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.
In logic, the law of excluded middle or the principle of excluded middle states that for every proposition, either this proposition or its negation is true. It is one of the three laws of thought, along with the law of noncontradiction, and the law of identity; however, no system of logic is built on just these laws, and none of these laws provides inference rules, such as modus ponens or De Morgan's laws. The law is also known as the law / principleof the excluded third, in Latin principium tertii exclusi. Another Latin designation for this law is tertium non datur or "no third [possibility] is given". In classical logic, the law is a tautology.
In philosophy and logic, the classical liar paradox or liar's paradox or antinomy of the liar is the statement of a liar that they are lying: for instance, declaring that "I am lying". If the liar is indeed lying, then the liar is telling the truth, which means the liar just lied. In "this sentence is a lie" the paradox is strengthened in order to make it amenable to more rigorous logical analysis. It is still generally called the "liar paradox" although abstraction is made precisely from the liar making the statement. Trying to assign to this statement, the strengthened liar, a classical binary truth value leads to a contradiction.
In traditional logic, a contradiction occurs when a proposition conflicts either with itself or established fact. It is often used as a tool to detect disingenuous beliefs and bias. Illustrating a general tendency in applied logic, Aristotle's law of noncontradiction states that "It is impossible that the same thing can at the same time both belong and not belong to the same object and in the same respect."
In logic, false or untrue is the state of possessing negative truth value and is a nullary logical connective. In a truth-functional system of propositional logic, it is one of two postulated truth values, along with its negation, truth. Usual notations of the false are 0, O, and the up tack symbol .
In logic, a three-valued logic is any of several many-valued logic systems in which there are three truth values indicating true, false, and some third value. This is contrasted with the more commonly known bivalent logics which provide only for true and false.
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.
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.
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.
Graham Priest is a philosopher and logician who 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 the University of St Andrews.
Logical truth is one of the most fundamental concepts in logic. Broadly speaking, a logical truth is a statement which is true regardless of the truth or falsity of its constituent propositions. In other words, a logical truth is a statement which is not only true, but one which is true under all interpretations of its logical components. Thus, logical truths such as "if p, then p" can be considered tautologies. Logical truths are thought to be the simplest case of statements which are analytically true. All of philosophical logic can be thought of as providing accounts of the nature of logical truth, as well as logical consequence.
Logic is the formal science of using reason and is considered a branch of both philosophy and mathematics and to a lesser extent computer science. Logic investigates and classifies the structure of statements and arguments, both through the study of formal systems of inference and the study of arguments in natural language. The scope of logic can therefore be very large, ranging from core topics such as the study of fallacies and paradoxes, to specialized analyses of reasoning such as probability, correct reasoning, and arguments involving causality. One of the aims of logic is to identify the correct and incorrect inferences. Logicians study the criteria for the evaluation of arguments.
Stephen Yablo is a Canadian-born American philosopher. He is David W. Skinner Professor of Philosophy at the Massachusetts Institute of Technology (MIT) and taught previously at the University of Michigan, Ann Arbor. He specializes in the philosophy of logic, philosophy of mind, metaphysics, philosophy of language, and philosophy of mathematics.
Jc Beall is an American philosopher working in philosophy of logic and philosophical logic, who since 2020, holds the O’Neill Family Chair of Philosophy at the University of Notre Dame. He was previously the Board of Trustees Distinguished Professor of Philosophy at the University of Connecticut.
The following is a list of works by philosopher Graham Priest.
This is a glossary of logic. Logic is the study of the principles of valid reasoning and argumentation.
