In his 1946 paper, "Knowing How and Knowing That," Ryle makes brief mention of Lewis Carroll's 1895 paper, "What the Tortoise Said to Achilles." (I discussed Carroll's argument and its relation to Ryle not so long ago.) Jason Stanley addresses the problem in his recent Know How (2011). He quotes Ryle's argument, which is not quite identical to Carroll's. Ryle writes:
A pupil fails to follow an argument. He understands the premises and he
understands the conclusion. But he fails to see that the conclusion follows from
the premises. The teacher thinks him rather dull but tries to help. So he tells him
that there is an ulterior proposition which he has not considered, namely, that if
these premises are true, the conclusion is true. The pupil understands this and
dutifully recites it alongside the premises, and still fails to see that the conclusion
follows from the premises even when accompanied by the assertion that these
premises entail this conclusion. So a second hypothetical proposition is added to
his store; namely, that the conclusion is true if the premises are true as well as the
first hypothetical proposition that if the premises are true the conclusion is true.
And still the pupil fails to see. And so on for ever. He accepts rules in theory but
this does not force him to apply them in practice. He considers reasons, but he
fails to reason. (This is Lewis Carroll’s puzzle in ‘What the Tortoise said to
Achilles’. I have met no successful attempt to solve it).
…knowing [a rule of inference] is not a case of knowing an extra fact or truth; itAccording to Stanley, Ryle's interest here is in whether or not epistemic justification amounts to having only "the right propositional states" (Stanley, p. 41). I don't think that's right. For one thing, Ryle never talks about anything called "propositional states." He is wary of the notion of literal mental states and he was highly critical of the contemporary notion of propositions. Ryle is interested in whether or not our accepting logical arguments can be reduced to our accepting a set of sentences. Furthermore, Ryle is not focusing on whether or not one might be justified or not in one's reasoning, but rather on whether or not one is compelled to accept a conclusion given certain set of sentences. So the focus is not so much on what constitutes epistemic justification, but on what compells us to accept certain logical arguments.
is knowing how to move from acknowledging some facts to acknowledging
others. Knowing a rule of inference is not possessing a bit of extra information
but being able to perform an intelligent operation. Knowing a rule is knowing
how. It is realized in performances which conform to the rule, not in theoretical
citations of it.
Ryle attempts to explain the absurdity of the example by claiming that reasoning is not reducible to knowledge of truths. The Rylean moral is that reasoning is not exhaustively modeled by a sequence of sentences representing the truths which are reasoned, and that if you try to model it that way, you end up with an infinite regress. Propositional knowledge alone does not force us to accept or draw logical conclusions.
Stanley makes the following objection. He supposes that Ryle is working under the assumption that propositional knowledge is behaviorally inert. That is why such knowledge supposedly does not compel the student to accept that the conclusion follows from the premises. Accepting that the conclusion follows from the premises would be a behavior, and Ryle's point is supposedly that the student's propositional knowledge does not facilitate any behaviors.
This is a mistake. Ryle does not take propositional knowledge, or any other kind of knowledge, to be behaviorally inert. In fact, Ryle's hypothetical student does produce behaviors based on his acceptance of the relevant propositions. He "dutifully recites" them and "considers" them. For Ryle, consideration, reflection and contemplation are forms of behavior, and their subject matter is propositional. Why should we think Ryle supposes that propositional knowledge was behaviorally inert? The problem confronting Ryle's hypothetical student is not that his propositional knowledge has no behavioral inertia, but that it does not have one very specific behavioral consequence: the acknowledgment that the conclusion follows from the premises.
Ryle distinguishes between theory and practice, but not such that only the latter is behaviorally operant. Ryle's claim is that, if a person only knows something in theory, they do not know how to apply it in practice. Ryle takes theoretical knowledge to be behaviorally limited, not inert. Theoretical knowledge involves certain sorts of dispositions and competences, and not others. Though Ryle's vocabulary is a bit outdated, his view is not so foreign. Today the distinction is more commonly drawn as between language and motor abilities and between higher and lower cognitive functions. There is good reason to appreciate such distinctions and to acknowledge their neurological bases, and I don't think Stanley wants to doubt them. He only fails to see how Ryle's view is a precursor to this contemporary way of thinking.
Stanley contrasts Ryle's view with Boghossian, who argues that understanding the logical constants may just be a matter of being disposed to and having the capacity to apply them in certain ways. But Ryle would certainly find some sympathy with Boghossian's assessment, though he would insist that the sort of competence Boghossian is talking about cannot be reduced to the justified true belief in propositions.
Stanley's objection at this point is likely thus: There is no reason to think of these distinctions as implying the non-reducablity of knowing how to knowing that. The crux is that Stanley takes the notion of propositional knowledge to be wide enough to encompass all kinds of knowing. Either these other competences and abilities are knowing that, or they are not knowledge, period. The fact that formal logic does not exhaustively model human reasoning is probably obvious to Stanley, and not in need of lengthy philosophical argument. Yet, in Ryle's defense, his Lewis Carroll argument wasn't all that lengthy. Moreover, the fact that we do not need this and similar arguments today might be in part due to the fact that Ryle so forcefully made them.