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Quantifiers Bind Variables
Suppose you had to work out whether this sentence is true in a certain possible situation.
That would be tricky given what we've said so far about the meanings of the quantifiers.
It would be tricky because we have talked about replacing variables with names without saying, in cases like this, which variables to replace.
To specify this we need the notion of binding ...
∀x( Square(x) → ∃x Blue(x) )
But first, to see the problem, think about this variable instance.
When do we replace it? Is it when removing the truth of the universal quantifier?
Or should we leave the variable in tact and replace it when removing the existential quantifier?
To answer this question we need the notion of binding ...
(Btw, this sentence is eqvuivalent to 'either not everything is square or something is blue')
