In 1931, a young Austrian mathematician published an epoch-making paper containing one of the most revolutionary ideas in logic since Aristotle. Kurt Giidel maintained, and offered detailed proof, that in any arithmetic system, even in elementary parts of arithmetic, there are propositions which cannot be proved or disproved within the system. It is thus uncertain that the basic axioms of arithmetic will not give rise to contradictions. The repercussions of this discovery are still being felt an...
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Gödel's incompleteness theorems - Wikipedia, the free ...
Gödel's incompleteness theorems are two theorems of mathematical logic that establish inherent limitations of all but the most trivial axiomatic systems capable of ...
Gödel's incompleteness theorems are two theorems of mathematical logic that establish inherent limitations of all but the most trivial axiomatic systems capable of ...
Extreme math: 1 + 1 = 2 – Good Math, Bad Math
Janne: If you follow the link in the original post, they have the entire principia online. The page that that image comes from is page 378. I can’t put a ...
Janne: If you follow the link in the original post, they have the entire principia online. The page that that image comes from is page 378. I can’t put a ...
Axiom -- From Wolfram MathWorld
Mathematica » The #1 tool for creating Demonstrations and anything technical. Wolfram|Alpha » Explore anything with the first computational knowledge engine.
Mathematica » The #1 tool for creating Demonstrations and anything technical. Wolfram|Alpha » Explore anything with the first computational knowledge engine.
Wittgenstein's Philosophy of Mathematics (Stanford ...
If, however, “∀nφ(n)” is not a meaningful (genuine) mathematical proposition, what are we to make of this proof? Wittgenstein's initial answer to ...
If, however, “∀nφ(n)” is not a meaningful (genuine) mathematical proposition, what are we to make of this proof? Wittgenstein's initial answer to ...
Recursive set - Wikipedia, the free encyclopedia
Formal definition. A subset S of the natural numbers is called recursive if there exists a total computable function f such that f(x) = 1 if x ∈ S and f(x) = 0 if x ...
Formal definition. A subset S of the natural numbers is called recursive if there exists a total computable function f such that f(x) = 1 if x ∈ S and f(x) = 0 if x ...
Analytic proposition - New World Encyclopedia
An analytic proposition is one whose truth depends on relations of ideas or concepts, and not on what it says about the world or the way the world is.
An analytic proposition is one whose truth depends on relations of ideas or concepts, and not on what it says about the world or the way the world is.
Kurt Godel | American mathematician |
Kurt Gödel, Gödel also spelled Goedel (born April 28, 1906, Brünn, Austria-Hungary [now Brno, Czech Rep.]—died Jan. 14, 1978, Princeton, N.J., U.S.), Austrian ...
Kurt Gödel, Gödel also spelled Goedel (born April 28, 1906, Brünn, Austria-Hungary [now Brno, Czech Rep.]—died Jan. 14, 1978, Princeton, N.J., U.S.), Austrian ...
Whitehead’s Early Philosophy of Mathematics
We examine Whitehead’s early philosophy of mathematics in this article because it was his only explicit philosophy of mathematics. After Principia Mathematica, ...
We examine Whitehead’s early philosophy of mathematics in this article because it was his only explicit philosophy of mathematics. After Principia Mathematica, ...
Gödel's Incompleteness Theorems (Stanford Encyclopedia of ...
Gödel's two incompleteness theorems are among the most important results in modern logic, and have deep implications for various issues. They concern the ...
Gödel's two incompleteness theorems are among the most important results in modern logic, and have deep implications for various issues. They concern the ...
Mathematical logic and set theory books - www.topology.org
Topic coverage summary table for mathematical logic and set theory books
Topic coverage summary table for mathematical logic and set theory books
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