Even within the English speaking, broadly analytic tradition 'philosophy of education' is a more than usually polymorphic concept, with ill-defined borders with educational theory, pious exhortation, and logical analysis. My own preference is for strengthening the links with 'main-line' analytical philosophy, for pursuing educational discussion with a more rigorous grasp of possible conceptual connections. This paper is intended to be a small contribution to such missionary endeavours. I shall begin by reporting and criticizing an argument, offered by J. M. Finnis1 that the pursuit of truth is objectively part of the good for man. I shall not here enquire how close Finnis' argument is to others, such as Peters', for a similar conclusion, but will stick closely to what Finnis presents. The utility of Finnis' argument for my larger purpose is, ironically, that he himself bases it upon an exhaustive and illuminating logical analysis of self-refutation, that offered by J.L. Mackie.2 I shall argue that despite his attempt to maintain rigorous standards of argument Finnis has still not probed the logical structure of his central claim carefully enough. If I am right I think some support is given to the contention that the logical tools of modern analytic philosophy are not esoteric luxuries but necessities for any adequate philosophy of education. A couple of more technical appendices seek to give further support to this claim, though the relegation of the material to an appendix testifies to its esoteric status at the moment. Of course, none of this, even if I am right, proves that philosophers of education must be able to employ notions of quantification, or different varieties of self-refutation, or any of the other concepts currently in vogue. I only claim that a demonstration of the usefulness of some of the tools is a demonstration of their usefulness. For those who would still rather not invest in them I hope that Finnis' argument, and the issues it opens up, will have an independent interest.
Finnis argues that truth, and the knowledge thereof, is self-evidently part of the good for man. He offered the argument in a Festschrift for H.L.A. Hart, and in that context he relates it to Hart's concern to explain law and morality by reference to human survival. What Finnis finds profoundly mistaken in this is Hart's suggestion that one might seriously reject the classical view that the good for man is not only a matter of biological survival above a certain minimal level of well-being but also a matter of the development of mind, of a concern for truth and goodness. Survival is generally taken to be a good, something everyone is, or can be assumed to be, committed to; but, in modern times at least, knowledge is not so honoured. Finnis seeks to re-instate the classical doctrine, to show that the pursuit of truth must be considered part of the good for man.
Clearly, Finnis' claim has important consequences beyond its bearing on Hart's theorizing; if he were correct, he would have plugged many a hole in attempted justifications of education, compulsory schooling, the promotion of rationality and so on, to mention only a few of the issues of peculiar concern to philosophers of education. I shall not, however, expatiate on what Finnis might do for us since it is the burden of this paper to show that Finnis has failed in his attempt to show us that the pursuit of truth is self-evidently good.
Finnis announces that "the principle that truth (and knowledge of it) is a good objectively worthy of human pursuit cannot be demonstrated. But it stands in need of no demonstration and itself is presupposed, as we shall see, in all demonstrations whatsoever" (p. 250). This claim that it is presupposed, not only in all demonstrations, but in all serious assertions, is supported by what he calls a kind of 'retorsive argument' or 'argument from retorsion' — an "argument which refutes a statement by showing that that statement is self-refuting" (p. 25O).3
Finnis employs an analysis of kinds of self-refutation first offered by J. L. Mackie, and it may not be amiss to follow Finnis in an informal review of Mackie's distinctions. (See Appendix 1 for Mackie's formalism.) Mackie leaves simple self-contradictions aside and concentrates on more involved cases which depend on the behaviour of proposition-forming operators on propositions. In general such operators are simply items like 'John believes that...,' 'either grass is green or...', or 'it is demonstrably false that...' which make a new proposition when added appropriately to an existing proposition. Mackie first finds a law for all such operators which explains in particular what he calls 'pragmatic self-refutation', in which the way something is presented conflicts with what is thereby presented — shouting 'I'm not shouting'. The logical law can be exemplified using the same example — if I am shouting that I am not shouting anything then it is not the case that I am not shouting anything. Of course, I may very well not be shouting anything, and I may be able to convey this fact — only not by shouting it.
