Re[2]: Logic Fundamentals (was: Re: Re[2]: [tied] PIE word for "peo

From: Brian M. Scott
Message: 41015
Date: 2005-10-04

At 3:31:21 PM on Monday, October 3, 2005, glen gordon wrote:

> Me:
>> Do you wish to prove the distinction between
>> statement and argument?

> Brian:
>> There's nothing to prove: it's a matter of
>> definition.

> It's an assumption that statement and argument are
> in different classes.

Formal logic is the main context in which statement
and argument are formally studied. In formal logic, whether
approached from philosophy or, as in my case, from
mathematics, it is not an assumption; as I said, and meant
quite literally, it's a matter of definition. The terms are
defined in such a way that no entity is both.

In a less technical setting it's still a useful distinction,
as is that between truth and validity-in-the-strict-sense,
for which you may prefer 'sound': 'Your argument is sound
enough, but since one of your premises is false, your
conclusion remains unsubstantiated'. Indeed, having taught
many students who habitually confused validity of inference
with truth of conclusion, I'd say that the distinction is
not just useful, but also a prerequisite to clear thinking.
What terms one uses for it, or even whether one uses any
terms at all, aren't important, but recognizing it is.

[...]

>> Hardly, since the following argument is valid:

>> All giraffes are pink with purple polka-dots.
>> gLeN is a giraffe.
>> Therefore gLeN is pink with purple polka-dots.

>> It seems likely that none of the individual
>> statements is true, however.

[...]

> Since the first statement is reasonably certain to be
> false, the conclusion is 'relatively untrue' as a whole.
> It is not an optimal conclusion and is therefore
> dismissed.

The fact that the premises are false tells you nothing about
the truth or falsity of the conclusion. You are not
logically entitled to conclude that the conclusion is
relatively untrue, probably false, or whatever. All you can
legitimately conclude is that the argument, despite its
impeccable inference, offers zero support the conclusion;
the conclusion itself may nevertheless be true, and it is
not made more or less likely by this argument. To put it
another way, the falsity of the premises entitles you to
dismiss the argument, but not its conclusion per se. Of
course, if the flawed argument was the only evidence offered
for the conclusion, the latter is now back to ground zero,
which might well put it behind one or more competing
hypotheses.

Brian