INTRODUCTION
Carroll's (Reference Carroll1895) short piece “What the Tortoise said to Achilles” in many ways anticipates issues that arise in a number of contemporary controversies. One might argue, for example, that initially plausible attempts to deal with the problem of easy knowledge will land one in the unfortunate position of Achilles who followed the Tortoise down a road that leads to vicious infinite regress. Or consider the conditions required for inferential justification. For idealized inferential justification, I have defended (Reference Fumerton1995, Reference Fumerton and Schantz2004, Reference Fumerton, Crisp, Davidson and Vander Laan2006) the view that to be justified in believing P on the basis of E one needs to be not only justified in believing E, but justified in believing that E makes probable P (where entailment is the upper limit of making probable). And again, critics have argued that such a strong requirement fails to learn the lesson that Achilles should have been taught by the Tortoise. Even more generally, one might well argue that strong access internalists will need to deal with a variation of Carroll's puzzle even for their accounts of non-inferential justification. In this paper I'll examine these controversies with a mind to reaching a conclusion about just exactly how one can accept intellectually demanding conditions on justified belief without encountering vicious regress.
Let's briefly remind ourselves of Carroll's puzzle. We don't need the rhetorical flourishes or the amusing asides that occur in Carroll's text. Nor do we need to worry much about the actual content of the propositions that were discussed. The Tortoise finds an excuse to discuss an inference from two propositions A and B which seem to entail unproblematically a third Z. The Tortoise gets Achilles to admit that one wouldn't be forced to accept the conclusion Z if one didn't accept either A or B. With an emphasis on the epistemology of the situation we might change that to the suggestion that there would be no reason to accept Z on the basis of A and B if we had no reason to accept either A or B. So far so good. The Tortoise is just appealing to the almost universally accepted principle that you can't get justification for believing the conclusion of an argument on the basis of its premises unless you have reason for believing the premises – more colorfully – garbage in; garbage out. However, the Tortoise suggests, having reason to believe A and B by itself won't force you to the conclusion Z unless you also see the connection between (A and B) and Z. The Tortoise suggests that we capture the relevant connection that must be accepted using a conditional whose antecedent is the conjunction of A and B and whose consequent is Z, but there are in fact different ways of formulating the conditional that is designed to assert the link between premises and conclusion. The Tortoise imbeds a modal operator in the conditional, one whose occurrence also gives rise to scope ambiguity:
(CM): If (A and B) are true Z must be true.
CM can be read (implausibly) as asserting that the necessity of Z follows from (A and B), or, much more plausibly, as asserting only that it is necessarily the case that if (A and B) then Z.
But it is not clear why we need a modal operator at all. Given the point the Tortoise is making, one would be in business simply adding to one's premises the truth:
(CC): If (A and B) then Z.
Either way, of course, it looks as if Achilles is in deep trouble if he accepts the invitation to include either CM or CC as an additional premise in his reasoning. Having bitten once, Achilles will no doubt continue to bite on the need for additional connecting principles to connect his new set of premises to his conclusion.
The Tortoise insists on connecting principles as premises in a case in which the premises seem to entail the conclusion. Such insistence might seem even more reasonable when we reason non-deductively. Suppose, for example, someone relies explicitly on the fact that he seems to remember having done something to reach the conclusion that he did it. To make the story a bit implausible our hypothetical reasoner formulates the explicit premise describing apparent memory and consciously infers the whereabouts of his car keys. If the Tortoise managed to inject himself into this conversation, he would no doubt suggest that one would only reach the relevant conclusion if one trusted apparent memory as a more or less reliable guide to past events. And since trust in that claim about the reliability of memory is a critical part of one's reasoning, its role should be acknowledged when one unpacks one's reasoning.
It might seem that one is out of the woods if one rejects the view that apparent memory supplies one with inferential justification. And these days, one is more likely to get the suggestion that beliefs based on apparent memory are non-inferentially justified (if justified at all). If that suggestion were correct, then we don't even have a conclusion based on premises and it will be hard for the Tortoise to raise the relevant question about belief in the connection between premises and conclusion. But this sort of move has never deterred skeptics. It seems clear to many that we are in some important sense relying on apparent memory, or committed to the reliability of memory, when we use it to form beliefs about the past.Footnote 1 And certainly once the Tortoise calls this (perhaps implicit) commitment to our attention, we can expect him to insist that we make explicit this commitment in the form of a premise.