Having established this perhaps rather obvious law for all proposition-forming operators on propositions, Mackie goes on to look at some special classes of operators. The first are what he labels 'truth-entailing' operators, where the proposition formed by the operator entails the proposition it is formed from. Thus 'John knows that...' belongs in this class whereas 'John believes that...' does not, 'John knows that grass is green' entails 'grass is green', while 'John believes that his wife is unfaithful' does not entail 'John's wife is unfaithful'. The law Mackie finds for truth-entailing operators is difficult to express informally, but can be exemplified by an instance such as 'it is not the case that John knows that John knows nothing'. John may in fact know nothing but it is logically impossible for John to know it. Mackie calls this a kind of absolute self-refutation since certain propositions are ruled out absolutely — 'John knows that John knows nothing' just cannot be true; it is not merely a matter of how we present it.
A second sort of absolute self-refutation arises with what Mackie calls 'prefixable' operators, those for which the proposition formed by the operator is entailed by the proposition it works on. 'It is true that...' belongs in this class but 'John knows that...' does not. 'Grass is purple' entails 'it is true that grass is purple', but not even 'grass is green' entails 'John knows that grass is green'. The law for this class is exemplified by the logical truth that it is not the case that there are no truths.
The sort of self-refutation that both Mackie and Finnis lay most stress upon is, however, different from any of these.4 Mackie labels it 'operational self-refutation' and calls the operators that create it 'weakly prefixable'. There is room for disagreement as to how best to characterize this type of self-refutation, but it is certainly concerned in some way with what the serious and coherent assertion of any proposition commits one to. One might see it as a way of uncovering the rules governing serious thought or dialogue. We have seen that for a prefixable operator the proposition formed by the operator is entailed by the original proposition itself; for weakly prefixable operators, the assertion of the proposition formed by the operator is entailed by the assertion of the original proposition. Informally this is perhaps rather involved; let us take a plausible example. One of the rules for polite discourse might be that if you assert that grass is green you believe that grass is green; one of the basic facts about thought might be that if you assert (if only to yourself) that grass is green you are thinking that grass is green. Mackie says that 'x coherently asserts that grass is green' entails 'x coherently asserts that x believes that grass is green', and he calls 'x believes that' a weakly prefixable operator. Finnis switches to examples with 'I assert that...', but the change is not germane to our discussion. What Mackie shows for any such weakly prefixable operators is something to the effect that you cannot coherently assert that you believe nothing. If 'I am thinking that...' is such an operator then I cannot coherently assert that I am not thinking anything; as Descartes claimed, 'I am thinking something' has got to be true whenever I think or assert it, or indeed anything else. But it is not a necessary truth; indeed it may not be a truth at all. Here Finnis departs from Mackie's account since he claims that an operationally self-refuting proposition is inevitably false "because it is inconsistent with the facts that are given in and by any assertion of it" (p. 252). But it is not the proposition that is inevitably false, rather asserting it in its characteristic ways makes it false (unlike pragmatic self-refutation where we can easily find another way of presenting the item) — what amounts to the same proposition may be true and coherently assertable. It was often true, certainly is now, that Descartes is not thinking, but Descartes could never coherently assert it or think it himself.5
To get any further we need to discover which operators are weakly prefixable, in other words, what coherent assertion does commit one to; and, as Finnis says, this is in large part a matter of fact (or value), not of logic, a matter of the facts surrounding coherent assertion. It is this location of the relevant facts that gives its peculiar power to this kind of retorsive argument. "The self-refuting interlocutor is overlooking these facts, but is himself creating or instantiating them by and in his act of asserting (disputing)" (p. 253). But rather than launch upon this general investigation it is time to turn to the specific argument Finnis offers for the claim that one cannot coherently deny the good of truth.
