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# First Order (formal) Logic Question Tweet

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1. First Order (formal) Logic Question
Logic professor wrote on the board today:

-Ax Ey Loves (y, x)

So, two questions:

(1) Is the negation operating on the entire statement, or only the universal quantifier? She said that she was 95% sure that convention has it that the negation will operate on the entire statement and not just the universal quantifier?

(2) Supposing that the negation is operating only on the universal, is this read as:

It is not the case that for every x there exists some y such that y loves x?

Simplified:

There exists some x such that there exists some y, such that y loves x?

I have no idea how it would be translated if the negation operated on the entire statement?

It is not the case that it is the case that for every x there exists some y, such that y loves x?
Last edited by NYU2012; 02-05-2012 at 19:26.
2. Re: First Order (formal) Logic Question
(Original post by Darkphilosopher)
Sorry but that made absolutely no sense what so ever.
What part of it didn't make sense?
Last edited by NYU2012; 02-05-2012 at 23:52.
3. Re: First Order (formal) Logic Question
The negation covers the quantifier and the statement quantified over, so that it would read: it is not the case that for all x there is some y such that y loves x.

You can't negate a quantifier by itself ... it's always quantifying over something ...
4. Re: First Order (formal) Logic Question
I would read that as negating the quantifier.

So you get either

it is the case that (for not all x (there exists some y such that (y loves x))

or

it is not the case that (for all x (there exists some y such that (y loves x))

I think these are actually equivalent - if somebody proved in the distant past that they're equivalent for all predicates that would explain the ambiguous notation.
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