In 1895 Lewis Carroll wrote his famous Mind article ‘What the tortoise said to Achilles’. The problem he raised can succinctly be put like this: can logic make the mind move? Or, less enigmatically, how do we describe what is wrong with the tortoise’s argument that, however many premises Achilles has him accept, he always has space to refrain from drawing the conclusion?

In this paper I am not so much concerned with movements of the mind, as movements of the will. But my question bears a similarity to that of the tortoise. I want to ask whether the will is under the control of fact and reason, combined. And I shall try to show that there is always something else, something that is not under the control of fact and reason, which has to be given as a brute extra, if deliberation is ever to end by determining the will. This is, of course, a Humean conclusion, and the only novelty comes in the way I wish to argue it. For I believe that many philosophers think, erroneously, that Hume relies on a naive and outdated conception of facts, or an even more naive and outdated conception of reason, in order to put passion on their throne. My tortoise defends Hume: what we do with our premises is not itself construed as acceptance of a premise.

As it stands the project is only described metaphorically. Presumably everything, including movement of the will, is under the control of facts in some sense, for even if they are only facts about our physiology or chemistry, still, they make us move. I am interested of course, only in cognitive control, or control by the apprehension of fact and reason.
 
 

Day 1

Achilles, then, had overtaken the tortoise and was sitting comfortably on its back. ‘You see’, he said, ‘the distances were constantly diminishing, and so...’

‘But if they had been constantly increasing?’; the tortoise interrupted, ‘how then?...Well now, would you like to hear of a race-course, that most people fancy they can get to the end of in two or three steps, while it really consists of an infinite number of distances, each one longer than the previous one?...let us take a little bit of an argument for acting’
 
 

(P) I would prefer eating lettuce to eating souvlaki

(B) The moment of decision is at hand

(Z) Let me choose to eat lettuce rather than souvlaki!
 
 

‘Well’, continued the tortoise, ‘there is no question of accepting (Z) as true, but there may be a question of accepting it. Let us agree that accepting (Z) amounts to actually doing whatever is involved in choosing lettuce rather than souvlaki. We accept (Z) only if the will is determined, and an intention is formed. Are we to suppose that if we accept (P) and (B), then we must accept (Z)?’

‘Wait a minute’, said Achilles, ‘I don’t want to rush you. It occurs to me that some philosophers make a distinction between what you prefer and what you think you ought to prefer, or would prefer if you were ideally placed, for a tortoise. Perhaps this affects the issue.’

‘If you like’, said the tortoise. ‘I too hate this modern fad for rushing past anything like that. Let us put it in’:
 
 

(P) I would prefer eating lettuce to eating souvlaki

(M) I think it is right to prefer lettuce to souvlaki

(B) The moment of decision is at hand

(Z) Let me choose to eat lettuce rather than souvlaki!
 
 

‘That’s better!’ said Achilles. ‘That certainly wraps it up for (Z). Surely you must accept (Z) if all those are true!’

‘I don’t quite know’ said the tortoise sadly. ‘Sometimes, well, I am not sure how important rightness is. I certainly get these urges to do what I think is wrong, don’t you know. I am really quite good at what you Greeks keep calling akrasia; in fact I rather enjoy it.’

‘Good heavens’, replied Achilles sternly yet compassionately. ‘if there is one thing modern moral philosophy will tell you, it is that any such behaviour is quite irrational. The norms of reason are foundations for the norms of ethics.’

‘And we don’t want to be unreasonable, do we?’ said the tortoise. ‘In fact, we had better add it, just to make sure.’
 
 

(RM) I think it is rational to do what I think is right
 
 

‘There we are’, announced Achilles in triumph. ‘reason prevails!’

‘Well, that is certainly a change’ said the tortoise ‘and yet sometimes, well, I am not sure how important rationality is. I certainly get these urges to act against reason, don’t you know. I am really quite good at that kind of akrasia; in fact I rather enjoy it.’

