Comment on Open Thread: May 2010, Part 2

Mon, 24 May 2010 06:49:43 GMT

Consider again the proposition "A true => (if A then B) OR (if A then not B)". Take B as: "This rock is heavier than this pencil." Now, assuming that the pencil does not lie in the weight range 1.5 plus/minus sigma, then this proposition must be true. And now, this statement is significantly more complicated than "A => ~~A", and it implies that (under proper restrictions) you can make longer logical statements, and continuing further, statements which are no longer trivial and just a property of human language.

I'm a little confused by this example. The proposition

A => (if A then B) OR (if A then not B)

is a logical tautology. It's truth doesn't depend on whether "the pencil does not lie in the weight range 1.5 plus/minus sigma". In fact, just the consequent

(if A then B) OR (if A then not B)

by itself is a logical tautology. So, I have two questions:

(1) Is there a reason why you didn't use just the consequent as your example? Is there a reason why it wouldn't "get to the heart" of your point?

(2) Just to be perfectly clear, are you claiming that the truth of some tautologies, such as A => ~~A , is "trivial and just a property of human language", while the truth of some other tautologies is not?

Discuss