Weckert - 'is Relativism Self-Refuting'

Educ. Phil. & Theory

Is Relativism Self-Re futing ?

JOHN WECKERT

Melbourne College of Advanced Education

I: Introduction

In recent issues of this journal, a number of articles have been addressed, in whole or in part, to the question of whether or not relativism is self-refuting.l This paper is a further contribution to the same debate.

I do not distinguish between conceptual relativism and cognitive or epistemological

I understand [epistemological relativism] as the doctrine that the basic epistemological properties are not such properties as that of belief B being justified, but rather such properties as that of belief B being justified relative to evidential system E2

This is certainly a legitimate variety of relativism, but it is not the one which concerns me here. Epistemological relativism is being taken as the doctrine that knowledge is relative to something or other, and it is assumed that what is known is true. The arguments to be examined which attack epistemological relativism interpreted thus, are also arguments against conceptual relativism.

relativism. By ‘epistemological relativism’, I do not mean what Field does. He writes:

Only a thoroughgoing relativism of course is normally charged with being self-refuting. A relativist then, can always avoid the charge by opting for a more moderate position. Instead of asserting that all truth is relative, he might just claim that most is. Even a thoroughgoing relativism, however, is not self-refuting, or so I will argue. Just as a sceptic can embrace scepticism with respect to his belief in s~epticism,~ so a relativist can accept that the statement of relativism itself is relative. Whatever other problems a conceptual relativist may encounter, self-refutation is not one of them.

Arguments to the effect that relativism is self-refuting take a variety of forms, a number of which are discussed by Husserl and Trigg. Some of these have been adequately answered by Meiland, and so will not concern us here? What will be of concern are several other versions of the argument, and an argument which Meiland considered but does not develop enough.

11: Mandelbaum

According to Mandelbaum an acceptance of relativism in the theory of knowledge frequently - and perhaps always - involves a prior commitment to non-relativistic interpretations of at least some judgments concerning matters of fact.5

30 JOHN WECKERT

He is saying, that is, that if relativism is true, then there are some things which are not relative, and he has two arguments designed to show this. (Two that is, with respect to conceptual relativism: there are others concerning other forms of relativism.) The first deals with Whorf. Whorfian conceptual relativism, he contends

holds that the influence of language on thought is so pervasive and so compelling that, insofar as it is a question of truth or falsity, one cannot legitimately compare statements made in one language with those made in another: the truth of each must be assessed within the framework provided by the conceptual system implicit in the structure of the language used.6

The argument is that if this Whorfian relativism were true, neither Whorf nor anyone else, could describe, in English, the languages which they do. They can do this because there are some non-relativistic facts, and so this all-embracing relativism must be false. Accep- tance of it depends on acceptance of something being objectively or absolutely true. Mandelbaum continues :

[Whorfl initially had to assume that the same objects and activities were being referred to in both languages. Therefore, it cannot be the case that how the world appears to those who speak a particular language is in all respects determined by the language they speak. . . languages presuppose a world of extra-linguistic objects to which the speakers of a language refer. Since, however, it is possible to refer to the same aspects of this world when using radically different languages . . . it cannot be maintained that those whose thought is expressed in different languages do not share a common world.7

There are two points here which suggest that relativism involves a reductio. One is that there is a ‘world of extra-linguistic objects’, and this, presumably, is an objective fact, and the other is that speakers of different languages share a common world. With respect to the second, it does not follow that if languages L1 ‘and L2 share a common world, what they share is aany way objective or absolute. What they share might not be what L 1 shares with L3, or what L2 shares with L3. Any two languages may share something, but no two need share the same. Whorf could say his account of the Apache or Nootka, or whatever, is relative to his language, that is, English, and its conceptual scheme. A linguist from a different background would give a different account.

The other point is more worrying for the relativist, but he can meet it. He might say that relative to our scheme, languages presuppose something extra-linguistic, but that this is not necessarily the case relative to all schemes. Perhaps we cannot understand what a language which did not would be like, but it does not follow that no-one can.

These replies to Mandelbaum may raise problems of their own, but they show that Whorf is not committed to any non-relativist facts, not at this level anyway. These criticisms then, as they are, fail.

Mandelbaum’s second argument is an attack on what he sees as relativism in Kuhn’sview of science. This requires little comment here, partly because it is an attempt to show incon- sistencies in Kuhn’s account in particular, and a conceptual relativist could always deny that Kuhn gives an adequate one, but more importantly because, as Mandelbaum acknowledges:

. . .his [Kuhn’s] thesis is less all-embracing than was Whorf s, for he confined his attention to what occurs within science, thus excluding any discussion of the more general world-pictures.8

Is Relativism Self-Refuting? 31

Our concem is with the more ‘all-embracing.’ I t might be that all scientific theories share something, but wh.at they share may still be relative to some conceptual scheme, or to several closely related ones. So again, even if Mandelbaum’s criticism, of Kuhn are successful, more than this is required to show that conceptual relativism presupposes some non-relativistic truths.

