Logic and the limits of explanation: the justification of deduction, Carrollian regress, logical validity and deductive inferential knowledge - Chapman, Dean (Department of Philosophy, 2023)
This essay engages with the problems of the justification of deduction, Carrollian regress, and deductive inferential knowledge. Also, it is considered whether Lewis Carroll's tale of what the tortoise said to Achilles can be interpreted as suggesting an argument against the possibility of logically valid argument. Such an argument is presented and shown to be unsound. Any justification of one of our basic rules of deductive inference, such as modus ponens, will inevitably make use of the very rule it means to justify. It will be a 'rule-circular' argument and invite charges that it begs the question and 'keeps bad company'. Following Paul Boghossian, the contention in this essay is that a thinker need not know that the rule according to which a given inference proceeds is sound in order to be entitled to carry out the inference. Thus, a rule-circular argument for the soundness of modus ponens does not beg the question. Also, by a conceptual role semantics which takes as its starting point that of Boghossian, and with insights gained from Robert Brandom's inferentialism, it is argued that a thinker who carries out an inference which is meaning-constituting of some concept for her is entitled to that act of inference, in part because she is epistemically blameless in it. One of the ways to counter a Cartesian sceptic is to maintain that some of our beliefs are beliefs we are entitled to have no doubt about. To make that claim good, it is argued, one must hold two things: first, that some of our beliefs are such that we have conclusive evidence for them, evidence which guarantees their truth; and second, that for some of these beliefs, we know that we have conclusive evidence for them - there are infallibilist and intemalist constraints on the possibility of us having knowledge that is certain. Pace Boghossian, the contention here is that anyone who carries out an inference which is meaning-constituting of some concept for her, in fact knows that inference to be valid. It is argued that knowing of the validity of an inference is sufficient for being entitled to carry it out so that one can thereby come to have what is here called 'certain knowledge' of the truth of its conclusion, given the satisfaction of other broadly applicable constraints. Thus, it is held that a thinker who carries out a meaning-constituting inference can thereby come to have certain knowledge of the truth of its conclusion. The central undertaking of this essay is therefore to face up to the problem of Carrollian regress, insofar as the main difficulty it raises for us has to do with the possibility of deductive inferential knowledge. By a conceptual role semantics it is argued that the error committed in allowing ourselves to be led into Carrollian regress is that of distinguishing too sharply between practical and propositional knowledge. It is a proper requirement that a reasoner must know that an inference is valid in order to be entitled to carry it out; but we need not think further that such knowledge must be deployed with the proposition of whose truth the thinker knows as a premise of the argument for her conclusion. A belief can serve as the basis of a subject's carrying out of an act - such as an assertion, or an inference - and an inferer's belief that an inference is valid being a case of knowledge is sufficient for her being entitled to that act of inference. The account is satisfyingly an account of both epistemic inferential entitlement as well as the rationality of inference.