Why “oughts” are not facts – or what the Tortoise and Achilles taught Mrs. Ganderhoot and me about practical reason

Why “oughts” are not facts – or what the Tortoise and Achilles taught Mrs. Ganderhoot and me about practical reason – Achilles, the Tortoise, and 100 Years

G.F. Schueler

A great deal of the moral philosophy of the last hundred years has been devoted to trying to understand “the relation between `is’ and `ought'”. On the one side, when we are engaged in genuine moral reasoning and debate, we seem to take it for granted that various factual claims support judgments about what we ought or ought not do. We even seem to regard some such judgments as true (and others as false). On the other side, when we reflect on such judgments, it seems difficult indeed to see how either of these things could be straightforwardly the case, in view of the very great difference between factual and evaluative (or normative) judgments. In this paper I will suggest that there is something to be learned about these issues by constructing a kind of practical reason analogue of Lewis Carroll’s famous dialogue between the Tortoise and Achilles (Carroll 1895), and then comparing the two. In particular I will argue that at least one of the issues Achilles’ encounter with the Tortoise raises is just exactly the same issue, the issue of how a judgment about what someone ought to do is related to the grounds that support it, that moral philosophers have struggled with under the title of “the relation between `is’ and `ought'”.

In Carroll’s dialogue at least part of the puzzle seems to be to explain how the Tortoise could fail to be moved (or led) to believe a conclusion even though he believes other things which seem to constitute the strongest possible reasons for believing this conclusion. It will be worthwhile to compare that sort of case, where the question is what someone has reason to believe, with the “practical” case where the question is what someone has reason to do.

In Carroll’s original version, the Tortoise claims to accept the following two propositions.

(A) Things that are equal to the same are equal to each other.

(B) The two sides of this Triangle are things that are equal to the same.

He then challenges Achilles to force him, logically, to accept

(Z) The two sides of this Triangle are equal to each other. Achilles’ tack is to ask him first to agree to the hypothetical

(C) If A and B are true, Z must be true.

This the Tortoise agrees to do, insisting however that since C is something distinct from A and B, which one might fail to accept, it should be written down after A and B as a third premise. Achilles then argues that now the Tortoise must accept Z since if A and B and C are true, Z must be true. This last being yet another distinct hypothetical which one could fail to accept, the Tortoise insists that it be added as a fourth premise:

(D) If A and B and C are true, Z must be true.

To the question of why one should accept Z, Achilles replies that since A and B and C and D are true, Z must be true. But this last, as the Tortoise points out, is yet another distinct hypothetical. And so it goes, or went.

Here is a practical reason analogue.(1) Suppose that as I am about to cross the street on my way to the library, old Mrs. Ganderhoot, who has obviously been standing on the comer in the rain for quite some time, points out the following things to me (each of which, we may suppose, I fully, sincerely and justifiably accept):

(a) Old Mrs. G. herself wants and needs to get across the street in order to cash her meager pensioner’s check for the week.

(b) It is cold and pouring rain.

(c) The traffic is very heavy.

(d) Mrs. G. is such a frail, timid old lady that she could be standing on the street comer well into next month unless someone helps her across.

(e) I myself am about to cross the street on the way to the library.

(f) I could very easily help Mrs. G. to get across the street by merely holding up my hand to stop the traffic and then escorting her across.

(g) Helping her in this way will not “cost” me anything to speak of; that is, I expend no extra money, I don’t significantly increase my chances of being hit by a car, etc.

Still, in spite of all this, I do not help her across the street and indeed am about to simply make a dash through a small gap in the cars when she points out to me that the above facts strongly support (though, she admits, they may not actually entail) the conclusion that

(h) I morally ought to help her across the street in these circumstances.

This stops me in my tracks and, ever ready for a philosophical discussion about morality, I return to the curb. I tell Mrs. G. that I certainly agree that the facts she has so skillfully marshaled seem overwhelmingly to support the claim that I morally ought to help her across the street in these circumstances.

