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33 relations: A priori and a posteriori, Analytic–synthetic distinction, Anti-psychologism, Arithmetic, Bertrand Russell, Edward N. Zalta, Empiricism, Equinumerosity, Evanston, Illinois, Evolution, Frege's theorem, Gottlob Frege, Hume's principle, Immanuel Kant, J. L. Austin, John Stuart Mill, Logic, Logicism, Ludwig Wittgenstein, Number, Parallel postulate, Peter Suber, Philosophy, Philosophy of mathematics, Principia Mathematica, Property, Psychologism, Russell's paradox, Set theory, Stanford Encyclopedia of Philosophy, Truth value, 0, 1884.
A priori and a posteriori
The Latin phrases a priori ("from the earlier") and a posteriori ("from the latter") are philosophical terms of art popularized by Immanuel Kant's Critique of Pure Reason (first published in 1781, second edition in 1787), one of the most influential works in the history of philosophy.
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Analytic–synthetic distinction
The analytic–synthetic distinction (also called the analytic–synthetic dichotomy) is a semantic distinction, used primarily in philosophy to distinguish propositions (in particular, statements that are affirmative subject–predicate judgments) into two types: analytic propositions and synthetic propositions.
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Anti-psychologism
In logic, anti-psychologism (also logical objectivism or logical realism) is a theory about the nature of logical truth, that it does not depend upon the contents of human ideas but exists independent of human ideas.
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Arithmetic
Arithmetic (from the Greek ἀριθμός arithmos, "number") is a branch of mathematics that consists of the study of numbers, especially the properties of the traditional operations on them—addition, subtraction, multiplication and division.
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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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Edward N. Zalta
Edward N. Zalta (born March 16, 1952) is a senior research scholar at the Center for the Study of Language and Information.
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Empiricism
In philosophy, empiricism is a theory that states that knowledge comes only or primarily from sensory experience.
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Equinumerosity
In mathematics, two sets or classes A and B are equinumerous if there exists a one-to-one correspondence (a bijection) between them, i.e. if there exists a function from A to B such that for every element y of B there is exactly one element x of A with f(x).
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Evanston, Illinois
Evanston is a city in Cook County, Illinois, United States, north of downtown Chicago, bordered by Chicago to the south, Skokie to the west, and Wilmette to the north.
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Evolution
Evolution is change in the heritable characteristics of biological populations over successive generations.
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Frege's theorem
In metalogic and metamathematics, Frege's theorem is a metatheorem that states that the Peano axioms of arithmetic can be derived in second-order logic from Hume's principle.
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Gottlob Frege
Friedrich Ludwig Gottlob Frege (8 November 1848 – 26 July 1925) was a German philosopher, logician, and mathematician.
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Hume's principle
Hume's principle or HP—the terms were coined by George Boolos—says that the number of Fs is equal to the number of Gs if and only if there is a one-to-one correspondence (a bijection) between the Fs and the Gs.
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Immanuel Kant
Immanuel Kant (22 April 1724 – 12 February 1804) was a German philosopher who is a central figure in modern philosophy.
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J. L. Austin
John Langshaw "J.
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John Stuart Mill
John Stuart Mill, also known as J.S. Mill, (20 May 1806 – 8 May 1873) was a British philosopher, political economist, and civil servant.
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Logic
Logic (from the logikḗ), originally meaning "the word" or "what is spoken", but coming to mean "thought" or "reason", is a subject concerned with the most general laws of truth, and is now generally held to consist of the systematic study of the form of valid inference.
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Logicism
Logicism is one of the schools of thought in the philosophy of mathematics, putting forth the theory that mathematics is an extension of logic and therefore some or all mathematics is reducible to logic.
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Ludwig Wittgenstein
Ludwig Josef Johann Wittgenstein (26 April 1889 – 29 April 1951) was an Austrian-British philosopher who worked primarily in logic, the philosophy of mathematics, the philosophy of mind, and the philosophy of language.
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Number
A number is a mathematical object used to count, measure and also label.
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Parallel postulate
In geometry, the parallel postulate, also called Euclid's fifth postulate because it is the fifth postulate in Euclid's ''Elements'', is a distinctive axiom in Euclidean geometry.
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Peter Suber
Peter Dain Suber (born November 8, 1951) is a philosopher specializing in the philosophy of law and open access to knowledge.
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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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Philosophy of mathematics
The philosophy of mathematics is the branch of philosophy that studies the assumptions, foundations, and implications of mathematics, and purports to provide a viewpoint of the nature and methodology of mathematics, and to understand the place of mathematics in people's lives.
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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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Property
Property, in the abstract, is what belongs to or with something, whether as an attribute or as a component of said thing.
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Psychologism
Psychologism is a philosophical position, according to which psychology plays a central role in grounding or explaining some other, non-psychological type of fact or law.
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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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Set theory
Set theory is a branch of mathematical logic that studies sets, which informally are collections of objects.
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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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Truth value
In logic and mathematics, a truth value, sometimes called a logical value, is a value indicating the relation of a proposition to truth.
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0
0 (zero) is both a number and the numerical digit used to represent that number in numerals.
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1884
No description.
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Redirects here:
Die Grundlagen der Arithmetik, Foundations of Arithmetic, The Foundations of Arithmetics.
References
[1] https://en.wikipedia.org/wiki/The_Foundations_of_Arithmetic
