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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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NTS: Coherence

September 27, 2011 Leave a comment

Today’s watch word is coherence, closely related to alignment.

Motivation for thinking about coherence is biology and coordination of cells in common action.

Issue is the success of coherence over randomness.  Why should there be coherence and coherent activity / coordinated activity of cells [of all kinds]. Absent some level of coherence  … randomness and perhaps chaos ensues.  Question arise about chaos.  Where does chaos fall? Is chaos ‘better’ or ‘worse’ than randomness?

 

Natural randomness appears easy, yet man-made randomness appears hard to generate.

 

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Automated Discovery

September 24, 2011 Leave a comment

on the todo list: Review progress in  Automated Discovery and MetaTools.

Categories: NTS

Its the economy xpid??

September 24, 2011 Leave a comment

Yes, the economy, economics, world trade, globalization, automation, resource allocation,… its kind of complicated and gets more complicated when the natural tendencies and temptations of those close to money and resources   exercise their influence …

lots to work on here …

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faster than light

September 23, 2011 Leave a comment

the physics buzz today was the story of an experiment suggesting neutrinos going faster than light ….

ok, maybe … so   some neutrinos are going faster than light … light is NOT going faster than light …    does everything stop working?  Is E=mc**2  not valid anymore,  does special relativity disappear?

No more event horizons?  No more black holes?

maybe c just gets demoted  and now we have to use c’  the speed of neutrinos instead?

can we crank up the speed of neutrinos, or is it just the new top speed?

does c become the ‘speed formerly known as the top speed’?

Do all neutrinos go faster than light?

maybe its really significant.

this IS  better than some of the other stuff taking up airtime …

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NTS: Progression of Prevailing Paradigms

September 23, 2011 Leave a comment

Work’s required on concurrent prevailing paradigms and paradigm shifts. Kuhn, where are you?

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Visual Presentation Software

September 23, 2011 Leave a comment

Currently evaluating visual presentation software alternatives. Primary candidates: Visio, SmartDraw