Philosophy – 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
Logicism, Formalism, and Intuitionism
The three main contemporary ways to understand the foundations of mathematics.
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
Philosophy
Is ‘Philosophy of Mathematics’ somehow useful?
What the philosophy of mathematics is useful for? Max Black, the author of The Nature of Mathematics (1933), thought the main task of the foundation of mathematics (and, consequently the main task of any philosophy of mathematics) would be to elucidate “and analyze the notion of integer or natural number”
Poincaré
Poincaré’s Philosophy of Mathematics
Was his philosophy of mathematics underrated?
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
Mathematics as Fiction: A Common Sense Approach
The following essay was written in 2014 when I was an undergraduate student at the University of Florida; it was the winner of the mathematics department’s Robert Long Prize for writing in the history and/or philosophy of mathematics. In the intervening time, my views on ontological/epistemological status
Philosophy
The Backstage of Mathematical Thinking: How Our Brains Bring About the Abstract
A brief survey of recent insights from cognitive science
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
Probability Theory
The Probabilistic Method
Maybe the most interesting proof method
Philosophy
Beginner’s Guide to Mathematical Constructivism
The foundational crisis in mathematics along with roughly four decades following it, was likely the most fertile period in the history of logic and studies in the foundations. After discovering the set-theoretic paradoxes, such as the paradox of the set of all sets, together with the logical ones, like Russell’