But even before the sigh of relief has left her frail, old lips, I have again stepped off the curb in preparation for darting between the motorcycles now roaring by. Mrs. G. (though still very polite about it) is clearly puzzled. She seems to think that perhaps I am not actually helping her across the street because, even though the facts she has mentioned support the view that I morally ought to help her, some other facts, unknown to her, show that morality requires that I get across the street as quickly as possible, or at least without assisting her. Perhaps someone on the other side of the street needs immediate first aid, for instance. My assurance that this is not the case clearly pleases her. She points out that if I admit that, other things being equal, I morally ought to help her across the street in these circumstances and that there is no moral reason whatsoever not to help her, then morality requires that I help her across.

Naturally I agree with what she says. In circumstances such as those described by (a) through (h), and since there are no moral reasons for not helping her, it certainly seems that I am morally required to help her across the street. I therefore step briefly (as I hope) back onto the curb just long enough to tell her that I agree that

(i) Since there is no moral reason for me not to help, I am morally required to help her across the street in these circumstances.

It seems to me, however, that there is a shade less of the glow of victory in her tired old eyes as she is writing this up (for she has by now gotten out a pad and pen with waterproof ink with which to record her unbroken string of argumentative successes). Nevertheless, just as I am stepping off the curb in order to dash between a convoy of motor homes which is rumbling by, it occurs to her that perhaps there is some other, nonmoral reason for me not to help. Perhaps some great financial advantage will accrue to me only if I cross the street without her. When I assure her that nothing like that is the case, she urges me to accept yet one more proposition:

(j) Since I have no reason not to help, all things considered I should help her across the street.

Always willing to be accommodating, I agree to this too but, unfortunately for her, the lure of the (momentarily) open road proves too great and before she can utter another word I have sprinted across the street and am gone.

In thinking, first, about Carroll’s story, we surely want to distinguish the following three questions:

(1) Do the two original premises, A and B, entail the conclusion Achilles wants the Tortoise to accept, Z?

(2) Given that the Tortoise believes (quite justifiably, let’s assume) A and B, is it reasonable for him to believe Z?

(3) Assuming that it is reasonable for the Tortoise to believe Z on the basis of his reasonable belief of A and B, what is it about this that is supposed to get him to believe Z? That is, we want to know the details of how the fact that it is reasonable for him to believe Z is supposed to explain his coming to believe it (and so how it can sometimes happen that, as in this case, he doesn’t come to believe it).

The answer to the first question is obviously yes. A and B entail Z, as both the Tortoise and Achilles agree when they accept C. It may well be that Achilles is not so clear about this as he should be since to judge by his method of arguing he seems to think that the original set of two premises is somehow made stronger (in the sense of giving the Tortoise more reason to accept Z) by the addition of C, D, E, and the others. But of course that can’t be. A and B entail Z all by themselves. C says that this is so (note the “must”). D says that A, B, and C entail Z (which of course they must if A and B alone do). And so on.

But the fact that A and B entail Z, even when combined with the Tortoise’s acceptance of this fact, and indeed even when we add that the Tortoise reasonably believes A and B, still doesn’t show that it is reasonable for the Tortoise to accept Z. Suppose for instance that Z were something which the Tortoise knew on independent grounds to be false (if, e.g., he had earlier measured the two sides and found one to be longer than the other). In that case the reasonable thing for him to do would be to reevaluate his acceptance of A and B.(2) The question of whether there is an entailment between A and B and Z, though it certainly bears on the question of whether it is reasonable for the Tortoise to believe Z (especially given that he reasonably believes A and B) does not settle that issue. And it is a separate and distinct confusion on Achilles’ part to think that it does. That is, it is one mistake for Achilles to think that adding the hypotheticals C, D, E, etc. to the set of premises somehow makes the argument stronger (in the way in which adding more evidence might make a different sort of argument stronger). But it is a quite different mistake to think that given that the Tortoise justifiably accepts A and B, the only remaining issue, when we are asking whether it is reasonable for him to believe Z, is whether A and B entail Z (or otherwise support Z strongly enough). There is a difference, that is, between the claim labeled “(C)” in Carroll’s dialogue (“If A and B are true, Z must be true”), which merely says that A and B logically entail Z, and a very similar sounding but different claim, that if the Tortoise accepts A and B then he must accept Z. This latter claim is about what is rationally required and could be false even if (C) is true.

