INTRODUCTION
It is a pleasure to have the opportunity to comment on ‘What the Internalist should say to the Tortoise’ by Richard Fumerton (Reference Fumerton2015), which makes detailed and intriguing use of the problem posed by Lewis Carroll in his dialogue between the Tortoise and Achilles to subtly reform and refine the principle of inferential justification which he has argued to be distinctive of inferential internalism. The Tortoise problem from Carroll, taken as a problem for internalists generally, seems well suited to motivate this refinement and also a useful tool in specifying exactly the nature of the needed reform to inferential internalism.
Or at least such a reform is motivated if Fumerton adopts the second of the two responses to the Tortoise that he considers at the end of his paper. Since he ends on a note of uncertainty about which response is preferable, I would like to use my comments to make the case for the second (and more reforming) response. I want to suggest that the second response is preferable in the way it addresses the Tortoise problem, and that taking the second response even further than suggested by Fumerton might lead to an even more satisfying response to the Tortoise
1. THE TWO RESPONSES TO THE TORTOISE
So, let us begin by clarifying the two responses that are on offer. Both can be explained with reference to Fumerton's Principle of Inferential Justification.
(PIJ) To be justified in believing P on the basis of another E, one needs to be
(1) justified in believing E and
(2) justified in believing that E makes probable P.Footnote 1
This formulation shows us that the two proposed responses only vary with respect to the second requirement. The first response consists in making no change to the formulation of the Principle of Inferential Justification, but rather to insist that the proposition that E makes probable P (which one must be justified in believing in accordance with the second requirement) “should not be treated as a premise.”Footnote 2 The regress of justification remains, but is then stopped by the suggestion that at least some (and hopefully sufficiently many) of the connecting principles “E makes probable P” are necessary truths, knowable a priori and not requiring any further inferential basis. If we understand “makes probable” in a Keynesian way, this necessary connection becomes more plausible, and inferential internalism need not imply skepticism through a regress of justification.
The second response to the Tortoise consists in making a change to the second requirement of the Principle of Inferential Justification. Rather than requiring justified belief that E makes probable P, Fumerton (and Sam Taylor) might only require “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.” I take this to be a modification of the original second requirement (2) to something like:
One must be (2’) aware that E makes probable P.
This second response stops the regress of justification by eliminating the requirement of justified belief which must then be further justified. Awareness of the probabilifying relation is also made plausible here by an appeal to the “Keynesian idea that evidential connections are internal relations” of which one can be directly aware.
2. THE TORTOISE AND ACHILLES
Which of these responses is better supported by the original problem of the Tortoise and Achilles? Certainly both address the conundrum that the addition of more premises to Achilles' argument will never lead the Tortoise to accept its conclusion. Premises alone are not enough for an inference (and hence for inferential justification), and the first response addresses this concern directly by insisting that what is added, though it takes the form of justified belief in a proposition, not be used as a premise. The second response avoids the pile-up of premises by not adding anything that could be used as a further premise. (When further premises are not needed. Of course, as noted by Fumerton in response to Mike Huemer, many arguments will be enthymemic and so require additional premises to be complete, but once those premises are added, the second response holds that needed for inference is an awareness of a relation – something that cannot be codified in an additional premise.) This seems to avoid the problem of further premises in a decisive way, and not to fall prey to the concern facing the first response that what is added should really be treated as a further premise – dragging us back into negotiation with the Tortoise.
An additional consideration here, might be highlighted by a slightly different application of the Tortoise problem in metaethics. Simon Blackburn, in his Practical Tortoise Raising (Reference Blackburn2010), expands the original dialogue to focus on cases where one might accept all the premises of a moral (or practical) argument and still not be motivated to act in accordance with its conclusion. In some metaethical contexts that focus might be on the motivation to act (e.g. when discussion motivational internalism) but in other metaethical (and particularly practical) contexts the focus might be on the action itself. How does seeing an action as instrumental to your own goals lead you to act? This focus on action simply highlights something that can already be found in the epistemic case. Though the epistemic inferential action is not as obvious, in reasoning we should be making inferences, drawing conclusions, and using our premises. Acceptance of a premise is required to support our reasoning, but it is not yet sufficient for the activity of reasoning.
Awareness of a probabilistic connection between premise and conclusion supports the following of that connection in a way that a simple justified belief in the connection might not. Following the Tortoise, one might accept the connecting proposition (though not as a premise) and still ask how one ought to follow that connection in one's reasoning. The reasoner needs to have and utilize the ability to make those supported inferences. And the awareness required by the second response could plausibly involve the possession of that ability. Just as we might say that one cannot have a full awareness of a fork (as a fork) if one does not understand how to use the fork, we might say that one cannot have a full awareness of a premise (as a premise) if one does not understand how to use the premise. Thus requiring awareness might better explain our abilities to reason.
