A fallacy is a fallacious argument. Someone who merely makes false statements, however absurd, is innocent of fallacy unless the statements constitute or express an argument. In one of its ordinary uses, of course, the word 'fallacy' means little more than 'false belief; but this use does not concern us. In logical tradition, a fallacy may be made up even out of true statements, if they occur in proper form; that is, if they constitute or express an argument that seems valid but is not.

The concept of an argument is quite basic to Logic but seldom examined. However, there are problems which require us to take a closer look at it. We have felt the advance rumblings of several of these already. I shall be concerned principally with three of them.

(i) First, consider the problem of 'nailing' a fallacy. In many cases of supposed fallacy it is possible for the alleged perpetrator to protest, with an innocent face, that he cannot be convicted because he has not been arguing at all. Consider the so-called argumentum ad hominem, in the sense of the modern books. Person A makes statement S: person B says 'It was C who told you that, and I happen to know that his mother-in-law is living in sin with a Russian': A objects, 'The falsity of S does not follow from any facts about the morals of Cs mother-in-law: that is an argumentum ad hominem': B may reply 'I did not claim that it followed. I simply made a remark about incidentals of the statement's history. Draw what conclusion you like. If the cap fits . . .' This would be disingenuous, but the point remains that B cannot be convicted of fallacy until he can have an argument pinned on him. And what are the criteria of that ?

To take another case, which is in earnest in that it is of a kind that can occur even in the relatively rarified atmosphere of philosophical discussion, consider the kind of move that we might be tempted to classify as argument in a circle, or question-begging. X asserts that the Principle of Non-Contradiction, 'A thing cannot have property P and property non-P at the same time and in the same respect', must be a valid principle and says 'If it were not, the world would be incoherent in that, for example, the chair I am sitting in might be existent and non-existent at the same time, or non-solid at the same time as it is solid*. But to show that such a world would be incoherent he must invoke the Principle of Non-Contradiction, which it is the object of the exercise to prove. Pressed, he says 'What I said is not circular because it is not an argument. I am not saying that the incoherence of a world containing contradictions is an argument for the Principle of Non-Contradiction. I am simply exemplifying the Principle in order to make clear what you could be committed to if you were to drop it'. So long as he can insist that he is merely elucidating his position, and not arguing, he can evade censure. If he is to be effectively answered, it must be on the grounds that what he says does constitute an argument, and based on an appreciation of what this involves.

(2) Secondly, consider the problems surrounding arguments on the fringe of Formal Logic: inductive arguments, arguments from authority. Is there such a thing as inductive validity, or is it a contradiction in terms? Although we accept in principle that some inductive arguments are better than others, what are the canons by which we judge an inductive argument's absolute, rather than relative, worth?

In the case of arguments from authority -- since we cannot abjure these arguments altogether -- how are we to balance authorities against one another, and arguments based on their opinions against arguments, such as inductive ones, from other sources? Is it always unreasonable to use an argument from authority against a deductive one (for example, in Mathematics)?

A prior question, both in the case of inductive arguments and in the case of arguments from authority, is: Are they really arguments? The logician commonly conceives arguments on the pattern 'P, therefore Q; but neither of these kinds of so-called argument fits easily into this mould. We do not normally say 'This crow is black; that crow is black; therefore, all crows are black', or 'The dealer said it's genuine Louis; therefore it's genuine Louis'. Instead, we frame, at most, a modified conclusion, in the form 'Therefore it is a reasonable conclusion that. . .', or 'So probably. . .', or 'So presumably. . .'. To call these 'arguments' is to mark a similarity to deductive arguments; but it might be as well to reassure ourselves that the similarities are really as great as the differences.

(3) A third problem involving re-examination of the concept of argument is the one raised by the assertion of Sextus Empiricus and J. S. Mill that every valid argument is question-begging. Mill says (System of Logic, Book II, ch. 3, § 2):

It must be granted that in every syllogism, considered as an argument to prove the conclusion, there is a petitio principii. When we say,

All men are mortal,
Socrates is a man, therefore
Socrates is mortal;

it is unanswerably urged by the adversaries of the syllogistic theory, that the proposition, Socrates is mortal, is presupposed in the more general assumption, All men are mortal. . .

The error committed is, I conceive, that of overlooking the distinction between two parts of the process of philosophising, the inferring part, and the registering part, and ascribing to the latter the functions of the former.

A presupposition of Mill's doctrine is that the primary and only true purpose of argument is to establish 'scientific' knowledge. But what of other contexts ? De Morgan complains (Formal Logic, pp. 296-7):

It is the habit of many to treat an advanced proposition as a begging of the question the moment they see that, if established, it would establish the question.

It does not occur to Mill, as it does to De Morgan, that there are dialectical criteria bound up in the notion of question-begging. Even a Millian argument from particulars to particulars could be open to the charge of question-begging on these other criteria. Thus someone who argues that democracy will be unsuccessful in New Guinea because it has been unsuccessful in Ghana, Ceylon, and Vietnam could have it conceded that his analogical inference process is a valid one but be charged with begging the question in his premisses.

Mill's doctrine has been important in helping to create a style of thought about philosophy, which is characteristically modern in its consequences. Philosophers grasp the proferred nettle and say 'Philosophical arguments, above all others, are circular really. A philosophical argument, having no empirical foundation, never teaches anyone anything he doesn't know already'. Yet they defend the so-called 'teaching' of Philosophy. They cannot have it both ways. If philosophical arguments really lead nowhere they should be dropped, and philosophers should stop drawing their pay. But perhaps, of course, there is more to be said about what an argument really is.

