Logical Thinking LO21633

John Gunkler (jgunkler@sprintmail.com)
Fri, 14 May 1999 16:10:53 -0500

Replying to LO21591 --


Please don't do this. I so often appreciate your messages, and enjoy
learning from your thinking in part because it often differs from the way
I've been thinking about things. But in your message about logical
thinking you have entirely missed my point.

It simply is not true that the logical fallacy of denying the antecedent
depends upon other "facts." Nor does my example depend upon other facts.
It really doesn't matter whether there actually is a corner drug store
where I could have purchased a toy. The point is that logically (not
empirically) there could have been one.

I know this is sometimes difficult for people to understand, but there is
a difference between a statement's logical status and its empirical
status. To object to a statement on logical grounds is to object to the
FORM of the statement, not its content. If the form of a statement is
fallacious (such as the form described as denial of the antecedent) it
doesn't matter what the "facts" are -- the statement is fallacious.

The only valid way to argue against what I just wrote is the way At argued
-- that there are other systems of logic (in particular, ones that do not
include the law of the excluded middle) in which the form named "denial of
the antecedent" is not fallacious. So, if we agree that our discourse is
to be ruled by this other system of logic, then I can't say what I said
validly. But if we do agree to "abide" by standard logic (as even At
admits holds in most ordinary discourse), then I can justify all that I
wrote in the original message about logical fallacies.

But, in neither case does it matter what the facts are -- in neither case
does it matter whether there is actually a corner drug store, nor whether
it actually sells toys.

You continue by adding,

>Another information would have made the conclusion valid: "The mall is
>the only place where toys can be bought."

Yes, that's an interesting thing to contemplate -- but it entirely changes
the FORM of the statement to include it. We can analyze what happens when
your statement is included, but (interesting as it may be to do so)that's
a different analysis than the one I cited as a example. My original
example did not include your statement of necessary conditions and it did
not need to include it.

Although you may understand all this, because it is so difficult for some
people, maybe I ought to try to clarify it a bit more. Here goes.

When someone argues: ""If p is true then q is true. p is not true.
Therefore, q is not true." what is happening?

I submit that they are asking me to believe that "q is not true." But,
more (and this is critically important), they are asking me to believe
that "q is not true" SOLELY ON THE BASIS OF the two other statements: "If
p is true then q is true." and "p is not true." The word "therefore"
means, in this context, that what I'm about to say is true solely on the
basis of what I just said.

In other words, the person making the (fallacious) argument is saying to
us: "Precisely and only because we know that 'If p is true then q is
true' and we know that 'p is not true' then we MUST conclude that 'q is
not true.'" But if there is even one case that could exist where, under
the given conditions (the first two statements), q is true -- then we have
shown that the argument is fallacious. And I provided one case. I could
have provided many others. I could have said, "Suppose I bought the toy
over the Internet." Or I could have said, "Suppose I bought the toy by
telephone order." etc., etc.

So the point is that, given the information provided by the person making
the argument, we should not be led to believe that the conclusion (q is
not true) must be true, because it may not be.

Now, as you say, if we are given other true statements, they may change or
merely confirm the truth value of the conclusion. For example, if we
added "p is true," then we would be able to conclude that "q is true" -
which means that "q is not true" is not true.

All of this is regardless of the empirical content of the statements p and
q -- it merely requires looking at the form of the argument we make with
those statements.


"John Gunkler" <jgunkler@sprintmail.com>

Learning-org -- Hosted by Rick Karash <rkarash@karash.com> Public Dialog on Learning Organizations -- <http://www.learning-org.com>