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31 relations: A. W. Moore (philosopher), Absolute (philosophy), Actual infinity, Axiom schema of specification, Burali-Forti paradox, Cardinal number, Class (set theory), Cumulative hierarchy, Element (mathematics), Ernst Zermelo, Georg Cantor, God, Infinity, Ivor Grattan-Guinness, Limitation of size, Mathematician, Mathematics, Metalanguage, Monadology, Naive set theory, Ordinal number, Paradox, Reflection principle, Richard Dedekind, Rudy Rucker, Set (mathematics), Set theory, Transfinite number, Well-order, Willard Van Orman Quine, Zermelo set theory.
A. W. Moore (philosopher)
Adrian William Moore (born 1956) is a Professor of Philosophy at the University of Oxford and Tutorial Fellow of St Hugh's College, Oxford.
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Absolute (philosophy)
In philosophy, the concept of The Absolute, also known as The (Unconditioned) Ultimate, The Wholly Other, The Supreme Being, The Absolute/Ultimate Reality, and other names, is the thing, being, entity, power, force, reality, presence, law, principle, etc.
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Actual infinity
In the philosophy of mathematics, the abstraction of actual infinity involves the acceptance (if the axiom of infinity is included) of infinite entities, such as the set of all natural numbers or an infinite sequence of rational numbers, as given, actual, completed objects.
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Axiom schema of specification
In many popular versions of axiomatic set theory the axiom schema of specification, also known as the axiom schema of separation, subset axiom scheme or axiom schema of restricted comprehension is an axiom schema.
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Burali-Forti paradox
In set theory, a field of mathematics, the Burali-Forti paradox demonstrates that constructing "the set of all ordinal numbers" leads to a contradiction and therefore shows an antinomy in a system that allows its construction.
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Cardinal number
In mathematics, cardinal numbers, or cardinals for short, are a generalization of the natural numbers used to measure the cardinality (size) of sets.
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Class (set theory)
In set theory and its applications throughout mathematics, a class is a collection of sets (or sometimes other mathematical objects) that can be unambiguously defined by a property that all its members share.
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Cumulative hierarchy
In mathematical set theory, a cumulative hierarchy is a family of sets Wα indexed by ordinals α such that.
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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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Ernst Zermelo
Ernst Friedrich Ferdinand Zermelo (27 July 1871 – 21 May 1953) was a German logician and mathematician, whose work has major implications for the foundations of mathematics.
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Georg Cantor
Georg Ferdinand Ludwig Philipp Cantor (– January 6, 1918) was a German mathematician.
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God
In monotheistic thought, God is conceived of as the Supreme Being and the principal object of faith.
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Infinity
Infinity (symbol) is a concept describing something without any bound or larger than any natural number.
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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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Limitation of size
In the philosophy of mathematics, specifically the philosophical foundations of set theory, limitation of size is a concept developed by Philip Jourdain and/or Georg Cantor to avoid Cantor's paradox.
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Mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in his or her work, typically to solve mathematical problems.
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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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Metalanguage
Broadly, any metalanguage is language or symbols used when language itself is being discussed or examined.
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Monadology
The Monadology (La Monadologie, 1714) is one of Gottfried Leibniz’s best known works representing his later philosophy.
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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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Ordinal number
In set theory, an ordinal number, or ordinal, is one generalization of the concept of a natural number that is used to describe a way to arrange a collection of objects in order, one after another.
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Paradox
A paradox is a statement that, despite apparently sound reasoning from true premises, leads to an apparently self-contradictory or logically unacceptable conclusion.
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Reflection principle
In set theory, a branch of mathematics, a reflection principle says that it is possible to find sets that resemble the class of all sets.
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Richard Dedekind
Julius Wilhelm Richard Dedekind (6 October 1831 – 12 February 1916) was a German mathematician who made important contributions to abstract algebra (particularly ring theory), axiomatic foundation for the natural numbers, algebraic number theory and the definition of the real numbers.
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Rudy Rucker
Rudolf von Bitter Rucker (born March 22, 1946) is an American mathematician, computer scientist, science fiction author, and one of the founders of the cyberpunk literary movement.
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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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Transfinite number
Transfinite numbers are numbers that are "infinite" in the sense that they are larger than all finite numbers, yet not necessarily absolutely infinite.
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Well-order
In mathematics, a well-order (or well-ordering or well-order relation) on a set S is a total order on S with the property that every non-empty subset of S has a least element in this ordering.
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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 set theory
Zermelo set theory, as set out in an important paper in 1908 by Ernst Zermelo, is the ancestor of modern set theory.
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Absolute Infinity, Absolute infinite, Absolute infinity, Absolute infinte, Absolutely infinite, Cantor's absolute, Cantor's absolute infinite.
References
[1] https://en.wikipedia.org/wiki/Absolute_Infinite
