On Aug 21, 2013, at 5:00 PM, raghu wrote:
On Wed, Aug 21, 2013 at 3:48 PM, Shane Mage <[email protected]>
wrote:
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."
Ok, all you are saying is that natural language contains sentences
that cannot be formalized into propositions that have truth values.
Great, but what have you really achieved? You will now just have to
accept that you cannot easily specify just what class of sentences
you can exclude in this way without in essence crippling the ability
of the language to express truth-claims.
All your "paradoxes" are exactly that--statements that have no truth
value (ie., cannot be refuted by factual data or *reductio ad
absurdam*). If a statement in "natural language" intends truth but
falls short of that specificity, it can be clarified through dialogue
in that same "natural language." Example: You say "this statement is
false." I ask: what does the demonstrative pronoun "this" refer to?
If (as is the case) it can't be shown to refer to anything at all your
statement is exposed as nonsense, not paradox.
The ways of paradox may be quaint, but every one of them reflects a
defective way of formulation.
There is nothing quaint about these paradoxes. You have a choice of
either (a) giving up on "natural language" and restrict yourself to
a stunted formal language in which logic can be used without running
into these paradoxes, or (b) accepting that natural language cannot
be completely formalized and reduced to logic consistently, and you
need to be cautious in making truth-claims in natural language terms.
How can you presume to dictate such a choice? Why do you exclude
clarifying the intended meaning of "natural language" statements
through dialogue (language, let me remind you, is a *social*
phenomenon) so as to be "cautious," so as to make sure that the "truth
claims" made in a phrase are indeed such (and therefore refutable) or
merely bullshit?
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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