- published: 07 May 2016
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Classical logic identifies a class of formal logics that have been most intensively studied and most widely used. The class is sometimes called standard logic as well. They are characterised by a number of properties:
While not entailed by the preceding conditions, contemporary discussions of classical logic normally only include propositional and first-order logics.
The intended semantics of classical logic is bivalent. With the advent of algebraic logic it became apparent however that classical propositional calculus admits other semantics. In Boolean-valued semantics (for classical propositional logic), the truth values are the elements of an arbitrary Boolean algebra; "true" corresponds to the maximal element of the algebra, and "false" corresponds to the minimal element. Intermediate elements of the algebra correspond to truth values other than "true" and "false". The principle of bivalence holds only when the Boolean algebra is taken to be the two-element algebra, which has no intermediate elements.
Graham Priest (born 1948) is Distinguished Professor of Philosophy at the CUNY Graduate Center, as well as a regular visitor at the University of Melbourne where he was Boyce Gibson Professor of Philosophy and also at St. Andrews University. He was educated at the University of Cambridge and the London School of Economics. His thesis advisor was John Lane Bell.
He is known for his defence of dialetheism, his in-depth analyses of the logical paradoxes (holding the thesis that there is a uniform treatment for many well-known paradoxes, such as the semantic, set-theoretic and Liar paradoxes), and his many writings related to paraconsistent and other non-classical logics.
Priest, a long-time resident of Australia, now residing in New York City, is the author of numerous books, and has published articles in nearly every major philosophical and logical journal. He was a frequent collaborator with the late Richard Sylvan, a fellow proponent of dialetheism and paraconsistent logic.
Non-classical logic Non-classical logics (and sometimes alternative logics) is the name given to formal systems that differ in a significant way from standard logical systems such as propositional and predicate logic.There are several ways in which this is done, including by way of extensions, deviations, and variations. -Video is targeted to blind users Attribution: Article text available under CC-BY-SA image source in video https://www.youtube.com/watch?v=vP5JqQRc65I
A definition of Logic as a field of philosophy, as well as several types of logic studied in philosophy, including second order logic, non-classical Logic, and modal logic. Sponsors: Prince Otchere, Daniel Helland, Dennis Sexton, Will Roberts and √2. Thanks for your support!
According to classical systems of logic, anything follows from a contradiction: the relation of logical consequence is explosive. But recent decades have seen growing interest in "deviant," paraconsistent systems that include non-explosive relations of logical consequence. Further, some deviant logicians, such as Priest, assert the existence of dialetheias (true contradictions). In this conversation, Eckert and Priest discuss whether and how deviant logic should be studied in the undergraduate classroom. Then (starting at 29:40) they look for dialetheias in the areas of emotions, legal norms, and contradictory fictions.
LOGIC: A SHORT INTRODUCTION - Lecture 3 Graham Priest, CUNY Graduate Center (NY), University of Melbourne
Automated reasoning in classical logic has received much attention in the literature. Mature resolution theorem provers such as Vampire and E can handle enormous problems in first-order classical logic with equality. Waldmeister, a theorem prover for unit equational logic, has been incorporated into Mathematica as an equational reasoning method. Somewhat surprisingly, there has been much less attention devoted to non-classical logics. This is unfortunate, since many interesting and useful logics are inherently non-classical. Well known examples include intuitionistic, substructural and modal logics. Additionally, many modern logics for specialized tasks such as those designed for security and authentication protocols are non-classical as well. The inverse method is a generalizat...
Christopher Gauker (Cincinnati) gives a talk at the MCMP Colloquium (9 Feb, 2012). In this talk, two definitions of logical validity for a simple first-order language are compared in order to decide which one provides a better model for the semantics for natural language. One of these is the standard model-theoretic definition. The other defines contexts as structures of linguistic objects and then defines validity as preservation of truth-in-a-context. The disadvantage of the model-theoretic definition is that it commits us to explicating the reference relation, which no one has ever been able to do. The context-logical definition avoids this commitment, although it takes on others. In particular, it commits to explaining what it takes for a given context to be the context that pertains t...
by Colin Ehlert through Professor Rev. Dr. James Kenneth Powell II, opensourcebuddhism.org In this nice piece we uncover the mystery of especially Indian logic and that, of Nagarjuna. Nagarjuna's logic follows the lines of the reductio ad absurdam. This argument "from infinity" is despised or ignored in the West for the most part, but it is Buddhism's "bread and butter."