There is a third confusion to which Achilles also seems to have fallen victim. For even if it is reasonable for the Tortoise to accept Z (i.e. because it is entailed by things he reasonably believes, there is little or no reason not to believe it, etc.) it doesn’t follow that the Tortoise will accept Z. People (and evidently also Tortoises) sometimes fail to believe things which they rationally should believe and which there is no justification for them not to believe. Sometimes this is explained by simple lack of intelligence or inattention or the like but failure to accept a conclusion can also be motivated. The evidence is all there, and I see it, but it is so damaging to my pet theory, or my friend’s reputation, or whatever, that I simply can’t accept it. Or rather, I “can’t accept” what it implies. There is nothing about the fact that one has overwhelming reason to believe something, and even sees that one has overwhelming reason, that automatically insures that one actually will believe it.

At one point Achilles conveniently makes all three of these mistakes at once, in a single, memorable sentence. Just after he has added the third or fourth extra “premise” to the argument and before he has quite seen the trend of the dialogue, the Tortoise innocently asks him what would happen if one were still to resist accepting Z. Achilles’ reply is that then “logic would take you by the throat and force you to do it” (Carroll 1895, p. 280); a reply which no doubt warms the heart of every teacher of introductory logic who reads it. If only it were so.

If we now turn to the practical reasoning case we find some interesting analogies. But it might be well to first note some disanalogies. The clearest of these is that whereas Achilles is trying to talk the Tortoise into believing something (Z), Mrs. G. is trying to talk me into doing something (help her across the street). That is, Carroll’s dialogue falls in the domain of “theoretical reason”, the one between Mrs. G. and myself in the domain of “practical reason.” A second disanalogy, connected to the first, is that while the “thing” which Achilles is trying to get the Tortoise to “do”, namely believe that the two sides of this triangle are equal to each other, has a propositional content (since it involves acquiring a propositional attitude), the thing Mrs. G. is trying to get me to do, help her across the street, being an action, has no such “content.”

In spite of such disanalogies between these two cases, there are some striking analogies as well. The two most important are also the most obvious. In both cases one person (Achilles/Mrs. G.) is trying to get another (the Tortoise/me) to do something. In each case the attempt to get the other person to do the thing essentially involves argument or reasoning (or perhaps it would be better to say, the giving of reasons). Both these cases are clear, even paradigmatic, examples of one person trying to persuade another by rational argument. At the same time it would be very misleading in either case to think that only arguments in the “logic textbook sense” (where an argument is simply a set of sentences some of which are premises and at least one of which is a conclusion) are involved. In both cases the arguments presented are arguments for doing something, acquiring a certain belief or performing a certain action. These are what are being claimed implicitly to be “supported by reason” or the like. And of course neither a belief (or an acquiring of a belief) nor an action are themselves sentences.

Given these analogies between the two examples, it is not surprising to find that there are at least potential confusions in the practical reason case which are analogous to the ones already listed in Carroll’s example. Let’s take them in the reverse of the order given: Achilles’ third mistake was in thinking that when it is overwhelmingly reasonable to believe something given what one already knows then, as he says, one is forced to believe it, i.e. that it is not possible not to believe it. Here the practical analogue would be to think that when one judged that, all things considered, one should do something, one could not then avoid doing it, or at least making every effort to do it. That is, the practical reason analogue of Achilles’ third mistake would be to deny that weakness of will is possible. Some weakness of this sort seems to have afflicted me in the story above, but whether Mrs. G. makes this mistake is perhaps not clear. Surely the mere fact that she tries to convince me to act by offering reasons for me to do so doesn’t by itself show that she thinks reason is always going to move people. In such a case the reasoner might see all the reasons for doing or believing something, and might believe that they support his doing or believing the thing. And yet he might fail to be moved by all this actually to believe the proposition or to perform the action in question. One of the virtues of Carroll’s paper is that it reminds us that whatever form of irrationality is involved in “weakness of will”, a strongly analogous form of irrationality can arise for beliefs.

