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John How do we define the situation where the whole and part are part of the same entity?
Such as a whole number? Regards! Ravi
On Wed, May 8, 2013 at 3:55 PM, John F Sowa <sowa@xxxxxxxxxxx> wrote:
Tara,
I didn't respond to this point earlier because I was tied up with
some critical deadlines. I also changed the subject line to avoid
mixing this discussion with the old thread.
JFS
>> Mathematics can be used to disprove a theory by showing that it is
>> inconsistent with observations.
TA
> I, and some others such as Karl Popper, wouldn't agree with your first statement.
>
> "In point of fact, no conclusive disproof of a theory can ever be produced; . . .
> If you insist on strict proof (or strict disproof) in the empirical sciences, you
> will never benefit from experience, and never learn from it how wrong you are."
>
> http://www.xenodochy.org/article/popper.html
That's a good point, and it applies to both science and ontology.
But note that one of Popper's most famous points is that a scientific
theory must be falsifiable. The following quotation by Popper comes
from the same web page:
KP
> In a theory thus axiomatized it is possible to investigate the mutual dependence
> of various parts of the system. For example, we may investigate whether a certain
> part of the theory is derivable from some part of the axioms. Investigations of
> this kind . . . have an important bearing on the problem of falsifiability.
> They make it clear why the falsification of a logically deduced statement may
> sometimes not affect the whole system but only some part of it, which may then
> be regarded as falsified.
In this quotation, he is talking about "a certain part of the theory"
which he is separating from "the whole system".
In mathematics, it is common to consider the conjunction of all the
parts of a theory as a bigger theory. If it makes a false prediction,
the entire conjunction is thereby falsified.
But as Popper and most scientists would agree, it is usually possible
to patch up a big theory by changing certain parts of it that lead to
the incorrect prediction.
In mathematics (and logic), if you make any change to a theory, it is
a different theory. But scientists and engineers usually name their
theories. When they change part of it, they keep the same name, but
update the version number.
In summary, if a theory makes a false prediction, a logician would say
it's false. An engineer would say it has a bug. And Microsoft would
say it has an "issue". But it's usually possible to make some revision
to some part, keep the same name, and update the version number.
John
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Thanks.
Ravi
(Dr. Ravi Sharma)
313 204 1740 Mobile
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