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diff --git a/content/zettel/4c1.md b/content/zettel/4c1.md new file mode 100644 index 0000000..4274bd4 --- /dev/null +++ b/content/zettel/4c1.md @@ -0,0 +1,19 @@ ++++ +title = "Different logical foundations" +author = "Yann Herklotz" +tags = [] +categories = [] +backlinks = ["4c"] +forwardlinks = ["4c2"] +zettelid = "4c1" ++++ + +There are different logical foundations to mathematics. The main one +that is used is Zermelo-Fraenkel set theory with the axiom of choice +(ZFC). However, there can be alternatives. For example, type theory +provides and alternative basis for the theory of mathematics, and also +result in a different logic. + +Propositional logic always needs set theory as a base to work with, +however, logical systems like intuitionistic logic can be built up using +type theory without ever needing set theory. |