I think that, if we give an accurate account of what an argument is, we completely dispose of this third problem, and go a long way towards drawing the sting from the other two. Moreover, we lay a foundation for an understanding of the fallacy-tradition and its place in the study of Logic.

An argument is generally regarded as being whatever it is that is typically expressed by the form of words 'P, therefore Q', 'P, and so Q', 'P, hence Q'; or, perhaps, 'Q, since P', 'Q, because P'. As a brief run-down on the appropriate terminology, let me quote from Whately (Elements of Logic, Bk. II, ch.III, § 1):

Every argument consists of two parts; that which is proved; and that by means of which it is proved. The former is called, before it is proved, the question; when proved, the conclusion (or inference); that which is used to prove it, if stated last (as is often done in common discourse) is called the reason, and is introduced by 'because,' or some other causal conjunction; e.g. 'Caesar deserved death, because he was a tyrant, and all tyrants deserve death.' If the Conclusion be stated last (which is the strict logical form, to which all Reasoning may be reduced) then, that which is employed to prove it is called the premises, and the Conclusion is then introduced by some illative conjunction, as 'therefore,'e.g.

'All tyrants deserve death:
Caesar was a tyrant;
therefore he deserved death.'

We might reasonably ask why Whately should refer to 'the strict logical form' and why, in fact, anyone should consider the precise order of the premisses and conclusion to be of any logical importance. One partial, though inconclusive, answer might be found in the comparative ambiguity of 'because', which may herald either a causal (in the natural scientific sense) or a rational explanation, either a fact allegedly related to the already-stated fact as cause to effect or a statement which is alleged to be related to the previous statement in accordance with the canons of Logic.¹ A formulation with 'therefore' might, for this reason, be preferred as less ambiguous. Perhaps, however, the attitude is merely conventional and no more than another example of how tied we still are to Aristotle's apron-strings. We have already noticed that the Indian tradition has even more elaborate predilections. We must dispense with this kind of bureaucracy.

When we divide the statements making up an argument into premisses and conclusion we are importing another fixed idea; for many arguments in practice have a 'thread', a 'development' that involves intermediate statements belonging to neither of these categories. It is usually assumed in logic books that a complex argument can always be broken down into simple steps in such a way that, in any given step, there are one or more premisses, just one conclusion and no intermediate statements. This is true of some arguments but not of all; and the word 'argument' is, in any case, regularly and properly used of the complex of steps as well as of the steps themselves. If we do not bear this in mind we are tempted to give too simple an account of various important logical phenomena. For example, 'circular' arguments may be quite misrepresented if we treat them as one-step events.

On the other hand, an argument is more than just a collection of statements. 'P, therefore Q' states P and states Q, but there are other ways of stating P and Q that do not amount to arguing from P as a premiss to Q as a conclusion. You can say 'P, and moreover Q', indicating that P and Q are true but that Q goes further than P; or 'P, neverthelessQ', indicating that P and Q are true but that you wouldn't expect to find them true together; or you can just say P and then say Q. When you choose to say 'P, therefore Q', the important feature of your utterance is that, as well as stating P and stating Q, you adduce P in support of Q.

Now it is important to notice that when P is adduced in support of Q, it may actually not support Q. This is only to say that an argument may be invalid. However, it is important to emphasize that an argument is not to be identified with an implication. There may be an argument where there is no implication: I may argue from P to Q when P does not, in fact, imply Q. 'Argument' is not synonymous with 'valid argument'. Although the existence, in some sense, of a valid implication may be a necessary condition of a valid argument it is not a necessary condition of an argument. Conversely, that P would support Q if it were adduced to do so does not, in itself, imply that, when both are stated, an argument is in process. A person may state P and then particularize it to Q; or state Q and then go to make the stronger statement P, without having argued in either case. He may even, in stating both P and Q, imply that it is Q that represents an argument for P instead of the other way round; or that P is an argument against Q and that therefore his joint statement poses a paradox; or any one of a number of other things. The forms 'P, and therefore Q', 'P, and moreover Q', 'P, and in particular Q', 'P, but nevertheless Q' are alike in that they all represent statements of both P and Q and imply a relation between them; but the actual relation between P and Q may not be that implied, just as P and Q may fail to be actually true as affirmed.

The actual logical relation between premisses and conclusion of an argument may be anything at all. It is even possible to find plausible arguments such that the conclusion is the precise contradictory of the premiss. People have argued²:

Every event has a cause.
Therefore (if you trace the causal sequence back far enough) some event has no cause.

Epimenides was telling the truth when he said 'I am lying'.
Therefore, Epimenides was lying when he said 'I am lying'.

No class is a member of itself.
Therefore (since it follows that the class of classes that are not members of themselves is not a member of itself, and from this that the class of classes that are not members of themselves is a member of itself), at least ont class is a member of itself.

I am not suggesting that logicians should accept defeat and abandon their quest for a paradox-free theory of deduction. The point is just that, whatever the result of that quest, there are various criteria of worth of arguments; that they may conflict, and that arguments may conflict; that when criteria conflict some are more dispensable than others, and that when arguments conflict a decision needs to be made to give weight to one rather than another. All this sets the theory of arguments apart from Formal Logic and gives it an additional dimension. This should now be abundantly clear, and we may turn our attention to the filling-in of details.

There is little to be gained by making a frontal assault on the question of what an argument is. Instead, let us approach it indirectly by discussing how arguments are appraised and evaluated. I shall stop using the words 'valid' and 'invalid' in case they cause concentration on too narrow a feature of this process of appraisal: the question interests in its broadest, rather than its narrowest, aspects. To avoid jargon as much as possible let good arguments be described simply as 'good'. There is no obvious or straightforward way of characterizing arguments that fall short of being 'good', because there are different ways of falling short; but I shall try to use the correct everyday word when there is one.