‘Holy Apollo!’ exclaimed Achilles. ‘Do you mean you have been reading the Romantics, so many millenia before their time? Are you in favour of short-termism and spontaneity, and against prudence and economics? Or is it something else?’

‘I don’t know’ said the tortoise, but perhaps you can explain to me: ‘must I be rational’?

‘Oh certainly’ said Achilles, ‘you must if...well, if you want to be rational, you know’

‘I love hypothetical imperatives’, said the tortoise. ‘but I am not sure this one is going to help. Still, we could make sure that rationality and ethics pull together, if you like’, he conceded helpfully.
 
 

(MR) I think it right to do what I think is rational
 
 

‘Hmmm’ said Achilles. ‘I hadn’t expected to put that in, but it is terribly decent of you to let me. And now at last we are home and dry!’

‘Only’, said the tortoise apologetically, ‘I get so terribly confused. We had to add (M) and I can’t help wondering that although I am sure it is right to do what is rational, these fits of akrasia still afflict me so chronically. I must have been badly brought up’ he added bashfully.

Achilles frowned as he replaced his pencil with a new one. ‘I think that is probably a bit morbid’ he said. ‘Surely in general you prefer to do what is right and rational?’ ‘Perhaps we should add it’, encouraged the tortoise:
 
 

(P’) I prefer to do what I think it right and rational to do.
 
 

‘And now’ said Achilles in triumph again, ‘We really are getting somewhere. The last time I talked with you, a century ago, you made me keep adding different premises! But now there is simply nothing more to add!’ And he did a little dance.

‘I love the way you move yourself’ said the tortoise, sitting comfortably. ‘All I admit is that I prefer to do what is right and rational. But then, after all, I preferred lettuce to souvlaki. And we had to add a bit to that, didn’t we?’ he laughed, modestly.

‘Sacred Zeno!’ expostulated Achilles. ‘You are not going to make me add another round are you! I can see it coming: you need that it is right to prefer to do what you think it is right and rational to do, and so on and so on. You really are the most stubborn animal.’

‘Well, I am a bit careful’ confessed the tortoise. ‘And I don’t really know that I am all that confident that it is right and rational to prefer to do what I think it is right and rational to do. After all, many people are wrong and stupid in preferring to do what they think it is right and rational to do. I wouldn’t want to act while I am worried in case I am like them!’

But great Achilles had flown to the libraries to collect some volumes on The Theory of Rational Choice. Munching some lettuce, the tortoise awaited his return.
 
 

Day II
 
 

‘You know’ resumed Achilles, ‘this whole business is off on the wrong foot. We have been talking as if there is a gap between preference and actual choice. Whereas I now read that in the best circles it is done to believe in the theory of revealed preference. Which means we read your preference back from your choice. It is not an antecedent state whose apprehension determines choices -- I admit that yesterday’s conversation made that idea puzzling -- but simply a logical construct from the choices you make!’

‘Pardon me’ said the tortoise. I must have misunderstood something. ‘Don’t these economists and game theorists get paid for giving advice -- advice about what to do?’

‘Absolutely’, said Achilles. ‘They are very rich and regarded as very good at it.’

‘Tell me more’, said the tortoise admiringly.

‘Well’ responded Achilles putting on his lecturer’s gown, ‘it seems to go like this.’

‘The reasoning behind talking of revealed preference comes in two parts . In the bad old days, it goes, it was thought that ‘utility’ wil be a Benthamite, empirical quantity which happened to be the object of desire, or ought to be the object of desire. But utilities so conceived prove both empirically and philosophically bogus, as indeed Bentham might have learned from Bishop Butler . It is neither true nor useful as an approximation that people or tortoises act so as to maximize the intensity or duration of some state of themselves. They do not even always act with their own interests in mind, where these interests are construed as states of themselves. Rather, we see them as having an interest in some object when that object figures in their decision making. But objects here include states that are not states of the subject: the survival of the whales, or the relief of the famine, or the death of the blasphemer, or the success of a friend. Indeed, notoriously, unless this is so the life resulting is apt to be unenviable and the selfishness is self-defeating. So let us instead reverse the equation: utilities are no longer empirically given, but are simply constructs from mathematically tractable ways of handling preferences. That is, given very weak assumptions an agent with an ordering of preferences over each of some set of options can be represented as if she had attached measurable ‘values’, called utilities, to those options. The provision of a scale is similar in principle to that of providing numerical measures for weights, given only the results from a balance. A balance is an empirical determination of when one object weighs at least as much as another. The results of tests for whether one object is at least as heavy as another can be presented numerically, with the numbers representing ‘weights’ of the objects in the set. An element has at least as great a weight as another if and only if the other does not outweigh it, which is to tip the balance against it.’

‘So if we have pairwise preferences across choices in a set, we can represent their utilities numerically. But what corresponds to the empirical results from the balance, telling us when choice a is preferred to choice b? The orthodox answer amongst economists and game theorists to accept the theory of revealed preferences. This was initially defended in the work of the economist Samuelson, and holds that preferences themselves are not antecedent psychological states that happen to control (most) decisions. Rather, true preferences are those that are revealed by decisions . It is, after all, a truism that to know what you or anyone else wants, see what you or anyone else chooses, or would choose given suitable options. To know that you prefer oil to butter, you see whether you choose it, at least when nothing further hangs on the decision. The theory of revealed preferences is perhaps less popular among philosopher than economists. But we shall see below good reason for accepting it, for there is really no other candidate for the necessary empirical test. Putting the two foundation stones together then, we have:
 
 

(Util) A utility function is defined such that the utility of a is at least as great as b if and only if a is weakly preferred to b (i.e. preferred to b, or at least as much as b). Such a function can be defined over a set of options if preference satisfies two consistency conditions: for all outcomes a, b either a is weakly preferred to b, or b to a (totality), and if a is weakly preferred to b, and b to c, then a is weakly preferred to c (transitivity).
 
 

(Revpref) Choice behaviour is primitive. If a player makes choices, then he is making choices as though he were equipped with a preference relation which has that choice preferred to others. An eligible agent is always interpretable as though he were seeking to further a preference.
 
 

In a nutshell, the first part of the approach makes utilities ‘logical constructions’ out of preferences, while the second makes preferences logical constructions out of actual choices.’

‘To whom do Util and Revpref apply? To anyone with consistent, transitive preferences over a set of options. I shall call such persons eligible persons (it is vital not to confuse the issue by calling them rational, as is frequently done). An ineligible person would be someone who cannot be interpreted in terms of utilities, just as a balance that cannot weigh some element in a set, or that weighs a > b, and b > c, but c > a cannot deliver a set of weights defined over the set. It is of the utmost importance, then, to realize that there are not two sorts of players in a prisoners’ dilemma, or other game theoretic structure, the eligible ones and the ineligible ones. ‘Ineligible’ refers not to a kind of player, but to someone who cannot be interpreted as playing at all. An ineligible player is like someone who approaches chess by knocking over the board. It is however, often a matter of judgement whether someone who appears to be ineligible through having intransitive preferences is so really, or is best interpreted as having redefined the options in front of her, but this is not our concern in what follows.’

‘Of course, both Util and Revpref have not gone uncriticized. Amartya Sen, for example, introduces notions of sympathy (having your welfare affected by the position of others) and and individual’s commitments (conceived of as standing outside, and even in opposition to their own welfare) as independent pressures on action . He points out that preference, in the economics literature, has two liaisons: one is with choice, but the other is with welfare. That is, increased preference satisfaction is supposed to increase welfare, and he denies that a notion of preference based on Revpref can fulfil this second condition. For people may behave as if they had certain preferences (those are the preferences we would read back from their behaviour) when their welfare, or even their expected welfare, would be better served if they behaved differently. Sen also believes that this undermines the authority of an approach based on Util. And if it does so, it also undermines Revpref, since if because of sympathy or commitment an agent acts against his preferences (what he would really like to do, if only the situation allowed it), then of course his action will not be revealing those preferences.’

‘The orthodox game theorist’s response is that their framework is quite elastic enough to encompass whatever motivations we believe to exist. As I have already sketched, there is no need to deny that a player may care about other things than their own interests, real or perceived, or their own welfare as opposed to that of others. In the apt phrase of David Gauthier, "it is not interests in the self, that take oneself as object, but interests of the self, held by oneself as subject, that provide the basis for rational choice and action". Choice is the upshot of whatever the player cares about, and as I have sketched, utility derives from choice. So it is wrong to criticize either axiom by reminding ourselves of the heterogeneous nature of desire. Rather, we must simply be careful to build any apparently ‘exogenous’ or external independent desires into the payoffs represented in the choice situation.’

‘The same caveats apply if we start to contrast preference with principle or with conscience. There is certainly a vernacular distinction here, for we talk of being obliged to do what we do not prefer to do. But the concepts defined by our two axioms do not match this distinction, and are not refuted by it. Rather, preference, revealed by choice, may include the preference for acting on any specific principle: the preference to keep a promise, or keep a vow to God, or to avoid the gaze of the man within, or the preference to do one’s bit, the preference for being the man who bought the Brooklyn bridge, rather than the man who sold it, or even the preference to try to live up to our better selves. The better way to describe the ‘conflict’ between a narrow sense of preference and what happens when principle is introduced is to say that sometimes we are obliged to do what we would not otherwise have preferred to do; but this leaves it open that now, in the presence of the obligation, our preference is actually that we conform to the requirements of obligation or duty. The counterfactual preference, that we would have had, had we not made the promise or felt obliged to cooperate, or whatever it is, is not our all-things-considered preference.’

‘Splendid, absolutely splendid’ interrupted the tortoise, a little sharply. ‘But now tell me how this translates into advice, for this is what we were hoping to find’

‘Well’ said Achilles, confidently ‘consider the familiar prisoner’s dilemma’.
 
 

                                                             A

                                             Hawk             Dove

                        Hawk             1,1                 0,3
B
                        Dove              3,0                 2,2
 
 

‘Each player acts independently, causally, of the other, and each knows the other’s utilities. Now, looking at this the game theorist can advise you to be a hawk. For whatever your opponent does, you do better by playing hawk. Yet this advice has been contested, and indeed some people think it is rational to play dove.’

‘Well, well,’ said the tortoise. ‘If the advice has been contested, then it must be significant advice! But tell me, to whom does it apply exactly?’

‘As we have explained’, said Achilles huffily ‘to anyone eligible, and who is presented with the game.’

‘Timeo Danaos et dona ferentes’ said the tortoise, smugly. ‘Tell me, what would happen if I didn’t follow the advice to choose hawk? Wouldn’t I reveal a preference for being a dove?’

‘Well, yes’ admitted Achilles, somewhat impatiently.

‘And if that is so’ continued the tortoise impeturbably ‘how does it happen that these little figures you have in the boxes, are the right ones? I mean, I can see how they might represent money, or years in prison or something but the game theorist is surely not telling me that it is rational to care only about money, or years in prison. I thought these figures represented the sum total of my preferences. But since these are revealed by choice, if I play dove, then they cannot be right’

‘Explain to me’ said Achilles, tottering slightly.

Here, the tortoise paused to put on the lecturer’s gown. ‘Suppose a player makes the dove choice. Then he preferred one or both of the options in which he acts as a dove to the others; by Revpref we must construct a utility function in accordance with that preference, and hence he was not actually in a prisoners’ dilemma. In the terms often used, his decision problem cannot have been accurately ‘modelled’ by presenting him as if he were in a prisoners’ dilemma. For a prisoners’ dilemma is defined so that the hawkish utilities outrank the doveish ones, and that in turn simply means that the hawkish options are the ones that get chosen. The conclusion ought to read that it is a tautology that an eligible player will necessarily choose hawk in the Prisoners’ dilemma.’

‘Aha’ said Achilles, ‘it is not quite as simple as that. For in such strategic problems, we have to consider the other player’s likely choice. Imagine, if you will, the poor agent lurching towards a choice, and knowing that on the other side of a mirror, as it were, but quite independently, his twin is doing the same. It will be better all round if they plump for dove, in spite of the way that such a choice is dominated. Mightn’t they each do so?’

‘Oh well’ replied the tortoise, ‘If they know that it is a real twin, who will magically do exactly the same as they do, then the upshots are restricted to the symmetric ones, and playing dove dominates. But in real situations they don’t know this, and they might do anything. If they have a minute to chose, then recalling what their twin is doing they might change their mind once in the first thirty seconds, again in the next fifteen seconds, again in half the remaining time, and so on. It would be like one of those lamps going on and off ever more quickly. I seem to remember you once modelled your running on just such a contraption’ he said, nostalgically remembering his first foray into philosophy, more than two thousand years ago. ‘Heaven knows where they end. All I am saying is that if they do go haywire, as well they might, and plump for dove, then if anything they reveal different preferences, and hence expected utilities, from the ones on show.’

‘For example’, continued the tortoise, ‘when on p. 27 of his book Binmore stresses that ‘it is tautological that homo economicus maximizes all the time’, we might think that this is peculiar to that kind of homo, or equally to testudo economicus, whom we then may or may not want to imitate. Whereas in the light of Util and Revpref, it is tautological that any eligible agent maximizes all the time. And in interpreting this it is well to remember the extremely weak imposition that consistency involves: only that you have transitive preferences over the entire set of options in play. In particular consistency does not entail any particular attitude towards risk, or towards other people, or action on principle. Nor does it entail constancy, or consistency over time, which means making the same choice on later occasions as you made on earlier ones.’

‘More importantly, it is to be remembered that inconsistent players are of no interest. For if a player is genuinely inconsistent, in any way that matters to the game, then we will be unable to construct a function from preferences to utilities. In such a case we cannot say what the utilities of the agent are under different choices, and the interpretation of him as in a prisoners’ dilemma, or any other kind of specific decision theoretic problem collapses. So in fact the tautology applies across the board: it is tautological than any player who can be intepreted as being in a prisoners’ dilemma, chooses the dominant strategy. There exists no theory about non-eligible players, so the restriction to eligible players is insignificant.’

‘Surely the game theorists know all this?’ queried Achilles.

‘Well’ said the tortoise, shaking his head mournfully, ‘they tend to be forthright about the official framework in some places, but more coy when they are offering all that richly-paid advice. For example Binmore frequently describes himself as arguing against those who think that strongly dominated choices are rational (p. 174); he sometimes describes his opponents as supposing that ‘out of equilibrium play can be sustained in the long run’ (p. 175), and by contrast presents himself as the realistic, Hobbesian man who is hard-headed enough to know that eventually if we can get more for ourselves, we will be tempted to do so. Theorists such as Gauthier and McLennan, who think it is sometimes rational to choose the dominated strategy, are particular targets.’

‘But isn’t that as it should be’, said Achilles, fumbling a little.

‘Well, I think it should be clear’ replied the tortoise, ‘that these attitudes are thoroughly incoherent. It is not that out of equilibrium play cannot be sustained in the long run, or needs psychologies that we have not got, or is the private preserve of benighted and irrational bleeding-heart Kantians, but that it cannot happen at all. In out of equilibrium play in the prisoners’ dilemma, an agent chooses the dominated strategy. But by Util and Revpref this is impossible: if an agent chooses a strategy, then this shows that the utility attached to it is higher than that attaching to any other strategy over which it was chosen.’

‘Hmmm’, said Achilles. ‘And yet, hasn’t the enterprise of bringing rational weight to bear against selfishness made the prisoner’s dilemma the central parable of modern political theory? How can that be so if you are right?’

