is a brother metaphysician with a rival theory. What we accuse metaphysicians of is disobeying the rules governing the significant use of language.

We shall now proceed to formulate the criterion of verifiability which we use to test the genuineness of apparent statements of fact.

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. This procedure is central to the argument of this book.

A simple example would be the proposition that there are mountains on the other side of the moon. No rocket has yet enabled me to check this, but I know it to be decidable by observation. Therefore this proposition is verifiable in principle and is accordingly significant. On the other hand with such metaphysics as "the Absolute enters into, but is itself incapable of, evolution and progress" [FH Bradley] one cannot conceive of an observation which would determine whether the Absolute did or did not enter into evolution; the utterance has no literal significance.

A proposition is verifiable in the strong sense if, and only if, its truth could be conclusively established by experience. It is verified in the weak sense if it is possible for experience to render it probable.

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. Nor can we accept that a sentence should be allowed to be factually significant if, and only if, it expresses something definitely confutable by experience [Karl Popper]. A hypothesis cannot be conclusively confuted any more than it can be conclusively verified.

Accordingly, we fall back on the weaker sense of verification. We say that the question that must be asked about any putative statement of fact is not, Would any observations make its truth or falsehood certain? but simply, Would any observations be relevant to determination of its truth or falsehood? This criterion seems liberal enough. In contrast to conclusive verifiability it does not deny significance to general or historical propositions. Let us see what kinds of assertion it rules out.

There has been dispute concerning the number of substances in the world. The monists maintain that reality is one substance, the pluralists maintain that reality is many. But it is impossible to imagine what observation could be made to solve the dispute. This metaphysical question about 'substance' is therefore ruled out by our criterion.

Consider the metaphysical version of the dispute between realists and idealists. Suppose a picture is discovered which may be by Goya. Experts examine it, and though they may disagree as to its genuineness, each knows what evidence would convince him. Suppose that these men have studied philosophy so that some maintain that the picture exists only in the mind, others that it is objectively real. What possible experience could any of them have which would be relevant to the dispute? They each have experienced the picture through correlated sensations of sight and touch, is there any similar process by which they could discover if the picture was 'real' or 'ideal'? There is none, the problem is fictitious.

There is no need for further examples. Our object is to show that philosophy, as a genuine branch of knowledge, must be distinguished from metaphysics. Metaphysical sentences are nonsensical; only tautologies and empirical hypotheses are significant propositions. Our task is to show how such mistakes come about.

There is a primitive superstition that every name must correspond to a single real entity, the metaphysician fails to see this because he is misled by a superficial grammatical feature of language. The proposition 'Unicorns are fictitious' resembles in structure the English sentence 'Dogs are faithful', creating the assumption that they are of the same logical type. Dogs must exist in order to be faithful, so it is held that unicorns must in some way exist in order to possess the property of being fictitious. This is a fallacy, a mistake that has been the source of many of the traditional 'problems of philosophy'.

Some speak of metaphysics as a type of poetry. Its statements may not have literal meaning, but they still express emotion and may have value as a means of moral inspiration. I am afraid that this assumption is false. Poets rarely produce sentences with no literal meaning, and even when they do their sentences are carefully chosen for rhythm. The metaphysician does not intend to write nonsense, he lapses into it through a failure to understand the workings of our language.

CHAPTER 2
THE FUNCTION OF PHILOSOPHY


AMONG the superstitions abandoned along with metaphysics is 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.

This is illustrated in the barrenness of Descartes system, where he attempts to base all our knowledge on the 'cogito'', a proposition which it would be self-contradictory to deny. In fact he was mistaken, for 'I exist' does not follow from 'there is a thought now'.

The only other course open to one who wished to deduce all our knowledge from 'first principles' would be to begin with a priori truths. But, as we shall show later, an a priori truth is a tautology. And from a set of tautologies alone, only further tautologies can be validly deduced. But it would be absurd to put forward a system of tautologies as constituting the whole truth about the universe.

We now see that the function of philosophy is wholly critical. In what does this critical activity consist?

One answer is to say that the philosopher's business is to test the validity of our scientific hypotheses and everyday assumptions. But this view, though widely held, is mistaken. The most that philosophy can do, apart from seeing whether beliefs are self-consistent, 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.

