Re: Blank nodes, "leaning", and the LEM

On Wed, 2011-03-23 at 08:38 -0500, Pat Hayes wrote:
> [ . . . ]
> OK, consider the two sentences
> A:  %E% x @ P(x)
> B: %E% z, y @ P(z) & P(y)
> Suppose A is true. Then there is something X such that P is true of X.
> Is the second sentence true under these circumstances? Yes, because
> that X can be the value for both z and y, and it makes both conjuncts
> true, and so the conjunction is true. Now suppose B is true: is A
> true? Obviously yes. Ergo, A and B each entail the other. Ergo, they
> are logically equivalent. 

Right.  And just to elaborate, the reason that the above equivalence may
not be obvious at first glance is because two different variable names
("z" and "y") were used in B, so the reader may erroneously make a
"unique name assumption" that z != y.  But in fact, B has no requirement
that z != y.

David Booth, Ph.D.

Opinions expressed herein are those of the author and do not necessarily
reflect those of his employer.

Received on Wednesday, 23 March 2011 20:22:20 UTC