‘Oh, it has nothing to do with rationality’ said the tortoise. ‘Or even being good. The same point applies even if you want to be bad’, and he shuddered slightly, which is hard for a tortoise.

‘Explain’, said Achilles wonderingly.

‘Well, take blackmail’ said the tortoise. ‘We can think of it in extended form in terms of a sequence of plays, one in succession by each of two players, Adam and Eve. At each node the player has to play one of two options, hawk or dove. In the following diagram, plays succeed each other in time. Hawkish behaviour is to the left, and doveish to the right. Adam’s payoffs are described first. We are assuming as usual that each of Adam and Eve’s payoffs is known to themselves, and to the other.

We can draw the choices thus:
 

Blackmail        (Adam's payoff is represented first)
 

        t1            A
----------------------
    Dove          1,2
    Hawk           *  >>>>>>>>>>>>>>>>>>>>    t2            E
                                                                         --------------------
                                                                           Dove        2,1
                                                                           Hawk       0,0
 

The story is that before the game starts Eve has committed an indiscretion. If Adam does nothing (doveish) he has 1 unit and Eve 2. If he blackmails Eve (hawkish) and she submits (doveish) he takes one of Eve’s units. But if she does not submit (hawkish) she blows the gaff on him, revealing him as a blackmailer, but also revealing her own indiscretion, leaving them both worse off, in the 0,0 finale.’

‘Orthodox decision theory has us reason as follows. In Blackmail, eligible Eve will not play the final hawkish option. For doing so represents simple loss. Eligible Adam knows that this is so. Hence he plays hawk, and since she then plays dove, his blackmail is successful.’

‘Suppose now that Adam knows in advance that this is the matrix. Then he knows in advance that eligible Eve will not choose to be a hawk when it comes to her turn. For it would be a contradiction (by Util and Revpref) for Eve to choose 0 units of utility when she can have 1. So eligible Eve will play dove, and eligible Adam will play hawk. For, once more, it would be a contradiction for Adam to play dove when he could play hawk, leaving him with 1 instead of 2. So Adam does not face a choice: once he knows the matrix, he knows what is going to happen.’

‘Now remember that expert game theorists endorse both Util and Revpref, and Binmore, for example, implies that all the rest of their kind do so as well . He believes that the "advantages of the methodology in clarifying the underlying logic are overwhelming". What this means is that the game theorist takes care of any facts about psychologies at the modelling stage (see esp. p. 162). We have successfully modelled a set of players only when they have no interests (nothing they care about) that are unrepresented in the game’s payoff structure. Often persons with other elements in their psychologies will not be in such games when others are.’

‘So what Eve needs to be is someone who is not modelled correctly as being in this game. In short, she needs to present herself as being vengeful and proud, disinclined to submit to blackmail, preferring her own financial ruin and that of Adam to the feeling of having been done down by him. Should she know she will face such situations regularly, she needs to cultivate a nice public vicious streak. Of course, if she hasn’t done that in advance, or had it done for her in a good school, she will be a plausible target for blackmail, poor thing.’

‘Good lord, or rather Zeus’ said Achilles, correcting himself quickly. ‘I suppose people like Gauthier would have to say that it is rational to be vicious.’ And he shuddered in his turn. ‘Let me try to sort it out. It certainly qualifies what we might have thought was meant by calling a strategy rational, or indeed calling the situation a game that calls for choices and strategies. We might have thought that if we talk of a game, and someone tells us that a particular strategy is rational, then we can interpret that as tantamount to giving us permission to follow it, or if it is uniquely rational, telling us to follow it. You do not in deliberation draw up two lists; one of what to do in given circumstances, and the other of what it is rational to do in the same circumstances . But in game theory as it is now being conceived, nothing can be translated into advice. For suppose we are ‘advised’ to follow the dominant strategy. This is null advice, equivalent to: behave so that a tautology is true of you. So if we don’t follow the advice, then our choice reveals that it wasn’t that game. But if it wasn’t that game then the advice was inapplicable, and if the advice was inapplicable, then there was no point in following it in any event, for the game theorist had failed to model the situation properly. As Wittgenstein might have said, anything could accord with the advice, and that means that no advice was given. The economists’ slogan ‘Maximize!’ turns out not to be an injunction at all, for nothing could count as failing to follow it . So the promise that we can learn something about rationality by these means collapses. Or, if we prefer it, the idea that the notion of rationality gains any purchase here is refuted. It is inevitable that so-called countertheoretical actions do not reveal the irrationality of the players, but the inadequacy of this application of the theory.’

