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. (shrink)

I describe the general structure of most infinite regress arguments; introduce some basic vocabulary; present a working hypothesis of the nature and derivation of an infinite regress; apply this working hypothesis to various infinite regress arguments to explain why they fail to entail an infinite regress; describe a common mistake in attempting to derive certain infinite regresses; and examine how infinite regresses function as a premise.

This paper discusses some of the ways in which circular definitions and circular explanations entail or fail to entail infinite regresses. And since not all infinite regresses are vicious, a few criteria of viciousness are examined in order to determine when the entailment of a regress refutes a circular definition or a circular explanation.

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. (shrink)

I argue that there are at least two kinds of tacit premises; describe a certain type of counterexample against the validity of arguments, and then use it to identify one kind of tacit premise. I distinguish two classes of tacit premises on the grounds that they are discovered or constructed differently, they have different roles in an argument or causal explanation, and have different logical relations to each other.

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. (shrink)

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 describe some pedagogical challenges of teaching critical thinking, and propose one way of partly meeting them: the application of critical thinking skills to beliefs responsible for our emotions. I suggest ways of introducing the topic of emotions in our critical thinking courses, describe a project assigned to my students, and provide a model of the project.

I mention the benefits, challenges, and costs of using small group activities to enhance our students’ learning of critical thinking skills in our courses, and then describe ten examples of these groups. Two of these examples are not commonly reported in the literature on small groups, so I describe them in greater detail to facilitate their use in our courses.

: 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. (shrink)

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. (shrink)

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. (shrink)

The author argues that there is no morally relevant distinction between letting and making death happen, and between withholding and withdrawing life-support. There is a discussion of possible adverse consequences in believing that there are moral distinctions. And then he shows that acknowledging the absence of such a distinction does not necessarily imply any endorsement of active euthanasia.

Book review of Gratton's Infinite Regress Arguments.

Hannah Arendt's (1906-1975) writings, both in public magazines and in her important books, are still widely studied today. She made original contributions in political thinking that still astound readers and critics alike. The subject of several films and numerous books, colloquia, and newspaper articles, Arendt remains a touchstone in innumerable debates about the use of violence in politics, the responsibility one has under dictatorships and totalitarianism, and how to combat the repetition of the horrors of the past. The Bloomsbury Companion (...) to Arendt offers the definitive guide to her writings and ideas, her influences and commentators, as well as the reasons for her lasting significance, with 66 original essays taking up in accessible terms the myriad ways in which one can take up her work and her continuing importance. These essays, written by an international set of her best readers and commentators, provides a comprehensive coverage of her life and the contexts in which her works were written. Special sections take up chapters on each of her key writings, the reception of her work, and key ways she interpreted those who influenced her. If one has come to Arendt from one of her essays on freedom, or from yet another bombastic account of her writings on Adolph Eichmann, or as as student or professor working in the field of Arendt studies, this book provides the ideal tool for thinking with and rediscovering one of the most important intellectuals of the past century. But just as importantly, contributors advance the study of Arendt into neglected areas, such as on science and ecology, to demonstrate her importance not just to debates in which she was well known, but those touched off only after her death. Arendt's approaches as well as her concrete claims about the political have much to offer given the current ecological and refugee crises, among others. In sum, then, the Companion provides a tool for thinking with Arendt, but also for showing just where those thinking with her can take her work today. (shrink)

Considers the problems of sovereignty through the work of Rousseau, Arendt, Foucault, Agamben, and Derrida.