Claude Gratton

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

Showing that the premises of an argument are not sufficient for (viz., do not entail) a conclusion a conclusion involves citing a counterexample that would show the premises of the argument to be true and the conclusion false. This paper distinguishes counterexamples by analogy (an argument with the same form as argument against which it is advanced but where it is clearly the case that the premises are true and the conclusion is false), counterexamples by possible conjunction (a conjunction of the premises and the negation of the conclusion), and counter-arguments (arguments directed against the truth of the conclusion). After detailing the logical differences between these concepts, the paper describes the pedagogical significance of this distinction and provides an assortment of test exercises for students.

Henry W. Johnstone (1996) attempts to use a notion of postponement to give a general account of viciousness of infinite regresses. Though some of his examples suggest that his notion applies to only beginningless regresses (...eRdRcRbRa), I will show that it also applies to endless ones (aRbRcRdRe...). Unfortunately, despite this expanded application, it does not apply to all vicious regresses, even to some of his own examples; it is cumbersome and unnecessary, and it fails to explain how some infinite regresses entail a contradiction.