‘You always did catch up fast’ said the tortoise admiringly, ‘And it also suggests that the question is not so much one of whether it is rational for Eve to be vicious, as whether she has been educated so that she and her peers thrive in the situations in which they will be put. Some have, some haven’t’, he added sententiously, and sat down, which is also quite difficult for a tortoise, and ate some more lettuce.
 
 

Day III
 
 

‘Look’ said Achilles, forlornly contemplating his bonfire of books on The Theory of Rational Choice, ‘decison making is at least under the control of fact and reason in another way. There will come after us one greater than us, who will show that it is a dictate of pure practical reason that we treat everyone as an end in themself. And his name shall be called Immanuel. But let’s not start on that’, he added hurriedly.

‘And every tortoise, I hope’ added the tortoise.

‘If they are rational’, assured Achilles, muttering something under his breath.

‘Tell me’, said the tortoise, ‘it sounds nice and impartial. Must I be impartial?’ he asked, innocently.

‘Absolutely’, said Achilles piously. ‘Even Hume, whom you somewhat resemble, realizes that we have to take up a common point of view. In a conversation with anyone else about what to do, there is a point where we must cease speaking the language of self-love, and correct our sentiments by invoking common standards, whereby we judge things and persons as they affect those surrounding them.’

‘And the penalty if we don’t?’ asked the tortoise.

‘Well, practical reasoning could not go forward’ said Achilles, ‘and we would lose the benefits of cooperation, or of putting the first person plural in place of the first person singular . We couldn’t even row boats together.’

‘We wouldn’t want that’, said the tortoise sociably. ‘But I remember a couple of days ago we thrashed out wants and preferences, and I am afraid I remained unmoved, if you remember. So what is new?’

‘Kant improves upon Hume’ said Achilles enthusiastically. ‘He shows how pure practical reason dictates respect for the law. For impartiality, fairness, and all that. All sorts of good things’ he finished lamely.

‘It sounds appetizing’ agreed the tortoise, ‘but tell me about this dictation and this respect. What is my awful fate if I find this respect is not actually dictated?’

‘Well if you don’t respect the law’ said Achilles, ‘you will not be free, not an autonomous self-governing tortoise.’

‘And I expect at least you are going to tell me that I wouldn’t want to be anything else’ chimed in the tortoise, ‘but that is not going to get us much further, is it? Presumably you really would like to tell me that it is contrary to reason not to respect the law, thereby achieving freedom and self-respect. And I doubt if I am going to believe you. For I believe that Kant will one day tell us that
 
 

‘But you are a just and fair and compassionate tortoise’, reminded Achilles.

‘You’re too kind’, said the tortoise blushing modestly. ‘But it is true. You will know how Adam Smith writes that
 
 

‘But it is not rational’ wailed Achilles, beating his head on the tortoise’s shell

‘Just as well’, said the tortoise, ‘given where that leaves us. And it is lucky my shell is so solid.’
 
 

Day IV
 
 

‘Listen’, began Achilles, his locks dishevelled by what appeared to have been a sleepless night. ‘At least you respect means-ends reasoning do you not? And quite possibly there exists argument that if you do that then you cannot remain unmoved in other ways. Once you have some musts then you have to allow others.’

