Paul Austin Murphy – Cantor's Archive
Logic
Formal Logic vs. Material Logic?
In a purely logical argument, even if the premises aren’t in any way (semantically) connected to the conclusion, the argument may still be both valid and sound. Professor Edwin D. Mares displays what he sees as a problem with purely formal logic when he offers us the following example
Logic
Lewis Carroll’s Infinite Premises
The British writer, mathematician and logician Charles Lutwidge Dodgson (which was Lewis Carroll’s real name) worked in the fields of geometry, matrix algebra, mathematical logic and linear algebra. Dodgson was also an influential logician. (He introduced the Method of Trees; which was the earliest use of a truth tree.
Philosophy
Who Says Nature is Mathematical?
This piece wouldn’t have been called ‘Who Says Nature is Mathematical?’ if it weren’t for the many other similar titles which I’ve seen. Take these examples: ‘Everything in the Universe Is Made of Math — Including You’, ‘What’s the Universe Made Of? Math, Says Scientist’ and ‘Mathematics
Constructivism
R.L. Wilder’s Constructivist Account of Early 20th Century Mathematics
This is the second part of my piece on Raymond Louis Wilder (1896–1982) and his philosophical, historical and anthropological account of mathematics. I suggest that the reader refer back to the introduction to my ‘Raymond L. Wilder’s Anthropology of Mathematics: Platonism and Applied Mathematics’for Wilder’s biographical
Philosophy
Mathematical Intuitionism and Anti-Realism Compared and Contrasted
Mathematical intuitionism (which is a subset of mathematical constructivism) has it (or had it) that mathematics is purely the result of the mental activities of human beings; not the discovery of mathematical entities which exist in an “objective” (or Platonic) realm. In terms of L. E. J. Brouwer’s original
Quantum Physics
Nature Isn’t Fuzzy: Quantum Uncertainty, Inconsistency and Paradox
… And Nature isn’t clear either. Nature is neither fuzzy nor not fuzzy.
Philosophy
Raymond L. Wilder’s Anthropology of Mathematics
Platonism and Applied Mathematics
Logic
The Basics of Logical Identity
Firstly we can say that logical identity is reflexive. In other words, everything (or every thing) is identical to itself. In symbols: ∀x (x = x) To translate: For every x (or for every thing), x must equal x (or everything must be identical to itself). That is, everything has the
Philosophy
Professor E. Brian Davies’s Mathematical Empiricism
This commentary is on the relevant parts of Davies’s book, Science in the Looking Glass. The following is not a book review.
Philosophy
A Modern Day Mathematical Platonist — Alain Badiou
Alain Badiou (1937-) is a French philosopher. At one point he was the chair of Philosophy at the École normale supérieure (ENS) and founder
Gödel
Gödel’s First Incompleteness Theorem in Simple Symbols and Simple Terms
The following piece explains a particular symbolic expression (or version) of Kurt Gödel’s first incompleteness theorem. It also includes a particular expression (or example) of a Gödel sentence (i.e., “This statement is false”)
Penrose
Is Roger Penrose a Platonist or a Pythagorean?
Roger Penrose is not only a mathematical physicist: he’s also a pure mathematician.