What are the criteria by which arguments are appraised?

The first thing we need to do is to deny one thing that most of the elementary logic books affirm. A distinction is faithfully made between the truth or falsity of the premisses and conclusion, on the one hand, and the validity or otherwise of the inference process on the other. A valid argument, it is said, may be built on completely false premisses and it may thus have a completely false conclusion. But this is a complete misrepresentation of the nature of argument. Take an example: I am arguing that the Viet Cong will be unable to last another year. I say 'American troops wear bright red uniforms. Bright uniforms excite envy in an enemy. Envious soldiers fall an easy prey to hardening of the arteries'. Given a couple of obvious additional premisses these imply the conclusion and those who follow the textbooks will have to say 'Well, it's a good argument. . . The conclusion is well supported by the premisses, and the fact that the premisses are not all they might be has nothing to do with the case'. This is obvious nonsense: whatever the textbooks say, in practice we like our premisses to be true, and we do not describe an argument as a good one if the premisses are false.

What about the conclusion? Presumably, if a good argument has true premisses and a satisfactory inference-process it must have a true conclusion too ? Unfortunately the case is not quite so simple as this. If logicians had found their perfect theory of deductive validity and we were to agree to work within the bounds of this theory, this would, of course, be so; and, in time, we might become so sure of our theory that we come to regard it as a simple tautology that it is so. But this is not the case at present, and may never be; and, in any case, there are good arguments that are not deductive. In practice, although we would want to say of a good argument that it supports its conclusion, it is not, as a rule, possible to say that it supports it beyond fear of reproach or criticism. It often occurs that there are good arguments for a given conclusion and also good arguments against it. We cannot demand of an argument that it be, all by itself, a knock-down one. If we did, we would risk running across a situation in which we found that there existed both a knockdown argument for a conclusion and a knock-down argument against it at the same time. It follows that our proposed stipulation that the conclusion of a good argument must be true cannot be sustained unqualified.

I shall enlarge on this in due course. For the moment, let us take some time off to answer an objection.

It will be said: Arguments occur not only in the form 'P, therefore Q or 'Q, because P' but also, sometimes, when we discuss the passage from the premiss to the conclusion, without being committed to the premiss or the conclusion themselves. We say 'If P, then Q'; and in this form an argument can be presented, discussed, validated and agreed to quite independently of whether P and Q are true or false. In some sense, in fact (it would be said), this is the proper form of an argument so far as the logician is concerned, because he is not involved in the question of the actual truth or falsity of the statements in his examples, but only with the inference-process that they exemplify. It must be added that good or valid inference-processes are good or valid all by themselves, independently of the material to which they are applied.

The answer to this is that 'If P, then Q' is not a real argument at all, but only a hypothetical argument. It says that a certain hypothetical statement P, which I am not now making, would serve, if I were to invoke it, as a premiss for a possible conclusion Q; but the argument remains hypothetical because I do not, or not necessarily, now argue in this way. A real argument has real premisses and conclusion, not hypothetical ones.

To those accustomed to logic's traditional terminology this use of the word 'hypothetical' looks like a pun, confusing (a) an argument which is hypothetical in the sense of not being real or actual, with (b) an argument which is hypothetical in grammatical form, having a clause introduced by 'if'. If we think this through, however, we may come to wonder whether the senses are really as different as they seem. If someone wishes to hypothesize an argument the natural way to do it is to use a 'hypothetical' form of words, and our reason for using the description 'hypothetical' for this relevant form of words is precisely that it is the standard method of representation of an argument that is only hypothesized, not used, as it were, in anger. Over the centuries the word has been detached from some of its proper associations and become an only semi-meaningful piece of logicians' jargon, often misused in that even actual arguments will sometimes be described as 'hypothetical' if they contain a premiss hypothetical in form.

That this terminological muddle is part of the wall which shuts reality out of much of our theory can be seen when we reflect that examples in logic books are mostly hypothetical ones anyway, even when they are in 'therefore' form. When logicians confine themselves to examples of the form 'If P, then Q' they are consequently confining themselves to hypothetical hypothetical cases. At the very least, we should move one step closer to reality. When we put up an example of an argument we should imagine someone actually arguing, not merely imagine someone imagining someone arguing. It is very easy, later, to ascend the theoretical ladder by condttionalizing what is said; but it is not nearly so easy, if we start from the other end, to restore the additional dimensions of actuality.

Now let us return to the task of formulating criteria of appraisal, and start to put them down systematically. This is, at first, only a first attempt, and we shall soon find reason to make some amendments. The first two criteria, however, are fairly obvious:

(1) The premisses must be true.
(2) The conclusion must be implied by them (in some suitable sense of the word 'implied').

Let us go on to another requirement. It is not enough that the conclusion follow from the premisses: it must follow reasonably immediately. Take some fairly advanced theorem of Geometry; say, that the opposite angles of a cyclic quadrilateral are supplementary. Although this follows from any suitably complete set of geometrical axioms, it would not be sufficient, by way of premisses for this conclusion, just to give such a set of axioms. The axioms are the starting-point of the argument, but the argument itself has not been given until it has been spelt out. So we shall have to stipulate:

(3) The conclusion must follow reasonably immediately.

