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]:

Being, existence, and ontological commitment" presents five theses of Quinian metaontology: (1-3) being is not an activity, is the same as existence, and is univocal; (4) the

existential quantifier adequately captures the sense of being; (5) ontological disputes can be settled by determining the ontological commitments implied by established beliefs (this last is restated and illustrated in chapters four, eight, and ten).

It appears, then, that the property on which K(Q-W) logically depends cannot be adequately formulated by embedding either a universal or

existential quantifier within the abstract with either internal or external scope relative to the modal operator.

Among the joint-carving terms, the most important one in this context is the

existential quantifier.

Hofweber asserts that we can distinguish between the internal and the external reading of the

existential quantifier.

checking in the process if he is in possession of or has developed a rudimentary but accurate feeling for syntax to concentrate afterwards in semantics, once we have informed him that the traditional symbol for the universal quantifier "for any" is "[for all]", an inverted letter "A", and for the

existential quantifier "there exists" is "[there exist]", a rotated letter "E".

Let the

existential quantifier '[there exists]x' range over the domain of all propositions [alpha] (that is, statements which have a definite truth-value).

It is pertinent to observe that the relative order of the

existential quantifier and negation in (3) is the opposite of the order of the indefinite some and negation in (1): adult English only licenses the "nonisomorphic" interpretation of sentences like (1).

The for all and every English phrases can be satisfied in SQL through negating its

existential quantifier construct EXISTS.

Now consider a quantifier that behaves exactly like the universal quantifier (over individuals) in models with domains of cardinality [greater than or equal to] n, but like the

existential quantifier in models with domains of cardinality < n.

Following this, Kolmogorov does not give the interpretation of the

existential quantifier, as we would expect, since intuitionistically the

existential quantifier cannot be defined using the universal and negation; but elsewhere in the paper he gives ample explanations of the meaning of existential claims in intuitionistic mathematics, and in particular, of the central point concerning them: that the person who makes the claim must be able to indicate a particular instance of it.

To eliminate an

existential quantifier [exists]z [element of] U, we use the lemma above, by translating its statement into first-order logic.