So what initial moral should we draw from Carroll's puzzle. Henny Youngman used to tell the following joke: Man goes into the doctor's office and says “Doctor: it hurts when I do this (he moves his elbow).” The doctor says: “Well, don't do that.” Mutatis mutandis, Achilles tells the philosopher that is head is starting to hurt as he contemplates the trouble he gets into adding connecting principles to his premises. The philosopher should respond as the doctor did: Well, don't do that. The problem is that it seems to some of us that we really do need to “see” in some sense that our premises support our conclusion before we could possibly have any sort of intellectually satisfying justification for believing our conclusion based on those premises. There are certainly examples one can give, where the refusal to address a Tortoise-like concern seems to be paradigmatically irrational.
1. THE PROBLEM OF EASY JUSTIFICATION
Consider what has come to be known, following Stew Cohen (Reference Cohen2002), as the problem of easy knowledge, though in what follows I'll talk mainly about easy justification rather than easy knowledge. There are different ways in which might try to get justification that seems so easy as to be suspicious. Consider first an old example, the problem of induction. As it was posed by Hume and Russell, the problem is how to get oneself a justified belief that inductive inference is a legitimate way of making predictions (either about an unknown part of the past, or an unknown future). We observe correlations between properties and are tempted to project those correlations into the unknown past and present. The skeptic asks how we can legitimately believe that our inductive reasoning is reliable. Here is one attempt to answer the question: We rely on memory to justify our belief that we have used enumerative induction and have been successful most of the time, and we project the observed correlation. Our skeptic quickly notices that this is an instance of the very pattern of reasoning that we were supposed to justify as legitimate and calls foul.
The above involves a straightforward reliance on a method to certify the reliability of that method. But there are more subtle versions of the same gambit. Consider Stew Cohen's kid wanting to know why he should rely on color appearance to reach conclusions about the real colors of things (Cohen Reference Cohen2002). Stew agrees to check it out with a slide show in which we get a sequence of objects that appear to have different colors. Off we go with another inductive argument, where the second conjunct of each premise is accepted based on the appearance the object presents:
(1) The screen looks red and it is red,
(2) The screen looks blue and it is,
(3) The screen looks green and it is,
And so on.
Conclusion:
(4) Color appearances usually get us at the real colors of things.
The reasoning is inductive but the problematic source circularity seems to occur with the justification of the premises and the unreflective reliance on subjective appearance to reach a conclusion about objective reality
We could of course supply indefinitely many more examples: Vogel (Reference Vogel2000) has his well-known example of the hapless car owner trying to check out the reliability of the car's gas gauge by checking the gas gauge against the level of gas in the tank, but where he also reaches the relevant conclusions about the level of gas in the tank solely by relying on the gas gauge! Or consider testimony. You need an argument for thinking that we can legitimately rely on testimony. Get testimony from a bunch of people, trust it, and inductively infer the reliability of testimony.
Now in some of these examples it is tempting to think that the explanation of why the arguments are pathetic is that there are underlying presuppositions upon which we rely in justifying our belief in the premises. In effect, we can't justify the premises without presupposing the conclusion. Once we follow Tortoise-like advice and include the implicit presuppositions required for the justification of each premise as an additional premise, we simply have familiar straightforward circular reasoning – the conclusion appears as a premise. Since one can only be justified in believing a conclusion based on premises if one is justified in believing the premises, one can't possibly acquire a justified belief in the conclusion of an argument this way. It seems to me that is surely the right conclusion to reach in some of the cases – Vogel's gas gauge case, for example. As he formulates the premise: The gas gauge reads half full and the tank is half full, the skepticial interlocutor is bound to interrupt with the question: How did you figure out that the tank is half full? And when the skeptic gets the answer that the gas gauge says it is, the skeptic will ask the obvious further question: How did you figure out that the gas gauge is reliable? When we have no independent reason to think that it is, the skeptic correctly won't count that as a legitimate observed correlation for use in an inductive argument designed to establish the reliability of the gas gauge. All this must at least remind one of the pressure Achilles felt to add to his premises critical claims that describe the link between one's evidence and one's conclusion.