However, the premisses of an argument are frequently not given in full and we need a supplementary criterion to deal with this possibility. There are rules or, at least, conventions governing what may be omitted. If I were to say, using Whately's example

Caesar deserved death because he was a tyrant,

All tyrants deserve death.

(4) If some of the premisses are unstated they must be of a specified omissible kind.

We may or may not be concerned with 'pure' Logic in this book, but we are certainly concerned with the Logic of practice. Consequently it is important to move on to the additional or modified criteria of appraisal that are relevant when Logic is put to work. It would not be acknowledged by everyone, of course, that the criteria given are in any need of alteration. It would be convenient if this were so. Unfortunately, there is one very important respect in which the alethic tests are not sufficient, and another important respect in which they are not necessary.

Let me first take up the respect in which they are not sufficient. By the alethic tests an argument is a good one if the premisses are true and the conclusion immediately follows from it. But what is the use of an argument with true premisses if no one knows whether they are true or not. If I argue that the Martian canals are not man-made because there never has been organic life on Mars, or that Australian aboriginal culture is related to European because there was extensive prehistoric migration from Assyria, my premisses may be true but the arguments will be quite useless in establishing my conclusions so long as no one knows them to be true. And the argument that oranges are good for orang-utans because they contain dietary supplements might or might not carry some weight in the second half of the twentieth century but would rightly carry none at all as between two ancient Romans who had never heard of vitamins. The recipient of an argument of this kind will rightly challenge it with 'How do you know?'; but this attacks not so much the truth of the statement as its epistemic status. It is not enough for the premisses of an argument to be true; they must also be known to be so, and we must replace the alethic rule (i) by a corresponding epistemic one

(E1) The premisses must be known to be true.

Furthermore, a similar point applies to the inference-process. We generally suppose that all inferences that are not complex ones are public and obvious, and this may be true of most; but it is possible in principle that Q should follow from P but that the step be an obscure or logically tricky one that would not be generally recognised or acknowledged. There is, perhaps, something philosophically repugnant about the suggestion that there should be inference-processes that nobody recognizes; but there is nothing in the least odd in supposing that someone or some group of people should, say, have immense difficulty with modus tollens or reductio ad impossibile. Such people would have to prefer other argument-forms.

We tried to rule this situation out earlier by specifying that inferences must be 'reasonably immediate'; but this phrase may have alternatively an alethic or an epistemic interpretation, and it is now clear that, in practice, it is the epistemic one that really matters. However immediately Q may follow from P in an alethic, or logical-systematic, sense, the argument from P to Q is less than inadequate if it is apt to strike people as obscure. It needs to be replaced by one "which is not merely immediate but acknowledged to be so. In an epistemic strengthening of the alethic rules (2) and (3) we shall be able to combine the two:

(E2, 3) The conclusion must follow clearly from the premisses.

A similar change of interpretation will now attend the rule about dropped premisses: 'omissible' can be regarded as explicated in some formal, non-epistemic way or it can alternatively be regarded as meaning 'acknowledged as omissible'. We can, in fact, make a contribution towards explaining what it is for premisses to be omissible: any premiss may be omitted that is known to be true and will be taken for granted in the context. That a premiss is 'known to be true' is not quite enough to licence its omission, since this would not distinguish it from premisses that need to be stated; and we frequently need to be reminded, in argument, of things that we know. However, if 'being taken for granted' is a concept admissible into epistemic Logic, we may state our next rule:

(E4) Premisses that are not stated must be such that they are taken for granted.

Whether the epistemic appraisal-criteria, taken together, are stronger than the alethic ones will depend on details of interpretation, such as whether 'taken for granted' in (E4) is really stronger than 'omissible' -- which must be regarded as an alethic term -- in (4). In the case of the epistemic criteria, however, there is an additional one; for an argument is surely unnecessary and dispensible unless its conclusion is not known to be true -- that is, is in doubt -- before the argument is put forward. It is true that there are 'academic' contexts, as we say, in which we produce or run over new arguments for old conclusions that are already well supported; but these, again, are hypothetical arguments or, at best, rehearsals for actual ones to be carried out on other victims on other occasions. It is as if we said: 'If Q were not already known to be true it could be supported as follows: P therefore . . .'. Our rule is:

(E5) The conclusion must be such that, in the absence of the argument, it would be in doubt.

This brings us to a difficulty. When epistemic logics have been formalized it has been usual to treat the 'knowledge' that is expressed in the symbolic operators as if the fictitious 'knower' were a person of infinite logical wisdom and rationality. It is implicit in the axioms and rules of the system that all logical theorems are 'known' to this person and that He draws all logical conclusions from whatever He knows. If 'K' is an operator meaning 'It is known that' it will commonly be regarded as a rule of the system that

If α is a theorem so is Kα

[Kp . K(p ⊃ q)] ⊃ Kq.

The answer is that epistemic concepts do not have to be logical concepts in this puristic sense for it to be worth our while to express them in symbols; and that the axioms and rules referred to do not satisfactorily express the logic of 'It is known that', when the knowers concerned are of less than perfect logical wisdom. Dropping these axioms and rules and replacing them with more reasonable ones does not present any very formidable difficulty; and it permits us to preserve rule (E5). One further comment should be made. The terms 'known', 'in doubt' and 'taken for granted' have been used as if there were no distinction to be made between different knowing subjects, so that what is known to one is known to all; but they are really doing duty for a range of concepts, 'known to me', 'known to you', 'known to John Smith', 'known to modern Science', 'known to most members of the diplomatic establishment', and so on. This does not make much difference so long as we stick systematically to one of relevant contexts. Thus, if the arguments we are discussing are arguments that John Smith produces within his own head and for his own edification the appraisal-criteria will refer exclusively to what is known to John Smith, in doubt to John Smith, and so on. However, the paradigm case of an argument is that in which it is produced by one person to convince another. Generally, the concepts relevant are those that refer to the person the argument is aimed to convince; but we can imagine complications in case, say, the arguer wishes to argue that the other person 'should know' such-and-such, or onlookers try to evaluate the outcome in their own terms. These make us wish for the simplicity, unfortunately illusory, of the alethic case. We shall see, however, that the task of building a formal model of some of the epistemic phenomena referred to is not unbearably difficult.