111: All truth is relative

We turn now to the more specific claim that T: All truth is relative,

or some variation like ‘No truth is absolute’, is self-refuting. It is self-refuting, it is claimed, because T itself is absolutely or objectively true if T is true at all. Mackie states the argument this way:

Since anything that simply is the case is an absolute and not merely relative truth . . . ‘There are no absolute truths’ is absolutely self-ref~ting.~

According to this, if it is simply the case that there are no absolute truths, then it is an absolute truth that there are no absolute truths.

This argument, as it stands, does nothing to show that T is indeed self-refuting. All it shows is that if whatever is the case is absolutely true, then T is self-refuting, and this is of course question begging, because it relies on the very notion, that of absolute truth, which the defender of T will reject.

A slightly different version of the argument comes from Trigg: If someone declares that truth is not objective, but only relative to societies, he may very well claim ‘there is no such thing as “objective truth”’ or ‘truth is relative to societies’. Both assertions, however, clearly purport to be objectively true, and are intended as truths about all societies. . . . He [the relativist] thus has to accept that sentences which state his thesisare apparently inconsistent with it.lo

The idea here, is that if T is about all truth in all societies, T must be absolutely true (or false). If it is true absolutely, it is false, because one truth is not relative, viz. T itself.

This argument is spelt out in more detail by Siegel. R is his version of T, (R is an epistemological, rather than a logical or metaphysical claim, but the issue is the same. The differences are, for our purposes, irrelevant.)

(R) For any knowledge-claim p, p can be evaluated (assessed,established, etc.) oniy according to. . , a set of background principles and standards of evaluation S1. . . S,; and, given a different set (or sets) of background principles and standards S’1 . . S’,. there is no neutral. . . way of choosing between the two. . . alternative sets in evaluating p.11

I am assuming here that truth relative to a set of background principles and standards of evaluation is just truth relative to a conceptual scheme. This is reasonable given that conceptual schemes contain these principles and standards.

The problem arises now, so Siegel believes, if R itself is substituted for p: (R) . . .R can be evaluated. . .only according to. . . a set of background principles and standards of evaluation S1 . . S,; and, given a different set. . . of background principles and standards of evaluation S’1. . . S’,. there is no neutral. . . way of choosing between the two. . . alternative sets in evaluating R.’ *

32 JOHN WECKERT

He continues: If R is true, then, as R states, R is itself relative to alternative, and equally legitimate, sets of background principles and standards of evaluation. Since these alternative sets will suggest differing evaluations of R, and since there is no way to neutrally pick one evaluation over and against any others, it follows that, if R is true, then R s truth unll vary according to the principles and criteria by which R is evaluated. In particular, it follows that, if according to some set of standards S1 . .Sn R is judged false. . , , then, if R is true (at least according to that set of standards S1. .Sn), R is false.13

The details of this argument are not altogether clear, and there seem to be two possible interpretations. One is that if R is true, it is true only relative to one set of standards, and therefore not true. The other interpretation is that if R is relatively true, it is not true relative to all standards, and so in an absolute sense, is false. Again if R is true it is false.

Doppelt replies to this argument, which is a criticism of an earlier paper of his own.

. . Siege1 claims that Kuhnian relativism as I present it is vulnerable to a reductio argument. The essence of the reductio is that Kuhn's relativism concerning standards of theoretical adequacy in science undermines the very methodological standards its own plausibility as a theory presupposes. But this argument mis- construes Kuhnian relativism as applying a prion and across the board to all standards and forms of evaluation whatsoever . . . Based, as it is, on a study of the standards implicit in scientific debate, it is illicit to abstract the form of Kuhn's

He writes:

argument and apply it willy nilly to-philosophical standards and arguments as well.14

The defence is that Kuhnian relativism is limited to scientific truths, not to all truths.

T'. All scientific truth is relative, If T is replaced by:

and if T' itself is not a scientific truth, then Doppelt is right, there is no reducfio. T' is not self-refuting. But self-refutation is avoided at some cost. Relativism on this account is much weakened. The problem also arises of why it does not apply to all truth. I will not pursue this line of argument further, because, as was mentioned earlier, my argument is that the stronger version of relativism is not self-refuting.

Doppelt does appear to be reluctant to take this way out, and continues: On the other hand, if Siegel thinks that there are some plausible standards of philosophical argument implicit in its historical or contemporary practice which makes relativism less plausible than its alternative(s), let him produce these standards.. .15

But produce these standards is something that Siegel does not have to do to show that relativism has a problem. Pointing out the incoherence is enough.

