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First-order logic—also known as predicate logic, quantificational logic, and first-order predicate calculus—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantified variables over non-logical objects, and allows the use of sentences that contain variables, so that rather than propositions such as "Socrates is a man", one can have expressions in the form "there exists x such that x is Socrates and x is a man", where "there exists" is a quantifier, while x is a variable. This distinguishes it from propositional logic, which does not use quantifiers or relations; in this sense, propositional logic is the foundation of first-order logic.
Truth is the property of being in accord with fact or reality. In everyday language, truth is typically ascribed to things that aim to represent reality or otherwise correspond to it, such as beliefs, propositions, and declarative sentences.
In philosophy, vagueness is an important problem in semantics, metaphysics and philosophical logic. Definitions of this problem vary. A predicate is vague if it has borderline cases. The predicate "is tall" is vague because there seems to be no particular height at which someone becomes tall. Alternately, a predicate is sometimes said to be vague if there are borderline cases of its application, such that in these cases competent speakers of the language may faultlessly disagree over whether the predicate applies. The disagreement over whether a hotdog is a sandwich suggests that “sandwich” is vague.
Saul Aaron Kripke is an American philosopher and logician in the analytic tradition. He is a Distinguished Professor of Philosophy at the Graduate Center of the City University of New York and emeritus professor at Princeton University. Since the 1960s, Kripke has been a central figure in a number of fields related to mathematical logic, modal logic, philosophy of language, philosophy of mathematics, metaphysics, epistemology, and recursion theory. Much of his work remains unpublished or exists only as tape recordings and privately circulated manuscripts.
Friedrich Ludwig Gottlob Frege was a German philosopher, logician, and mathematician. He worked as a mathematics professor at the University of Jena, and is understood by many to be the father of analytic philosophy, concentrating on the philosophy of language, logic, and mathematics. Though he was largely ignored during his lifetime, Giuseppe Peano (1858–1932), Bertrand Russell (1872–1970), and, to some extent, Ludwig Wittgenstein (1889–1951) introduced his work to later generations of philosophers.
In philosophy, a proposition is the meaning of a declarative sentence, where "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.
Moral realism is the position that ethical sentences express propositions that refer to objective features of the world, some of which may be true to the extent that they report those features accurately. This makes moral realism a non-nihilist form of ethical cognitivism with an ontological orientation, standing in opposition to all forms of moral anti-realism and moral skepticism, including ethical subjectivism, error theory ; and non-cognitivism. Within moral realism, the two main subdivisions are ethical naturalism and ethical non-naturalism.
In the philosophy of language, the distinction between sense and reference was an innovation of the German philosopher and mathematician Gottlob Frege in 1892, reflecting the two ways he believed a singular term may have meaning.
Bernard Bolzano was a Bohemian mathematician, logician, philosopher, theologian and Catholic priest of Italian extraction, also known for his liberal views.
Peter Thomas Geach (1916–2013) was an English philosopher and professor of logic at the University of Leeds. His areas of interest were philosophical logic, ethics, history of philosophy, philosophy of religion and the theory of identity.
In philosophy, term logic, also known as traditional logic, syllogistic logic or Aristotelian logic, is a loose name for an approach to logic that began with Aristotle and was developed further in ancient times mostly by his followers, the peripatetics, but largely fell into decline by the third century CE. Term logic revived in medieval times, first in Islamic logic by Alpharabius in the tenth century, and later in Christian Europe in the twelfth century with the advent of new logic, and remained dominant until the advent of modern predicate logic in the late nineteenth century. This entry is an introduction to the term logic needed to understand philosophy texts written before it was replaced as a formal logic system by predicate logic. Readers lacking a grasp of the basic terminology and ideas of term logic can have difficulty understanding such texts, because their authors typically assumed an acquaintance with term logic.
Gertrude Elizabeth Margaret Anscombe, usually cited as G. E. M. Anscombe or Elizabeth Anscombe, was a British analytic philosopher. She wrote on the philosophy of mind, philosophy of action, philosophical logic, philosophy of language, and ethics. She was a prominent figure of analytical Thomism.
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.
The theory of descriptions is the philosopher Bertrand Russell's most significant contribution to the philosophy of language. It is also known as Russell's theory of descriptions. In short, Russell argued that the syntactic form of descriptions is misleading, as it does not correlate their logical and/or semantic architecture. While descriptions may seem fairly uncontroversial phrases, Russell argued that providing a satisfactory analysis of the linguistic and logical properties of a description is vital to clarity in important philosophical debates, particularly in semantic arguments, epistemology and metaphysics.
Norms are concepts (sentences) of practical import, oriented to effecting an action, rather than conceptual abstractions that describe, explain, and express. Normative sentences imply "ought-to" types of statements and assertions, in distinction to sentences that provide "is" types of statements and assertions. Common normative sentences include commands, permissions, and prohibitions; common normative abstract concepts include sincerity, justification, and honesty. A popular account of norms describes them as reasons to take action, to believe, and to feel.
The Categories is a text from Aristotle's Organon that enumerates all the possible kinds of things that can be the subject or the predicate of a proposition. They are "perhaps the single most heavily discussed of all Aristotelian notions". The work is brief enough to be divided, not into books as is usual with Aristotle's works, but into fifteen chapters.
In logic, a categorical proposition, or categorical statement, is a proposition that asserts or denies that all or some of the members of one category are included in another. The study of arguments using categorical statements forms an important branch of deductive reasoning that began with the Ancient Greeks.
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 solely by virtue of their meaning, whereas synthetic propositions are true based on how their meaning relates to the world.
In analytic philosophy, philosophy of language investigates the nature of language, the relations between language, language users, and the world. Investigations may include inquiry into the nature of meaning, intentionality, reference, the constitution of sentences, concepts, learning, and thought.
The Frege–Church ontology is an ontology, a theory of existence. Everything is considered as being in three categories, object, name, or concept (sense). The ontology was developed by Alonzo Church based on ideas of Gottlob Frege to resolve some paradoxes. The ontology is related to certain modal logics.
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