Some Remarks on the Generalized Scheme of Reduction to Absurdity and Generalized Hypothetical Syllogism in Fuzzy Logic

In this paper we investigate two generalizations, in fuzzy logic, of classical scheme of reduction to absurdity. We compare them with two possible generalizations of classical hypothetical syllogism (in fuzzy logic) and we show that generalized hypothetical syllogism is more general. We present new results concerning solutions of an inequality and an equation connected directly with generalization of scheme of reduction to absurdity in fuzzy logic

Galen's Institutio Logica

Originally published in 1964. This book is a translation of Institutio Logica, which was probably written by Galen, although scholars disagree on the possibility of this work being a forgery. It provides a survey on the history of logic written around the third century

What is a logical diagram?

Robert Brandom’s expressivism argues that not all semantic content may be made fully explicit. This view connects in interesting ways with recent movements in philosophy of mathematics and logic (e.g. Brown, Shin, Giaquinto) to take diagrams seriously - as more than a mere “heuristic aid” to proof, but either proofs themselves, or irreducible components of such. However what exactly is a diagram in logic? Does this constitute a semiotic natural kind? The paper will argue that such a natural kind does exist in Charles Peirce’s conception of iconic signs, but that fully understood, logical diagrams involve a structured array of normative reasoning practices, as well as just a “picture on a page”

Ancient Logic and its Modern Interpretations: Proceedings of the Buffalo Symposium on Modernist Interpretations of Ancient Logic, 21 and 22 April, 1972

Articles by Ian Mueller, Ronald Zirin, Norman Kretzmann, John Corcoran, John Mulhern, Mary Mulhern,Josiah Gould, and others. Topics: Aristotle's Syllogistic, Stoic Logic, Modern Research in Ancient Logic

Deconstructing Ethics: The Search for New Origins

Derrida’s theory of différance deconstructs essentialist and transcendental truths. Derrida—and others—often position this theory as a tool for achieving some ethical objective. This usage of deconstructive theory implies that the project of the ethical cannot be deconstructed. More precisely, it raises the question of if ethics can be derived without either essentialist or transcendental truths. If it cannot, then an ethical usage of deconstructive theory is self-defeating. This thesis will first show that Derridean theory deconstructs the grounds for ethics without providing another viable source for moral conclusions. Given this seemingly pre-ethical state, it will then present the Lacanian Real as a possible source for deriving moral conclusions. Ultimately, the thesis concludes that the ethical project in critical studies must find new origins; the paper gestures towards those origins

Human reasoning and cognitive science

In the late summer of 1998, the authors, a cognitive scientist and a logician, started talking about the relevance of modern mathematical logic to the study of human reasoning, and we have been talking ever since. This book is an interim report of that conversation. It argues that results such as those on the Wason selection task, purportedly showing the irrelevance of formal logic to actual human reasoning, have been widely misinterpreted, mainly because the picture of logic current in psychology and cognitive science is completely mistaken. We aim to give the reader a more accurate picture of mathematical logic and, in doing so, hope to show that logic, properly conceived, is still a very helpful tool in cognitive science. The main thrust of the book is therefore constructive. We give a number of examples in which logical theorizing helps in understanding and modeling observed behavior in reasoning tasks, deviations of that behavior in a psychiatric disorder (autism), and even the roots of that behavior in the evolution of the brain