Doppelt concludes: Relativism may well turn out to be inferior to some alternative hilosophical

A reductio hardly constitutes a facile route. If conceptual relativism is self-refuting, it ought to be rejected. But the relativist need not concede defeat just yet.

system, but it cannot be dismissed by the facile route of a reductio. I t

Is Relativism Self-Refuting? 33

It has been argued that T must be true absolutely if true at all, and if so, T is self- refuting. But why, if true, must it be absolutely true? If the relativist denies that there is any absolute truth, he must maintain that T itself is relatively true, and as Meiland points out, ‘saying that relativism is only relatively true does not produce inconsistency’.17 To see this more clearly, we will make use of an undeveloped idea of Meiland’s - that absolute truth is a two-term relation between a statement and a state of affairs, and a relative truth is a three-term relation between a statement, a state of affairs, and a con- ceptual scheme.18 (This is slightly different from his formulation, but the difference is insignificant.) Call relative truth, ‘truth3’, absolute truth, ‘truthz’, and truth in general, where the matter is undecided, ‘truthl’. If T, ‘All truthl is relative’, is true2, then T is false2, in which case it is self-refuting. But if we accept Meiland’s suggestion that T should be taken as relatively true, then no inconsistency is generated. We can say either that if T is true3, it is not true3, or if it is true3, it is not true2. In the latter case two different concepts of truth are at work so there is no contradiction. In the former, there is no contradiction in saying that T is true relative to one scheme and false relative to a different one. On this view it cannot be said, as Mackie says, that if something is the case it is absolutely true. It is rather only the case relative to some scheme. And objectivity need not be presupposed by any statement which purports to make a cognitive claim. All that is presupposed is a relationship between the statement, some state of affairs, and some conceptual scheme.

IV: T as a relative truth

So relativism is saved for a moment longer from self-refutation, but I want to examine more carefully now what is involved in the claim that relativism, that is T, is itself relatively true.

IV: 1 : Can T be relatively true?

Suppose that T is true relative to some conceptual scheme S1. Then T must be true relative to every possible scheme, or there is some possible S relative to which T is not true. Assume that the former is correct. But if T is true relative to every scheme, it becomes unclear in what sense T is only relatively true. The three term relation, true3, has one free-wheeling member, which can be dropped with no loss, and so becomes true2 . A truth which is true relative to every scheme is surely just an absolute truth. The velocity of light is constant relative to every frame of reference, so we are commonly told, so we say that it is one thing the velocity of which is not relative. It is certainly not relative in the sense that the speed of a person walking down the aisle of an aeroplane is relative, say four kilometers per hour relative to the plane and 804 kilometers per hour relative to the ground. So truth gS relative to every framework or scheme is nothing other than truth which is not relative, but which is absolute. (More will be said about this shortly.)

How does the relativist fare if the other disjunct is accepted? Now it is the case that T is true relative to S1, but not true relative to some other scheme, S2. There are again two alternatives. Either T is false relative to S2, or T is neither true nor false relative to S2. If T is false relative to S2, then relative to S2 some truths are absolute. Put another way, some truths are absolute relative to S2. That is, if T is false relative to S2, then ‘some sentence p is absolutely true’ is true relative to S2. But what is the force of ‘absolute’ here? It seems that it has little, if any. We might say of the person walking down the aisle

34 JOHN WECKERT

of the aeroplane that it is absolutely true that he or she is moving at the speed of four kilometers per hour relative to the plane and 804 kilometers per hour relative to the ground. But ‘absolute’ seems to do little work here, except perhaps as emphasis, and that is of no help. It appears then that truth which is absolute relative to some scheme, is just truth relative to that scheme. If this is so, then there is no sense in saying that if T is true only relative to S, it is false relative to S. If it is true relative to S, it is true relative to any scheme, and so is true absolutely. And if it is absolutely true, it is of course self- refuting.

However this argument against the relativist fails. It fails because it depends on the identification of truth which is absolute relative to some scheme, with truth which is relative to that scheme, that is, the following is assumed to hold:

The relativist can deny this identification. If p is absolutely true relative to S2, then relative to s2 p is true relative to every S. This is different from saying that p is true relative to S2, which claims only that p is true relative to S2. Put another way, saying that consistent with the other truths of S2, ‘p is true relative to every S’, is different from saying that ‘p is true’ is consistent with those truths. They might both be consistent with the other truths of S2, but they certainly need not be. So despite appearances, ‘absolute’ does have a job to do in ‘p is absolutely true relative to S2) and so cannot be dropped.

p is absolutely true relative to S = p is true relative to S.

