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.
The problem of universals is an ancient question from metaphysics that has inspired a range of philosophical topics and disputes: "Should the properties an object has in common with other objects, such as color and shape, be considered to exist beyond those objects? And if a property exists separately from objects, what is the nature of that existence?"
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".
Zeno's paradoxes are a series of philosophical arguments presented by the ancient Greek philosopher Zeno of Elea, primarily known through the works of Plato, Aristotle, and later commentators like Simplicius of Cilicia. Zeno devised these paradoxes to support his teacher Parmenides's philosophy of monism, which posits that despite our sensory experiences, reality is singular and unchanging. The paradoxes famously challenge the notions of plurality, motion, space, and time by suggesting they lead to logical contradictions.
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.
Analytic philosophy is a broad, contemporary movement or tradition within Western philosophy and especially anglophone philosophy, focused on analysis. Analytic philosophy is characterized by a style of clarity of prose and rigor in arguments, 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, and as a consequence the argument fails to persuade. 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.
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, dealing with philosophy, philosophical topics, and philosophers. The IEP publishes only peer reviewed and blind-refereed original papers. Contribution is generally by invitation, and contributors are recognized and 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.
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 British Academy Reader in Humanities, University of Oxford, 1982–84.
Western philosophy refers to the philosophical thought and work of the Western world. Historically, the term refers to the philosophical thinking of Western culture, beginning with the ancient Greek philosophy of the pre-Socratics. The word philosophy itself originated from the Ancient Greek philosophía (φιλοσοφία), literally, "the love of wisdom" Ancient Greek: φιλεῖν phileîn, "to love" and σοφία sophía, "wisdom").
The following outline is provided as an overview of and topical guide to metaphysics:
Adrian William Moore is a British philosopher and broadcaster. He is Professor of Philosophy at the University of Oxford and tutorial fellow of St Hugh's College, Oxford. His main areas of interest are Kant, Wittgenstein, history of philosophy, metaphysics, philosophy of mathematics, philosophy of logic and language, ethics and philosophy of religion.
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 due to the structure of arguments alone, independent of their topic and content. Informal logic is associated with informal fallacies, critical thinking, and argumentation theory. It examines arguments expressed in natural language while formal logic uses formal language. When used as a countable noun, the term "a logic" refers to a logical formal system that articulates a proof system. Logic plays a central role in many fields, such as philosophy, mathematics, computer science, and linguistics.
