Applied Logic presents logic as a relevant tool for interpreting arguments, not simply as an abstract discipline such as mathematics or physics. Through English-language arguments that are debated today—health care, economic problems, AIDS, and so on—the author strives to give students an appreciation of logic's applicability. An appendix provides answers to selected exercises. Applied Logic and the Instructor's Manual will be of great value to those teaching elementary logic.

Logic is a celebrated representation language because of its formal generality. But there are two senses in which a logic may be considered general, one that concerns a technical ability to discriminate between different types of individuals, and another that concerns constitutive norms for reasoning as such. This essay embraces the former, permutation-invariance conception of logic and rejects the latter, Fregean conception of logic. The question of how to apply logic under this pure invariantist view (...) is addressed, and a methodology is given. The pure invariantist view is contrasted with logical pluralism, and a methodology for applied logic is demonstrated in remarks on a variety of issues concerning non-monotonic logic and non-monotonic inference, including Charles Morgan’s impossibility results for non-monotonic logic, David Makinson’s normative constraints for non-monotonic inference, and Igor Douven and Timothy Williamson’s proposed formal constraints on rational acceptance. (shrink)

Kant identifies knowledge [Wissen], belief [Glaube], and opinion [Meinung] as our three primary modes of “holding-to-be-true” [Fürwahrhalten]. He also identifies opinion as making up the greatest part of our cognition. After a preliminary sketch of Kant’s system of propositional attitudes, this paper will explore what he says about the norms governing opinion and empirical hypotheses. The final section will turn to what, in the Critique of Pure Reason and elsewhere, Kant refers to as “General Applied Logic”. It concerns (...) the “contingent conditions of the subject, which can hinder or promote” good inquiry; and, though rarely mentioned in the secondary literature, it offers Kant’s methodological alternative to the traditional epistemological goal of finding “a sufficient and at the same time general criterion of truth”. (shrink)

Contemporary logicians have expanded upon the old notions of psychologism in logic and proposed new, weakened versions of it. Those weakened versions postulate that psychologistic logic does not have to inform about the ontology or metaphysics of reasoning. Instead, logic applied in cognitive science could serve as one of many paradigms for making empirical predictions about the observable process of human reasoning. The purpose of this article is to entertain this notion and answer the question: what (...) properties should a logical system formally representing actual human reasoning have? Based on the existing evidence from cognitive science and neuroscience we identified three potential candidates: context-sensitivity (satisfied for example by adaptive logics), content-sensitivity (satisfied by non-Fregean logics) and probabilism (satisfied for example by fuzzy logics). (shrink)

This instructor's manual, to accompany Applied Logic, contains answers to the exercises found in the text and a workbook useful for preparing students for exams. The text itself presents logic as a relevant tool for interpreting arguments, not simply as an abstract discipline such as mathematics or physics. Through English-language arguments that are debated today—health care, economic problems, AIDS, and so on—the author strives to give students an appreciation of logic's applicability. This book will be of (...) interest to those teaching elementary logic. (shrink)

This special issue of the Journal of Applied Logics deals with the logical aspects of the concept of God. It contains the following articles: Logic and the Concept of God, by Stanisław Krajewski and Ricardo Silvestre; Mathematical Models in Theology. A Buber-inspired Model of God and its Application to “Shema Israel”, by Stanisław Krajewski; Gödel’s God-like Essence, by Talia Leven; A Logical Solution to the Paradox of the Stone, by Héctor Hernández Ortiz and Victor Cantero; No New Solutions (...) to the Logical Problem of the Trinity, by Beau Branson; What Means ‘Tri-’ in ‘Trinity’ ? An Eastern Patristic Approach to the ‘Quasi-Ordinals’, by Basil Lourié; The Éminence Grise of Christology: Porphyry’s Logical Teaching as a Cornerstone of Argumentation in Christological Debates of the Fifth and Sixth Centruies, by Anna Zhyrkova; The Problem of Universals in Late Patristic Theology, by Dirk Krasmüller; Intuitionist Reasoning in the Tri-unitrian Theology of Nicolas of Cues, by Antonino Drago. (shrink)

This classic text, written by philosopher and mathematician William Thomson, presents a systematic exposition of the laws of thought and their role in science, logic, and philosophy. The book is still widely used in philosophy and mathematics courses today. This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work is in the "public domain in the United States of America, and possibly other nations. (...) Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

This Is A New Release Of The Original 1883 Edition.

Twenty-four U.S. states have enacted HIV exposure laws that prohibit HIV-positive persons from engaging in sexual activities with partners to whom they have not disclosed their HIV status. There is little standardization among existing HIV exposure laws, which vary substantially with respect to the sexual activities that are prohibited without prior serostatus disclosure. Logical analysis and mathematical modeling were used to explore the HIV prevention effectiveness of two types of HIV exposure laws: “strict” laws that require HIV-positive persons to disclose (...) their serostatus to prospective partners prior to any sexual activity and “flexible” laws that require seropositive status disclosure only prior to high-risk sex . These laws were compared relative to each other and to a no-law alternative. The results of these analyses indicate that, under most circumstances, both strict and flexible exposure laws can be expected to reduce HIV transmission risk relative to the no-law alternative, with flexible exposure laws producing the greater reduction in risk. This study demonstrates how logical analysis and mathematical modeling techniques can make an important contribution to the construction of a rational basis for decisions about a highly contested public health policy issue. (shrink)

Twenty-four U.S. states have enacted HIV exposure laws that prohibit HIV-positive persons from engaging in sexual activities with partners to whom they have not disclosed their HIV-status. From a public health perspective, HIV serostatus exposure laws can be viewed as structural interventions that seek to limit the spread of HIV by acting at the policy level. A central premise of these laws is that informed partners are more likely to protect themselves by declining sex, by substituting less risky activities for (...) higher-risk ones, or by using condoms, than are uninformed partners. However, the effectiveness of these laws at preventing HIV transmission is not known.There is little standardization among existing HIV exposure laws, which vary substantially with respect to the sexual activities that are prohibited without prior serostatus disclosure. Among the strictest laws are those in Arkansas, Michigan, New Jersey, and Ohio which mandate disclosure prior to almost any type of sexual contact. (shrink)

This paper presents an adaptive logic enhancement of conditional logics of normality that allows for defeasible applications of Modus Ponens to conditionals. In addition to the possibilities these logics already offer in terms of reasoning about conditionals, this way they are enriched by the ability to perform default inferencing. The idea is to apply Modus Ponens defeasibly to a conditional and a fact on the condition that it is ‘safe' to do so concerning the factual and conditional knowledge at (...) hand. It is for instance not safe if the given information describes exceptional circumstances: although birds usually fly, penguins are exceptional to this rule. The two adaptive standard strategies are shown to correspond to different intuitions, a skeptical and a credulous reasoning type, which manifest themselves in the handling of so-called floating conclusions. (shrink)