It is time, therefore, to look into the problem of scientific induction; the problem of finding a way to prove that certain empirical generalizations derived from past experience will also hold good in the future. There are only two ways of approaching this problem; from a purely formal principle or from an empirical principle. In the former case one commits the error of supposing that from a tautology it is possible to deduce a proposition about a matter of fact; in the latter case one simply assumes what one is setting out to prove. Thus, there is no possible way of solving the problem of induction. It is a fictitious problem, since all genuine problems are at least theoretically capable of being solved. Actually, the only test to which scientific procedure is subject is the test of its success in practice - that is, that it enables us to predict future experience.

What gives one the right to believe in the existence of a certain material thing is simply the fact that one has certain sensations; for, whether one realizes it or not, to say that a thing exists is equivalent to saying that such sensations are obtainable. It follows that the philosopher has no right to despise the beliefs of common sense. The philosopher must confine himself to works of clarification and analysis of a sort which we shall presently describe.

While the 'history of philosophy' contains some metaphysics, the majority of the great philosophers were primarily not metaphysicians but analysts.

The little of Locke which is not philosophical, is not metaphysics, but psychology. Nor is it fair to regard Berkeley as a metaphysician. He did not, in fact, deny the reality of material things but discovered that material things must be defined in terms of sense-contents.

Hume explicitly rejected metaphysics. He has been accused of denying causation, whereas in fact he was concerned only with defining it. He laid the way open for the view, which we now adopt, that every assertion of a particular causal connexion involves the assertion of a causal law, that every general proposition of the form 'C causes E' is equivalent to the form 'whenever C, then E', where the symbol 'whenever' refers to the infinite number of possible instances.

When we consider Hobbes, Bentham and the best part of John Stuart Mill's, we may claim that English empirical philosophy has been essentially analytic, while a more complete list of the analytic philosophers would certainly include Plato, Aristotle and Kant.

The propositions of philosophy are not factual, but linguistic in character- 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.

A striking instance of this is the proposition that a material thing cannot be in two places at once. This looks like an empirical proposition, but critical inspection shows that it is actually linguistic. It simply records the fact that as a result of certain verbal conventions, the proposition that two sense-contents occur in the same visual or tactual sense-field is incompatible with the proposition that they belong to the same material thing. And this is a necessary fact. But it has not the least tendency to show that we have certain knowledge about the empirical properties of objects.

Although it is misleading to write about linguistic questions in 'factual' language, it is often convenient for the sake of brevity. And we shall not always avoid doing it ourselves. But it is important that no one should be deceived by this practice into supposing that the philosopher is engaged on an empirical or metaphysical inquiry. We may speak loosely of him as analysing facts, or notions, or even things. But we must make it clear that these are simply ways of saying that he is concerned with the definitions of the corresponding words.

CHAPTER 3
THE NATURE OF PHILOSOPHICAL ANALYSIS


FROM our assertion that philosophy provides definitions it must not be inferred that it is the function of the philosopher to compile a dictionary. In a dictionary we look for what may be called explicit definitions; in philosophy, for definitions in use.

We define a symbol explicitly when we put forward another symbol synonymous with it. Thus, when we define an oculist as an eye-doctor, we are asserting that, in English, the two symbols 'oculist' and 'eye-doctor' are synonymous.

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. A good example of this process is Bertrand Russell's theory of definite descriptions, which is not a theory at all but an indication of the way in which all phrases of the form 'the so-and-so' are to be defined. It proclaims that every sentence which contains a symbolic expression of this form can be translated into a sentence which does not contain any such expression, but does contain a sub-sentence asserting that one, and only one, object possesses a certain property, or else that no one object possesses a certain property. Thus, 'The round square cannot exist' is equivalent to 'No one thing can be both square and round; and the sentence 'The author of Waverley was Scotch' is equivalent to 'One person, and one person only, wrote Waverley, and that person was Scotch'. These examples show us how to express what is expressed by any sentence which contains a definite descriptive phrase without employing any such phrase. And thus they furnish us with a definition of these phrases in use.

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'. But when we come to translate the sentences, we find that the first is equivalent to 'He, and no one else, wrote that book', and the second to 'The class of mammals contains the class of cats. 'Is' is an ambiguous symbol for existence, class-membership, identity and entailment.

What we are saying is that all sentences in which symbol e occurs can be translated into sentences which do not contain e or any synonym of e, but do contain symbols b, c, d....

