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.

Showing that the premises of an argument are not sufficient for 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 , counterexamples by possible conjunction , and counter-arguments . 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.

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.

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.

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 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 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 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, I will show that it also applies to endless ones. 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.

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)