‘Respect means-ends reasoning?’, queried the tortoise, ‘Explain to me what you mean’

‘Well, suppose you want some of that lettuce across the road. And you apprehend that the only way to get it is to cross the road, since lettuce is even less likely to move than you are. In other words, you know that if you want the lettuce, you must cross the road. So it follows that you conceive yourself under a necessity to cross the road. There would then be a kind of inconsistency in not crossing the road.’

‘I think I only know one kind of inconsistency’, said the tortoise. ‘The kind that goes p & -p. Do you mean I am contradicting myself? It doesn’t feel as if I am.’

‘But don’t you agree that if you want the lettuce you must cross the road? And you want the lettuce (and the moment of decision is at hand)...so you must cross the road.’

‘By modus ponens’ said the tortoise, a nasty glint coming into his eye.

‘Grrr’, said Achilles warningly.

‘Alright’, said the tortoise backing off relatively hastily, ‘but it isn’t even modus ponens is it? I mean, if I want a million pounds I must buy a lottery ticket, and I do want a million pounds, but I don’t see that I must buy a lottery ticket. It is one of those off-colour conditionals where musts and oughts make the conclusion non-detachable. And in fact, I am not going to buy a lottery ticket’ he concluded with a flourish.

‘Aha’, replied Achilles, ‘that must mean you want something else more, such as avoiding lotteries or sitting still’

‘I rather think we are back in the world of Revpref’ said the tortoise. ‘Of course I recognize that if I am to get what I want, I must adopt the only means available. If I am to get the lettuce I must cross the road, and wanting the lettuce as I do I expect in time to cross the road. If I don’t do so, we might agree that I really didn’t want the lettuce all that much, or perhaps that I wanted something else more. Maybe I just didn’t want to cross the road. No harm in that’ he concluded smugly.

‘You make it sound a kind of accident if you choose the means to the end’ complained Achilles. ‘Whereas I am trying to show that reason enjoins the choice! To coin a phrase, it is an a priori principle constitutive of practical rationality!’

‘Not an accident, and not that, whatever it is’ said the tortoise. ‘Naturally, some difficult radical interpretation has to be done. If I prefer lettuce to starvation, and recognize crossing the road as the only means to lettuce, yet act as if I prefer the joint outcome <starvation, sit still> to <lettuce, cross the road> then we will cast around for other objects of concern to explain my choice. And equally obviously tortoises of a race that does not choose necessary means to ends will fail to achieve their ends; assuming their ends include satisfying their needs, then they will die out rather rapidly. I expect that is why I may be about to cross the road. On the other hand, tortoises who rush around buying lottery tickets may not do all that well either. The race is not always to the swift’ he mused.

‘But wouldn’t you call a fellow tortoise who persistently failed to adapt means to ends unreasonable? Don’t there have to be authoritative, instrumental norms?’ fumed Achilles.

‘Oh, I call lots of people unreasonable’, said the tortoise, ‘people who get angry too quickly or eat too much so that they can get sick and lose weight, or who enter dwarf-throwing competitions. It doesn’t signify very much except that their behaviour doesn’t make sense to me, or even that I disapprove of them. But as for norms, yes, indeed I am glad I am not the kind of tortoise who constantly fails to adopt means to ends. I am not sure I am ever going to meet any who do so fail, both because it is so hard to identify them, and because we agreed that they will have died out pretty quickly. But if I did, well I am sure they would really arouse my passions -- good-for-nothing, useless animals, every last tortoise of them’ he said with a frown.

‘At least I can agree to that’ replied Achilles, sadly.

‘Why so sad?’, asked the tortoise, caringly.

‘Nothing’, said Achilles, ‘It is just that I thought I had a different thought, and now I think I didn’t.’
 
 

Day V
 
 

‘But look’, said Achilles, ‘you have resisted all the arguments I could muster. And yet I notice that this pile of lettuce has steadily shrunk. So what is going on?’

‘Oh, didn’t I tell you?’ said the tortoise, pausing surprised in mid-mouthful. ‘I have an absolute passion for the stuff. In fact, I scarcely ever resist it. Would you like some too?’