# Re: [isabelle] Free variables aren't quantified, it's that simple (by all appearances)

On 9/14/2012 6:13 PM, Alfio Martini wrote:

`So, they do not get quantified, but they have the same "denotation"
``(that is to say, they are equivalent under all interpretations.)
`

Alfio,

`To try and summarize it, for you "they" are the formulas with free
``variables that get proved. I'm going to label these propositions that
``you're talking about as tautologies. They have the same denotation as
``some quantified formula.
`

`For me, "they" are the formulas with free variables which have no
``definite truth value, like the (3) that I gave as an example. For these
``formulas, there is not an equivalent quantified formula.
`

`You're focusing on the free variable formulas that can be proved, and
``their equivalency to a quantified formula.
`

`I'm focusing on the free variable formulas that can't be proved, and
``which don't have an equivalency to a quantified formula.
`
I think that's the way it is.
Regards,
GB

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