Finnis offers us one version of the argument in extenso which I shall reproduce here both in fairness to Finnis and because I want to argue that his way of presenting it is both potentially misleading and confused in detail.
For all p
1 If I assert that p I am implicitly committed to 'I assert that p'.2 If I assert that p I am implicitly committed to anything entailed by 'I assert that p'.3 'I assert that p' entails' 'I believe that p [is true]'.4 'I assert that p' entails 'I believe that p' is worth asserting'.5 'I assert that p' entails that 'I believe that p' is worth asserting qua true'.6 'I assert that p' entails 'I believe that truth is [a good] worth [pursuing or] knowing'.Therefore from (3)
7 If I assert 'It is not the case that truth is [a good] worth [pursuing or] knowing' I am implicitly committed to 'I assert that it is not the case that truth is [a good] worth [pursuing or] knowing'.And from (3) and (7)
8 If I assert 'It is not the case that truth is [a good] worth [pursuing or] knowing' I am implicitly committed to 'I believe that it is not the case that truth is [a good] worth [pursuing or] knowing'.But from (2) and (6)
9 If I assert 'It is not the case that truth is [a good] worth [pursuing or] knowing' I am implicitly committed to 'I believe that truth is [a good] worth (pursuing or] knowing'.So, from (8) and (9)
If I assert 'It is not the case that truth is [a good] worth [pursuing or] knowing' I am implicitly committed both to 'I believe that truth is a good worth pursuing or knowing' and to 'I believe that it is not the case that truth is a good worth pursuing or knowing'.Thus, if I assert that truth is not a good, I am implicitly committed to formally inconsistent beliefs (pp. 258-9).
I am not very sure how Finnis conceives the earlier steps in his argument, in particular what he intends by saying that "steps (4) and (5) . . . are introduced into the argument only in order to prepare for step (6)" (p. 261). In fact, lines (1) to (6) are independent permisses; they do not receive any support from each other or from the argument as a whole. If they are true then (10) is true too, but the argument gives us no reason to think they are true. I am not sure whether Finnis' talk of preparing for step (6) shows that he fails to realize this.
The first three lines of the argument express rules for coherent assertion that Finnis has taken over from Mackie. Line (4) is the first of Finnis' innovations, which introduce evaluative implications of assertion. While I am sure Mackie and I differ from Finnis on the ontological status of evaluations I think he is right not to worry about that question in this context. There is something odd about asserting 'p, but I don't think p is worth asserting'; in understanding serious assertion we do take the asserter seriously, as someone who thinks he is not totally wasting his time, and this is true whatever be our final account of worthwhileness. And, remembering the exalted aims of our idealized discourse, the same goes for (5). If these be granted, it is, I think, rather strange that Finnis does not immediately make use of Mackie's results to show that it is impossible to coherently assert that no proposition is worth asserting or that I don't care whether any proposition is true or false.
One reason may be that they are still a long way from the central contention of line (6). Using Mackie's result on (5) we know that we cannot coherently assert that we don't care whether any proposition is true or false; any attempt at serious assertion commits us to claiming that the truth of some proposition is worth knowing. There is nothing in Mackie's results, or anywhere else I know of, to get us from that minimal commitment to a commitment that the truth of all propositions is worth knowing. But isn't it this that (6) requires? The pity is that (6) is crucially indeterminate; Finnis is exploiting the elliptical logical structure of such abstract nouns as 'truth', 'justice', and so on. If we want to generalize about just actions or just social arrangements we can hardly avoid facing the question 'how many such cases are we dealing with? all just acts, or most, or only a few?' But when we generalize by using the abstract noun 'justice' such mundane considerations are all too easily forgotten.
