Logic and Foundations of Mathematics Commons^™

Vagueness, Ignorance, And Margins For Error, Kenton Machina, Harry Deutsch

Faculty Publications - Philosophy

We argue that the epistemic theory of vagueness cannot adequately justify its key tenet–that vague predicates have precisely bounded extensions, of which we are necessarily ignorant. Nor can the theory adequately account for our ignorance of the truth values of borderline cases. Furthermore, we argue that Williamson's promising attempt to explicate our understanding of vague language on the model of a certain sort of "inexact knowledge" is at best incomplete, since certain forms of vagueness do not fit Williamson's model, and in fact fit an alternative model. Finally, we point out that a certain kind of irremediable inexactitude postulated by …

What's The Reason?, Kenton Machina, Mark Siderits

Faculty Publications - Philosophy

"What's the Reason?" is an informal applied logic textbook in 5 chapters. It includes discussions of the nature of good everyday and academic reasoning, common mistakes in everyday reasoning, and overall informal argument assessment.

Induction And Deduction Revisited, Kenton Machina

Faculty Publications - Philosophy

Most authors seem to assume there are two types of argument, deductive ones and inductive ones. But there is wide disagreement about how those two are to be distinguished from one another, and about whether there are two kinds of logic, deductive and inductive, relevant to evaluating arguments of each type. In this paper, I argue that all attempts to distinguish a logic of inductive arguments from a logic of deductive ones fail. I argue that the distinction between induction and deduction is not a logical distinction, but is rather a pragmatic one, pertaining to how “tight” the argument needs …

Basic Applied Logic, Kenton Machina

Faculty Publications - Philosophy

From the preface:

This is a practical book, intended to help its users develop logical reasoning skills. It is designed for any introductory course that focuses on the development of those skills—whether that course takes an "informal" nonsymbolic approach or a more formal approach. Although it contains optional sections in which modern symbolic logic is carefully developed through first-order predicate calculus, the book maintains a practical orientation, emphasizing only those aspects of logical theory that bear on argument evaluation and argument construction. Thus, the book is well-suited for use in a wide range of introductory applied logic courses, introductory philosophy …

Truth, Belief, And Vagueness, Kenton Machina

Faculty Publications - Philosophy

Formal mathematical logic is designed to capture the logical form of mathematical statements, all of which employ precisely defined concepts, unlike the concepts found in natural languages, almost all of which are vague. In this paper I argue that in order to more accurately represent the logical form of vague natural language statements, formal logic should employ degrees of truth and falsehood, rather than assuming just the two truth “values” T and F. I explore in detail the most reasonable definitions for basic logical operations in a system that allows for degrees of truth, concluding that one of the multi-valued …