What one must not say is that logical constructions are fictitious objects. While it is true that the English State, for example, is a logical construction out of individual people, and this table is a logical construction out of sense-contents, it is not true that either the English State or this table are fictitious, in the sense in which Hamlet or a mirage is fictitious.

Material things are logical construction out of sense-contents. The problem of 'reducing' material things to sense contents is the philosophical problem of perception. The solution we will give of this problem will serve as a further illustration of the method of philosophical analysis.

One may assert with regard to any two of one's visual or tactual sense-contents that they are elements of the same material thing if, and only if, they are related to one another by a relation of direct, or indirect, resemblance and continuity. Each of these relations is symmetrical - that is to say, a relation which cannot hold between terms A and B, and terms B and C cannot hold between A and C. This means that no visual, or tactual, sense-content can be an element of more than one material thing.

However, interpretation of language depends on the 'meaning' ascribed to its symbols. it is possible for two sentences to be equivalent, by our criterion, without having the same effect on anyone who employs the language. For instance, 'p is a law of nature' is equivalent to 'p is a general hypothesis which can always be relied on': but the associations of the symbol 'law' are such that the former sentence gives rise to belief in an orderly power 'behind' nature. This, I suspect, accounts for the widespread reluctance to admit that the laws of nature are merely hypotheses, just as the failure of some philosophers to recognize that material things are reducible to sense-contents is very largely due to the psychological effect of the term 'material thing'.

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. But the deduction of relations of equivalence from the rules of language is a purely logical activity; and it is in this logical activity that philosophical analysis consists.

It is to be remarked that the process of analysing a language is facilitated if it is possible to use an artificial system of symbols whose structure is known, such as Russell and Whitehead's so-called system of logistic. But it is not necessary.

CHAPTER 4
THE A Priori


THE view of philosophy which we have adopted is a form of empiricism. So we must deal with the objection brought against empiricism; that it is impossible on empiricist principles to account for our knowledge of necessary truths. For, as Hume showed, the fact that a law has been substantiated in n-1 cases affords no logical guarantee that it will be substantiated in the nth case also, no matter how large we take n to be. This means that no general proposition referring to a matter of fact can ever be shown to be necessarily and universally true.

Where the empiricist encounters difficulty is with the truths of formal logic and mathematics, for they appear to everyone to be necessary and certain. The empiricist must deal with these truths in one of two ways: either say that they are not necessary truth, and then account for the universal conviction that they are; or say that they have no factual content, and then explain how a proposition without factual content can be true and useful and surprising.

If neither of these courses proves satisfactory, we shall be obliged to give way to rationalism, to accepting that thought is an independent source of knowledge more trustworthy than experience and thereby upset the main argument of this book.

The course of maintaining that the truths of logic and mathematics are not necessary or certain was adopted by Mill. He maintained that these propositions were inductive generalizations based on an extremely large number of instances. I do not think that this solution is acceptable. In rejecting it, we are obliged to be somewhat dogmatic. We can do no more than state the issue clearly and then trust that Mill's contention will be seen be discrepant with the relevant logical facts.

The best way to substantiate our assertion that the truths of formal logic and pure mathematics are necessarily true is to examine cases in which they might seem to be confuted. It might easily happen, for example, that when I counted what I had taken to be five pairs of objects, I found instead that they only amounted to nine. One would not say that the mathematical proposition '2x5=10' had been confuted. One would say that I was wrong in supposing that there were five pairs to start with, or that one object had been taken away while I was counting, or that two of them had coalesced, or that I had counted wrongly.

To take another example: if what appears to be a Euclidian triangle is found by measurement not to have angles totalling 180 degrees, we do not say that we have met with an instance which invalidates mathematical laws. We say that we have measured wrongly or that the triangle is not Euclidean.

For formal logic we may take an example relating to the so-called law of excluded middle, which states that a proposition must be either true or false. On might suppose that a proposition of the form 'x has stopped doing y' would in certain cases constitute an exception to this law. For instance, if my friend has never written to me, it seems fair to say that it is neither true nor false that he has stopped writing to me. But in fact the proposition 'My friend has not stopped writing to me' is not, as it appears to be, contradictory to 'My friend has stopped writing to me', only contrary to it. For it means 'My friend wrote to me in the past, and he still writes to me'. Thus we preserve the law of the excluded middle by showing that the negating of a sentence does not always yield the contradictory of the proposition originally expressed.