Achilles’ second mistake was thinking that when the premises one reasonably or justifiably believes entail a conclusion, it is then automatically reasonable to believe the conclusion. Since this point involves entailment, it only applies strictly speaking to cases where the original premises entail the desired conclusion. But the point is more general. It applies equally, perhaps even more obviously, to cases where the premises support or provide evidence for a conclusion without actually entailing it. The fact that one has strong, even very strong, evidence for some conclusion doesn’t automatically mean it is reasonable of one to believe that conclusion. One might, e.g., discover strong, independent grounds for doubting it.

But there is an analogous mistake that can be made in practical reasoning, though in fact Mrs. G. does not make it. It could arise in either of two places, in the move from (h) to (i) or in the move from (i) to (j). In the first move it would be the mistake of thinking that when there is some moral reason for doing something then you are morally required to do it, period (i.e., roughly, that when you morally ought to do it other things being equal then you morally ought to do it all things considered). This is a mistake, and an obvious one, because the issue of what you morally ought to do may not be settled by the considerations you have looked at. Other moral considerations may outweigh or cancel them. This would happen in the case of Mrs. G. and my helping her in crossing the street if, e.g., someone had collapsed on the other side of the street and I was needed at once to administer first aid. But, as we saw, Mrs. G. took care to rule out this sort of possibility.

An exactly similar mistake is possible in moving from (i) to (j). It would be the mistake of thinking that if you are morally required to do something then that always or automatically settles the issue; this is, in the end, what you should do. This would be to overlook the possibility that some nonmoral factors may outweigh the moral ones, i.e. it is the idea that moral considerations are always or automatically overriding. This is of course a controversial claim in moral philosophy but the question of whether or not it is true is moot in this case since, as we saw, Mrs. G. was careful to rule out the possibility that there was some non-moral reason for me not to help her across the street. So we can set this sort of mistake aside as well.

Achilles’ first mistake is perhaps the most interesting. It was a mistake for Achilles to think that by adding the extra claims C, D, E, etc. he somehow strengthened his argument for Z. To be fair to Achilles we should notice that even though these extra claims don’t make his argument any stronger logically, it was reasonable to expect that at least the first one (C: If A and B are true, Z must be true.) might have had some persuasive effect on the Tortoise, since it is possible that the Tortoise had just not noticed (or had not “fully appreciated” the fact) that A and B entailed Z. (After the failure of C to persuade him, of course, that expectation was less reasonable. Though this point is clearest when, as in Carroll’s story, the premises in question (A and B) entail the conclusion being argued for (Z), the point is equally valid for “evidential” arguments, i.e. where the premises somehow support the conclusion but do not entail it. If some truths, say A’ and B’, provide strong or even overwhelming evidence that Z’ is true, it adds nothing to the evidence if the claim (call it C’) that A’ and B’ provide overwhelming evidence for Z’ is added by the person making the argument (Achilles’?).

Though the three claims Mrs. G. adds are quite different from the ones Achilles keeps heaping on, interestingly similar problems afflict them. The question here is whether, in adding her extra claims, (h), (i) and (j), Mrs. G. has in any way strengthened her argument, beyond the “persuasive” point that I just may not have noticed these things. Let’s concentrate on (h) to start with. Does her claim that I morally ought to help her cross the street add anything to her argument (given in (a) through (g)) for my doing so? The clearest case will be when “other things are equal”, i.e. when (h) is true and true just because (a)-(g) are true.(3) So let’s assume both these things. One way (I think the most obvious way) to take (h) here would be to read it as saying, or at least entailing, that I have some reason (or some “moral” reason) to help Mrs. G. across the street. But if that is what (h) means then it won’t add anything to Mrs. G.’s argument, any more than C, D, etc. added anything to Achilles’ argument. On this reading (h) says that I have reason to help, and of course I have reason to help only because of the situation as described in (a)-(g). It is this situation which gives me reason to help Mrs. G. (if anything does). (h), on this way of understanding it, just says that I have reason to help.

