logic on The Dan MacKinlay family of variably-well-considered enterprises
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Recent content in logic on The Dan MacKinlay family of variably-well-considered enterprisesHugo -- gohugo.ioen-usMon, 04 Jan 2016 11:40:53 +1100Foundations of mathematics
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Mon, 04 Jan 2016 11:40:53 +1100https://danmackinlay.name/notebook/foundations.htmlThis is a long story which I would not attempt to tell here even if I were qualified at a level beyond undergraduate. ZFC set theory (“Zermelo–Fraenkel plus axiom of choice”) and its relatives are the default foundations for mathematics used by working mathematicians, and they are certainly better than no foundations. They have many irritating features, however, such as tying up armies of mathematicians in disputes about the Axiom of Choice, and leaving people such as me who do measure theory spending far too much time on the pathologies of set theory in infinite limits because of said axiom.