Whatever instance we take, 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. In other words, the truths of logic and mathematics are analytic propositions or tautologies. This is a controversial statement.

Analytic propositions or judgements, as defined by Kant, are ones in which the predicate B of a subject A is covertly contained in the concept of A. In contrast, in a synthetic judgement the predicate B lies outside the subject A, though standing in connection with it. Analytic judgements, Kant explains, add nothing to the concept of the subject. Synthetic judgements, on the other hand, 'add to the concept of a subject a predicate... which no analysis could possibly extract from it'. Kant gives 'all bodies are extended' as an example of an analytic judgement, on the ground that the required predicate can be extracted from the concept of 'body'; as an example of a synthetic judgement he gives 'all bodies are heavy', and '7+5=12' on the grounds that the concept of twelve is by no means already thought of in merely thinking of the union of seven and five.

I think this is a fair summary of Kant's position. But, even ignoring Kant's neglect of the difficulties of language, he does not give us one straightforward criterion for distinguishing between analytic and synthetic propositions; he gives us two. His holds that '7+5=12' is synthetic because of the way we think about numbers, whereas 'all bodies are extended' is held to be analytic due to the principle of contradiction alone.

I think we can avoid Kant's confusions if we say that 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. Thus the proposition 'There are ants which have established a system of slavery' is synthetic while the proposition 'Either some ants are parasitic or none are' is analytic.

When we say that analytic propositions are devoid of factual content, we are not suggesting that they are senseless in the way that metaphysical utterances are senseless. Thus if I say that all Bretons are Frenchmen, and all Frenchmen are Europeans, then all Bretons are Europeans, I am not describing any matter of fact. But I am indicating the convention which governs our usage of the words 'if' and 'all'.

We see, then, that analytic propositions can give us new knowledge. They call attention to linguistic usages and reveal unsuspected implications in our beliefs. Thus, if I know that May Queens are a relic of tree-worship and I discover that May Queens still exist in England, I can employ the tautology 'If p implies q, and p is true, q is true' to show that there still exists a relic of tree worship in England. But it would not provide new knowledge in the way that evidence that May Queens had been forbidden by law would provide new knowledge.

If one had to set forth all the information one possessed, with regard to matters of fact, one would not write down any analytic propositions. But one would make use of analytic propositions, besides enabling one to make one's list complete, the formulation of analytic propositions would enable one to make sure that the synthetic propositions of which the list is composed formed a self-consistent system.

Traditionally, the analytic character of the truths of formal logic was obscured in speaking always of judgements instead of propositions, and introducing irrelevant psychology, giving the impression that logic was concerned with the workings of thought. What it was actually concerned with was the formal relationship of classes, as is shown by the fact that all its principles of inference are subsumed in the Boolean class-calculus, which is subsumed in turn in the propositional calculus of Russell and Whitehead, itself probably only one among many possible logics, each of which is composed of tautologies as interesting to the logician as the arbitrarily selected Aristotelian 'laws of thought'.

A point not sufficiently brought out by Russell is that every logical proposition is valid in its own right. Its validity does not depend on it being incorporated into a system, that is to say, it being deducible from other analytic propositions. This 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. Mathematics may form a special class of analytic propositions containing special terms, but is analytic all the same.

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. While this was plausible when Euclid's was the only known geometry, the subsequent invention of non-Euclidian geometries has shown it to be mistaken.

Geometry is a purely logical system, its propositions purely analytic, its diagrams not essential to completely rigorous geometry. The fact that most of us need the help of actual diagrammatic examples to be made aware of the consequences of geometric applications shows merely that our intellects are unequal to the task of carrying out very abstract processes of reasoning without the assistance of intuition.

Our knowledge that no observation can ever confute the proposition '7+5=12' depends simply on the fact that the symbolic expression '7+5' is synonymous with '12'. And the same explanation holds good for every a priori truth.

What is mysterious at first sight is that these tautologies should o occasion be so surprising, that there should be in mathematics and logic the possibility of invention and discovery. 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'.

The explanation is very simple. The power of logic and mathematics to surprise us depends, like their usefulness, on the limitations of our reason. 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.

