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Mar
03

Collections of axioms and information on theories dependency

List of Axioms from Computer Science Department, University of Miami Documentation, Computer Science Department, University of Miami List of axioms collected from Wikipedia. MBase: A Mathematical Knowledge Base. A collection of definitions, theorems and proofs. The Mathematical Atlas. Methamath. Proof symbolic visualizations, University of Texas.

Mar
03

“The ways of paradox”: Quine on Berry’s paradox.

“Ten has a one-syllable name. Seventy-seven has a five-syllable name. The seventh power of seven hundred seventy-seven has a name that, if we were to work it out, might run to 100 syllables or so; but this number can also be specified more briefly in other terms. I have just specified it in 15 syllables. [...]

Mar
03

Book on self-reference (comprising papers by various contributors)

Table of contents and introduction: http://www.imm.dtu.dk/~tb/genintro.pdf

Mar
03

On single and shortest axioms

Both the philosopher Charles Sanders Peirce in 1880 and the American logician H. M. Sheffer in 1913 realized that the truth-functions of elementary logic could all be defined from a single operation. The Sheffer stroke, also known as the NAND operation, is a logical operator with the following meaning: p NAND q is true if [...]

Nov
12

Human Readable Proofs Visualization

- Symbolic Visualizations, University of Texas:http://cvcweb.ices.utexas.edu/ccv/projects/VisualEyes/SymbVis/index.php- Proof nets and zero-knowledge proofs.

Nov
12

Kurt Godel: The writings. Université de Lille III

Kurt Godel workshop for studying his legacy and writings. Lille, France, May 19-21, 2006 My thoughts, ideas, references, comments and informal notes: – The wheel machine, a machine for real computation which I am proposing -as a thought experiment- in a forthcoming paper  on the Church-Turing thesis -Yes, one more paper on the CT thesis!- [...]

Jul
30

Experimental Metamathematics

Metamathematics is to mathematics what metaphysics is to philosophy. It is about stepping outside the discipline and attempting to grasp it as a single entity/ object of study; it is an investigation into the foundations of mathematics. (For an elucidation of  Foundations of Mathematics see http://www.math.psu.edu/simpson/hierarchy.html) Some mathematicians have begun to practice  a quasi-empirical brand of mathematics and insist on results for which there [...]