Johann asked:

"Premise: This argument is valid.

Conclusion: I am the Pope."

Am I? If the premise is false then the argument is valid, and thus the premise is true and the
argument sound. So it seems that I am, therefore, the Pope.

============

If the premise is false, then it is false that the argument is valid, and you are notthe Pope. You have
not set up a paradox correctly.

The following:

"1) This sentence below is NOT valid

2) I am the Pope."

and

"1) This sentence below IS valid

2) I am the Pope."

are NOT paradoxes. The first is simply true, the second is simply false.

Try this one:

"1) the sentence below is true

2) the sentence above is false."

You need self-referentiality to set up a paradox. You could add Popes or whatever to the last one if
you want.

Steven Ravett Brown

Whether an argument is deemed formally valid has nothing at all to do with whether anything it says
is true, but only has to do with whether the various things that are asserted in it are connected in a
proper way. Conceivably and for the sake of argument, Johann's one premise argument passes that
test, and ifit does, then what we are saying is that any conclusion whatsoever could have been
validlyadduced from this initial premise. Now, it is important to remember that with a valid argument,
you can put garbage in and get garbage out. This is because validity is entirely to do with the process
from input to output, and not to do with the quality of either inputs or outputs.

Soundness is an entirely different matter. For an argument to be sound, it must be not only valid in its
proper connection of premise(s) and conclusion, but also derive its conclusion from a true premise.
For something to be a sound argument, you need to take sure to put truths in at the front end of a
valid argument. Soundness is validity plus true premises.

Validity and Soundness properly distinguished, we can look again at Johann's two clause central
assertion. Johann asserts:

"If the premise is false then the argument is valid..."

Well, we can accept this because we accept that the argument is valid, and that this is so irrespective
of whether the premise in it is true or false.

But Johann then continues:

"...and thus the premise is true and the argument sound."

This is a wrong move. From the fact that the argument is valid, nothing whatsoever follows about the
truth or falsity of the premise. Just because the argument is valid, it doesn't follow that the premise is
true or that the argument is sound.

"So it seems that I am, therefore, the Pope."

No, Johann isn't the Pope. And he hasn't done anything to show that he is either, because his
argument is confused about validity and soundness.

David Robjant

Formal logic is abstract and needs to be given content. In his book Logical Forms,Mark Sainsbury
suggests that for an argument to be valid in ordinary language it must be "useful" so that is not
enough for propositions to be true or false for validity. Your argument is not useful at all and there is
no relevant connection between the premises. You would find Sainsbury's whole book very useful, in
fact. He shows differences between ordinary language arguments and the workings of formal logic.

Otherwise put, by Avrum Stroll in a paper "Broadened Logic": An argument should be "cogent" as
opposed to "nonsense" or "absurd". As ordinary language users we just know what is nonsensical
and absurd, and we also have prior knowledge as to what is useful. Stroll says that traditional logic
has been "acontextualised" by Russell and Frege and contains no information about the world. As
humans beings we acquire knowledge about the world which has to be used as content in an
argument in a way which makes sense.

Logic might not reflect the way we think at all. Experience in the world makes a difference to the
inferences we are able to draw and formal logic is rather artificial as a way of describing natural
inferences. "The kinds of logic described by logicians simply seem irrelevant to normal individuals.
We do not construct truth tables and look up the result: We do not use formal rules of inference" —
this is a only a statement made by Howard Gardner in The Mind's New Science— but you could read
the whole book to check out the detailed way in which he backs this up.

When Aristotle introduced the idea of a syllogism, he didn't have as much knowledge of the way the
mind works as we have today. I have always found the idea that logic underpins our use of language
and form of argument highly persuasive, but it seems that it is time to rid ourselves of this idea.

Rachel Browne

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