Thus we have shown that the truths of pure reason, the propositions which we know to be valid independently of all experience, are so only in virtue of their lack of factual content. To say that a proposition is true a priori is to say that it is a tautology

CHAPTER 5
TRUTH AND PROBABILITY


HAVING shown how the validity of a priori propositions is determined, we shall now put forward the criterion used to determine the validity of empirical propositions and so complete our theory of truth. It is commonly supposed that the business of philosophers is to answer the question 'What is truth ?' But when we come to consider this famous question, we find that it does not gives rise to any genuine problem.

If we analyse statements of truth (or assertion, judgement, assumption, opinion or belief) we find that in all sentences of the form 'p is true', the phrase 'is true' is logically superfluous. When, for example, one says that the proposition 'Queen Anne is dead' is true, all that one is saying is that Queen Anne is dead. Similarly, when one says that proposition 'Oxford is the capital of England' is false we are just saying that Oxford is not the capital of England. The terms 'true' and 'false' are just marks of assertion or denial, there is no sense in asking us to analyse the concepts further.

This point seems too obvious to mention, yet philosophers preoccupied with the 'problem of truth' have overlooked it. Their excuse is that references to truth generally occur in sentences whose form suggests that the word 'true' stands for a genuine quality or relation.

To take two typical examples, the sentence 'A proposition is not made true by being believed' is equivalent to 'For no value of p or x, is "p is true" entailed by "x believes p": and the sentence 'Truth is sometimes stranger than fiction' is equivalent to 'There are values of p and q such that p is true and q is false and p is more surprising than q.' In every case the question 'What is truth?' is reducible to 'What is the analysis of the sentence "p is true" ? This question raises no genuine problem, since we have shown that to say p is true is simply a way of asserting p.

Thus the question 'What makes a proposition true or false?' is a way of asking how propositions are validated.

Many philosophers would say that 'ostensive' propositions, those recording immediate experience, are not mere hypotheses, but are absolutely certain. We cannot admit this, for one cannot in language point to an object without describing it. And description is classification, which means going beyond what is immediately given. However, we shall leave speculation about false doctrines to the historian.

When one speaks of hypotheses being verified in experience, it is never just a single hypothesis but a system of hypotheses. If a scientific law is found to be invalid by experience we can say that conditions were not what they seemed to be or we had dismissed some relevant factor, or that we were hallucinating. A man can always sustain his convictions if he is prepared to make the necessary ad hoc assumptions. A proposition which we maintain in the face of all experience is not a hypothesis, but a definition. That many of our 'laws of nature' are merely disguised definitions is incontestable, confused by the fact that our definitions are not immutable. If experience says that all A's have property B, we tend to take possession of this and ultimately refuse to call anything A unless it has B. And in that case 'All A's have B', originally a synthetic generalization, comes to express a plain tautology. The famous 'All men are mortal' is a case in point.

We formulate hypotheses, in science for instance, to enable us to make accurate predictions. We assume that a system of hypotheses which has broken down once is likely to break down again, and we alter our hypotheses to increase the probability of them anticipating experience. It is therefore necessary to make clear what is meant by 'probability'.

Roughly speaking, increased probability means increased confidence, and confidence is what we place on rational belief. There is no absolute standard of rationality. We trust contemporary science because they have been successful in practice. In future we may adopt different methods, and view the present ideas as irrational.

We conclude our discussion of validity by observing that every synthetic proposition is a rule for the anticipation of future experience, distinguished from other synthetic propositions in that it is relevant to different situations.

CHAPTER 6
CRITIQUE OF ETHICS AND THEOLOGY


BEFORE we can claim that all synthetic propositions are empirical hypotheses, we must address "Judgements of value", which we will contend are simply expressions of emotion which can be neither true nor false.

The systems of ethics is very far from a homogeneous whole, not only is it apt to contain pieces of metaphysics but its content is of different kinds:

(1) Propositions giving definitions of ethical terms, or judgements about definitions

(2) Propositions describing the phenomena of moral experience and their causes (which belong to psychology or sociology)

(3) Exhortations to moral virtue (which are not propositions at all, and don't belong to philosophy or science)

(4) Actual ethical judgements (which can't be classified at all, but are not definitions, so don't belong to philosophy)

It is easy to see that only the first of our four classes can be said to constitute ethical philosophy.