Before moving on to a further modification of the criteria it is worth remarking that one tempting generalization of them, the introduction of degrees of knowledge and doubt -- that is, epistemic probability -- turns out, when an attempt is made to formulate it in detail, to be much less clear than it seems at first. We feel that it should be possible to weaken (E1) to

(P1) The premisses must be reasonably probable

(P5) The conclusion must be less probable a priori than the premisses.

Now let us consider the respect in which the alethic criteria are too strong. Since the epistemic criteria are, on most counts, stronger than the alethic ones, it will follow that the epistemic ones are too strong also.

The point concerns the strong connotations of the word 'know'. We felt the need to alter criterion (1), which says that the premisses must be true, to (Ei), which says that the premisses must be known to be true; but, besides being a strengthening, this was also a change of emphasis, from theory to practice. In practice we often proceed on less than knowledge; namely, on more or less strong belief or acceptance. An argument that proceeds from accepted premisses on the basis of an accepted inference-process may or may not be a good one in the full, alethic sense, but it is certainly a good one in some other sense which is much more germane to the practical application of logical principles.

And here it may be that the puristic logician will feel that I am lowering my sights, and declaring a preference for, or satisfaction with, arguments that persuade, as distinct from possibly unpersuasive arguments that are valid. This is a half-truth, and we must distinguish the different possible purposes a practical argument may have. Let us suppose, first, that A wishes to convince B of T, and discovers that B already accepts S: A can argue 'S, therefore T' independently of whether he himself accepts S or T and independently of whether S and T are really true. Judged by B's standards, this is a good argument and, if A is arguing with B and has any notion at all of winning, he will have to start from something B will accept. The same point applies to the inference-procedure. One of the purposes of argument, whether we like it or not, is to convince, and our criteria would be less than adequate if they had nothing to say about how well an argument may meet this purpose.

Conviction, of course, may be secured by threat, water-torture or hypnotism instead of by argument, and it is possible that Logic should have nothing to say about these means; but we can hardly claim that an argument is not an argument because it proceeds ex concesso, or that such arguments have no rational criteria of worth. We are, in fact, talking about the class of arguments that Aristotle called dialectical, and that Locke called ad hominem. The dialectical merits of an argument are, no doubt, sometimes at variance with its merits judged alethically or otherwise; but we would still do well to set down a set of criteria for them.

However, there is also more to be said against the alethic criteria and in favour of a set based on acceptability or acceptance rather than truth. The case in which Smith tries to convince Jones on grounds which Jones will accept but Smith may not, is, after all, somewhat less general than will satisfy us: we should consider, also, the case in which someone, with good reason, accepts a given set of premisses and a given inference-process, and becomes convinced of a consequent conclusion. In other words, we should consider a case in which we are not at all tempted to make quasi-moral judgements. The question of whether there are any circumstances in which it is permissible to argue a case on someone else's grounds -- though it would almost certainly be answered in the affirmative -- is not really relevant, and we can dodge it by remarking on the relativity of the word 'accepted' which like 'known', is really doing duty for a range of concepts, 'accepted by me', 'accepted by you', 'accepted by modern Science' and so on. What good reasons various people may have for accepting various statements and procedures are, no doubt, themselves sometimes relevant to the worth of argument erected on them; but, if we are to draw the line anywhere, acceptance by the person the argument is aimed at -- the person for whom the argument is an argument -- is the appropriate basis of a set of criteria.

Somewhat more tentatively, one might push the claims of this reformulation even further. So long as it is the logic of practice that is being discussed, it is important to relate the concepts of truth, validity, and knowledge to dialectical concepts in the right way. Dialectical concepts have a certain claim to be considered as the fundamental ones, in that the 'raw' facts of the dialectical situation are that the various participants put forward and receive various statements. In the limiting case in which one person constructs an argument for his own edification -- though we might follow Wittgenstein in finding something peculiar about this case⁴ -- his own acceptance of premisses and inference are all that can matter to him; and to apply alethic criteria to the argument is surreptitiously to bring in the question of our own acceptance of it. When there are two or more parties to be considered, an argument may be acceptable in different degrees to different ones or groups, and a dialectical appraisal can be conducted on a different basis according to which party or group one has in mind; but again, if we try to step outside and adjudicate, we have no basis other than our own on which to do so. Truth and validity are onlookers' concepts and presuppose a God's-eye-view of the arena. When Smith and Jones argue and I am looking on, I can say to you 'Smith's argument is valid', or 'Jones's premisses are false', in judgement of what I observe, and these statements are different from and irrelevant to anything about what Smith or Jones accept. But if Smith says 'S is true', the words 'is true' are empty and he might as well have said simply 'S'; and if he says 'The argument "S, therefore T" is a good one' he might just as well have argued 'S, therefore T'. Used by participants in the argument, these terms cannot have the same function as for onlookers. And alternatively, if I as a former onlooker decide to intervene to give Smith the glad tidings that his argument is valid or Jones the news that his premisses are false, I am likely to find that I have become simply another participant in an enlarged dialectical situation and that the words 'true' and 'valid' have become, for me too, empty stylistic excrescences. To another onlooker, my statement that so-and-so is true is simply a statement of what I accept.

