Claude Gratton

: I explore the logic of counterexamples by possible conjunction in order to extend their use to estimate the degree of support of premises; address some problems with my proposal; discuss some ways of teaching this extended use; and argue that conditional probability fails to express the degree of support of premises. The scant literature on this topic sometimes presents the degree of support of premises P1…Pn for conclusion C in terms of conditional probability, Pr. I will argue that the degree of support is better expressed by the probability of the conditional statement expressing the inference, Pr; and prove that Pr is not equivalent to Pr.

I investigate various logical and contextual factors involved in the derivation and use of infinite regresses in infinite regress arguments. I discuss the concept of a regress; identify different kinds of infinite regresses; clarify the core structure of most infinite regress arguments; use the logic of binary relations to explain the derivation of the most common kind of infinite regress encountered in my research; explain how circular definitions and circular explanations entail infinite regresses; discuss the rhetorical features of infinite regress arguments that are presented or analyzed in terms of recurring questions and answers; examine different conditions under which an infinite regress is used to refute a statement; identify different structures of infinite regress arguments that are presented or analyzed in terms of recurring problems and solutions