The other case is that where T is neither true nor false relative to S2. Here truth is neither relative nor non-relative. This must be so, because if truth were relative in S2 then in S2, T would be true, and if all truths were not relative, T would be false. Therefore, if all truth is either relative or not relative, and if S2 truth is neither relative nor non-relative, there is no truth relative to S2. That is, in S2 either ‘All truth is relative’ is meaningless, or it has a different meaning from what it has in S1. This does not necessarily pose any problem for relativism. If T is true relative to some scheme, false relative to another, and neither true nor false relative to a third, T is not incoherent if interpreted as being relatively true. However, if in all schemes T is either true or neither true nor false, then there is at least the appearance of a difficulty. It is not clear in what sense the T which is true in S1 is the same T as that which is neither true nor false in S2. If T1 is the T in S1, and T2 the one in S2 then T1 is true relative to S1 and T2 is neither true nor false relative to S2. But now T1 is true relative to all schemes in which it occurs, and so could be argued to be true absolutely. However it can also be argued that since T is not true relative to all schemes it is reasonable to call it only relatively true. We will return to this issue later, and for the moment give T the benefit of the doubt.

IV: 2: Tris’s objection

So far we have been able to save T from the self-refutation charge, but perhaps this has been done at some considerable cost. Consider this objection to relativism raised by Trigg, part of which was quoted earlier:

If someone declares that truth is not objective but only relative to societies, he may very well claim ‘there is no such thing as “objective truth” ’, or ‘truth is rela- tive to societies’. Both assertions, however, clearly purport to be objectively true, and are intended as truths about all societies. There would not be much point in the relativist uttering them if he did not wish to convince someone else of them. He thus has to accept that sentences which state his thesis are apparently incon- sistent with it. He can always claim that the truth of his words is only relative to

Is Relativism Self-Refuting? 35

his own society, but as their whole point is to describe other societies as well, this just serves to emphasise the incoherence in the position.l9

Trigg’s basic argument here seems to be that unless there are absolute or objective truths, it is not possible to convince anyone of anything, and it is not possible to make any general claims. The second of these need not concern the relativist too much. He can still describe other societies from his own point of view, and make general claims which are true relative to his own scheme. No careful relativist would of course want to do more than that. The former claim of Trigg’s, that it is not possible to convince anyone of any- thing if relativism is true, is discussed by Meiland. Meiland distinguishes three strands in this Trigg-type objection: (1) There is no possibility of a non-relativist accepting relativism. (2) The non-relativist can have no reason - can have no rational basis - for accepting

relativism. (3) The relativist can have no motive in uttering the doctrine of relativism, particular-

ly in uttering it to the non-relativist.20 (1) is clearly false. One may change one’s mind simply as a result of conversion. There is nothing to stop the relativist from trying to convert the non-relativist. Against (2) it can be argued that relativism does not necessarily rule out all rational discussion and argument. Two people who share, or for the sake of the argument assume, the same pre- suppositions, may argue rationally, while admitting that their arguments are relative to those presuppositions, which in turn are acknowledged to be true relative to some scheme or schemes. The relativist may be able to show a non-relativist that on the basis of the non-relativist’s own presuppositions he is logically committed to relativism. So relativism does not rule out all rational arguments, and there may be rational grounds for a non- relativist to become a relativist.

The third strand discussed by Meiland can easily be refuted. The relativist can surely have motives for expressing relativist views. He may just feel like it, in the same way that someone may feel like expressing something in poetry or on the piano.

IV: 3 : Passmore’s objection

Trigg’s objection, stated baldly as it is, does not show that a relativist can have no motives for expressing T and saying that it is only relatively true. However, the germs of a problem lie in Meiland’s reply to (2). This will be approached via Passmore’s discussion of one of Socrates’ attempts to show that Protagoras’ ‘Man is the measure of all things’, is self-refuting. The crux of the problem, Passmore says, is this:

Protagoras is . . . asserting that ‘p is true for x’ and ‘p is not true for y’; these propositions he is taking to be true. It has to be true not only for x but for every- body that ‘p is true for x’ since this is exactly what is involved in asserting that ‘man is the measure of all things’.21

If ‘p is true for x’ is true for everybody, then ‘p is true for x’ is one truth which is absolute, so Protagoras’ doctrine implies that man is not the measure of all things. Some things must be true for all men. But it is not clear why this is so. If man is the measure of all things, then it would seem to follow that while it is true for x that ‘p is true for x’ it might be true for y that ‘p is not true for x’. No contradiction appears to be involved here. ‘p is true for x’ is not both true and not true relative to the same person.