Our strictly philosophical treatise on ethics will make no ethical pronouncements, but give an analysis of ethical terms.

Ethical philosophers often discuss the possibility of reducing all ethical terms to one or two fundamental terms. We are not concerned with which terms these might be (whether 'right' is 'good' etc), just if ethical terms can be translated into statements of fact.

We reject subjectivist and utilitarian analyses of ethical terms. Subjectivists view 'right' and 'good' as those things which are generally approved of, but it is not self-contradictory to assert that some generally approved actions are not right. A similar argument is fatal to utilitarianism. We cannot agree that to call an action right is to say that it would cause the greatest happiness, because sometimes it is wrong [cf slavery]. We should conclude that the validity of ethical judgements is not determined by their felicity [causing happiness], nor by people's judgements. We reject subjectivism and utilitarianism not as proposals of a new ethical system, but as ways of analysing ethical notions.

If we say 'x is wrong', this may be a normative moral judgement about 'x', or it may be a descriptive statement that 'x' is repugnant to a particular society. We are only concerned with normative ethics.

Moralists claim that they 'know' their moral judgements are correct. This is of purely psychological interest, is not verifiable and has not the slightest tendency to prove the validity of any moral judgement.

The correct treatment of ethical statements is afforded by a third theory, compatible with our empiricism.

We begin by admitting that fundamental ethical concepts are unanalysable, as there is no criterion of validity. They are mere pseudo-concepts. If I say "You acted wrongly in stealing that money", I am saying no more than "You stole that money", but attended with a certain feeling of the speaker. Another man may disagree with me about the wrongness of stealing, he may quarrel with my moral sentiments but he cannot, strictly speaking, contradict me. The ethical word is purely "emotive".

It is impossible to find a criterion for determining the validity of ethical judgements. Not because they have an 'absolute' value mysteriously independent of sense-experience, but because they have no objective validity whatsoever. If a sentence makes no statement, there is no sense in asking whether it is true or false. Pure expressions of feeling do not come under the category of truth or falsehood.

The orthodox subjectivist holds that ethical propositions are about the speaker's feelings. If this is so, they could be true or false depending on whether the speaker had the relevant feelings. I can say "I am bored" by tone or gesture without speaking at all, or may be lying about my feelings. We say that ethical statements are excitants of feeling which do not necessarily involve any assertions.

We hold that it is impossible to dispute about questions of value, and that no-one really ever does so. This may seem paradoxical, but 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. Our judgement that it is so is itself a moral judgement, and so outside the scope of argument. We finally resort to mere abuse. We praise or condemn in the light of our own feelings.

If anyone doubts this, let him try to construct an argument about values which does not reduce itself to an argument about logic or empirical fact. All that one may legitimately enquire is, What are the moral habits of a given person or group, and what causes them to have these? This is a job for the Social Sciences.

If anyone thinks we have overlooked casuistry [investigation of how a moral code causes effects]- casuistry is not a science, it is the analytical investigation of a given moral system, it is an exercise in formal logic.

Our conclusions about ethics apply equally to æsthetics. Words like "beautiful" and "hideous" are employed as ethical words are employed. We conclude that there is nothing in æsthetics or ethics to justify the view that embodies a unique knowledge.

This brings us to God. It is now admitted by philosophers that the existence of a (non-animist) god cannot be proved. We can't deduce the existence of god because the conclusion of a deductive argument is contained in its premises and the premises are uncertain. We can't prove god a priori, because such judgements are tautologies from which nothing further can be found. 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. Thus we offer the theist the same comfort we gave to the moralist.

Where [cf animism] 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.

There is no logical ground for antagonism between religion and science, in fact our views accord with theists, to whom God is a mystery which transcends human understanding, and therefore cannot significantly be described. Religious experience is psychologically interesting, but that does not imply that an act of intuition can reveal truth about matter of fact unless it is a verifiable proposition.

CHAPTER 7
THE SELF AND THE COMMON WORLD


It is customary for authors of epistemological treatises to assume that empirical knowledge must have a basis of certainty. But we have shown that our claims to empirical knowledge are not susceptible of logical justification, only of pragmatic justification. We shall apply this to the traditional 'problem' of knowledge of our own and others existence.