This point is of such fundamental philosophical importance that more needs to be said about it. The empty or, at best, parenthetical character of 'is true' and 'is valid' when applied to my own statements or arguments is paralleled by the similarly empty or parenthetical character of 'I think', 'I believe', or 'I accept'. Broadly, it would seem that the man who says 'S is true' or 'I accept S' might as well say simply 'S'; and, if he needs to paint in some subtle shade of meaning, can do so as easily by a gesture or an intonation as with extra words. What function do these extra words have? One answer is that one or other formula is essential to the case in which S is specified by description rather than explicitly: thus, I can affirm 'Jones's last statement but one is true' where it would not make sense to utter the verbless sentence 'Jones's last statement but one'. However, in the context of a discourse in which all parties understood the reference of the descriptive phrase, I could still dispense with 'is true' by substituting Jones's actual statement; and, in any case, we still have to discriminate between 'is true' and 'I accept'. Although my saying that X accepts S is not at all the same as my saying that S is true, my saying that I accept S seems, on the face of it, to have precisely the same function and practical effect.

The two formulations differ, as it happens, in a dialectical subtlety that involves not so much the speaker as the addressee. If Smith says 'S is true' and Jones agrees, he indicates that he, Jones, accepts S in the same way as Smith does; but if Smith says 'I accept S' and Jones agrees straightforwardly, he indicates not that he accepts S but only that he understands that Smith does. Hence it makes a difference to the addressee, Jones, which form is used, and either form to some extent restricts the degrees of freedom of his reply. Knowing this, Smith himself will choose to say 'S is true' if he seeks acceptance of S by Jones, and 'I accept S' if he does not seek or expect this acceptance. Generally, a formulation in terms of what I accept, rather than in terms of what is true, does not issue so strong a challenge to the hearer.

So much for the participant; but consider, now, the position of the onlooker and, particularly, that of the logician, who is interested in analysing and, perhaps, passing judgement on what transpires. If he says 'Smith's premisses are true' or 'Jones's argument is invalid' he is taking sides in the dialogue exactly as if he were a participant in it; but, unless he is in fact engaged in a second-order dialogue with other onlookers, his formulation says no more nor less than the formulation 'I accept Smith's premisses' or 'I disapprove of Jones's argument'. Logicians are, of course, allowed to express their sentiments but there is something repugnant about the idea that Logic is a vehicle for the expression of the logician's own judgements of acceptance and rejection of statements and arguments. The logician does not stand above and outside practical argumentation or, necessarily, pass judgement on it. He is not a judge or a court of appeal, and there is no such judge or court: he is, at best, a trained advocate. It follows that it is not the logician's particular job to declare the truth of any statement, or the validity of any argument.

While we are using legal metaphor it might be worth while drawing an analogy from legal precedent. If a complaint is made by a member of some civil association such as a club or a public company, that the officials or management have failed to observe some of the association's rules or some part of its constitution, the courts will, in general, refuse to handle it. In effect the plaintiff will be told: 'Take your complaint back to the association itself. You have all the powers you need to call public meetings, move rescission motions, vote the manager out of office. We shall intervene on your behalf only if there is an offence such as fraud.'⁵ The logician's attitude to actual arguments should be something like this.

My statement of this position is, perhaps, more forthright than the support I can give it warrants; but some of those who disagree will still follow along with the idea of a weakening of the criteria of worth of an argument. The modified criteria, which I shall call dialectical ones, are formulated without the use of the words 'true' and 'valid'; or of the word 'known', which would imply truth. With this difference they run closely parallel to the epistemic criteria.

(D1) The premisses must be accepted.

(D2, 3) The passage from premisses to conclusion must be of an accepted kind.

(D4) Unstated premisses must be of a kind that are accepted as omissible.
(D 5) The conclusion must be such that, in the absence of the argument, it would not be accepted.

Now, an onlooker who wishes to apply these criteria to the assessment of an argument must decide from whose point of view he wishes it assessed -- the arguer's, the addressee's, or his own. When an onlooker pretends to give an 'absolute' or 'impersonal' assessment the point of view is largely his own.

It is not uncommon for an argument to be assessed from a mixed point of view, by the construction of a hypothetical argument-situation having only some of the features of the actual one. Thus a logically-minded onlooker who judges 'That argument is valid' will frequently mean 'If I accepted those premisses and did not accept that conclusion, that argument would persuade me'; or, given an example of an argument insufficiently spelt out, he will puzzle through it and conclude 'The argument is really valid', meaning, in our analysis, 'The argument is acceptable to me as supplemented with these steps'. We cannot, perhaps, legislate for the various special kinds of hypothetical argument-situation that a theorist can construct for himself, and we must content ourselves with regarding them as non-primary.

Why do I use the word 'accepted' in my primary formulation, rather than the word 'believed'? It would be natural to weaken 'S is known' to 'S is believed' rather than 'S is accepted'. My reason for preferring 'accepted' is that 'believed' is too much a psychological word, conjuring up pictures of mental states. I can accept something simply by putting on the appropriate linguistic performance; and this behavioural manifestation is the only necessary constituent of the argument-situation. I can conceive that a machine might be made to accept or reject arguments, though I would hesitate to describe it as having beliefs.

Now let us return to the three problems with which we started. I shall take them in reverse order, dealing, first with the thesis of Sextus and Mill that every argument is question-begging.

