Relations and Multiple Quantification:
Overlapping Quantifiers

The relational statements we've examined so far have a variable in one of the subject positions, bound by a single quantifier. However, we can also have variables in more than one position, each bound by a separate quantifier, as long as we observe a few simple rules.

When we have more than a single quantifier, how do we tell which one goes first? If the quantifiers are of the same kind, it doesn't matter.

Everything is related
to everything.
(x)(y)Rxy
OR
(y)(x)Rxy
Something bumped
into something.
(x)(y)Bxy
OR
(y)(x)Bxy
For everything that exists, there's
something that causes it.
(y)(x)Cxy
There is a single
cause for everything.
(x)(y)Cxy
In general, when the existential quantifier comes before the universal quantifier, it means there is some one thing that the rest of the statement is about.

When the existential quantifier comes after the universal quantifier, it means "something or other."


Relations | Overlapping Quantifiers

Relations and Multiple Quantification

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