Logic and arguments

Lloyd Eby (leby@nova.umuc.edu)
Sat, 20 Jun 1998 22:49:53 -0400 (EDT)

On Sat, 20 Jun 1998, Glenn R. Morton wrote:
Replying to Stephen Jones on the subject of arguments:

> Stephen, you own citation proves what I was trying to say. IF the premises
> are true, then the conclusion is true. But if they are false, then the
> conclusion is false. If an argument is to be true, the premises must be true.
> And then below you go on to argue my position.
> >GM>If they aren't, then the argument is false. If Johnson is
> >>so expert in analyzing argumentation, he should know this.
> >
> >Clearly if "the facts" are not "correct" then "the argument is
> >false." You didn't have to go into such a preamble about
> >"logic" to establish that!

Logicians usually use this terminology:

Premises and/or conclusions can be true or false. Arguments can be valid
or invalid, sound or unsound.

A valid argument is one that has an argument-form such that *if* all the
premises are true, then the conclusion *must be true*. Another way of
saying this is that a valid argument is truth-conveying, meaning that if
the premises are true, the argument guarantees that truth is conveyed to
the conclusion. (But note that an argument that has a valid form *may*, in
fact, have one or more false premises, in which case the conclusion may be
either true or false.)

An invalid argument is one that fails to be valid, i.e. it has a form such
that it does not guarantee that if the premises are true, then the
conclusion must be true.

A sound argument is one that is *both* valid and that has all true
premises. (Thus, a sound argument also necessarily has a true
conclusion.) An unsound argument is one that fails to be sound, i.e. it
either has at least one false premise or it is invalid (or both).

(Logicians do not usually use `true' or `false' for arguments or argument
forms, but for statements, namely premises or conclusions.)

So, in summary, `true' and `false' are used for premises or conclusions
(i.e. statements). `Valid', `invalid', `sound', and `unsound' are used for

Lloyd Eby Avoid the legal nets
That entangled Bernie Goetz,
Just shout "Help! Help! Police!"
Like Kitty Genovese ...

The time for action has passed;
now is the time for recriminatory bickering.