Talk:Implementation of mathematics in set theory: Difference between revisions

Revision as of 06:26, 22 December 2005

Revision as of 08:42, 23 December 2005

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typing by allowing only index sets of singletons. It is not completely general but is a little

easier -- but I still made some mistakes setting it up! [[User:Randall Holmes|Randall Holmes]] 06:26, 22 December 2005 (UTC)

==terminology==

I find it a little problematic to refer to doing these things "in" ZFC or NFU. ZFC and NFU only prove things; they don't construct or define anything. I've had quite a job explaining this at articles like [[definable number]] (people want to talk about things like "real numbers definable in ZFC", which is nonsense).

What the article seems to be about is how to define various concepts in the ''language of set theory'' (not ZFC or NFU) in such a way that ZFC (resp. NFU) proves that they behave the way one wants them to. I think that's fine; I just would rather not see this called "doing things in ZFC or NFU". That's a reasonable shorthand when everyone understands each other, but is likely to cause or reinforce misconceptions among neophytes.

A subordinate but related point is that, of course, the implementations said to be "done in ZFC" could equally well be done in weaker or stronger theories with the same intended interpretation (say, ZC, or ZFC+"there exists a huge cardinal). So it's really the intended interpretation that controls, not the precise formal theory, at least in the "ZFC" case. For NFU it's harder to say, because I'm unaware whether or not NFU has an intended interpretation (you'd know more about that than I). --[[User:Trovatore|Trovatore]] 08:42, 23 December 2005 (UTC)