We can set out this criticism of Passmore’s more fully by reverting to our previous

36 JOHN WECKERT

terminology. Suppose that T is true relative to Sly and that some proposition, p, is true relative to S1. Now relative to S1 there must be some scheme S2, relative to which it is not true that p is true relative to S1. If this were not so, ‘p is true relative to S’, would be true in all schemes, and so would be true absolutely. So it must be the case that Telative to S1, p is true relative to S1, and relative to S2, p is not true relative to S1. This certainly generates no contradiction. So Protagoras and the defender of T do not succumb to Passmore’s criticism.

IV: 4 : a is decidable

However, the non-relativist can push the argument a little further. Suppose again, that relative to S1 , p is true relative to S1 , and that relative to S 2 , p is not true relative to S1 , Let a stand for ‘p is true relative to Sl’. Now, is it decidable whether a is true or false? Assume that it is. If it is, then either the S1 adherent is correct, or the S2 adherent is. That is, it must be possible to show either that p follows from, or is consistent with, the other truths or presuppositions of S1, or that it does not follow from, or is inconsistent with, those truths and presuppositions. So a must be either absolutely true or absolutely false, in which case the relativist would be committed to an absolute truth.

An immediate objection might be raised by a relativist. It is that the question ‘Is it decidable whether a is true or false?’ is illegitimate as it stands. a is only true or false relative to some scheme. The non-relativist might then ask whether this is decidable, that is, if OT is true or false relative to that scheme, to which the relativist will again say that this is an illegitimate question. In order to make things as difficult as possible for the relativist, we will assume that the question, as it stands, is legitimate. So we return to the original problem, the supposition that a is decidable.

Meiland’s way out will not do for the relativist now. He claims that it is not incom- patible with relativism to say that a relativist can argue, even with a non-relativist, provided that, at least for the sake of the argument, they assume the same presuppositions. Here it must be remembered, they are both arguing about the truth value of p relative to the presuppositions of S1. So for the sake of the argument, the S2 adherent must work within the confines of S1. His argument is simply that given the presuppositions of S1, p is not true. The problem here clearly seems to be whether a: is reall,, true or whether it is reall,, not true, and ‘really’ carries the force of ‘absolutely’. So if the S1 adherent can show that a is really true, a’s truth might be an absolute truth, and if the S2 adherent can show that it is really not true, that must be not true absolutely.

IV: 5: a is not decidable What is the situation if a is not decidable? We immediately want to know why it is

not. If the adherents of S1 and S2 are both rational it might be because S1 and S2 are incommensurable. Exactly what incommensurability involves is not clear, but for now I will assume that if two schemes are incommensurable, none of the terms of one can be translated or explained in any way, in terms of the other. It would follow from this that incommensurable schemes have different criteria of rationality. This must be so because none of the logical connectives of one scheme could be translated into the other, nor could terms like ‘is true’, ‘is rational’, and so on. Whether the incommensurability thesis needs to be interpreted as strongly as this can be debated, but it commonly is, or at least appears to be.

Is Relativism Self-Refuting? 31

There are problems with the imcommensurability thesis, but I will ignore these and concentrate on the self-refutation objection. If S1 and S2 are incommensurable it could make no sense relative to S2 to talk about truth relative to S1, and vice versa. If the terms ‘true’, ‘absolute’ and ‘relative’, are terms in S1, they are completely foreign to any other scheme. In so far as other schemes may use these terms, they must have different mean- ings from what they have in S1. Now from this, if it makes sense, it follows that all truth is truth relative to S1. T then, if true, is true relative to S1 only, not because it is false in all other schemes, but simply because the relevant concepts do not occur in any other. What work then does ‘relative to S1’ do in ‘T is true relative to S1? It seems that there is nothing for it to do. ‘Relative to S1’ only does something if it makes sense to say that relative to some other scheme T may not be true. But this cannot make sense if the incommensurability thesis holds, because now we cannot ascribe truth in any sense to any scheme other than S1, And if all other schemes lack the concepts of truth, absoluteness and relativity, nothing about T can be asserted from within them either.

What follows from this for the self-refutation argument? It might be argued that if there is incommensurability, T must be true absolutely. This conclusion might be reached on the grounds that there is no scheme relative to which T is false. If this is correct, relativism, that is, T, is self-refuting. The chief difficulty in arguing in this way, however, is that, while it is true that T is false in no scheme, it is also the case that T is not true relative to all schemes. It is only true relative to S1. This may be enough to show that T is only relatively true. Against this it might be objected that T is true in all of the schemes in which it is possible for it to occur, so if true, it is true absolutely.