Since existence is not a predicate, 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. But when one says that sense-experience, or sense-content, exists, one is making a different type of statement from the one made by saying that a material thing exists. Accordingly, it seems advisable to speak of the 'occurrence' of sense-contents and experience.

The problems concerning the gulf between mind and matter are fictitious problems arising out of the senseless metaphysical conception of mind and matter. Freed from metaphysics we see that there can be no a priori objections to the connections between mind and matter.

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.

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. We commonly speak of a man as surviving memory loss or personality change, but it is self-contradictory to speak of a man surviving his body. Those who look forward to life after death do not expect an empirical but a metaphysical existence, and this is one which has no logical connection whatever with the self.

As to other persons, it may be argued that the sense-experiences of another person cannot possibly form part of one's own experience and that while such a solipsistic doctrine cannot be shown to be self-contradictory, it is known to be false. We maintain that, although one cannot observe the mental existence of other people, one can infer their existence through analogy with a high degree of probability.

While analogy cannot render probable a completely unverifiable hypothesis, I can legitimately use analogy to establish the probable existence of an object provided that it could conceivably be manifested in my experience. 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.

CHAPTER 8
SOLUTIONS OF OUTSTANDING PHILOSOPHICAL DISPUTES


We cannot acquiesce in the existence of party divisions or 'schools' among philosophers. For, as we have seen, the function of the philosopher is to analyse the consequences of our linguistic usages. I propose, therefore, to examine the three great issues concerning which philosophers have differed in the past, and sort out each problem.

RATIONALISM AND EMPIRICISM

Rationalists uphold, and empiricists reject, the idea that there is a supra-sensible world accessible to intuition and alone wholly real. We have already dealt with this doctrine in the course of our attack on metaphysics, and seen that it is not only false but senseless. We therefore deny the possibility of such a world and dismiss as nonsensical the descriptions which have been given of it.

REALISM AND IDEALISM

Comparatively little attention has been paid to the realist-idealist controversy. For realists 'x is real' or 'x exists' is equivalent to 'x is perceived'. Realists maintain that the concept of reality is unanalysable. We shall find that realists are right in what they deny, but wrong in what they assert.

Berkeley held that nothing could exist other than through perception, but allowed that a thing might exist unperceived by any human inasmuch as it could still be perceived by God. The fact that things very probably do exist when no human is perceiving them was construed as proof of the existence of a personal god; whereas, in truth, it proves there is an error in Berkeley's reasoning.

We may allow that his dictum 'Esse est percepti' [essence IS perception] is true with regard to sense-contents. But it is a mistake to conclude, as Berkeley did, that a material thing cannot exist unperceived. 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. We maintain that a man must define his own existence, and the existence of other people, no less than that of material things.

Descartes believed that he could deduce his own existence from the existence of a mental entity, a thought, and concluded that mental states were not physical. We have shown that we have no empirical grounds for believing that mind and matter are independent.

Some philosophers may argue against us that as the sensible appearance of a material thing varies with the point of view, and the psychology, of the viewer so it cannot be said that appearance is any more than 'in the mind'. All that this argument from 'illusion' proves is that the relationship of sense-content to material thing is not that of a part to a whole.

The view that whatever is thought of must necessarily be real depends on the mistaken assumption that a sentence like 'Unicorns are thought of' is of the same logical form as 'Lions are killed'. The realist view that imaginary objects 'have reality' has already been shown to be metaphysical, and need not be discussed further.

MONISM AND PLURALISM

The monist assertion that Reality is One is nonsensical, since no empirical situation could have any bearing on its truth. Monists declare that everything is related to everything else in some way or other so that to state a fact about something involves stating everything about it. And this is tantamount to saying that any true proposition can be deduced from any other.

We have no a priori ground for either accepting or rejecting the Monist doctrine that every event is causally connected with every other and that Reality is One, but there are good empirical grounds for rejecting it, in that it denies the possibility of natural science.

To predict tomorrow's weather, I need not take into account the state of mind of the Emperor of Manchukuo. The fact that our predictions are very often successful gives us reason to believe that at least some of our judgements of irrelevance are correct, and so to reject the monist doctrine.

If science may be said to be blind without philosophy, it is also true that philosophy is virtually empty without science.


AJ 'Freddie' Ayer
1910-1989
Ayers remains were cremated at Golders Green Crematorium, London






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