Jim Donegan ✅ · @jimdonegan
1553 followers · 4634 posts · Server mastodon.scot
Jim Donegan ✅ · @jimdonegan
1477 followers · 4214 posts · Server mastodon.scot
· @e7_87
24 followers · 25 posts · Server mathstodon.xyz

plato.stanford.edu/entries/mat

Constructive math is distinguished from its traditional counterpart, classical math, by the strict interpretation of the phrase “there exists” as “we can construct”.

1 Intuitionistic Math
"math unfolds itself internally, formalization, although not unacceptable, is unnecessary."(from SEP entry)

2 Recursive Constructive Math

3 Bishop’s Constructive Math
"the building blocks of mathematics were the positive integers"

4 Martin-Löf’s Type Theory

#PhilosophyOfMathematics

Last updated 2 years ago

· @e7_87
24 followers · 22 posts · Server mathstodon.xyz

philosophy.stackexchange.com/a

"Naive set theory is the theory used historically by G. Frege to show that all mathematics reduces to logic. Type theory was proposed and developed by B. Russell and others to put a restriction on set theory to avoid Russell's paradox...category theory has been offered as an alternative to ZFC as a foundational theory...

... set theory (by way of ZFC) is important to the logicist program, and category theory appeals to structuralists"

#PhilosophyOfMathematics

Last updated 2 years ago

· @e7_87
24 followers · 21 posts · Server mathstodon.xyz

"there are two conflicting views: a set is considered either a collection of things (Cantor), or synonymous with a property (attribute, predicate) of things. "

"in addition to logic we rely on this existential creed and the idea of iteration. ... Poincaré has proved right in his defense of mathematical induction as an indispensable and irreducible tool of mathematical reasoning."

-- "Mathematics and Logic", Hermann Weyl

#PhilosophyOfMathematics

Last updated 2 years ago

Jim Donegan ✅ · @jimdonegan
1388 followers · 3825 posts · Server mastodon.scot
Jim Donegan ✅ · @jimdonegan
964 followers · 1983 posts · Server mastodon.scot
Ted Talbot · @tedtalb
24 followers · 5 posts · Server zirk.us
Jim Donegan ✅ · @jimdonegan
955 followers · 1921 posts · Server mastodon.scot
Jim Donegan ✅ · @jimdonegan
955 followers · 1921 posts · Server mastodon.scot
Jim Donegan ✅ · @jimdonegan
956 followers · 1921 posts · Server mastodon.scot