The indecision evident in the preceding paragraph about which conclusion to draw, stems, I think, from doubts about whether to place more weight on the claim that T is not true relative to all schemes, or on the claim that it is true in all of the schemes in which it can occur. The relativist might be able to avoid self-refutation here, but another problem cannot be avoided. That is, that ‘relative to’, whether in ‘T is relative to S1’ or ‘p is true relative to S1 ’, has a very different meaning from ‘relative to’ as it occurs in state- ments like ‘I am travelling at four kilometers per hour relative to the plane and 804 kilo- meters per hour relative to the earth’. In this case it is meaningful but wrong to say that I am moving at four kilometers per hour relative to the earth, but with ‘T is true relative to S1’ the situation is quite different. T has no relationship whatsoever with any scheme apart from S1, so it is unclear what ‘relative to’ in this context means.

IV: 6 : Adilemma

To recapitulate briefly, the dilemma posed for the relativist is this: if a, that is, ‘p is true relative to S1’ is decidable, then the relativist is committed to an absolute truth, viz. that a is either absolutely true or absolutely false. On the other hand, if a is not decidable there is incommensurability between schemes and the very meaning of the relativist thesis becomes unclear. There are a number of ways in which the relativist can attempt to avoid impalement on the horns of this dilemma, and it is to these which we now turn.

First, it might be argued that all the argument for the first horn of the dilemma shows is that statements like a are absolutely true relative to some scheme, but not just absolutely true. And it has already been shown that absolute truth relative to a scheme does not reduce to absolute truth. If this is right, then if a is decidable it is either

38 JOHN WECKERT

absolutely true or absolutely false relative to S1, but not just absolutely true or false. This however misses the point of the argument, which was, if the truth or falsity of a is decidable, then a is either true or false relative to all schemes, and this is absolute truth or falsity.

A second way of avoiding the dilemma is to argue that while S1 may be in- commensurable with some schemes, it is not with all. Suppose that S1 and S2 are not incommensurable but that S1 and S3 are. It might make sense now to talk of a being true relative to S1, because that is not the only scheme relative to which it is both meaningful and true. This, however, does not really advance the relativist cause, because a is still true relative to all schemes in which it can occur. A new problem is raised too, which concerns the identity of conceptual schemes. If S1 and S 2 are not incommensur- able what reasons have we for saying that they are two schemes rather than one? Perhaps incommensurability is what individuates schemes. This is a problem which I will not attempt to answer now.

A third possibility is that we may be able to weaken the incommensurability claim and so slip between the horns. Of course it cannot be weakened too much, or we will be back with decidability. The main question now is whether or not it is possible to have a position where S1 and S2 are not totally incommensurable, but where a is still not decidable. There is such a position, and that is where a is discussable. S1 and S2 may not be totally incommensurable, but a may still not be decidable, even though it might be discussable. This possibility avoids entirely the problems raised by the dilemma. On the one hand, a might be both true relative to S1 and not true relative to S 2 , without the matter being decidable, and on the other the problems of incommensurability do not arise. S1 and S 2 may share many statements, one of which may be T. This does not imply that T must be true relative to S 2 , merely that it is meaningful in that scheme, and that the meaning is the same as in S1. If they both share T, 01 should at least be discussable.

V: Discussability and decidability

So the relativist is out of trouble again, if only temporarily. But now two more questions arise. Can a statement be discussable but not decidable, and does discussability appeal to some absolute criterion of rationality?

The second question can be answered quickly. What discussability does imply is some appeal to a shared criterion of rationality. This is necessary, at least if truth and validity are to be discussed, and it is difficult to see how they can be avoided. But an appeal to shared criteria is very different from an appeal to absolute criteria. If a is to be discuss- able between S1 and S 2 , those two schemes must share some criteria of rationality, but the criteria they share need not be absolute, and it need not be what S1 and S3 share. 22

The answer to the first question appears obvious. Arguments are conducted at great length over politics, for example, with no agreement being reached, except perhaps an agreement to differ. But this is hardly good enough. It can be attacked from two directions. One is to say that no real discussion is taking place in arguments of this sort, because the antagonists talk past each other, and for this reason never reach agreement. The alternative objection is that agreement could be reached, but only if people were more rational and more inclined to listen to rational argument, rather than adhering

Is Relativism Self-Refuting? 39

stubbornly to their prejudices. In order to avoid these objections some accounts of discussability and decidability are required.

V: 1 : Discussability

We will say that some sentence p is discussable by two disputants, D1 and D2, only if D1 can understand the meaning or usage of p as employed by D2, and vice versa. Most discussions of p, and certainly the ones which are of concern here, involve an attempt to assess the truth of p, or perhaps its probability, or, as some sociologists of knowledge prefer to say, its credibility. For the sake of simplicity, we will only talk about truth. If D1 and D2 are to discuss p, not only must they understand what the other means by p, but they must also understand the other’s meaning or usage of ‘truth’, or variants like ‘is the case’, ‘is the fact’, and so on. If they operate only at the object language level, they may not need to understand each other’s usage of ‘truth’ and the like, but I am assuming that any thorough discussion does involve some use of these terms.

