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130 relations: Abstract and concrete, Alfred North Whitehead, Alfred Tarski, Ancient Greek, Antisymmetric relation, Aristotle, Arity, Artificial intelligence, Asymmetric relation, Atomism, Axiom, Axiom of extensionality, Axiom of regularity, Axiom schema, Axiomatic system, Bertrand Russell, Binary relation, Boolean algebra, Boolean algebra (structure), Boundary (topology), Category theory, Complement (set theory), Complete lattice, Computer science, Countable set, David Lewis (philosopher), Distributive property, Domain of discourse, Edmund Husserl, Element (mathematics), Empty set, Extensionality, First-order logic, Formal ontology, Foundations of mathematics, Free logic, Free variables and bound variables, G. Spencer-Brown, Gabriel Kron, Geometry, Georg Cantor, Giuseppe Peano, Grammatical aspect, Group polarization, Gunk (mereology), Hasse diagram, Identity (philosophy), Implicate and explicate order, Integrity, Intersection (set theory), ..., Ivor Grattan-Guinness, John Lucas (philosopher), Join and meet, Joseph Goguen, Kit Fine, Lattice (order), Laws of Form, Logical truth, Mass noun, Mathematical logic, Mathematics, Mereological essentialism, Mereological nihilism, Mereotopology, Meronomy, Meronymy, Metaphysics, Michel Weber, Mihajlo D. Mesarovic, Modal logic, Model theory, Monad (philosophy), Naive set theory, Natural language, Natural number, Natural science, Nelson Goodman, Nihilism, Nominalism, Occam's razor, Ontology, Ordered pair, Parmenides (dialogue), Partially ordered set, Peano axioms, Philosophy, Physical body, Plato, Plural quantification, Predicate (mathematical logic), Principia Mathematica, Process and Reality, Quantifier (logic), Quantifier variance, Quantum mechanics, Real number, Reflexive relation, Richard Milton Martin, Roderick Chisholm, Russell's paradox, Semantics, Semilattice, Set (mathematics), Set theory, Set-builder notation, Sheaf (mathematics), Ship of Theseus, Simple (philosophy), Singleton (mathematics), Stanford Encyclopedia of Philosophy, Stanisław Leśniewski, Steve Vickers (computer scientist), Subset, Symmetry, Syntax, Systems theory, Temporal logic, Temporal parts, Theoretical physics, Topology, Topos, Transitive relation, Trinity College, Cambridge, Union (set theory), Universal set, Universe, Well-founded relation, Whitehead's point-free geometry, Willard Van Orman Quine, Zermelo–Fraenkel set theory. Expand index (80 more) »
Abstract and concrete
Abstract and concrete are classifications that denote whether a term describes an object with a physical referent or one with no physical referents.
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Alfred North Whitehead
Alfred North Whitehead (15 February 1861 – 30 December 1947) was an English mathematician and philosopher.
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Alfred Tarski
Alfred Tarski (January 14, 1901 – October 26, 1983), born Alfred Teitelbaum,School of Mathematics and Statistics, University of St Andrews,, School of Mathematics and Statistics, University of St Andrews.
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Ancient Greek
The Ancient Greek language includes the forms of Greek used in ancient Greece and the ancient world from around the 9th century BC to the 6th century AD.
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Antisymmetric relation
In mathematics, a binary relation R on a set X is anti-symmetric if there is no pair of distinct elements of X each of which is related by R to the other.
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Aristotle
Aristotle (Ἀριστοτέλης Aristotélēs,; 384–322 BC) was an ancient Greek philosopher and scientist born in the city of Stagira, Chalkidiki, in the north of Classical Greece.
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Arity
In logic, mathematics, and computer science, the arity of a function or operation is the number of arguments or operands that the function takes.
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Artificial intelligence
Artificial intelligence (AI, also machine intelligence, MI) is intelligence demonstrated by machines, in contrast to the natural intelligence (NI) displayed by humans and other animals.
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Asymmetric relation
In mathematics, an asymmetric relation is a binary relation on a set X where.
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Atomism
Atomism (from Greek ἄτομον, atomon, i.e. "uncuttable", "indivisible") is a natural philosophy that developed in several ancient traditions.
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Axiom
An axiom or postulate is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments.
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Axiom of extensionality
In axiomatic set theory and the branches of logic, mathematics, and computer science that use it, the axiom of extensionality, or axiom of extension, is one of the axioms of Zermelo–Fraenkel set theory.
