| Summary: | 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.
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