Discussion may involve considerably more mutual understanding than has been indicated here, but it involves at least this much. On the account given, if D1 and D2 both have the same conceptual scheme, it is easy to see why they can discuss p. Each under- stands the other because they use the terms involved in the same way, and they share the same criteria of rationality. If they have different conceptual schemes, they can discuss p only if each can understand what the other says. This, however, does not involve them sharing the meaning or usage of p, merely that for the sake of the discussion they assume certain common presuppositions. The same is the case with ’truth’. They need not share the concept of truth in the sense of accepting the same one, but if the discussion is to proceed, they must at least understand and use the same one for the purposes of the discussion. Suppose for example, that D1 holds a correspondence theory of truth and D2 a preference theory, that is, that p is true if preferred by the majority of the community. If D1 understands D2’s use of p and his preference theory, of if D2 understands D1 in the equivalent way, they can discuss p.

V: 2 : Decidability

This account of discussability sets some limits as to what can be discussed between schemes, but we will leave that for the moment, and briefly consider decidability. In general a statement or argument is decidable if there is a decision procedure which can tell in a finite number of steps whether or not the statement or argument is true or valid. If a problem has an algorithmic solution, that is, if it can be solved by a computer, it is decidable.

Suppose that D1 and D2 can discuss p but that they cannot agree on its truth value, despite both being creatures of good-will. Why are they unable to reach agreement? One obvious answer is that the knowledge each possesses with respect to p differs. Each might be justified in what he believes, given the state of his knowledge. However, p.might eventually be decidable here if each acquired the same knowledge relevant to p. The situa- tion will be different if what divides them is a difference in relevant presuppositions. Perhaps they can examine these presuppositions and reach a reement on them. (I am assuming that presuppositions can be discussed and examined).k But that may not be so. In cases where alternative presuppositions are equally reasonable and equally useful,

40 JOHN WECKERT

which one we hold may be purely a matter of preference. Although these presuppositions may be discussable, there is no guarantee that any agreement will be reached, even if D1 and D2 are equally rational and knowledgeable, just as it may be undecidable whether cabbage really is nice tasting or not.

It might be argued that p is only discussable but not decidable because we are fallible, preference-dominated creatures. Could a preference-free, infallible machine do better? In many cases undoubtedly it could, but not in all.

We know from the work of Church and others that certain parts of number theory and quantification theory are undecidable in the sense that there are no decision procedures to tell whether any arbitrary formula or its negation is provable.24 We also know of many other problems for which there exist no algorithms. A consequence of this in quantifica- tion theory is that there is no general, step by step way of showing that some sentence follows from, or is entailed by, some other sentence or set of sentences, or that it is not. So some undecidability must be admitted, and that in areas where discussion in the sense outlined above is clearly possible. The general conclusion then must be that discussability does not imply decidability, which is what the relativist needed. Moreover, undecidability has emerged in just those areas where it was needed most. The issue under consideration was whether or not it could be decided if a is true or false. a can be interpreted as ‘S1 entails p’, and if p is a sentence and S1 a set of sentences, the question is whether a certain sentence is entailed by some particular set of sentences, or in a more formal way, is ‘S -+ p’ valid? And it is just in such cases that there is no general decision procedure.

It might be objected that I have misinterpreted the significance of Church’s theorem. What Church showed was that there is no general decision procedure in quantification theory, not that it can never be shown that some sentence is entailed by some other, or others. If it can be shown that some p is entailed by some S, then that is absolutely true and the relativist is still in trouble, even if this kind of entailment cannot in general be established.

To answer this it must be kept in mind what the original problem was. The problem was: can it be decided whether a is true, as claimed in S1, or not true, as claimed in S2? If there is a decision procedure it must be relative to S1 and S2. Suppose that a can be decided relative to these two schemes, what follows? Nothing, except that a is decidable relative to S1 and S 2 . It does not follow that it is also decidable relative to S 1 and some third scheme S3, even though a may be discussable between these two schemes. What S1 and S2 share which makes a discussable in them, is not necessarily the same as what S1 and S3 share which allows them to discuss it. This argument does not go through simply because the decidability of a has been relativised. To see this, suppose that decidability is relativised but that discussability entails decidability. Now, if a is decidable, it is decid- able relative to every scheme in which it is discussable, so it will be true relative to all schemes in which ,it can be discussed, or not true relative to all of them, and we are back with an absolute truth, or with incommensurability. However, once the discussable- decidable nexus has been cut in general, this condition is avoided.