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Axiom of regularity
In mathematics, the axiom of regularity (also known as the axiom of foundation) is an axiom of Zermelo–Fraenkel set theory that states that every non-empty set A contains an element that is disjoint from A. In first-order logic, the axiom reads: The axiom implies that no set is an element of itself, and that there is no infinite sequence (an) such that ai+1 is an element of ai for all i. With the axiom of dependent choice (which is a weakened form of the axiom of choice), this result can be reversed: if there are no such infinite sequences, then the axiom of regularity is true.
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Axiom schema
In mathematical logic, an axiom schema (plural: axiom schemata or axiom schemas) generalizes the notion of axiom.
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Axiomatic system
In mathematics, an axiomatic system is any set of axioms from which some or all axioms can be used in conjunction to logically derive theorems.
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Bertrand Russell
Bertrand Arthur William Russell, 3rd Earl Russell, (18 May 1872 – 2 February 1970) was a British philosopher, logician, mathematician, historian, writer, social critic, political activist, and Nobel laureate.
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Binary relation
In mathematics, a binary relation on a set A is a set of ordered pairs of elements of A. In other words, it is a subset of the Cartesian product A2.
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Boolean algebra
In mathematics and mathematical logic, Boolean algebra is the branch of algebra in which the values of the variables are the truth values true and false, usually denoted 1 and 0 respectively.
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Boolean algebra (structure)
In abstract algebra, a Boolean algebra or Boolean lattice is a complemented distributive lattice.
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Boundary (topology)
In topology and mathematics in general, the boundary of a subset S of a topological space X is the set of points which can be approached both from S and from the outside of S. More precisely, it is the set of points in the closure of S not belonging to the interior of S. An element of the boundary of S is called a boundary point of S. The term boundary operation refers to finding or taking the boundary of a set.
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Category theory
Category theory formalizes mathematical structure and its concepts in terms of a labeled directed graph called a category, whose nodes are called objects, and whose labelled directed edges are called arrows (or morphisms).
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Complement (set theory)
In set theory, the complement of a set refers to elements not in.
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Complete lattice
In mathematics, a complete lattice is a partially ordered set in which all subsets have both a supremum (join) and an infimum (meet).
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Computer science
Computer science deals with the theoretical foundations of information and computation, together with practical techniques for the implementation and application of these foundations.
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Countable set
In mathematics, a countable set is a set with the same cardinality (number of elements) as some subset of the set of natural numbers.
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David Lewis (philosopher)
David Kellogg Lewis (September 28, 1941 – October 14, 2001) was an American philosopher.
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Distributive property
In abstract algebra and formal logic, the distributive property of binary operations generalizes the distributive law from boolean algebra and elementary algebra.
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Domain of discourse
In the formal sciences, the domain of discourse, also called the universe of discourse, universal set, or simply universe, is the set of entities over which certain variables of interest in some formal treatment may range.
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Edmund Husserl
Edmund Gustav Albrecht Husserl (or;; 8 April 1859 – 27 April 1938) was a German philosopher who established the school of phenomenology.
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Element (mathematics)
In mathematics, an element, or member, of a set is any one of the distinct objects that make up that set.
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Empty set
In mathematics, and more specifically set theory, the empty set or null set is the unique set having no elements; its size or cardinality (count of elements in a set) is zero.
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Extensionality
In logic, extensionality, or extensional equality, refers to principles that judge objects to be equal if they have the same external properties.
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First-order logic
First-order logic—also known as first-order predicate calculus and predicate logic—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science.
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Formal ontology
In philosophy, the term formal ontology is used to refer to an ontology defined by axioms in a formal language with the goal to provide an unbiased (domain- and application-independent) view on reality, which can help the modeler of domain- or application-specific ontologies (information science) to avoid possibly erroneous ontological assumptions encountered in modeling large-scale ontologies.
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Foundations of mathematics
Foundations of mathematics is the study of the philosophical and logical and/or algorithmic basis of mathematics, or, in a broader sense, the mathematical investigation of what underlies the philosophical theories concerning the nature of mathematics.
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Free logic
A free logic is a logic with fewer existential presuppositions than classical logic.
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Free variables and bound variables
In mathematics, and in other disciplines involving formal languages, including mathematical logic and computer science, a free variable is a notation that specifies places in an expression where substitution may take place.
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G. Spencer-Brown
George Spencer-Brown (2 April 1923 – 25 August 2016) was an English polymath best known as the author of Laws of Form.
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Gabriel Kron
Gabriel Kron (1901 – 1968) was a Hungarian American electrical engineer who promoted the use of methods of linear algebra, multilinear algebra, and differential geometry in the field.
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Geometry
Geometry (from the γεωμετρία; geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space.
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Georg Cantor
Georg Ferdinand Ludwig Philipp Cantor (– January 6, 1918) was a German mathematician.
