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Full-Text Articles in Logic and Foundations of Mathematics
What's The Reason?, Kenton Machina, Mark Siderits
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
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 …
Truth, Belief, And Vagueness, Kenton Machina
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 …