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.
A paradox is a logically self-contradictory statement or a statement that runs contrary to one's expectation. It is a statement that, despite apparently valid reasoning from true or apparently true premises, leads to a seemingly self-contradictory or a logically unacceptable conclusion. A paradox usually involves contradictory-yet-interrelated elements that exist simultaneously and persist over time. They result in "persistent contradiction between interdependent elements" leading to a lasting "unity of opposites".
A fallacy is the use of invalid or otherwise faulty reasoning in the construction of an argument that may appear to be well-reasoned if unnoticed. The term was introduced in the Western intellectual tradition by the Aristotelian De Sophisticis Elenchis.
Deductive reasoning is the process of drawing valid inferences. An inference is valid if its conclusion follows logically from its premises, meaning that it is impossible for the premises to be true and the conclusion to be false. For example, the inference from the premises "all men are mortal" and "Socrates is a man" to the conclusion "Socrates is mortal" is deductively valid. An argument is sound if it is valid and all its premises are true. One approach defines deduction in terms of the intentions of the author: they have to intend for the premises to offer deductive support to the conclusion. With the help of this modification, it is possible to distinguish valid from invalid deductive reasoning: it is invalid if the author's belief about the deductive support is false, but even invalid deductive reasoning is a form of deductive reasoning.
Analytic philosophy is an analysis focused, broad, contemporary movement or tradition within Western philosophy, especially anglophone philosophy. Analytic philosophy is characterized by a clarity of prose; rigor in arguments; and making use of formal logic and mathematics, and, to a lesser degree, the natural sciences. It is further characterized by an interest in language and meaning known as the linguistic turn. It has developed several new branches of philosophy and logic, notably philosophy of language, philosophy of mathematics, philosophy of science, modern predicate logic and mathematical logic.
Circular reasoning is a logical fallacy in which the reasoner begins with what they are trying to end with. Circular reasoning is not a formal logical fallacy, but a pragmatic defect in an argument whereby the premises are just as much in need of proof or evidence as the conclusion. As a consequence, the argument becomes a matter of faith and fails to persuade those who don't already accept it. Other ways to express this are that there is no reason to accept the premises unless one already believes the conclusion, or that the premises provide no independent ground or evidence for the conclusion. Circular reasoning is closely related to begging the question, and in modern usage the two generally refer to the same thing.
Logical reasoning is a mental activity that aims to arrive at a conclusion in a rigorous way. It happens in the form of inferences or arguments by starting from a set of premises and reasoning to a conclusion supported by these premises. The premises and the conclusion are propositions, i.e. true or false claims about what is the case. Together, they form an argument. Logical reasoning is norm-governed in the sense that it aims to formulate correct arguments that any rational person would find convincing. The main discipline studying logical reasoning is logic.
A temporal paradox, time paradox, or time travel paradox, is a paradox, an apparent contradiction, or logical contradiction associated with the idea of time travel or other foreknowledge of the future. While the notion of time travel to the future complies with the current understanding of physics via relativistic time dilation, temporal paradoxes arise from circumstances involving hypothetical time travel to the past – and are often used to demonstrate its impossibility.
Carl Gustav "Peter" Hempel was a German writer, philosopher, logician, and epistemologist. He was a major figure in logical empiricism, a 20th-century movement in the philosophy of science. Hempel articulated the deductive-nomological model of scientific explanation, which was considered the "standard model" of scientific explanation during the 1950s and 1960s. He is also known for the raven paradox and Hempel's dilemma.
Bastiaan Cornelis van Fraassen is a Dutch-American philosopher noted for his contributions to philosophy of science, epistemology and formal logic. He is a Distinguished Professor of Philosophy at San Francisco State University and the McCosh Professor of Philosophy Emeritus at Princeton University.
The Internet Encyclopedia of Philosophy (IEP) is a scholarly online encyclopedia with 880 articles about philosophy, philosophers, and related topics. The IEP publishes only peer-reviewed and blind-refereed original papers. Contribution is generally by invitation, and contributors are recognized as leading international specialists within their field.
Timothy Williamson is a British philosopher whose main research interests are in philosophical logic, philosophy of language, epistemology and metaphysics. He is the former Wykeham Professor of Logic at the University of Oxford, and a fellow of New College, Oxford.
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.
Kit Fine is a British philosopher, currently university professor and Silver Professor of Philosophy and Mathematics at New York University. Prior to joining the philosophy department of NYU in 1997, he taught at the University of Edinburgh, University of California, Irvine, University of Michigan and UCLA. The author of several books and dozens of articles in international academic journals, he has made notable contributions to the fields of philosophical logic, metaphysics, and the philosophy of language and also has written on ancient philosophy, in particular on Aristotle's account of logic and modality.
A priori and a posteriori are Latin phrases used in philosophy to distinguish types of knowledge, justification, or argument by their reliance on experience. A priori knowledge is independent from any experience. Examples include mathematics, tautologies and deduction from pure reason. A posteriori knowledge depends on empirical evidence. Examples include most fields of science and aspects of personal knowledge.
Laurence Jonathan Cohen,, was a British philosopher. He was Fellow and Praelector in Philosophy, 1957–90 and Senior Tutor, 1985–90 at The Queen's College, Oxford and was a British Academy Reader in Humanities, University of Oxford, 1982–84.
Philosophy is a systematic study of general and fundamental questions concerning topics like existence, reason, knowledge, value, mind, and language. It is a rational and critical inquiry that reflects on its own methods and assumptions.
A mathematical object is an abstract concept arising in mathematics. In the usual language of mathematics, an object is anything that has been formally defined, and with which one may do deductive reasoning and mathematical proofs. Typically, a mathematical object can be a value that can be assigned to a variable, and therefore can be involved in formulas. Commonly encountered mathematical objects include numbers, sets, functions, expressions, geometric objects, transformations of other mathematical objects, and spaces. Mathematical objects can be very complex; for example, theorems, proofs, and even theories are considered as mathematical objects in proof theory.
Philosophy of logic is the area of philosophy that studies the scope and nature of logic. It investigates the philosophical problems raised by logic, such as the presuppositions often implicitly at work in theories of logic and in their application. This involves questions about how logic is to be defined and how different logical systems are connected to each other. It includes the study of the nature of the fundamental concepts used by logic and the relation of logic to other disciplines. According to a common characterisation, philosophical logic is the part of the philosophy of logic that studies the application of logical methods to philosophical problems, often in the form of extended logical systems like modal logic. But other theorists draw the distinction between the philosophy of logic and philosophical logic differently or not at all. Metalogic is closely related to the philosophy of logic as the discipline investigating the properties of formal logical systems, like consistency and completeness.
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.