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Giuseppe Peano
Giuseppe Peano (27 August 1858 – 20 April 1932) was an Italian mathematician and glottologist.
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Grammatical aspect
Aspect is a grammatical category that expresses how an action, event, or state, denoted by a verb, extends over time.
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Group polarization
In social psychology, group polarization refers to the tendency for a group to make decisions that are more extreme than the initial inclination of its members.
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Gunk (mereology)
In gunkology, an area of philosophical logic, the term gunk applies to any whole whose parts all have further proper parts.
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Hasse diagram
In order theory, a Hasse diagram is a type of mathematical diagram used to represent a finite partially ordered set, in the form of a drawing of its transitive reduction.
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Identity (philosophy)
In philosophy, identity, from ("sameness"), is the relation each thing bears only to itself.
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Implicate and explicate order
Implicate order and explicate order are ontological concepts for quantum theory coined by theoretical physicist David Bohm during the early 1980s.
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Integrity
Integrity is the quality of being honest and having strong moral principles, or moral uprightness.
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Intersection (set theory)
In mathematics, the intersection A ∩ B of two sets A and B is the set that contains all elements of A that also belong to B (or equivalently, all elements of B that also belong to A), but no other elements.
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Ivor Grattan-Guinness
Ivor Owen Grattan-Guinness (23 June 1941 – 12 December 2014) was a historian of mathematics and logic.
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John Lucas (philosopher)
John Randolph Lucas FBA (born 18 June 1929) is a British philosopher.
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Join and meet
In a partially ordered set P, the join and meet of a subset S are respectively the supremum (least upper bound) of S, denoted ⋁S, and infimum (greatest lower bound) of S, denoted ⋀S.
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Joseph Goguen
Joseph Amadee Goguen (28 June 1941 – 3 July 2006) was a US computer scientist.
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Kit Fine
Kit Fine (born 26 March 1946) is a British philosopher, currently University Professor and Silver Professor of Philosophy and Mathematics at New York University.
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Lattice (order)
A lattice is an abstract structure studied in the mathematical subdisciplines of order theory and abstract algebra.
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Laws of Form
Laws of Form (hereinafter LoF) is a book by G. Spencer-Brown, published in 1969, that straddles the boundary between mathematics and philosophy.
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Logical truth
Logical truth is one of the most fundamental concepts in logic, and there are different theories on its nature.
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Mass noun
In linguistics, a mass noun, uncountable noun, or non-count noun is a noun with the syntactic property that any quantity of it is treated as an undifferentiated unit, rather than as something with discrete subsets.
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Mathematical logic
Mathematical logic is a subfield of mathematics exploring the applications of formal logic to mathematics.
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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Mereological essentialism
Mereological essentialism is a philosophical thesis about the relationship between wholes, their parts, and the conditions of their persistence.
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Mereological nihilism
Mereological nihilism (also called compositional nihilism, or rarely simply nihilism) is the mereological position that objects with proper parts do not exist.
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Mereotopology
In formal ontology, a branch of metaphysics, and in ontological computer science, mereotopology is a first-order theory, embodying mereological and topological concepts, of the relations among wholes, parts, parts of parts, and the boundaries between parts.
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Meronomy
A meronomy or partonomy is a type of hierarchy that deals with part–whole relationships, in contrast to a taxonomy whose categorisation is based on discrete sets.
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Meronymy
Meronymy (from Greek μέρος meros, "part" and ὄνομα onoma, "name") is a semantic relation specific to linguistics, distinct from the similar meronomy.
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Metaphysics
Metaphysics is a branch of philosophy that explores the nature of being, existence, and reality.
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Michel Weber
Michel Weber is a Belgian philosopher, born in Brussels in 1963.
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Mihajlo D. Mesarovic
Mihajlo D. Mesarovic (Serbian Latin: Mihajlo D. Mesarović, Serbian Cyrillic: Михајло Д. Месаровић; born 2 July 1928) is a Serbian scientist, who is a professor of Systems Engineering and Mathematics at Case Western Reserve University.
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Modal logic
Modal logic is a type of formal logic primarily developed in the 1960s that extends classical propositional and predicate logic to include operators expressing modality.
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Model theory
In mathematics, model theory is the study of classes of mathematical structures (e.g. groups, fields, graphs, universes of set theory) from the perspective of mathematical logic.
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Monad (philosophy)
Monad (from Greek μονάς monas, "singularity" in turn from μόνος monos, "alone"), refers in cosmogony (creation theories) to the first being, divinity, or the totality of all beings.
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Naive set theory
Naïve set theory is any of several theories of sets used in the discussion of the foundations of mathematics.