What I am suggesting, then, is that Finnis has underplayed the importance of the quantifiers buried in 'truth is worth pursuing'. All truths or some truths? He would not, I think, reject this question as irrelevant to the logic of claims about truth or justice; indeed, elsewhere in his discussion, he explicitly puts the quantifiers in — he tells us that his fundamental claim does not mean that every true proposition is equally worth knowing, and he sums up the claim by saying "for any p it is better to believe (assert) p where p is true than to believe (assert) p where p is false, and than to disbelieve (deny) p where p is true" (p. 263). But in presenting his formal argument this explicit universal quantification was elided — one might swallow 'I assert that p, so truth matters to me' but only, I suggest, so long as one does not face its ambiguity between 'I assert that p, so the truth value of at least one proposition matters to me' (which is what Mackie's results give us) and 'I assert that p, so for all q, the truth value of q matters to me' (which is what Finnis wants). Perhaps one ought to have such a commitment, but it needs argument to show that a man's concern for truth must extend so far beyond the matters he is currently disputing; I simply deny that, properly understood, line (6) is self-evident.
Argument could be offered, I think, for extending concern beyond those propositions explicitly disputed to others entailing or entailed by those in dispute (by rules such as line (2)); but this does not seem likely to catch all propositions in its net. But without an argument, Finnis is making (6) analytically true, and thereby losing the retorsive force of his argument since it now concerns a kind of serious assertion we have no reason to think employed by those to whom his original argument should be addressed.
Finnis has made the valuable point that since there are evaluative elements in our understanding of serious assertion certain evaluative claims are operationally self-refuting; the asserter is refuted out of his own mouth. But we have also seen that the plausible candidates here are, just as in Mackie's discussion, very weak claims; we cannot coherently deny that some truths matter, that some assertions are worth making. But practically, educationally, this much (or this little) has never been denied. Finnis seemed to promise much more, a way of showing that truths matter in every area, that one should never believe the false. But his argument, when examined more closely, seems to trade on elision; the powerful assertion remaining mere assertion, unsupported by the retorsive argument.
In this appendix I shall first summarize Mackie's account of self-refutation in his formalization, which is a lot clearer than the contortions of the preceding informal account; and then I shall offer a formalization of the argument quoted above from Finnis. This will serve to illustrate the confusion of details of the argument that I have I not touched upon earlier.
Mackie uses fairly standard Polish notation supplemented by the symbol 'd' to stand for any proposition-forming operator on propositions. He also is quite happy to quantify over propositions. The basic law of pragmatic self-refutation is Cd(NΣpdp)N(NΣpdp) — if d that nothing is d'd then it is not the case that nothing is d'd; if I write that I am writing nothing then it is not the case that I am writing nothing.
The first kind of absolute self-refutation occurs with truth-entailing operators, d such that dp entails p. For these, Nd(NΣpdp) is also a law. The second sort of absolute self-refutation involves prefixable operators, d such that p entails dp. For these, N(KΣpdp) is a law, so NΣpdp is absolutely self-refuting. Assuming classical laws of double negation, one can say that for these operators Σpdp is a logical truth and self-verifying.
For operational self-refutation we have to invoke a special operator, a, to be understood as 'x coherently asserts that . . .', or as Finnis prefers, 'I assert that . .. Weakly prefixable operators are then d such that ap entails adp. For these Mackie proves that Na(NΣpdp) is a law, so that NΣpdp cannot be coherently asserted.
To formalize Finnis' argument I add to the above machinery the following: B for 'I believe that . . .'; W for 'is worth asserting'; ? for 'is worth asserting qua true' or 'I care whether or not . . .'; t for 'truth is worth pursuing'; and I follow Mackie in sometimes reading material implication as the much more involved 'if ... then I am implicitly committed to ---'. I now suggest the following formalization:
For all p
1 Capaap 2 If ap entails q then Capaq 3 ap entails Bp which amounts to 3* CapaBp 4* CapaWp 5* Capa?p 6 ap entails Bt 6* Capat 7 CaNtaaNt from (1) 8 CaNtaBNt from (3*) 9 CaNtaBt from (6*) and (3*) 10 CaNtKaBtaBNt from (8) and (9)
However little this reflects what Finnis intended, it is at least, so I believe, a valid argument, and I have tried to capture Finnis' none too perspicuous presentation. A casual comparison with his version will, however, reveal some interesting differences. He claims that his line (7) comes from (3), whereas my line (7) comes from (1), and moreover my lines (1) and (7) play no role at all in the actual argument. Again my line (8) is a simple consequence of my (3*) whereas Finnis claims to derive his (8) from (3) and (7). Yet again Finnis thinks that line (2) is involved in the derivation of line (9).