2. INFERENTIAL INTERNALISM
Consider another controversy on which the dialogue between the Tortoise and Achilles might seem to bear even more directly. I have often defended a view I call inferential internalism. In its strongest form the view holds that one is justified in believing that P on the basis of E only if one is justified in believing that E makes probable P (where, again, entailment can be viewed as the upper limit of making probable). In the past I have tried to support the principle by relying on examples that I now concede weren't fair. For example, I imagined the astrologer who makes predictions about the love lives of people by relying on information about their date of birth and the present alignment of stars, or the tea-leaf reader who makes predictions based on the pattern made by the remains of leaves in a tea cup. I then asked the rhetorical question: Wouldn't you reject such inferences as obviously illegitimate if the astrologer had no reason to believe that there is some sort of connection between birth dates and stars and the love lives of people, or the tea-leaf reader had no reason to believe that the pattern in the tea cup had something to do with the relevant events predicted? And we certainly wouldn't let the astrologer attempt to satisfy our insistence on a justified belief about the connection by reading in the stars that astrology is reliable, or let the tea-leaf reader read in the tea leaves that this way of making predictions is pretty good!
Mike Huemer (Reference Huemer2002) has argued, successfully I think, that the examples given above are bad examples. They neither show the plausibility of inferential internalism, nor do they bolster the Tortoise's suggestion that when we infer conclusions from premises we always need to add an extra premise describing the relevant connection between premises and conclusion. The examples of astrological inference and tea-leaf reading do show that the astrologer and the tea-leaf reader need to add a premise asserting a contingent (probably law-like) connection between stars and people, and tea remains and the future, but that's only because without those premises the arguments are simply bad arguments. There is no relevant connection between the arguments' premises and their conclusions. If the arguments are to have any chance of being respectable, they need to be construed as enthymematic. Those putting forth the arguments are relying on critical, but suppressed premises.
Much of the reasoning we actually articulate is enthymematic in this way. I come home to find my windows smashed, valuables missing, and I conclude that I have been robbed. As we ordinarily talk, no-one would complain if I describe the broken windows and the missing valuables as my evidence that I have been robbed. But again, it is hardly the case that I could legitimately infer from those truths, and those truths alone, that I have been robbed. I could only legitimately reach that conclusion if I have good reason to believe such things as that windows don't typically break spontaneously and cause the disappearance of valuables, that around here it isn't legal for neighbors to borrow things in this manner, that there is a legally defined notion of property in the first place. I suppose a philosopher might insist that these truths are background presuppositions, not premises, but this seems to me to be a distinction without a difference. The fact is that the reasoning is far more complex than our surface discussion of these matters might indicate.
The terminology we use to make the distinctions made above may invite confusion. I'd prefer to say that the premises of enthymematic argument simply do not describe the evidence from which we infer our conclusions. At most they describe part of that evidence. So, in the strict sense, for example, litmus paper's turning red isn't even putative evidence of the solution's being acidic, someone's telling me that her name is “Susan” isn't evidence that her name is “Susan,” the alignment of planets wasn't even offered by the astrologer as evidence of any of the astrologer's predictions. The evidence from which we infer our conclusions includes everything that we take to be critically relevant to our conclusion. But the terminology doesn't really matter. If you prefer to retain our ordinary way of talking and describe partial evidence as evidence, that's fine, as long as you concede that the evidence about which you speak is very often just that – partial evidence.
Having made these distinctions, we can now reframe the Tortoise's question to Achilles. When we are considering an argument whose premises purport to accurately describe the complete evidence from which we infer a conclusion, do we need an additional premise describing the relevant connection between premises and conclusion. And the answer had better be “No.” By contrast, when we are dealing with enthymematic arguments, the answer to the question of whether we need to “add” additional premises in order to have an argument that is respectable is trivially “Yes.” We have already described the argument as enthymematic, and that just means that the stated premises don't include all of the relevant premises.
We haven't yet given a principled account of how to distinguish enthymematic from non-enthymematic reasoning. My own suggestion, not very popular, is that when we present a non-enthymematic argument we intend the connection between premises and conclusion to hold necessarily. If P entails Q, then, of course, it is a necessary truth that P entails Q. But similarly if P makes probable Q (in the sense relevant to the evaluation of non-deductive reasoning), it is also necessarily true that P makes probable Q. And we can know that P makes probable Q a priori. We can't know a priori or a posteriori that P makes probable Q when P represents incomplete evidence for Q, since, incomplete evidence for Q doesn't make probable Q!
