Re: OT: Once again Inez delves into the murky waters of philosophy.

Inez <savagemouse123@xxxxxxxxxxx> wrote:

On another thread there has been a bit of a discussion about "proving
an negative," and it's got me thinking. It is often said on this
newsgroup that you can't prove a negative. However, it's clear that
in some cases you can.

For example, I may not be able to prove that there's no such thing as
a three-eyed Barbie doll anywhere in the world, but I can't prove that
there isn't one under my bed.

So what is the real long hand version of this? You can't prove a
universal negative, or something like that?

You *can* prove a negative if you can list (enumerate) all the items
under discussion. You only can't prove a negative if the domain is
infinite or indefinitely large.

Suppose I say "There are no red balls in that bag". I can prove the
negative by taking all the balls out and classifying them under colours.
If the red basket is empty, I have proven it.

Suppose I say "There are no humans elsewhere in the universe". Since we
have no access to the universe in general, that is practically
unproveable.

In traditional logic, this is called modus tollens and it has the form
"If P then Q; Not-Q, therefore Not-P". If not-Q is true, that is, if Q
is false, then you have shown Not-P is true, or P is false.

But if the domain in which Q may occur is too big, or unexplorable, then
you cannot prove that Not-P. In ordinary induction, in which we try to
generalise from observed cases, no number of not-Qs is enough to show
that all items are not-Q if the "bag" is too big or we cannot open it.

The classical example is "No swans are not-white" (= "All swans are
white"). Suppose we assert this in 1500. Each observed swan is white,
and hence the negation is not proven. Does this mean all swans are
white? No, because swans in West Australia are black. But in 1500 they
hadn't been observed, so even though the claim was shown to be false
later, and was false when stated, it could not be proven to be false at
the time.

Hope this helps.
--
John S. Wilkins, Postdoctoral Research Fellow, Philosophy
University of Queensland - Blog: scienceblogs.com/evolvingthoughts
"He used... sarcasm. He knew all the tricks, dramatic irony, metaphor,
bathos, puns, parody, litotes and... satire. He was vicious."

.

Relevant Pages

  • Re: First Causes
    ... the inherently self contradictory form of Q "not not". ... Put simply you seem to be saying that if negation is universal then ... this depends on your universe of discourse. ... It is not even a fundamental operator - if we consider the ...
    (sci.cognitive)
  • Quantum Gravity 285.7: Are "Mass Operators" Missing From Quantum Logic?
    ... namely to a point at which mass itself ... of the Universe outside the set), and double negation is ... "affirmation", but what in the world is affirmation? ... Universe", as opposed to an "unreality" operator that claims that the ...
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  • Re: OT: Once again Inez delves into the murky waters of philosophy.
    ... Suppose I say "There are no humans elsewhere in the universe". ... and hence the negation is not proven. ... because swans in West Australia are black. ... This is exactly what Apo was using, since he said god was all around ...
    (talk.origins)
  • Re: OT: Once again Inez delves into the murky waters of philosophy.
    ... is false, then you have shown Not-P is true, or P is false. ... no number of not-Qs is enough to show ... because swans in West Australia are black. ... every statement is the negation of some other statement. ...
    (talk.origins)
  • Re: OT: Once again Inez delves into the murky waters of philosophy.
    ... no number of not-Qs is enough to show ... because swans in West Australia are black. ... "Proving a negative" without context doesn't make much sense, ... every statement is the negation of some other statement. ...
    (talk.origins)
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