On Aug 21, 2013, at 3:47 PM, raghu wrote:
On Tue, Aug 20, 2013 at 5:43 PM, Shane Mage <[email protected]>
wrote:
On Aug 20, 2013, at 1:43 PM, Chuck Grimes wrote:
... These can be modeled on the liar's
paradox which leads to a contradiction in the formation of
definitions.
Example. This statement is false. (A)\
But---what statement does "this statement" refer to? If some prior
statement, no problem or paradox.
There are ways to recreate the Liar's paradox without self-
referential statements (e.g. with a number of sentences that refer
to each other).
If the statement is "this statement is false" then we must say "
'this statement is false' is false." Again, no paradox because the
contradiction in Aristotelian logic is between false and not-false,
and not-false in no way implies true: a statement may be
performative, emotional, or meaningless and as such neither true nor
false.
Not false indeed equals true unless you reject the "excluded middle"
principle, which very substantially cripples logic and prevents you
from doing all kinds of interesting and useful stuff with it.
The "excluded middle" says: Either A or notA. If "false" is A, then
"true" can be termed notA ONLY if statements must be either true or
false. Which is manifestly NOT the case. Frederic's birthday was not
his twenty-first, but that didn't in fact, in logic, or in law (even
Pirate law) make him "a little boy of five." The ways of paradox may
be quaint, but every one of them reflects a defective way of
formulation.
Shane Mage
"L'après-vie, c'est une auberge espagnole. L'on n'y trouve que ce
qu'on a apporté."
Bardo Thodol
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