So where are we? We know that we shouldn't accept the Tortoise's invitation to add a connecting principle as a premise in the case of non-enthymematic reasoning. That would begin a regress that we couldn't stop. And we might suppose, therefore, that we should abandon inferential internalism, the principle that to be justified in inferring Q from P one must be justified in believing that P makes probable Q. But that would be a mistake, I think. Even if we focus on deductively valid reasoning, we can still make a distinction between someone who is caused to believe Q by his justified belief that P where P entails Q, but who can't recognize that P entails Q, and someone who is caused to believe Q by his justified belief that P where that person also recognizes the entailment and where his seeing the entailment is part of what causes him to believe Q. And it still seems to me that only the latter is fully justified in believing Q on the basis of P.Footnote 2
But how do we avoid regress? One straightforward way is to claim that while justified belief in the connecting principle is necessary for justification, the proposition in question should not be treated as a premise. There is still the threat of regress in gaining justification for believing connecting principles, particularly if those asserting probabilistic connections are treated as empirical truths that themselves can only be inferred from other truths. As I suggested earlier, however, there is a way out if one can make plausible the claim that such truths are necessary truths (they would probably need to be construed as synthetic necessary truths) knowable a priori. The proposal for avoiding regress proposed here is straightforward, but one can understand why the critic might think it too clever by half. The inferential internalist argues that one needs to have a justified belief in the connecting principle to have propositional justification for believing the conclusion of an inference based on the premises, and that one needs to base one's belief on the conclusion, in part, on that justified belief in the connecting principle asserting a connection between premises and conclusion in order to have justified belief in the conclusion based on the premises. In short, the critic will argue that the proposition asserting a connection between premises and conclusion is starting to look and function just like a premise. If it looks like a premise, and epistemically acts like a premise, how do I expect to get away with arguing that it is not a premise? While I concede the objection has initial force, my answer is intended to be disarmingly simple. I read “What the Tortoise said to Achilles” and I don't want to be in the position of Achilles facing a vicious regress. To avoid Achilles' fate one simply can't treat the connecting principle as a premise among other premises.
3. AN ALTERNATIVE
As we noted earlier, the threat of the nagging Tortoise is not confined to inferential justification. We talked about the problem of easy justification, and it is useful to remember that the problem was raised by Cohen and others primarily as a dilemma for those who seek to characterize basic justification – non-inferential justification. Take some account of basic justification that identifies having non-inferential justification with exemplifying some property J. A philosopher (like BonJour (Reference Bonjour1985) when he was a coherentist) is bound to ask why you think that J beliefs are usually true. And again it is initially hard to see why one couldn't in principle use an inductive argument relying on J beliefs and introspective knowledge that they are J beliefs to get a track record argument of reliability. When exemplifying the relevant J property I believe P and P (I conclude justifiably since I exemplify the J property). When exemplifying the relevant J property I believe Q and Q (I conclude justifiably since I exemplify the J property). Given that I have some way of discovering that I exemplify the J property, the inductive argument in support of the reliability of forming beliefs this way seems straightforward – straightforward but all too “easy.” And again, it might be tempting to suppose that the problem with the argument is that in some sense or other I am implicitly relying on the conclusion in forming the second conjunct of each of the premises. My foundational justification relies on a justified belief in the proposition that J beliefs are usually true. But this time it is absolutely clear that the foundationalist must resist the temptation to concede that a justified belief in this other proposition is a critical part of being justified in believing P. That's fatal to foundationalism—the doctrine that there is a kind of justification for believing a proposition that does not consist, even in part, in the having of another different justified belief.
