Monique Y. Mudama said:
Hmm, there's a lot of things I don't agree with on that page. It seems
to differentiate between circular reasoning and (valid) deductive logic
based on how much of the premise the conclusion is based upon. For example,
it considers "P implies Q. P. Therefore Q." to be valid, but "Q. Therefore
Q." to be "invalid" (or circular reasoning). To me, both are valid deductive
arguments.
I think the author is confusing "truth value" with "validity". The
arguments are deductively valid because if the assumptions are true, then
the conclusion must be true (this is the case for "Q. Therefore Q" for
example). However, the even though the arguments are deductively valid, that
does not nescessarily mean that they are true. If the assumptions are false,
then a deductively valid argument could end up being false as well.
Of the exercise at the end of the page, I particularly disagree with the
explanation for answer "B", on police brutality. To me, it seems like a
valid deductive argument (though its truth value depends entirely on the
truth value of the assumptions made). I'd formulate the statement like this
"P if and only if Q. Not P. Therefore not Q." where Q is "The charges are
true." and P is "The police did it.". Nowhere in that statement is it
assumed that the claim is false; rather, it is assumed that the police
didn't commit physical abuse, and from that, the claim being false is
derived.
"Often, however, circular reasoning is more subtle than this: it
depends on an assumption not stated but assumed. Consider the famous
argument of the French philosopher, René Descartes: "I think,
therefore I am." Descartes has begged the question here, because when
he said "I think," he'd already implied "I am" (or how else could he
think?). Yet his fallacy continues to persuade people, over three
hundred years later."
So once again, I'm in disagreement with the author. Nowhere is there an
assumption that Descarte exists. Instead, Descarte assumes he is thinking,
and assumes that as a requirement to think, one needs to exist. From these
two assumptions, Descarte derives that he must exist.
Anyway, I was a bit imprecise when I said Descartes' statement is an
axiom. It's actually an argument based on two more fundamental axioms. Those
axioms are of course, the two assumptions I listed above: that Descarte is
thinking, and that one needs to exist to think. As far as I know, there's no
way to prove either assumptions, but they're taken to be "self-evidently"
true.
- Oliver