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Natural language
In neuropsychology, linguistics, and the philosophy of language, a natural language or ordinary language is any language that has evolved naturally in humans through use and repetition without conscious planning or premeditation.
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Natural number
In mathematics, the natural numbers are those used for counting (as in "there are six coins on the table") and ordering (as in "this is the third largest city in the country").
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Natural science
Natural science is a branch of science concerned with the description, prediction, and understanding of natural phenomena, based on empirical evidence from observation and experimentation.
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Nelson Goodman
Henry Nelson Goodman (7 August 1906 – 25 November 1998) was an American philosopher, known for his work on counterfactuals, mereology, the problem of induction, irrealism, and aesthetics.
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Nihilism
Nihilism is the philosophical viewpoint that suggests the denial or lack of belief towards the reputedly meaningful aspects of life.
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Nominalism
In metaphysics, nominalism is a philosophical view which denies the existence of universals and abstract objects, but affirms the existence of general or abstract terms and predicates.
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Occam's razor
Occam's razor (also Ockham's razor or Ocham's razor; Latin: lex parsimoniae "law of parsimony") is the problem-solving principle that, the simplest explanation tends to be the right one.
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Ontology
Ontology (introduced in 1606) is the philosophical study of the nature of being, becoming, existence, or reality, as well as the basic categories of being and their relations.
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Ordered pair
In mathematics, an ordered pair (a, b) is a pair of objects.
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Parmenides (dialogue)
Parmenides (Παρμενίδης) is one of the dialogues of Plato.
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Partially ordered set
In mathematics, especially order theory, a partially ordered set (also poset) formalizes and generalizes the intuitive concept of an ordering, sequencing, or arrangement of the elements of a set.
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Peano axioms
In mathematical logic, the Peano axioms, also known as the Dedekind–Peano axioms or the Peano postulates, are axioms for the natural numbers presented by the 19th century Italian mathematician Giuseppe Peano.
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Philosophy
Philosophy (from Greek φιλοσοφία, philosophia, literally "love of wisdom") is the study of general and fundamental problems concerning matters such as existence, knowledge, values, reason, mind, and language.
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Physical body
In physics, a physical body or physical object (or simply a body or object) is an identifiable collection of matter, which may be constrained by an identifiable boundary, and may move as a unit by translation or rotation, in 3-dimensional space.
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Plato
Plato (Πλάτων Plátōn, in Classical Attic; 428/427 or 424/423 – 348/347 BC) was a philosopher in Classical Greece and the founder of the Academy in Athens, the first institution of higher learning in the Western world.
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Plural quantification
In mathematics and logic, plural quantification is the theory that an individual variable x may take on plural, as well as singular, values.
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Predicate (mathematical logic)
In mathematical logic, a predicate is commonly understood to be a Boolean-valued function P: X→, called the predicate on X. However, predicates have many different uses and interpretations in mathematics and logic, and their precise definition, meaning and use will vary from theory to theory.
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Principia Mathematica
The Principia Mathematica (often abbreviated PM) is a three-volume work on the foundations of mathematics written by Alfred North Whitehead and Bertrand Russell and published in 1910, 1912, and 1913.
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Process and Reality
Process and Reality is a book by Alfred North Whitehead, in which Whitehead propounds a philosophy of organism, also called process philosophy.
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Quantifier (logic)
In logic, quantification specifies the quantity of specimens in the domain of discourse that satisfy an open formula.
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Quantifier variance
The term quantifier variance refers to claims there is no uniquely best ontological language with which to describe the world.
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Quantum mechanics
Quantum mechanics (QM; also known as quantum physics, quantum theory, the wave mechanical model, or matrix mechanics), including quantum field theory, is a fundamental theory in physics which describes nature at the smallest scales of energy levels of atoms and subatomic particles.
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Real number
In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.
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Reflexive relation
In mathematics, a binary relation R over a set X is reflexive if every element of X is related to itself.
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Richard Milton Martin
Richard Milton Martin (1916, Cleveland, Ohio – 22 November 1985, Milton, Massachusetts) was an American logician and analytic philosopher.
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Roderick Chisholm
Roderick Milton Chisholm (November 27, 1916 – January 19, 1999) was an American philosopher known for his work on epistemology, metaphysics, free will, value theory, and the philosophy of perception.
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Russell's paradox
In the foundations of mathematics, Russell's paradox (also known as Russell's antinomy), discovered by Bertrand Russell in 1901, showed that some attempted formalizations of the naïve set theory created by Georg Cantor led to a contradiction.
