P is P
x is x
y is y
true is true
talse is false
In all these cases the least form is REI , such that 'P', 'x', 'y', 'true', 'false' represent elements and 'is' represents relation.
So your ‘REI’ only holds if you deliberately insert ‘is’ and then duplicate the
P,
x,
y,
True or
False on the other side of your unnecessary and trivial ‘is’? Thanks Doron, for directly asserting that your ‘REI’ is simply unnecessary.
In the case of P(x,y) P is the relation and x or y are elements.
No
P is the predicate name wile
x and
y are variables. You do not get to redefine some other language to turn it into your self-contradictory, trivial and ill defined ‘REI’ language. How do you define a predicate name as a ‘relation’ in your ‘REI’ or for that matter how do you define any ‘relation’ within your ‘REI’, since your ‘REI’ can only ‘relate’ ‘elements’ where you claim ‘elements and ‘relations’ are ‘mutually independent’ as the ‘relater’ and the ‘related’ which of course makes them, well, mutually dependent as ‘relater’ and the ‘related’.
In both cases REI is the basis of any WFF.
In both cases you had to go out of your way to insert an unneeded and trivial ‘is’ so you can call it a 'relation' for your ‘REI’. Oh wait since your ‘REI’ can only 'relate' 'elements' then nothing ‘is’ defined as a 'relation' in your ‘REI’, not even ‘is’, so you have just wasted your time inserting an ‘is’ that even in your ‘REI’ can not define itself as a 'relation'.
P alone
x alone
y alone
true alone
false alone
is alone
are not WFF
Try looking up the language and grammar that was being applied, it was First Order Predicate Logic and not your trivial contradictory ‘REI’, if you do not recall. Oh but that would require you to do some actual research which your ‘framework of everything researchable’ does not seem to enable you to do.
The least WFF is A=A, where A (Element) refers to itself by = (Relation) (it is not less than REI) as follows:
[qimg]http://www.geocities.com/complementarytheory/AAA.jpg[/qimg]
Again asserting that a ‘relation’ can not refer to itself as a ‘relation’ thus making the ‘relations’ your ‘REI’ requires indefinable and nonexistent in your ‘REI’.
That 'is' it Doron just keep cheating yourself by trying to label people instead of addressing the inadequacies and inconsistencies of your notions.
You used REI in this quote, where P,x,y are Element(s) and 'are' is the Relation (self-relation in this case, where each element at least refers to itself (as shown by the A=A diagram) in order to be considered as WFF).
No Doron I used English in that quote, another language and grammar you should consider researching, if your notions would only permit it.
In other words, no REI no WFF.
You actually used REI as follows:
'X is, on its own, ...' where 'X' represents Element and 'is' represents Relation.
REI is inevitable.
No, Doron your ‘REI’ is inevitably self contradictory unless you can show how ‘is’ can reference itself as a ‘relation’ in your ‘REI’. If you can not then ‘is’ is not definable as a ‘relation’ but only as an ‘element’ in your ‘REI’. However, if you can show ‘is’ ‘self-referenced’ as a ‘relation’ then you show that your ‘REI’ is not required.