So even though it might be persuasive of Mrs. G. to point out to me that (h) is true (that I have a moral reason to help, that I morally ought to help), because I may not have noticed this point, the truth of (h), thus understood, does not give me any further reason to help, beyond what is provided by the truth of (a)-(g). (h) merely says that I have a reason. It doesn’t, so to speak, provide or describe a reason (in the way that, e.g., (a) does). So (h) adds nothing to the strength of Mrs. G.’s argument. If we were to deny this, and hold that even though (h) is only true because (a)-(g) are, still (h) somehow strengthens Mrs. G.’s argument for my helping her, in the sense of providing some further element not contained in (a)-(g) which gives a further reason for me to help, then we would find ourselves in a regress analogous to the one Achilles gets into by thinking that his extra claims strengthen his argument for Z. For if the truth of (a)-(g) are all that make the “ought” judgment (h) true and yet the truth of (h) gives a further reason, beyond that of (a)-(g), for my helping Mrs. G., then in order to completely spell out the argument here in full detail, so as not to leave any reasons out, we would have to add (h) to the premises and express the conclusion with some further “ought” judgment, say (h’), which will be true because (a)-(g) and (h) are true. But then the same question arises again for (h’). (h’) is now in the same relation to (a)-(g) and (h) as (h) itself was to (a)-(g). Hence (h’) should also add a further reason for me to help Mrs. G. in just the way (h) itself supposedly did. So like (h), (h’) in its turn should be added to the premises if they are to be a complete list of the reasons for helping Mrs. G. across the street. And then of course as a conclusion to this new argument there will be a still further “ought” judgment, say (h”), which will be true because (a)-(g), (h) and (h’) are true. And so on.

The lesson here is that just as it was a mistake for Achilles to think that adding his extra claims (to the effect, really, that his earlier premises entailed the desired conclusion) somehow strengthened his argument, equally it would be a mistake for Mrs. G. to think that the addition of the claim that I morally ought to help strengthens her argument in any way, in the sense of giving me any further reason to help.

This same point applies even more obviously to (j) (which was, roughly, “All things considered, I ought to help her across the street”). Presumably (j) says, or at least entails, that I have sufficient reason to help and that I have more reason to help than not.(4) Clearly we cannot take this to mean that the fact that all things considered this ought to be done is yet another reason for doing it, beyond those given by (a)-(g), (h) and (i). For if we say that this fact, that reason is, so to speak, on the side of my helping, is itself straightforwardly a reason for me to help then it looks as if the argument for my helping won’t be complete until we list this fact among the premises. But then as soon as we step back to look at this new set of premises and conclude that

(j’) These premises show that this is, finally, what I ought to do

(or the like) we will have yet another new reason which will have to be added to the list for it to be complete. And so on just as with (h). Thus true, final or all-things-considered “ought” judgments cannot themselves be reasons for performing whatever act is in question. The mistake of thinking that they are would lead one into a regress analogous to the one in which Achilles finds himself caught.

There is a moral here for moral philosophy. In the century following the publication of “What the Tortoise Said to Achilles” a very large percentage of the effort expended in moral philosophy has been devoted to trying to make sense of one or the other or (especially) both of two features of moral judgments which ordinary use of those judgments seems to presuppose but which seem, individually, quite puzzling and, jointly, virtually impossible. Moral judgments seem both to be “about the world” and “action guiding.” There would be no point here in going over the history of “metaethics” in this century, but I think it safe to say, that many philosophers who have concentrated on how moral judgments can be action guiding have virtually given up the hope of showing them to be about the world (or straightforwardly true, etc.).

