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First-order logic—also called predicate logic, predicate calculus, quantificational logic—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. Rather than propositions such as "all men are mortal", in first-order logic one can have expressions in the form "for all x, if x is a man, then x is mortal"; where "for all x" is a quantifier, x is a variable, and "... is a man" and "... is mortal" are predicates. 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 or verity is the property of being in accord with fact or reality. In everyday language, it is typically ascribed to things that aim to represent reality or otherwise correspond to it, such as beliefs, propositions, and declarative sentences.
In linguistics and philosophy, a vague predicate is one which gives rise to borderline cases. For example, the English adjective "tall" is vague since it is not clearly true or false for someone of middling height. By contrast, the word "prime" is not vague since every number is definitively either prime or not. Vagueness is commonly diagnosed by a predicate's ability to give rise to the Sorites paradox. Vagueness is separate from ambiguity, in which an expression has multiple denotations. For instance the word "bank" is ambiguous since it can refer either to a river bank or to a financial institution, but there are no borderline cases between both interpretations.
Friedrich Ludwig Gottlob Frege was a German philosopher, logician, and mathematician. He was 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. Frege is widely considered to be the greatest logician since Aristotle, and one of the most profound philosophers of mathematics ever.
The history of logic deals with the study of the development of the science of valid inference (logic). Formal logics developed in ancient times in India, China, and Greece. Greek methods, particularly Aristotelian logic as found in the Organon, found wide application and acceptance in Western science and mathematics for millennia. The Stoics, especially Chrysippus, began the development of predicate logic.
A proposition is a central concept in the philosophy of language, semantics, logic, and related fields, often characterized as the primary bearer of truth or falsity. Propositions are also often characterized as the type of object that declarative sentences denote. For instance the sentence "The sky is blue" denotes the proposition that the sky is blue. However, crucially, propositions are not themselves linguistic expressions. For instance, the English sentence "Snow is white" denotes the same proposition as the German sentence "Schnee ist weiß" even though the two sentences are not the same. Similarly, propositions can also be characterized as the objects of belief and other propositional attitudes. For instance if someone believes that the sky is blue, the object of their belief is the proposition that the sky is blue.
In the philosophy of language, the distinction between sense and reference was an idea 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 was a British philosopher who was 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 logic and formal semantics, term logic, also known as traditional logic, syllogistic logic or Aristotelian logic, is a loose name for an approach to formal logic that began with Aristotle and was developed further in ancient history mostly by his followers, the Peripatetics. It was revived after the third century CE by Porphyry's Isagoge.
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, a Fellow of Somerville College, Oxford, and a professor of philosophy at the University of Cambridge.
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 like 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 metaphysical elements.
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.
In metaphysics, the A series and the B series are two different descriptions of the temporal ordering relation among events. The two series differ principally in their use of tense to describe the temporal relation between events and the resulting ontological implications regarding time.
A truth-bearer is an entity that is said to be either true or false and nothing else. The thesis that some things are true while others are false has led to different theories about the nature of these entities. Since there is divergence of opinion on the matter, the term truth-bearer is used to be neutral among the various theories. Truth-bearer candidates include propositions, sentences, sentence-tokens, statements, beliefs, thoughts, intuitions, utterances, and judgements but different authors exclude one or more of these, deny their existence, argue that they are true only in a derivative sense, assert or assume that the terms are synonymous, or seek to avoid addressing their distinction or do not clarify it.
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.
Philosophy of language investigates the nature of language and 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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