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Re: Mathematics as discourse about form:
Posted:
Jan 1, 2013 12:22 PM
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On Jan 1, 7:04 pm, Charlie-Boo <shymath...@gmail.com> wrote:
> On Jan 1, 6:55 am, Zuhair <zaljo...@gmail.com> wrote:
>
> > Add a new primitive to the language of ZFC,
> > this primitive is the binary relation "exemplifies" denoted by
> > the infix dyadic symbol ~
>
> > Define:
>
> > R is a form defining relation iff
> > R is an equivalence relation &
> > For all x. ~x=0 -> For all s. Exist y. y R x & s in TC(y)
>
> You are not giving the domains of symbols, nor using a consistent
> syntax first ~x=0 is not dyadic
The monadic logical symbol ~ stands for NEGATION, while the dyadic
infix symbol ~ stands for 'exemplifies'
then y ~ $ which is but uses multiple
> punctuation characters in a row!?!?
>
What multiple punctuation do you mean ~ and $, if that what you mean
then it doesn't matter.
> ?If you can't explain it simply, you don't understand it well enough?
> - Albert Einstein
>
> "A mathematical theory is not to be considered complete until you have
> made it so clear that you can explain it to the first man whom you
> meet on the street." - David Dilbert
>
> What is the difference between math and the other branches of science?
>
> C-B
Math is not a branch of science.
Math is about supplying discourse about form, it has nothing to do
with the Truth of that discourse.
Science is about the Truth of discourse about its objects, and its
objects are not "forms".
A 'form' is a free standing universal, i.e. an object exemplified by
objects that bears some equivalence relation between them in such a
manner that EVERY object of the universe of discourse is an object of
the transitive closure of an object that exemplify it. So a form is a
universal that "involves" the whole universe of discourse in its
exemplification, and its exemplification is dictated by having an
equivalence relation to a some object. For example each natural number
is a form because each natural number can be interpreted as a
universal that is exemplified by sets of objects and all those sets
are 'bijective' to a common object. Of course it is clear that
'bijection' is an equivalence relation that involves the whole
universe of discourse and so it is a form defining relation. So
"number" is interpretable as a form. In a similar manner a "point" can
be interpreted as a tuple of numbers, etc..
The basic difference between universals that constitute 'forms' and
those that not, is that the later ones do not involve the whole
universe of discourse in its exemplification, we can even have some
universals the exemplification of which follows some equivalence
relation like for example the relation equality "=" but yet still that
exemplification is not a one what involves the whole universe of
discourse and accordingly that universal is not a form. ALL universals
in science like physics, biology, chemistry etc.. are actually what I
call as PRIVET universals or Local universals or sometimes I call them
also Native universals, all actually mean the same thing, that those
universals only involves a SECTOR of the universe of discourse with
its exemplification and not all of it, for example the universal "cat"
can only be exemplified by animal objects, and the exemplification of
cat certainly doesn't involve the whole universe with it, we don't
have the case that EVERY object in the universe is a member of the
transitive closure of a cat. In philosophy sometimes the term "form"
is used to describe any universal, but here in this account 'form' is
only used to denote the Free standing universals (those that involve
the whole universe with their exemplification) provided that all
objects exemplifying them must have an equivalence relation to a
common object. This will strip those forms of any privet properties
other than abstract form which is the kind of objects mathematics
tries to provide discourse about.
Hope that helps
Zuhair
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