In logic, the law of non-contradiction (LNC) states that contradictory propositions cannot both be true in the same sense at the same time, e. g. the two propositions "p is the case" and "p is not the case" are mutually exclusive. Formally, this is expressed as the tautology ¬(p ∧ ¬p). The law is not to be confused with the law of excluded middle which states that at least one, "p is the case" or "p is not the case", holds.
Pluralism is a term used in philosophy, referring to a worldview of multiplicity, often used in opposition to monism or dualism. The term has different meanings in metaphysics, ontology, epistemology and logic. In metaphysics, it is the view that there are in fact many different substances in nature that constitute reality. In ontology, pluralism refers to different ways, kinds, or modes of being. For example, a topic in ontological pluralism is the comparison of the modes of existence of things like 'humans' and 'cars' with things like 'numbers' and some other concepts as they are used in science.
Understood in a narrow sense, philosophical logic is the area of logic that studies the application of logical methods to philosophical problems, often in the form of extended logical systems like modal logic. Some theorists conceive philosophical logic in a wider sense as the study of the scope and nature of logic in general. In this sense, philosophical logic can be seen as identical to the philosophy of logic, which includes additional topics like how to define logic or a discussion of the fundamental concepts of logic. The current article treats philosophical logic in the narrow sense, in which it forms one field of inquiry within the philosophy of logic.
Logical possibility refers to a logical proposition that cannot be disproved, using the axioms and rules of a given system of logic. The logical possibility of a proposition will depend upon the system of logic being considered, rather than on the violation of any single rule. Some systems of logic restrict inferences from inconsistent propositions or even allow for true contradictions. Other logical systems have more than two truth-values instead of a binary of such values. Some assume the system in question is classical propositional logic. Similarly, the criterion for logical possibility is often based on whether or not a proposition is contradictory and as such, is often thought of as the broadest type of possibility.
Paraconsistent logic is a type of non-classical logic that allows for the coexistence of contradictory statements without leading to a logical explosion where anything can be proven true. Specifically, paraconsistent logic is the subfield of logic that is concerned with studying and developing "inconsistency-tolerant" systems of logic, purposefully excluding the principle of explosion.
Richard Sylvan was a New Zealand–born philosopher, logician, and environmentalist.
Dialetheism is the view that there are statements that are both true and false. More precisely, it is the belief that there can be a true statement whose negation is also true. Such statements are called "true contradictions", dialetheia, or nondualisms.
In classical logic, intuitionistic logic, and similar logical systems, the principle of explosion is the law according to which any statement can be proven from a contradiction. That is, from a contradiction, any proposition can be inferred; this is known as deductive explosion.
In logic, a strict conditional is a conditional governed by a modal operator, that is, a logical connective of modal logic. It is logically equivalent to the material conditional of classical logic, combined with the necessity operator from modal logic. For any two propositions p and q, the formula p → q says that p materially implies q while says that p strictly implies q. Strict conditionals are the result of Clarence Irving Lewis's attempt to find a conditional for logic that can adequately express indicative conditionals in natural language. They have also been used in studying Molinist theology.
Philosophy is the study of general and fundamental problems concerning matters such as existence, knowledge, values, reason, mind, and language. It is distinguished from other ways of addressing fundamental questions by being critical and generally systematic and by its reliance on rational argument. It involves logical analysis of language and clarification of the meaning of words and concepts.
Non-classical logics are 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 commonly the case, including by way of extensions, deviations, and variations. The aim of these departures is to make it possible to construct different models of logical consequence and logical truth.
Jean-Yves Beziau (French:[bezjo]; born January 15, 1965, in Orléans, France is a Swiss Professor in logic at the University of Brazil, Rio de Janeiro, and Researcher of the Brazilian Research Council. He is permanent member and former president of the Brazilian Academy of Philosophy. Before going to Brazil, he was Professor of the Swiss National Science Foundation at the University of Neuchâtel in Switzerland and researcher at Stanford University working with Patrick Suppes.
Noneism, also known as modal Meinongianism, is a theory in logic and metaphysics. It holds that some things do not exist. It was first coined by Richard Routley in 1980 and appropriated again in 2005 by Graham Priest.
Trivialism is the logical theory that all statements are true and, consequently, that all contradictions of the form "p and not p" are true. In accordance with this, a trivialist is a person who believes everything is true.
Meinong's jungle is a term used to describe the repository of non-existent objects in the ontology of Alexius Meinong. An example of such an object is a "round square", which cannot exist definitionally and yet can be the subject of logical inferences, such as that it is both "round" and "square".
Lorenzo Peña is a Spanish philosopher, lawyer, logician and political thinker. His rationalism is a neo-Leibnizian approach both in metaphysics and law.
Eduardo Barrio is an Argentine logician.
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical truths. It examines how conclusions follow from premises based on the structure of arguments alone, independent of their topic and content. Informal logic is associated with informal fallacies, critical thinking, and argumentation theory. Informal logic examines arguments expressed in natural language whereas formal logic uses formal language. When used as a countable noun, the term "a logic" refers to a specific logical formal system that articulates a proof system. Logic plays a central role in many fields, such as philosophy, mathematics, computer science, and linguistics.
The following is a list of works by philosopher Graham Priest.
