The same problem occurs if we try to bring the abstract within the scope of a single existential quantifier
by embedding it in a restatement of K(Q-W) assumption (1) in the expression, [there exists]x[for all]y[[x = y [conjunction] [F.
Now I need the existential quantifier
for an integer .
On the assumption of the existential quantifier
ranging over the domain of all possible propositions in conjunction with the domain being constant, it is impossible that in any possible world W there exists a proposition the concept of which includes the property D.
It is pertinent to observe that English presents a different linguistic expression which is also ordinarily rendered as an existential quantifier
, but which shows the opposite pattern from some.
In addition, [for all], the universal quantifier, and [there exists], the existential quantifier
, can occur in formulas.
Similarly use existential quantifiers
to eliminate z-variables from L(SC)-atomic formulas.
Since (Two) is a logical consequence of 0 [not equal to] 0, then according to our logicist (Two) is itself analytic and logically true, provided that analyticity and logical truth are closed under logical consequence, or at least the introduction rule for the first-order existential quantifier
The rules for the independent existential quantifier
elimination require the introduction of function letters (to express the independence).
Fitch's Paradox is presented as a problem for realism, and is 'solved', I think, by denying that existential quantifier
elimination is legitimate.
However, the relation between these two representations, as well as the relation between the universal and the existential quantifier
representation, is not made clear (it seems to me that the two exercises devoted to these issues are not very helpful).
For (ii), we slightly modify the previous formula [Phi] by turning the existential quantifier
[exists]z into a universal quantifier [inverted] Az, and by replacing the last two conjuncts with
Then, letting "([sigma]-x)" be a substitutional existential quantifier
, we can try formulations like
Puntel finds here an alternative to the materialist ontology that analytic philosophers take for granted when translating everyday speech into first-order predicate logic, using an existential quantifier
that carries illegitimate ontological baggage: there is no "x" apart from the facts themselves.
This second-order property is of course expressed by the existential quantifier
(and its dual by the universal quantifier).
Questions of ontological import are considered from a perspective that does not accord existential import to the so-called (though only called so since Frege) Existential Quantifier