The prisoners dilemma is a hypothetical game set up showing a situation where people won't want to work together even when it's beneficial to do so. It's just a long way of saying people don't like to be taken advantage of. Is often game theory 101. Patreon https://patreon.com/user?u=849925 ITERATED PRISONER'S DILEMMA AND THE EVOLUTION OF COOPERATION https://www.youtube.com/watch?v=BOvAbjfJ0x0 EXTRA NOTES Concerning "Cooperation" Cooperation refers to cooperation between the two players. Not necessarily with outside parties like the police.
Non-classical logic Non-classical logics (and sometimes alternative logics) is the name given to formal systems that differ in a significant way from standard logical systems such as propositional and predicate logic.There are several ways in which this is done, including by way of extensions, deviations, and variations. -Video is targeted to blind users Attribution: Article text available under CC-BY-SA image source in video https://www.youtube.com/watch?v=vP5JqQRc65I
A definition of Logic as a field of philosophy, as well as several types of logic studied in philosophy, including second order logic, non-classical Logic, and modal logic. Sponsors: Prince Otchere, Daniel Helland, Dennis Sexton, Will Roberts and √2. Thanks for your support!
According to classical systems of logic, anything follows from a contradiction: the relation of logical consequence is explosive. But recent decades have seen growing interest in "deviant," paraconsistent systems that include non-explosive relations of logical consequence. Further, some deviant logicians, such as Priest, assert the existence of dialetheias (true contradictions). In this conversation, Eckert and Priest discuss whether and how deviant logic should be studied in the undergraduate classroom. Then (starting at 29:40) they look for dialetheias in the areas of emotions, legal norms, and contradictory fictions.
LOGIC: A SHORT INTRODUCTION - Lecture 3 Graham Priest, CUNY Graduate Center (NY), University of Melbourne
Automated reasoning in classical logic has received much attention in the literature. Mature resolution theorem provers such as Vampire and E can handle enormous problems in first-order classical logic with equality. Waldmeister, a theorem prover for unit equational logic, has been incorporated into Mathematica as an equational reasoning method. Somewhat surprisingly, there has been much less attention devoted to non-classical logics. This is unfortunate, since many interesting and useful logics are inherently non-classical. Well known examples include intuitionistic, substructural and modal logics. Additionally, many modern logics for specialized tasks such as those designed for security and authentication protocols are non-classical as well. The inverse method is a generalizat...
Christopher Gauker (Cincinnati) gives a talk at the MCMP Colloquium (9 Feb, 2012). In this talk, two definitions of logical validity for a simple first-order language are compared in order to decide which one provides a better model for the semantics for natural language. One of these is the standard model-theoretic definition. The other defines contexts as structures of linguistic objects and then defines validity as preservation of truth-in-a-context. The disadvantage of the model-theoretic definition is that it commits us to explicating the reference relation, which no one has ever been able to do. The context-logical definition avoids this commitment, although it takes on others. In particular, it commits to explaining what it takes for a given context to be the context that pertains t...
by Colin Ehlert through Professor Rev. Dr. James Kenneth Powell II, opensourcebuddhism.org In this nice piece we uncover the mystery of especially Indian logic and that, of Nagarjuna. Nagarjuna's logic follows the lines of the reductio ad absurdam. This argument "from infinity" is despised or ignored in the West for the most part, but it is Buddhism's "bread and butter."
The prisoners dilemma is a hypothetical game set up showing a situation where people won't want to work together even when it's beneficial to do so. It's just a long way of saying people don't like to be taken advantage of. Is often game theory 101. Patreon https://patreon.com/user?u=849925 ITERATED PRISONER'S DILEMMA AND THE EVOLUTION OF COOPERATION https://www.youtube.com/watch?v=BOvAbjfJ0x0 EXTRA NOTES Concerning "Cooperation" Cooperation refers to cooperation between the two players. Not necessarily with outside parties like the police.
According to classical systems of logic, anything follows from a contradiction: the relation of logical consequence is explosive. But recent decades have seen growing interest in "deviant," paraconsistent systems that include non-explosive relations of logical consequence. Further, some deviant logicians, such as Priest, assert the existence of dialetheias (true contradictions). In this conversation, Eckert and Priest discuss whether and how deviant logic should be studied in the undergraduate classroom. Then (starting at 29:40) they look for dialetheias in the areas of emotions, legal norms, and contradictory fictions.
