instrumentalism; consequences of set theory

[gusl]

I want to call myself an instrumentalist. Can anyone provide reasons why I shouldn't want to?

By the way, ordinal arithmetic (where addition and multiplication are not commutative) seems cool, though a bit of "abstract nonsense". I don't like non-computational things... I like to think of infinity as a limit.

What do instrumentalists think of set theory? Does a transfinite ordinal ever come in handy?

Do different set theories have any consequences for physicists, or any scientists at all, for that matter?



Some PoS readings for later:

The Empiricist Challenge: Knowledge Empiricism and the Underdetermination Argument

Some important concepts of PoS

Comments

[easwaran.livejournal.com]

As far as I understand it, instrumentalism is always instrumentalism about something. It's the idea that such things don't actually really exist or have value in themselves, but rather just as means towards something else. So I don't think it's possible to be a global instrumentalist.

Actually, ordinal arithmetic is quite computable. I did some searches a few months ago and actually found some online programs that implement addition, multiplication, and exponentiation for ordinals given in Cantor normal form, using the \aleph function and the \epsilon function (which enumerates the fixed-points of the \aleph function).

[gustavolacerda.livejournal.com]

I want to call myself an instrumentalist about mathematics: "mathematics is only good as far as it helps model real situations (whether these situations are physical, social phenomena or the intuitions that live inside our head)".

[easwaran.livejournal.com]

I think I can endorse that.