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Semantics
Semantics (from σημαντικός sēmantikós, "significant") is the linguistic and philosophical study of meaning, in language, programming languages, formal logics, and semiotics.
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Semilattice
In mathematics, a join-semilattice (or upper semilattice) is a partially ordered set that has a join (a least upper bound) for any nonempty finite subset.
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Set (mathematics)
In mathematics, a set is a collection of distinct objects, considered as an object in its own right.
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Set theory
Set theory is a branch of mathematical logic that studies sets, which informally are collections of objects.
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Set-builder notation
In set theory and its applications to logic, mathematics, and computer science, set-builder notation is a mathematical notation for describing a set by enumerating its elements or stating the properties that its members must satisfy.
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Sheaf (mathematics)
In mathematics, a sheaf is a tool for systematically tracking locally defined data attached to the open sets of a topological space.
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Ship of Theseus
In the metaphysics of Identity, the ship of Theseus (or Theseus's paradox) is a thought experiment that raises the question of whether a ship—standing for an object in general—that has had all of its components replaced remains fundamentally the same object.
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Simple (philosophy)
In contemporary mereology, a simple is any thing that has no proper parts.
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Singleton (mathematics)
In mathematics, a singleton, also known as a unit set, is a set with exactly one element.
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Stanford Encyclopedia of Philosophy
The Stanford Encyclopedia of Philosophy (SEP) combines an online encyclopedia of philosophy with peer-reviewed publication of original papers in philosophy, freely accessible to Internet users.
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Stanisław Leśniewski
Stanisław Leśniewski (March 30, 1886 – May 13, 1939) was a Polish mathematician, philosopher and logician.
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Steve Vickers (computer scientist)
Steve Vickers (born c. 1953) is a British mathematician and computer scientist.
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Subset
In mathematics, a set A is a subset of a set B, or equivalently B is a superset of A, if A is "contained" inside B, that is, all elements of A are also elements of B. A and B may coincide.
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Symmetry
Symmetry (from Greek συμμετρία symmetria "agreement in dimensions, due proportion, arrangement") in everyday language refers to a sense of harmonious and beautiful proportion and balance.
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Syntax
In linguistics, syntax is the set of rules, principles, and processes that govern the structure of sentences in a given language, usually including word order.
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Systems theory
Systems theory is the interdisciplinary study of systems.
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Temporal logic
In logic, temporal logic is any system of rules and symbolism for representing, and reasoning about, propositions qualified in terms of time.
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Temporal parts
In contemporary metaphysics, temporal parts are the parts of an object that exist in time.
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Theoretical physics
Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict natural phenomena.
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Topology
In mathematics, topology (from the Greek τόπος, place, and λόγος, study) is concerned with the properties of space that are preserved under continuous deformations, such as stretching, crumpling and bending, but not tearing or gluing.
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Topos
In mathematics, a topos (plural topoi or, or toposes) is a category that behaves like the category of sheaves of sets on a topological space (or more generally: on a site).
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Transitive relation
In mathematics, a binary relation over a set is transitive if whenever an element is related to an element and is related to an element then is also related to.
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Trinity College, Cambridge
Trinity College is a constituent college of the University of Cambridge in England.
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Union (set theory)
In set theory, the union (denoted by ∪) of a collection of sets is the set of all elements in the collection.
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Universal set
In set theory, a universal set is a set which contains all objects, including itself.
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Universe
The Universe is all of space and time and their contents, including planets, stars, galaxies, and all other forms of matter and energy.
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Well-founded relation
In mathematics, a binary relation, R, is called well-founded (or wellfounded) on a class X if every non-empty subset S ⊆ X has a minimal element with respect to R, that is an element m not related by sRm (for instance, "s is not smaller than m") for any s ∈ S. In other words, a relation is well founded if Some authors include an extra condition that R is set-like, i.e., that the elements less than any given element form a set.
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Whitehead's point-free geometry
In mathematics, point-free geometry is a geometry whose primitive ontological notion is region rather than point.
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Willard Van Orman Quine
Willard Van Orman Quine (known to intimates as "Van"; June 25, 1908 – December 25, 2000) 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 of philosophy and a teacher of logic and set theory, and finally as a professor emeritus who published or revised several books in retirement.
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Zermelo–Fraenkel set theory
In mathematics, Zermelo–Fraenkel set theory, named after mathematicians Ernst Zermelo and Abraham Fraenkel, is an axiomatic system that was proposed in the early twentieth century in order to formulate a theory of sets free of paradoxes such as Russell's paradox.
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Improper part, Mereological fusion, Part (mathematics), Proper part, Special Composition Question, Special composition question.
References
[1] https://en.wikipedia.org/wiki/Mereology
