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


--- On Wed, 15/12/10, Eric Yost <mr.eric.yost@xxxxxxxxx> wrote:

> On 12/14/2010 5:50 AM, Donal McEvoy wrote:
> > The proposition "e = mc2" is our invention but the
> invariant it describes is not.>
> 
> You assume that "E=Mc(2)" is true throughout the universe.

This line of mine came in a paragraph that began
"Let us say it is true that "e = mc2". 
So, yes, for _the purposes of the argument_ it was assumed that "E=Mc(2)". It 
need not be assumed otherwise; I had likewise assumed, for the purposes of the 
argument, that "2+2=4" and "a2+b2=c2".

The argument or question was about the status and character of such claims, 
given their truth - not about whether such claims were true. That is why 
"E=Mc(2)" could be assumed to be true for the purposes of this argument - just 
as it could be assumed that "2+2=4" and "a2+b2=c2" were true for the purposes 
of considering whether the status and character of these claims was such that 
these 'truths' [or perhaps, more precisely, the invariant structural relations 
described by the relevant propositions] existed at least from the beginning of 
the universe.

No one need be put to proof of a specific empirical or mathematical truth for 
the purposes of this kind of argument - or so I assumed. 

> Do we know this ["E=Mc(2)"] in the same way that we know of right
> triangles a-squared plus b-squared = c-squared?

The analogy between a proposition asserting a physical law and a proposition 
asserting a mathematical 'law' was not claimed to be that we "know" them "in 
the same way" (or that we don't): it was not so much an epistemic as an 
'ontological' analogy that was being offered for consideration - an analogy as 
to the status and character of such laws, whether physical or mathematical, 
irrespective of how they are "known", proved or tested. It lay in what we might 
call our 'ontological' intuitions/assumptions about the 'laws' so asserted - 
that such laws pre-exist and exist independently of the means we develop or 
invent to describe them.

This was the point of my writing:-
"This "e = mc2" describes a structural property of the universe. This 
'structural property' we might say is a physical or natural law. Such a law of 
physics is posited as holding anywhere in the physical universe, from the 
beginning until the end - it describes an invariant. We can conceive logically 
possible universes where this invariant does not obtain, so this invariant is 
not a law of logic that must hold in all possible worlds. In the case of "e = 
mc2" we do not think that the invariant it describes is our invention, rather 
it is our discovery. The proposition "e = mc2" is our invention but the 
invariant it describes is not. Nor is the truth of the proposition our mere 
invention: as the truth of the proposition depends on its correspondence with 
an invariant that we do not invent. We invent or develop a means to describe 
something invariant that pre-exists, and exists independently of, any such 
description of it."

The analogy here goes to whether such structural invariants, be they physical 
or mathematical, pre-exist and/or exist independently of their description. 
Thus the analogy does not raise Eric's epistemic question, namely:
> Do we know ["E=Mc(2)"] in the same way that we know of right
> triangles a-squared plus b-squared = c-squared?

The answer to that question is, I suggest, that there are both similarities and 
differences between how we 'know' physical laws and how we 'know' mathematical 
laws. But this is not, I think, a question directly raised by the analogy. 

As to why these laws must apply throughout the universe, the simple answer is 
that they would lack the character of universal laws if they did not. A more 
sophisticated answer is that if, say, we found that there was a portion of the 
universe where the 'invariant' did not apply [where perhaps it appeared that 
"E=mc4" and "2+2=35"], the invariant would be falsified as a universal law; we 
would have to abandon it as a law altogether or explain why the structural 
invariant was limited in its application so that those limitations themselves 
were explained in invariant terms.   

Donal
London








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