Automated reasoning in classical logic has received much attention in the literature. Mature resolution theorem provers such as Vampire and E can handle enormous problems in first-order classical logic with equality. Waldmeister, a theorem prover for unit equational logic, has been incorporated into Mathematica as an equational reasoning method. Somewhat surprisingly, there has been much less attention devoted to non-classical logics. This is unfortunate, since many interesting and useful logics are inherently non-classical. Well known examples include intuitionistic, substructural and modal logics. Additionally, many modern logics for specialized tasks such as those designed for security and authentication protocols are non-classical as well. The inverse method is a generalizat...
Christopher Gauker (Cincinnati) gives a talk at the MCMP Colloquium (9 Feb, 2012). In this talk, two definitions of logical validity for a simple first-order language are compared in order to decide which one provides a better model for the semantics for natural language. One of these is the standard model-theoretic definition. The other defines contexts as structures of linguistic objects and then defines validity as preservation of truth-in-a-context. The disadvantage of the model-theoretic definition is that it commits us to explicating the reference relation, which no one has ever been able to do. The context-logical definition avoids this commitment, although it takes on others. In particular, it commits to explaining what it takes for a given context to be the context that pertains t...
This is the first of the two video lectures associated with Chapter 10: Argument in "College Composition and Reading: Information and Strategies" by L. Dawn Lukas, and discusses classic logic, with a focus on syllogisms. You can access a PDF of the syllogism validity chart at http://online.santarosa.edu/homepage/dwidler/Eng1A_general/syllogism_chart.pdf
A comprehensive map of all of the disciplines, areas and subdivisions of philosophy. Including logic, History of philosophy, philosophical traditions, value theory, epistemology, metaphysics, philosophy of religion, philosophy of science, philosophy of mind, philosophy of language, philosophy of action, ethics, aesthetics, social philosophy, political philosophy, philosophical methods and more! This video breaks down and offers a brief explanation of each area of study, and should serve as a good introduction for beginners, a solid refresher for journeymen and a cool illustration for experts. Enjoy! Table of Contents: 00:00 Introduction 01:44 Logic and Philosophical Methods 02:14 Formal Classical Logic 04:55 Non-Classical Logic 06:35 Informal Logic 08:00 Philosophical Methods 10:20 The...
In the lecture "Do We Need any Paraconsistent Logic in Theology?" prof. Lambert, outlined several situations when non-classical logics may be useful in theological thinking and remarked that paraconsistent logic should be used carefully. His belief was that paraconsistent logic can be applied only to describe singularities and discontinuities. Otherwise, contradictions would invade whole system of ideas and make it useless. Prof. Lambert underlined the fact that there are two possible interpretations of paraconsistency: the epistemological interpretation (contradiction is in our language and not in reality) and the ontological interpretation (contradictions exist in reality). Prof. Lambert mentioned two main theological issues which can be fruitfully addressed by paraconsistent logic: solv...
Presented Oct. 9, 2013, in the Info-Metrics Seminar Series at American University in Washington, DC. http://www.american.edu/cas/economics/info-metrics/ Abstract: The development of the concept of information is traced from Plato to the Port-Royal Logic, on through Mill, Boole, Frege, Carnap, Bar-Hillel, Montague, Kripke, Shannon, and I relate it to algebraic representations of Stone, Priestley, myself, and others. I finish by introducing the concept of an information frame, generalizing the Routley-Meyer ternary frame semantics for relevance logic, and show how it can be employed to model the static and dynamic aspects of information (information as data, information as program) and hence model combinatory logic, relation algebras, and some other logics of interest to computer science....
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Professor Graham Priest (City University of New York) speaks at the Epistemology Research Group, 12th April 2017. Abstract: Elsewhere I have endorsed a model of rational choice between logical theories, in terms of computing the weighted average of the various good-making criteria of theories. There is currently a debate between those (like Williamson) who hold that counterfactuals with impossible antecedents are all vacuously true, and those (such as myself), who hold that this is not the case. In this talk I will show how the debate can be understood in terms of the above-mentioned model of rational theory-choice. I shall argue that non-vacuism is the better theory. The main point of the talk, however, is to illustrate the model of theory-choice, and so support its plausibility.