My suggestion is that for judgments about what we should, or ought to (or even must) do, Carroll’s little dialogue and its “practical reason analogue” show us that if there really is a puzzle here, it is a puzzle about rationality itself, and it is very widespread indeed. Moral philosophers who discuss the nature of “ought” or “should” judgments (“must” is usually ignored) have generally held such judgments to be about morality, sometimes also acknowledging that judgments of prudence or etiquette can be couched in these terms as well. It is almost universally taken for granted, however, that such judgments are about actions. But this is just mistaken. Judgments about what we should, or ought to, or even must, do are made, in exactly the same sense, about beliefs, hopes, fears, and wants, as well as actions. In fact these locutions apply to anything we can “do” which is subject to rational criticism. What such judgments say is that the person in question has some (or enough, or overwhelming, etc.) reason to do, believe, hope, or fear whatever is in question.

So there should be no more (or less) of a puzzle about how it can be true (or false) that I ought to help Mrs. G. across the street than there is about how it can be true that the Tortoise ought to (indeed must) believe or “accept” the things entailed by what he already believes. And there should be no more (or less) of a puzzle about how my acceptance of the thought that I should help Mrs. G. across the street can actually get me to do so (as well as sometimes fail to) than there is about how the Tortoise’s acceptance of the thought that if he believes A and B he must believe Z can actually get him to believe Z (as well as sometimes fail to).

There can be no genuine doubt that judgments of this latter sort are frequently and straightforwardly true. (You ought to doubt that your car will make it in to town, given the way the engine sounds. You ought to suspect that our team is not going to win many games, given the difficulty of their schedule and the recent injuries to some of our best players.) Similarly, by far the most frequent way of explaining why someone in fact believes (or wants, fears, suspects, etc.) something is by citing the evidence available to that person which makes it the case the he or she should believe (or want, fear, etc.) just this. Such explanations are so common, in fact, that we virtually never notice them. (Why does the coach think we won’t win many games this season? Well, he knows how difficult our schedule is and he knows that several of our best players are injured.)

So moral philosophers who worry about how practical “ought” judgments could possibly be true, and about how the acceptance of such judgments could possibly get those who accept them to perform the action in question, should take heart. Such judgments of rational assessment are among the most common in life, applying not only to actions but to everything humans do that is subject to rational assessment. So either the same sort of answer is available for practical rationality as is available everywhere else, or the same sort of difficulties that have been encountered in practical rationality arise everywhere else as well. (I think it is the former, but I suppose Achilles might be forgiven for suspecting that it is the latter.)(5)

Philosophy Department G. F. SCHUELER University of New Mexico Albuquerque, NM 87131 USA

(1) A somewhat different version of this example appears in my The Idea of a Reason for Acting (1989, pp. 21-23) (2) This point is made by Gilbert Harman (1970). (3) The “because” here is thought to be problematic since we don’t want to say that (a)-(g) entail (h), presumably. But we also don’t want to say that A’ and B’ entail C’ (which says “A’ and B’ provide overwhelming evidence for Z'”) . Yet surely C’ is true, at least when “other things are equal”, just because A’ and B’ are. (4) Both clauses are needed. One might have sufficient reason to do something without it being the case that, all things considered, one ought to do it, since one might have still better reason to do something else. (5) This paper was read at the “Achilles and The Tortoise” Conference at Glasgow University, July 1995. Garrett Cullity responded. Brom Anderson, Barbara Hannan and Raul Orayen provided helpful comments on an earlier draft.


Carroll, Lewis 1895: “What the Tortoise Said to Achilles”, Mind, 4, pp. 278-80.

Harman, Gilbert 1970: “Induction”, in Swain, M. (ed. , Induction, Acceptance and Rational Belief. Dordrecht: D. Reidel, 1970, pp. 83-99.

Schueler, G. F. 1989: The Idea of a Reason for Acting. Lewiston: Mellen.

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