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Mathematical fictionalism, weaselism, and castles in the air …

September 27, 2011 Leave a comment

what  are we to make of Mathematical fictionalism?

 

the post linked above states:

 

  Platonism is the view that (a) there exist abstract mathematical objects (i.e., nonspatiotemporal mathematical objects), and (b) our mathematical sentences and theories provide true descriptions of such objects. … snip snip … And abstract objects, platonists tell us, are wholly nonphysical, nonmental, nonspatial, nontemporal, and noncausal. Thus, on this view, the number 3 exists independently of us and our thinking, but it does not exist in space or time, it is not a physical or mental object, and it does not enter into causal relations with other objects.

Fictionalism, on the other hand, is the view that (a) our mathematical sentences and theories do purport to be about abstract mathematical objects, as platonism suggests, but (b) there are no such things as abstract objects, and so (c) our mathematical theories are not true.

 

and essentially that things like the number three or 2+2=4  don’t even exist  …

and that my friends, is what some philosophers debate …  so for sure, one case question the existence of trillion dollar deficits and debts 🙂

SEP entry also mentions  easy-road fictionalism, or weasel fictionalism.

 

but on a  more serious note the article discusses the serious issue of the continuum hypothesis and undecidability,

 

The most famous example here is probably the continuum hypothesis (CH), which is undecidable in currently accepted set theories, e.g., Zermelo-Frankel set theory (ZF). (In other words, ZF is consistent with both CH and ~CH; i.e., ZF+CH and ZF+~CH are both consistent set theories.) Given this, it follows from Field’s view that neither CH nor ~CH is part of the story of mathematics and, hence, that there is no objectively correct answer to the CH question.

 

and that is a topic actually worth thinking about … what is it that we CAN prove, and what is it that we CANNOT prove, and CAN there be machines we create that could prove [really hard] things that we couldn’t [unaided?]

 

 

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