Post #1042183

2026-04-09 13:51 UTC

IMAGINE, IF YOU WILL, A PERSON WHO HAS BUILT HIS IDENTITY AND CAREER ON HIS LOVE AND KNOWLEDGE OF LOGIC; WHO HAS SPENT YEARS AND CONSIDERABLE MONEY STUDYING LOGIC; WHO HAS GRADUATED WITH A DEGREE IN LOGIC; WHO PERHAPS TEACHES LOGIC TO CHILDREN OR EVEN LECTURES ON IT AT A UNIVERSITY. NOW IMAGINE DISCOVERING THAT THIS PERSON HAS ONLY EVER HEARD ABOUT ONE FOUNDATION IN THEIR ENTIRE LIFE: IT IS THE ZERMELO–FRAENKEL SET THEORY.

Replies (2)

@ncf@types.pl 2026-04-09 13:54

(ref)

Open ##2061454
@mjd@mathstodon.xyz 2026-04-09 14:21

@ncf It's often striking to me how, for so many people, the entire conceptual universe is circumscribed by ZF(C). That theory has become so dominant over last last 100 years that many people can't escape it. Their motto, and they really believe it, is “everything is a set”. For them there's no collection that isn't a ZF set, and it's incoherent to suggest the idea of a mathematical object that isn't somehow isomorphic to a ZF set. J.H. Conway laments this in an epigraph to _On Numbers and Games_. For example, he says that one should be able to postulate the existence of ordered pairs without being expected to identify a particular ZF construction with the required properties. Of course he's right, ZF is irrelevant here. But I've had many conversations with people on Math SE who said that no, an ordered pair _is by definition_ a set of the form {{x}, {x,y}}, nothing more or less.

Open ##2061455