Claude Gratton

Infinite regress arguments are part of a philosopher's tool kit of argumentation. But how sharp or strong is this tool? How effectively is it used? The typical presentation of infinite regress arguments throughout history is so succinct and has so many gaps that it is often unclear how an infinite regress is derived, and why an infinite regress is logically problematic, and as a result, it is often difficult to evaluate infinite regress arguments. These consequences of our customary way of using this tool indicate that there is a need for a theory to re-orient our practice. My general approach to contribute to such a theory, consists of collecting and evaluating as many infinite regress arguments as possible, comparing and contrasting many of the formal and non-formal properties, looking for recurring patterns, and identifying the properties that appeared essential to those patterns. Two very general questions guided this work: How are infinite regresses generated in infinite regress arguments? How do infinite regresses logically function as premises in an argument? In answering these questions I clarify the notion of an infinite regress; identify different logical forms of infinite regresses; describe different kinds of infinite regress arguments; distinguish the rhetoric from the logic in infinite regress arguments; and suggest ways of improving our discussion and our practice of constructing and evaluating these arguments.

I examine a number of infinite regress arguments whose infinite regresses are presented or described in terms of recurring questions and answers in order to determine whether such recurring questions have any role in generating these infinite regresses, or in disqualifying the recurring answers. I argue that despite the existence of such infinite regress arguments and the suggestions of some philosophers, these recurring questions have no such roles. Some ways of handling these infinite regress arguments are then proposed.

: 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.