Sextus was interested in this thesis to support the sceptical view that no knowledge is possible: Mill, to destroy deduction as a source of knowledge by comparison with observation and analogy. In either case the thesis is an epistemological one, and, in retrospect, it can be seen that we would be right to expect a purely alethic analysis of argument to lack the richness to deal with it. Sextus and Mill could be regarded, in other words, as criticizing the alethic conception of argument in favour of one incorporating epistemological considerations. Aristotle, as we saw earlier in discussing his treatment of Begging the Question, was inclined to object to any argument that did not fit into the pattern he thought appropriate for the orderly or 'scientific' deduction of knowledge from first principles. Mill produces an empiricisms version of the same predilection; and Sextus the sceptic's version which disallows all knowledge and hence all argument.

The revised set of criteria of argument -- whether epistemic criteria or dialectical -- goes some distance towards meeting these three authors' objections to the alethic conception of argument, but then leaves them to go their separate ways; though with weakened separate theses. A question-begging argument has frequently been defined as one whose premisses are at least as much in need of proof as its conclusion, and this is precisely the kind of argument that is ruled deficient by criteria (E5) and (D5), which have no correlates in the alethic set. So long as we are using one of these more sophisticated sets of criteria, the truth is not that all good arguments are question-begging, but that none are. Moreover, not all alethically good arguments are question-begging; they are question-begging only if they fail to satisfy these additional non-alethic criteria. Put generally, the thesis of Sextus and Mill is hardly plausible once we have moved away from an alethic conception of argument.

Mill, of course, has done us a service in pointing out that there is a restricted conception of knowledge -- the naive empiricist conception -- that gives approximately the result he states. If we are prepared to accept, first, that the only true knowledge is that which is obtained from direct observation and, secondly, that direct observation gives us always singular facts and never general, we shall have to regard any argument from a general premiss to a singular conclusion as wrong-headed and unscientific; and if we think thirdly, as Mill apparently does, that all deductive arguments are in the form of traditional syllogisms and, fourthly (and unhistorically), that syllogisms are inferences from general propositions to singulars, it will follow that anyone who increases his knowledge by the use of deductive argument is increasing it improperly or by the wrong means. This is not the place to debate the assumptions, but the special nature of them needs emphasis.

Different special stipulations are made by Aristotle and by Sextus. Mill, of course, has done little more than turn Aristotle on his head. For Aristotle, self-evident first principles are at the start of the epistemological argument-chain and all scientific knowledge is obtained deductively, though not all deduction is scientific. For Sextus the acquisition of true knowledge is not possible at all, and it would follow that not only deductive arguments are question-begging but every other kind too.

On the other hand, we need only relax these writers' special stipulations concerning the acquisition of knowledge to destroy their thesis. Let them say what they will about true knowledge; but, when it is knowledge of a more mundane variety that is being considered -- and, particularly, if it is not so much 'knowledge' in any strict sense but beliefs, hypotheses, and theses -- any kind of argument can be question-begging but no kind is more clearly so than any other.

Science and empirical (or other) method doesn't superannuate or by-pass dialectical criteria of argument. Even Science must progress by building on 'accepted' knowledge, and every scientific thesis needs to be supported by a dialectically sound case. It is perhaps even a danger for Science that it should be regarded as an enterprise built co-operatively on universally public empirical facts, rather than as a give-and-take market-place activity.

While we are berating philosophers for neglect of non-alethic criteria of argument we should take time off to accord special dispraise to the modern formal logician, whose field of view is perhaps more blinkered in this respect than that of almost any of his predecessors. His conception of argument is well illustrated by the formal concept of proof. A proof, for the formal logician, is a display of formulae of his system, either in a list or in a two-dimensional table, that satisfies certain structural properties, namely, that formulae later in the list or lower in the table are related by 'rules of inference' to relevant earlier or higher ones. Formal proofs, so conceived, have the virtue of precision but it is totally misleading to take such a proof as a model of rational argument.

In a formal proof the conclusion, or last formula, may be proved either absolutely, or relatively to certain other formulae higher in the table. If it is proved absolutely, this is either because no relevant formulae have been introduced unproved, or because those that have been introduced are axioms or (in some systems) because all unproved formulae have been prefixed in a 'conditionalization' process. If it is proved relatively to other formulae, then it would be said that the 'conditional' proof has been absolutely validated, which amounts to very much the same thing as saying that a certain formula of conditional form has been proved absolutely. The rules of inference and, if any, the axioms are supposed to be beyond question.

A proof, I take it, is just a knock-down argument; but this model of proof, far from setting a high standard of argument-worth for us, completely lets slip certain important desiderata. For example, it quite fails to ban circular reasoning for us, and one is encouraged to imagine that there is 'really nothing wrong' with using a formula to prove itself, or an axiom to prove an axiom, or a rule to prove a formula (such as modus ponens) interpretable as the expression of the rule. Equivocation is apparently also regarded as impossible, or the invalid arguments that it may lead to as 'formally valid'. The shortness of the steps and the transparency of the axioms and rules, whose rationale is the provision of a guarantee against error, is not only not a protection against these other sources of invalidity but a smoke-screen that can help them to slip through unnoticed; and it is not uncommon for the fussiness of a formal proof to defeat its own end by making it extremely laborious to follow, if not actually obscure. Yet in spite of it all it is a commonplace of modern Logic that highly paradoxical theorems have been 'proved' from harmless-looking axioms and rules. The complicated shuffle involving the construction of 'alternative' systems disguises the fact that nothing is proved absolutely at all, and that an unpalatable theorem can sometimes be a ground for going back and altering the axioms or rules.