I have argued elsewhere (Reference Fumerton1995, Reference Fumerton, Crisp, Davidson and Vander Laan2006) that the key to evaluating accounts of foundational justification is to test such accounts against the apparent felt need to add a further premise of the sort we are considering, either to get justification in the first place, or even to increase the level of one's justification. So, for example, if we take a straightforward reliabilist account of non-inferential justification, it's almost impossible to resist the suggestion that we would be epistemically much better off with respect to gaining assurance that P if we had not only a reliably-produced belief, but also good reason to believe that our belief that P was produced by a belief-independent, unconditionally reliable process. Or even if we find ourselves relying on seemings (as the seeming evidentialist suggests), one can't help but yearn for an independent reason to think that seemings are reliable indicators of what the seemings represent.Footnote 3 Some of our beliefs might be the result of a “design” that causes us to react to sensory stimuli in certain ways, but if I find myself wondering if those beliefs are true, it would sure be nice to have a good reason for thinking that they are the result of such a design plan. The worry, of course, is that one will be able to say similar things about any proposed account of non-inferential justification. If that's right, then I suspect that there is no alternative to Sosa's (Reference Sosa2009) suggestion that one can always, in principle, do better by moving to higher and higher levels of justified belief. But I'm not convinced that one is left with that conclusion. This is not the place to convince you, but I have argued for the view that when one has non-inferential justification of the sort I recognize, there is no better sort of justification one could have, even in principle. When, for example, one is in pain, while one thinks that one is and one is directly acquainted with the correspondence or “fit” between the thought and the pain, one has all one needs, all one could possible want, by way of epistemic justification for believing that one is in pain. One can form the higher-belief that one stands in the relevant relations of acquaintance, and for the first two or three levels up, one can probably get oneself non-inferential justification for believing that one does stand in those relations to the relevant facts, but it doesn't seem to me that one would gain any more reason for believing that one is in pain than one had initially (though one might get a more philosophically sophisticated set of beliefs employing a set of concepts that most people lack).
My former student, Sam Taylor, has suggested (Reference Taylor2013) that if all of the above is true, then one might suggest that there is a lesson for the inferential internalist. Notice that in trying to give an account of non-inferential justification, I argued that our direct awareness of fit between thought and fact was sufficient to give one the kind of intellectually satisfying justification one seeks as a philosopher. I specifically cautioned against the view that one needed justification for believing the proposition that there was the relevant correspondence between thought and fact. And this was important not just to preserve the justification as non-inferential – to preserve it as justification that does not require the having of other different justified beliefs – but also to allow that those who are relatively unsophisticated conceptually could still have fully justified beliefs.
To avoid the appearance of a Lewis-style regress, or the charge that one is simply employing a premise without calling it a premise, the inferential internalist might argue, as I have said the foundationalist should argue, that the awareness of connection between premises and conclusion that is needed to generate inferential justification is not justified belief in a proposition. When one infers P from E one does need awareness of an evidential connection between E and P, but that awareness doesn't need to take the form of a justified belief in a proposition asserting the existence of the connection. Again, this might provide a nice symmetry between what I have argued one should say about non-inferential justification and what I am suggesting one might say about inferential justification. The closest analog to evidential connection in non-inferential justification is the correspondence or “fit” between thought and fact. And if I am content to have awareness of fit do the work of justifying the non-inferentially justified belief, why shouldn't I be content to let awareness of probabilistic connection do the work in the case of inferential justification. To be sure, for those who possess the relevant concept of probabilistic or evidential connection, a justified belief that the connection exists would be easily formed. But the question here is whether one would lack justification if one had the relevant awareness without forming the belief made true by the relationship of which one is aware.
All this presupposes, of course, that the relation of entailment and the relation of making probable are relations of which one could become directly aware. And, this will inevitably take us right back to the controversial Keynesian idea that evidential connections are internal relations that hold between their relata – that if E makes probable P, the mere existence of E and P guarantee that the relation of making probable obtains (Keynes Reference Keynes1921). But that is a view that I think all internalists will eventually need to accept if they are to avoid problematic regress.
In the end I'm not sure which of the two options I have discussed in this paper is preferable. I'm worried that one can be directly aware of, say, entailment without seeing it as entailment, and that in such cases the awareness won't give one the kind of assurance that the epistemologist seeks. But Bergmann (Reference Bergmann2006) has argued that awareness of correspondence between thought and fact could occur without someone seeing it as correspondence and that in such cases the awareness won't achieve the relevant epistemic goal either. The two seem to me different, but in the end, it is hard to see just why one should be satisfied with mere awareness of fit in the case of non-inferential justification while worrying about mere awareness of probabilistic connection in the case of inferential justification.
