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.
The use of universal quantifiers to comprehend and express the for all and every phrases is more natural and intuitive than negating existential quantifiers
. Consider the following statement: Every company, which is destroying at least one forest, is savage, and every person who lives in Canada is concerned (1) about such companies.
(We need at most m extra variable for existential quantifiers
, where m is the maximum arity of a schema relation.)
If negation, identity, and the first-order existential quantifier
are indeed logical terms, and if the analytic (or logical) truths are closed under consequence, then no analytic (or logical) truth can entail (Two).
In the syntax, only existential quantifiers
and disjunctions can be made independent of previous choices (and so only the verifier is handicapped by independence).
order existential quantifier
can be read "there is a class" or "there is a property", in which case, it seems, the locution invokes classes or properties.
Now I need the existential quantifier
for an integer ...
(the existential quantifier
) which explicitly carries existential import.
Among the joint-carving terms, the most important one in this context is the existential quantifier
. Sider's main argument--the argument from the indispensability of using quantifiers--against ontological deflationists is the following: 'Questions framed in indispensable vocabulary are substantive; quantifiers are indispensable; ontology is framed using quantifiers; so ontology is substantive--that's the best argument for ontological realism' (188).
Hofweber asserts that we can distinguish between the internal and the external reading of the existential quantifier
. The question "Are there numbers?" is underspecified, having both an internal and an external reading.
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.sub.k] = [lambda]y [x = y]] [right arrow] [[F.sub.k]x [right arrow] [F.sub.k]y]].
By placing an existential quantifier
[there exists] before x ("for some x") and an universal quantifier [for all] before y ("for all y"), we can bind these variables, as may be seen bellow [Bird, 2009]: