Re: existential quantifier necessary?

From: Owen (oorionus_at_yahoo.com)
Date: 01/30/05 

Date: Sun, 30 Jan 2005 13:00:34 -0500

  "alex goldman" <hello@spamm.er> wrote in message
news:1410070.KI6dqmXISo@yahoo.com...
> Is it really necessary to give the existential quantifier a special
status,
> including it in BNF grammars, etc., as opposed to treating it just like
any
> other relation (similarly to treating equality) ?
>
> Greater(X, Y) => Exists(Z) ^ Greater(Z, Y) ^ Greater(X, Z)

  It seems that the existential quantifier has special status in classical
logic, only because,
  Ax(x=x) is an axiom. That is to say, we grant, in vitue of this axiom,
that all things referred to
  by our variables (pronouns) exist. i.e. AxE!x <-> Ax(x=x).

  "To be is to be a value of a variable"
  "No entity without identity"
  "To be something is to be identical to some existent thing"

  All of that which is, is.