Talk:Internal set

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 Field: Foundations, logic, and set theory

How many notions of "internal set" are there?[edit]

I find this stub deeply confusing. Could someone who knows something about one of these notions (how many? 1? 2? 3?) please clarify this a bit. --Hans Adler (talk) 12:42, 20 November 2007 (UTC)

Nelson[edit]

If Nelson's theory can be characterized as constructivist, he should be included in the list of people who contributed to constructivism at constructivism. Has Nelson's theory been described as constructivist in print? Katzmik (talk) 11:26, 7 September 2008 (UTC)

I am really puzzled why IST is characterized constructivist in the article. As is shown in Nelson's paper IST is a conservative extension of ZFC so in whatever sense IST is constructivist, ZFC is as well. Am I overlooking something? --CSTAR (talk) 16:49, 2 February 2009 (UTC)

Certainly Nelson is widely viewed as a constructivist. I'm surprised to see it stated that he's not in a list of contributors to constructivism. Michael Hardy (talk) 17:12, 2 February 2009 (UTC)

It is indeed true Nelson has written a book on finitism (Predicative Arithmetic, 1986 Princeton University Press, which is now available online). Nelson's finitism is quite a radical position. In part, this finitism is motivated from his finitistic probability theory (I think he may have said so himself, but I can't find the reference), although I don't think anybody seriously believes that the radical finitism of Predicative Arithmetic is sufficient for "Radically Elementary Probability Theory". That said, IST is not constructivist under any common interpretation of constructivism --CSTAR (talk) 18:23, 2 February 2009 (UTC)