Re: All panduks are green
- From: stevendaryl3016@xxxxxxxxx (Daryl McCullough)
- Date: 10 Apr 2008 06:37:57 -0700
Aatu Koskensilta says...
On 2008-04-10, in sci.logic, Daryl McCullough wrote:
(x) (Px -> Qx)
has exactly the same meaning as
~(Ex) (Px)
or
(x) (Px -> Qx)
Does it? These formulas are logically equivalent, but it seems to me
they differ in meaning, though in a rather trivial way.
When someone clarifies a statement by spelling out all the details,
does the clarification have the same meaning as the original, or not?
In the case of statements involving logical connectives, it is typical
for those not trained in logic to assume that statements have implications
that don't actually have. For example, "A or B" does not imply
that exactly one of {A,B} is true, although many people assume
that that's what is meant. So if you want to be clear about it,
you would, redundantly, "Either A is true, or B is true, or both are true".
The third clause "or both are true" is logically unnecessary,
because "A or B" by itself allows for both to be true.
Similarly, saying "all Xs are Ys" can give some people (such
as our friend Newberry) the false impression that we are saying
that there is at least one X. To avoid that false impression,
we can spell it out as
"Either there are no Xs at all, or there are some Xs, and
all of them are Ys"
Expanding the sentence in excruciating detail like that isn't
changing the *meaning*, but it may make some invalid inferences
less likely.
--
Daryl McCullough
Ithaca, NY
.
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