[lit-ideas] Re: Beg to differ, say, about fractals

  • From: Donal McEvoy <donalmcevoyuk@xxxxxxxxxxx>
  • To: lit-ideas@xxxxxxxxxxxxx
  • Date: Sat, 11 Dec 2010 16:42:24 +0000 (GMT)

> >>> On 10/22/2010 8:18 PM, near the date of someone's milestone birthday he 
> >>> unfortunately forgot, Donal McEvoy wrote:
> >>>>   We may say there was no number system on earth before humans invented 
> >>>> one.

Eric wrote:

> >> Yet of right triangles, a-squared plus b-squared
> >> equals c-squared, as theorem, will remain true
> after the last star has flickered out. It was also true
> before the planets formed.

My reply should have read:-

> > ..it is not clear from the "Yet"
> whether or not Eric is denying the proposition that "there
> was no number system on earth before humans invented one."
> >
> > If he is denying it, perhaps he might clarify how the
> alleged fact that a true mathematical theorem (at least of
> the kind he gives) will be true for eternity, shows there
> was a number system on earth before humans invented one?
> >
> > If not, what is the connection between the
> proposition 'a mathematical truth is true forever' and
> 'there was no number system on earth before humans invented
> one'?

To these points and questions, might be added:-

Eric's post raises the question of what was always there, from when the 
universe began say, and what ‘emerged’.

Was the ‘triangle’, the mathematical perfect ‘triangle’ and not some physical 
approximation to it, there when the universe began? Was maths? Was logic?

We might accept that what is true logically, and mathematically, was true from 
the beginning of the actual world (in some sense) and did not become true by 
virtue of something happening after the beginning; this is especially the case 
with 'logical truth' if we accept the view that a 'logical truth' must be true 
in all possible worlds. But does this show logical and mathematical 'truth' 
existed from the beginning or merely that these truths are atemporal or 
ahistorical, standing outside the universe of space and time? 

Does it help to say propositions expressing these 'truths' did not exist from 
the beginning but nevertheless these 'truths' existed from the beginning? 

A universe devoid of the sequence of natural numbers is not a universe in which 
the proposition ‘2 + 2 = 4’ can exist or have any actuality or instantiation as 
a proposition. Can we admit that even in a universe in which '2 + 2 = 4' does 
not exist as a proposition it would still be true(and as what?)? Can we admit 
therefore that something (a proposition?) may be already true even though it 
does not yet exist (as a proposition?)? Or do we incline to the view that, if 
it would be true in any given universe, it must exist (in some sense) as a 
truth in any given universe?

When we produced the sequence of natural numbers (or, say, the 'triangle' as a 
mathematical entity) were we inventing, or were we discovering something that, 
in some sense, was waiting to be discovered? If the latter, what is the sense 
in which natural numbers (and triangles) existed prior to their discovery? 

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