Another point is worthy of comment here. If a, that is, ‘p is true relative to S1’ is interpreted as ‘S1 entails p’, then contrary to what was argued earlier, Q could occur in schemes in which there were no concepts of truth or relative to, provided only that there

Is Relativism Self-Refuting? 41

was a concept of entailment. But this just shifts the issue. If ct is in S1, and if ‘entails’ in S1 is the same as ‘entails’ in S2, then ct could occur in S2. But if they are not the same concept, then it could not. So our previous claim about the schemes in which a could occur needs only slight modification.

V : 3 : Conclusion

Finally, to illustrate what has been argued, let us briefly consider an example discussed by Evans-Pritchard in Nuer Religion. 25 The Nuer, according to Evans-Pritchard, believe that human twins are birds. Let Sn be the Neur conceptual scheme, and Sw the Western, scientific one. The sentence ct then will be ‘Human twins are birds relative to Sn’. Relative to S, this appears not only false but absurd. ‘The Nuer do not really believe that twins are birds’, we might be tempted to say from within Sw. In order to discover whether or not it is true that ‘Human twins are birds relative to Sn’, we can attempt to see exactly what they mean by ‘human twin’, ‘bird’, and by the verb ‘to be’. We can also examine their principles of rationality. Once this has been done we might find that ct is really true, and that we in Sw were wrong to deny it. But even if the matter can be decided relative to S, and Sw, it does not follow that it could be relative to some other scheme in which ct is discussable. The fact that we in Sw may not be able to comprehend how this would be possible shows very little, except perhaps our limitations.

Conceptual and epistemological relativism may have their problems. But they do not fall in the face of the self-refutation objection.

42 JOHN WECKERT

REFERENCES

1

2 3

4

5

6 7 8 9

10 11 12 13 14

15 16 17

18 19 20

21 22

23

24

25

Marshall, J., Peters, M., and Shepheard, M., “Self Refutation Arguments Against Young’s Epistemology”, Educational Philosophy and Theory, Vol. 13, No. 2, 1981, pp. 43-50. White, F.C., “Knowledge and Relativism I”, Educational Philosophy and Theory, Vol. 14, No. 1, 1982, especially pp. 5-6. Watt, A.J., “Sense and Relativism”, Educational Philosophy and Theory, Vol. 14, No. 2, 1982, especially pp. 29-32. Siegel, H., “Relativism Refuted” Educational Philosophy and Theory, Vol. 14, No. 2, 1982, pp. 47-50. Field, H., “Realism and Relativism”, Journal of Philosophy, Vol. LXXIX, 1982, p. 563. See Oakley, I.T., “An Argument for Scepticism Concerning Justified Beliefs”, Amencan Philosophical Quarterly, Vol. 13, 1976 p. 228. See Husserl, E., Logical Investigations, Vol. 1. Translated J.N. Findlay, Routledge and Kegan Paul, London, 1970, pp. 138-143; R. Trigg, Reason and Commitment, Cambridge University Press, Cambridge, 1974; J.W. Meiland, “Concepts of Relative Truth”,Monist, Vol. 60,1977,

Mandelbaum, M., “Subjective Objective and Conceptual Relativism”, Monist, Vol. 62, 1979, p. 403. ibid., p. 417 loc. cit..

pp. 568-582.

ibid., p. 418 Mackie, J.L., “Self-refutation - A Formal Analysis”, Philosophical Quarterly, Vol. 14, 1964, D. 200. TrGg, R., op. cit., pp. 2-3. Siegel, H., “Epistemological Relativism in Its Latest Form’’, Inquiry, Vol. 23, 1970, p. 115. ibid., pp. 115-116. ibid., p. 116. Doppelt, G., “A Reply to Siegel on Kuhnian Relativism”, Inquiry, Vol. 23, 1980, pp. 121 -122. ibid., p. 122. loc.’ cit . , Meiland, J., “On the Paradox of Cognitive Relativism”, Metaphilosophy, Vol. 11, 1980, p. 121. Meiland, J., “Concepts of Relative Truth”,Monist, Vol. 60, 1977 p. 571. Trigg, R, op. cit., pp. 2-3. Meiland, J., “On the Paradox of Cognitive Relativism”, Metaphilosophy Vol. 11, 1980, pp. 2 12ff. Passmore, J., Philosophical Reasoning, Duckworth London, 1961, p. 67. See Hesse, M., Revolutions and Reconstructions in Science, Harvester Press, Brighton Sussex, 1980, pp. 42-45. See Collingwood, R.G. An ESSUJ) on Metaphysics, Ckdrendon Press, Oxford, 1948, especially chapters IV and V for discussion of presuppositions. Church, A., “A Note on the Entscheidungsproblem”, Journal of Symbolic Logic, Vol. 1, 1936, pp. 40-41; 101-102. See also Quine, W.V., Selected Logic Papers, Random House New York, 1966, chapter XX. Evans Pritchard, E., Nuer Religion, Clarendon Press, Oxford, 1970.