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.