The worst feature of this model is the appearance of definitiveness given to the concept of proof, and the impression that it is unrelated to the problem of filling out out knowledge or of actually convincing real people. Short steps are neither necessary nor sufficient to carry conviction: there is no guarantee of freedom from equivocation: conviction on one occasion or of one person is no guarantee of conviction on another occasion or of another: deductive 'proof' does not put a conclusion beyond rejection on other grounds. Formal validity, that is, is no guarantee of validity or vice versa.

This brings us to the second of our problems, that of 'non-deductive' argument-forms. Actually, it should be clear by now that we cannot always classify an argument uniquely as 'deductive' or 'non-deductive'. Arguments are more than mere inference-steps, and may have a structure with different elements in them. Nevertheless there are clear cases of arguments that are non-deductive: inductive arguments, statistical or probabilistic arguments, arguments from authority and arguments which rely on one or another kind of emotive appeal. Our earlier question, 'Are they really arguments?' can now be seen to be misplaced: certainly they are arguments, and if we are questioning any credentials at all we should rather question those of what often pass for deductive arguments.

When we have filled out the concept of an argument and realize that it is more than an inference schema, what, precisely, is the difference between deductive arguments and others? Does deductive argument give greater certainty? Not always: sometimes we rely for preference on the others. We rely on authority rather than deduction if we back the word of a distinguished mathematician against our own calculations; and on induction against deduction if we back a highly-confirmed experimental generalization against a theoretical prediction. (There is more, of course, to be said here, but it does not destroy the main point.) Is deductive argument more systematic than other kinds? Unfortunately, yes, for it is a scandal of modern Philosophy that, despite all the miles of writing, the question of induction or confirmation of hypotheses remains in such a state, utterly un-mechanizable. But much has been done, and we should not regard deductive Logic as perfect. Is deductive validity, when we are sure we have the details correct, 100 per cent in a way other kinds of argument-worth are not? All sorts of things can go wrong with a deductive argument. Many a mathematician or logician has solemnly proved a contradiction, sure that he had the details correct. When we invoke the 100 per cent character of deduction as characteristic of it we are talking about pure theory, not practice.

Excessive obscuratism on this point is out of place: one is tempted to overstate a case purely because it is usually not stated at all. I shall assume that the reader really does know the difference between deductive arguments and others, and that I do not need to go into it. What is, above all, necessary is to dethrone deduction from its supposed pre-eminent position as a provider of certainty. This is not-at-all for Sextus's or Mill's reasons, but simply because we sometimes cheerfully and properly prefer other arguments against it.

The stumbling-block for many people is the mistaken idea that a good deductive argument compels the acceptance of a conclusion which, in turn, entails unequivocal action on it. Nothing has been said in this chapter about the rationality or otherwise of accepting the conclusions of good arguments and of acting on them, and it should be clear that this is not an entirely simple matter -- when, for example, there are good arguments pointing in opposite directions. Once this question is separated, it should be clear that the very existence of different argument forms is a part of the problem with which, in the long run, the logician must deal, since there must be rules for weighing one against the other. Here, it must be sufficient to protest against the theory that the weighting of deductive arguments is determinate, and infinite, and that of inductive arguments totally the reverse.

Now let us turn to the problem of 'nailing' a fallacy. Is it a genuine problem? Good arguments (we hear the plaintiff saying) should be seen as good by all reasonable people, whereas some people refuse to be impressed and our knock-down arguments leave them still standing up. What is a rational man to do about those who are irrational and will not admit it?

This complaint must be dismissed as frivolous. It amounts to the demand that there should be a precise equation between logical soundness and practical efficacy: Right must be Might. And the answer to this demand is, first, that there is no royal road to success in practical dialectics; but, secondly, and most importantly, that no argument, even when wilful sophistry is set aside, ever settles a dispute once and for all, beyond the possibility of being reopened.

What argument ever is knock-down? Some, of course, are sometimes accepted as being so. But it is not at all unusual to find that an apparently knock-down argument -- which, perhaps, satisfies all of somebody's rules of validity -- is later found to be faulty. Either it is discovered that one of the premisses was untrue or insufficiently substantiated, or it is found that there was an equivocation on some term, or that the question was begged, or that there was a confusion concerning exactly what was being proved; or, though perfectly valid and drawn from true premisses it was not straightforwardly drawn and should have had some filling-out or marginal explanations; or, though it was valid and from true premisses, the arguer's or hearer's reasons for thinking it so were misplaced, the actual truth or validity being only accidentally achieved. Or it is discovered that there are other powerful arguments contradicting the conclusion reached and that a reappraisal of the earlier argument should be undertaken in spite of its strength; or that there is an unexpected repugnance between the conclusion and newly-discovered other facts; and so on, virtually ad infinitum.

This sceptical doctrine needs to be balanced, of course, with the well-known countermoves to scepticism. Do I really think, in the case of such-and-such well-accepted arguments, that there is any likelihood of reversal? When someone describes an argument as 'knock-down' and it seems to him, to me and to everyone else to be so, are we wrong so to describe it? No. The use of the term remains what it was. But if the philosophical point has been well made, something follows about the attitudes that should be taken towards the concept of argument, and those that should not be. Many of the latter are current.

1 cf. Ryle, 'If, so and because'.

2 I owe the example to D. C. Stove, who gave it in a paper read in Sydney in 1964.

3 An Essay in Modal Logic, p. 1.

4 I refer to the well-known 'private languages' argument, in Philosophical Investigations, 258, which can be adapted here.

5 See, for example, Head, Meetings, p. 101.