Finnis in his later discussion claims that his line (2) is entailed by (1), given "the definitional relation between asserting that p and implicit commitment to whatever is entailed by p. For 'I assert that p' is an instance of 'p'"(p. 26O). This is not exactly pellucid. The definitional relation is one Mackie suggested and it could be formulated 'if p entails q then Capaq'. Replacing 'p' with 'ap' yields 'if ap entails q then Caapaq', which isn't quite my version of (2), but will in fact give it with (1) and the law CKCrCpqCspCrCsq. I submit that the greater degree of formalization I have employed here would have made Finnis' task, and that of his reader, somewhat easier — though it may also have revealed the vanity of his retorsive argument
In my main argument I suggested that it was strange that Finnis did not avail himself of Mackie's results at line (5), though I also suggested that if he had he would have seen the impossibility of getting from 'the truth of some proposition is worth knowing' to 'the truth of every proposition is worth knowing'. I also noted that his crucial claim lacks any determinate quantification. All of Mackie's examples involve explicit quantifiers. I gave reasons for thinking that Finnis would not wish to take refuge in this quantificational indeterminacy, but it is worth asking whether the kind of item Finnis invokes ('truth is worth pursuing') raises any logical problems for the kind of analysis Mackie gave and Finnis adopted.
One noticeable feature of this item is that it is not obviously a matter of an operator on propositions. But there are, arguably, several items entailed by any assertion, and which therefore generate cases of operational self-refutation, but which do not seem to involve weakly prefixable operators. Just as with the operators themselves, there is room for disagreement as to which items belong in this class, but a plausible case can be made for 'there are tokens', 'x exists', 'x is using a language', and so on. But there seems to me to be a natural extension of Mackie's account that takes care of these cases. Let us use 'e' to stand for any such proposition, for which ap entails e. The following proof:
| 1 ap entails e | rule for this class |
| 2 aNe | supposed assertion |
| 3 aNe entails e | by (1) |
| 4 If aNe entails e then CaNeae | cf. (2) in Finnis' argument |
| 5 ae | (4), (3); (2) modus ponens |
| 6 NaNe | (2)—(5),and the rule NKapaNp |
A general moral that one might properly draw from these discussions is that it is worth noticing the logical diversity of modes of self-refutation (and conversely, self-verification). A diet of examples restricted to my e class may encourage one to overlook the more complex cases that involve operators and thereby possible quantifications over propositions operated upon. An instructive example of such an over-restricted data base occurs in an argument by Richard Gale6 who says that if 'I do not promise to do a' is self-verifying then 'I promise to do a' must be self-refuting, which is absurd. Gale's other examples are from my e class, and it is this fact, I suggest, that blinds him to the role of a general performative operator (which one might call 'happy assertion') which is truth-entailing.7 When this is conjoined with explicit performative operators such as 'I promise that . . .' the analysis becomes rather messy, but my present point is that one has to be careful where you put the negation signs in moving from self-verification to refutation or vice versa. In general, nothing follows from the fact that d is able to generate a special kind of self-refutation about what Nd will do (apart, of course from pragmatic self-refutation). Thus, 'it is certain that ...' is a truth-entailing operator, but 'it is not certain that. . .' belongs to none of our special classes.
2
© E.P. Brandon, 2002, HTML last revised 30 December 2002.
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