Benjamin Udell wrote:

> In standard first-order logic, the phrase "everything exists" would be taken
> to trivially mean "“that, that is, is," or the like. Is there a way to say it
> in a non-trivial sense in first-order logic at all? Is it an idea that can be
> logically expressed at that basic level? What would it mean if it can't? I'm
> not a logician, but there does appear to be a way to say it in a specially
> restricted kind of first-order logic, by use of a special kind of
> quantificational functor. As for whether this leads to a coherent logical
> idea in less restricted logic, you be the judge. The result is, at least, a
> kind of statement which seems to lead to an area of logical issues raised by
> the "Everything Exists" picture, in any case, with regard to saying that
> every "potential" particular definite individual is actualized somewhere and
> somewhen, or the negative, that the world in all times and places lacks some
> particular definite individual. Now, in defining the existential particular
> quantification, one may start with a finite universe of objects named by
> constants "a" through "h", and say “There is a such that...Ja...or there is b
> such that...Jb...or... [etc.] ...or there is h such that...Jh....” and agree
> to write this as "Ex ...Jx...." Then one drops the substitutionalist
> requirement that x shall range over only named objects a, b, c, etc. Then the
> variable x is no longer _substitutional_ but instead is _objectual_. To get
> to our new special functor will be a matter of replacing the repeated "or"
> with a repeated "and". Let’s define a functor "Æ" such that "Æx ...x...." is
> equivalent to "There is a such that...a...AND there is b such
> that...b...AND... [etc.] ...AND there is h such that...h...." In effect one
> is saying that every name names something. Now, what happens when the
> substitutionalist requirement is dropped? In considering just what it is that
> x now ranges over, and whether the objectual statement "Æx ...x..." is
> contingently or formally true or contingently or formally false or formally
> or contingently undecidable or (despite its fraternal-twin relationship with
> the existential particular) just plain ill-defined, 

To me this seems confusing because you're not distinguishing between names and 
objects.  Let yNx be the relation "y names x".  Then your functor is equivalent 
to Ex("x"Nx).  But that is really no different that Ex(yNx) unless you 
postulate 
that there is an operator " " that produces a canonical name of an object, i.e. 
given x then "x" is (by construction) a name for x.  But if you use such a 
naming operator then you've already assumed that every name so generated names 
something.  The question is the converse; whether every name names something. 
The usual way of addressing this is to reinterpret  the name as a definite 
description: "Did Moses exist?" -> "Did a person who took the ten commandments 
from God exist?"

>one is led to consider
> some of the logical problems which arise in any case in entertaining the
> general idea that “everything exists.” In other words, we seem to arrive at
> some of the right problematics. Then if you negate it, you're saying that
> there lacks a something, some particular thing is failing to exist. If you
> say "~Æx Jx," you're saying that something's missing or it exists but isn't J
> (e.g., but isn't jumping). So you could say "[AxJx] & ~[ÆxJx]" (Note: "Æx"
> should NOT be called the "existential universal" which would instead be
> properly applied to whatever is equivalent to the conjunction or predicative
> combination of the existential particular and the hypothetical universal,
> where you say, e.g., "there's some food that’s good, and any food is good" or
> "there's some food that's good such that any food is good" or “there’s food
> and any food is good” I suppose that "Æx” could be called the
> "omniexistential."

There are also logics in which existence is treated as a predicate instead a 
quatifier, e.g.  http://en.wikipedia.org/wiki/Free_logic

Brent Meeker

--~--~---------~--~----~------------~-------~--~----~
You received this message because you are subscribed to the Google Groups 
"Everything List" group.
To post to this group, send email to everything-list@googlegroups.com
To unsubscribe from this group, send email to [EMAIL PROTECTED]
For more options, visit this group at 
http://groups.google.com/group/everything-list
-~----------~----~----~----~------~----~------~--~---

Reply via email to