And this suggests to me that a virtue epistemology, with a focus on epistemic abilities, might have the mechanisms to provide an even clearer response to the Tortoise problem. Of course, to accept an externalist Virtue Epistemology would be to abandon, not modify, the second requirement of Fumerton's Principle of Inferential Justification, but an internalist virtue epistemology (such as those offered by James Montmarquet (Reference Montmarquet1993), Jason Baehr (Reference Baehr2011), and myself (Reference Wright2010, Reference Wright2013)) might be a resource to provide an account of the awareness (and related abilities) required in the modified (2’). I am certainly intrigued by this suggestion, and think that it deserves further consideration.
3. PROBABILITIES AND INFERENCE
To return to the main line of our argument, we have seen how the second response to the Tortoise, might better resolve the original problem from Carroll. Awareness of a probabilifying relation is sufficiently different from justified belief in a proposition to be poised to stop the Tortoise's regress. However, while awareness might be of the right form to be followed as an action, we can still ask why we should trust that awareness. What is our justification for taking the inferential action that it suggests? Though this justification takes a different form than justification of a belief in a proposition, we can still ask what provides that justification.
Why should we trust our awareness that E makes probable P? Fumerton's answer to this question depends upon the special features of the relation of making probable, how it is interpreted and the access we have to the probabilifying relation thus interpreted. He suggests that we adopt a Keynesian logical interpretation of probability on which the probabilifying relation is knowable a priori. The plausibility of this claim depends on probabilistic reasoning being the analog of deductive reasoning; both can be known a priori, even though deductive reasoning is certain and probabilistic reasoning is not.
However, the fruitfulness of this proposal can be put into question when we consider recent arguments that Keynes himself abandoned “Keynesian probability” as he developed his economic theories.Footnote 3 Keynes moved away from the logical conception of probability, partly because he noted the way in which our judgments about uncertainty are influenced by the judgments of others in our communities. If the probabilifying relation were available a priori, we would expect to see convergence in probability judgments, but not a convergence that changes over time; the variation in probability judgments, particularly in boom and bust economic cycles, give us some reason to doubt that we have an a priori grasp of probabilifying relations. If we follow Keynes in shifting to an “intersubjective interpretation” of probability (as Donald Gillies (Reference Gillies, Runde and Mizuhara2003) argues that Keynes did), to understand the probabilifying relation we must study those around us and particularly their ideas about probability. But such an empirical requirement would bring back the Tortoise's regress.
When looking for a justification for following (2’) in our reasoning, we have been looking for special features of the “making probable” relation that might give us a reason to trust our awareness of it. But if the probabilifying relation is not accessible a priori, what further reason could we have for trusting our awareness that E makes probable P? I suggest that the most fruitful alternative is to shift from a focus on the “making probable” relation to a focus on our awareness. If awareness is taken to be a factive attitude, then one clearly has reason to follow our awareness of a probabilifying relation. However, awareness should not be understood to be factive here; one can be aware of something, in this sense, without its being the case. Rather than looking for a factive attitude, we should instead look at the individual having the attitude, the one reasoning.
Instead we should note that awareness of a relation is not itself a state in need of further justification; it is not justified belief in a proposition. Rather than referring us back to a further proposition, awareness brings the focus to the individual, the one being aware. In that individual, we can characterize awareness of a relation as an endorsement of the inference from E to P. The source of this endorsement could depend on trust in the person who is making the inference rather than on the content of the inference. This would be to base our endorsement of our own inferences on self-trust. Note that this self-trust can be characterized as either self-trust in our awareness of the relation between E and P or self-trust in our action of making the inference from E to P. In either case self-trust gives us a reason to endorse our own inferences. And this reason is not one that can be added as a further premise in the Tortoise's notebook. Of course there is still the further question of what makes it reasonable or rational for us to trust ourselves. Both Keith Lehrer (Reference Lehrer1997) and Linda Zagzebski (Reference Zagzebski2012) have argued that self-trust is a basic requirement for any rationality. Such arguments might be supplemented by the consideration that self-trust also seems poised to provide a satisfying resolution to the Tortoise problem.
Moving to a dependence on self-trust is clearly beyond the scope of Fumerton's suggested second response. But it seems to me that reliance on self-trust is the next natural step in the proposed direction, that it gives clear response to the Tortoise problem, and that the introduction of self-trust allows us to solve Carroll's problem even if we are forced to reject a logical interpretation of probability.
