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Willard Van Orman Quine was an American philosopher and logician in the analytic tradition, recognized as "one of the most influential philosophers of the twentieth century." From 1930 until his death 70 years later, Quine was continually affiliated with Harvard University in one way or another, first as a student, then as a professor. He filled the Edgar Pierce Chair of Philosophy at Harvard from 1956 to 1978.
In logic and proof theory, natural deduction is a kind of proof calculus in which logical reasoning is expressed by inference rules closely related to the "natural" way of reasoning. This contrasts with Hilbert-style systems, which instead use axioms as much as possible to express the logical laws of deductive reasoning.
In linguistics and logic, a proposition is the meaning of a declarative sentence. In philosophy, "meaning" is understood to be a non-linguistic entity which is shared by all sentences with the same meaning. Equivalently, a proposition is the non-linguistic bearer of truth or falsity which makes any sentence that expresses it either true or false.
A propositional attitude is a mental state held by an agent toward a proposition.
In philosophy and logic, a deflationary theory of truth is one of a family of theories that all have in common the claim that assertions of predicate truth of a statement do not attribute a property called "truth" to such a statement.
A possible world is a complete and consistent way the world is or could have been. They are widely used as a formal device in logic, philosophy, and linguistics in order to provide a semantics for intensional and modal logic. Their metaphysical status has been a subject of controversy in philosophy, with modal realists such as David Lewis arguing that they are literally existing alternate realities, and others such as Robert Stalnaker arguing that they are not.
"Two Dogmas of Empiricism" is a paper by analytic philosopher Willard Van Orman Quine published in 1951. According to University of Sydney professor of philosophy Peter Godfrey-Smith, this "paper [is] sometimes regarded as the most important in all of twentieth-century philosophy". The paper is an attack on two central aspects of the logical positivists' philosophy: the first being the analytic–synthetic distinction between analytic truths and synthetic truths, explained by Quine as truths grounded only in meanings and independent of facts, and truths grounded in facts; the other being reductionism, the theory that each meaningful statement gets its meaning from some logical construction of terms that refer exclusively to immediate experience.
In logic, the law of identity states that each thing is identical with itself. It is the first of the historical three laws of thought, along with the law of noncontradiction, and the law of excluded middle. However, no system of logic is built on just these laws, and none of these laws provide inference rules, such as modus ponens or DeMorgan's laws.
David Benjamin Kaplan is an American philosopher. He is the Hans Reichenbach Professor of Scientific Philosophy at the UCLA Department of Philosophy. His philosophical work focuses on the philosophy of language, logic, metaphysics, epistemology and the philosophy of Frege and Russell. He is best known for his work on demonstratives, propositions, and reference in intensional contexts. He was elected a Fellow of the American Academy of Arts & Sciences in 1983 and a Corresponding Fellow of the British Academy in 2007.
In philosophy of language, an extensional context is a syntactic environment in which a sub-sentential expression e can be replaced by an expression with the same extension and without affecting the truth-value of the sentence as a whole. Extensional contexts are contrasted with opaque contexts where truth-preserving substitutions are not possible.
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.
Frege's puzzles are puzzles about the semantics of proper names, although related puzzles also arise in the case of indexicals. Gottlob Frege (1848–1925) introduced the puzzle at the beginning of his article "Über Sinn und Bedeutung" in 1892 in one of the most influential articles in analytic philosophy and philosophy of language.
The analytic–synthetic distinction is a semantic distinction, used primarily in philosophy to distinguish between propositions that are of two types: analytic propositions and synthetic propositions. Analytic propositions are true or not true solely by virtue of their meaning, whereas synthetic propositions' truth, if any, derives from how their meaning relates to the world.
A priori and a posteriori are Latin phrases used in philosophy to distinguish types of knowledge, justification, or argument by their reliance on empirical evidence or experience. A priori knowledge is that which is independent from experience. Examples include mathematics, tautologies, and deduction from pure reason. A posteriori knowledge is that which depends on empirical evidence. Examples include most fields of science and aspects of personal knowledge.
An interpretation is an assignment of meaning to the symbols of a formal language. Many formal languages used in mathematics, logic, and theoretical computer science are defined in solely syntactic terms, and as such do not have any meaning until they are given some interpretation. The general study of interpretations of formal languages is called formal semantics.
In logic, the term statement is variously understood to mean either:
- a meaningful declarative sentence that is true or false, or
- a proposition. Which is the assertion that is made by a true or false declarative sentence.
Following the developments in the philosophical study of formal logic with symbolic logic in the late nineteenth century and mathematical logic in the twentieth, topics traditionally treated by logic not being part of formal logic have tended to be termed either philosophy of logic or philosophical logic if no longer simply logic.
Salva congruitate is a Latin scholastic term in logic, which means "without becoming ill-formed", salva meaning rescue, salvation, welfare and congruitate meaning combine, coincide, agree. Salva Congruitate is used in logic to mean that two terms may be substituted for each other while preserving grammaticality in all contexts.
In modal logic and the philosophy of language, a vivid designator is a term which is believed to designate the same thing in all possible worlds and nothing else where such an object does not exist in a possible world. It is the analogue, in the sense of believing, of a rigid designator, which is the same in all possible worlds, rather than is just believed to be so.