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

*From*: Donal McEvoy <donalmcevoyuk@xxxxxxxxxxx>*To*: lit-ideas@xxxxxxxxxxxxx*Date*: Tue, 14 Dec 2010 10:50:30 +0000 (GMT)

--- On Tue, 14/12/10, Eric Yost <mr.eric.yost@xxxxxxxxx> wrote: > From: Eric Yost <mr.eric.yost@xxxxxxxxx> > Subject: [lit-ideas] Re: Beg to differ, say, about fractals > To: lit-ideas@xxxxxxxxxxxxx > Date: Tuesday, 14 December, 2010, 7:16 > > > On 12/13/2010 7:53 PM, Donal McEvoy wrote: > > This still leaves open, it seems to me, whether the > right-angled triangle somehow existed from the beginning and > whether all we did was discover this entity and its > attendant structural properties - all of which were there > from the beginning. Or did we invent the right-angled > triangle, which not only was never perfectly physically > embodied but never existed prior to our development of this > mathematical 'object' or 'concept'?> > > The right triangle, from before any beginning, was a set of > relations such that the truth of > a-squared+b-squared=c-squared, in reference to right > triangles, was always the case. This would seem to posit the right triangle as a mathematical object constituted by "a set of relations", the truth about which "was always the case". If so, does that not entail that the "set of relations" "was always the case"? And, if so, does that not entail that the right triangle, constituted by that set of relations, "was always the case" - or was somehow there from the beginning? Let us say it is true that "e = mc2". 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. Let us say it is true that "2 + 2 = 4". This "2 + 2 = 4" describes a structural property - an invariant. So, if true, does "a-squared+b-squared=c-squared in reference to right triangles". We might say these invariants are mathematical laws rather than physical laws. It seems we might nevertheless say that we do not invent these 'laws' but discover them, just as we do not invent but discover the physical invariants or laws of the universe (our invention being limited to the means of describing them, though we might say even this is more of a 'discovery' than invention). We are soon back with our problem (or a variant of it). This problem disappears if we view it as entirely unproblematic that mathematical invariants were there from, or pre-existed, the beginning of the physical world: for any physically possible world must also be a mathematically possible world and both must also be a logically possible world. When we talk of the law-like structures of the universe, we are talking about structures within structures - with the most general being the law-like structures of logic that must hold in any possible world. But surely, even if it is correct, it is not entirely unproblematic that mathematical invariants were there from, or pre-existed, the beginning of the physical world? Surely there are meaningful questions we might pose here and even attempt to answer? > However Donal also certainly knows that the word "exists" > is not a predicate, nor are its verb-form declensions > meaningful verbs. (Ask Robert Paul, which I have already > done by asking you to do so.) "Contrite unicorns exist." Donal is open-minded as to whether "exists" can (or cannot) be deployed as a "predicate" (fearing the answer may turn into a rather empty one hingeing on the definition of "predicate"), but does not see how this much answers or tackles the problems here. > The questions seems to be, "Where does the truth of > a-squared+b-squared=c-squared, in reference to right > triangles, exist?" > > Am I asking the right question? I am not sure. A simple answer to this question, following Tarski, might be that the truth of "a-squared+b-squared=c-squared" exists in the correspondence between that proposition and the existence of an invariant that it describes. Whatever the problems with this, another more fundamental problem is to address the character of "the existence of an invariant" of this mathematical sort - an existence that we understand can never be (perfectly) physically embodied. Donal London ------------------------------------------------------------------ To change your Lit-Ideas settings (subscribe/unsub, vacation on/off, digest on/off), visit www.andreas.com/faq-lit-ideas.html

**Follow-Ups**:**[lit-ideas] Re: Beg to differ, say, about fractals***From:*Eric Yost

**References**:**[lit-ideas] Re: Beg to differ, say, about fractals***From:*Eric Yost

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