Sharing paradoxes
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Transcript of Sharing paradoxes
SHARING PARADOXESthe Role of Self-Contradictory Structures in Arts and Sciences
Or
This is not a conference
By Félix Lambert
WHAT IS A PARADOX
• Contradict itself
• Shapes of paradoxes: Self-referential, Circular
• Quine’s Classification: Veridical, Falsifical, Antinomy.
FALSIFICAL PARADOX
• 0=0+0+0+0+0+0+0…..
• 0=(1-1)+(1-1)+(1-1)+(1-1)…
• 0=1-1+1-1+1-1+1-1+1-1…
• 0=1+(-1+1)+(-1+1)+(-1+1)+(-1+1)…
• 0=1+0+0+0+0+0+0…
• 0=1
EXAMPLES OF PARADOXES
• The Liar’s Paradox
• Curry‘s and Löb’s Paradox A:A implies B
• Russel’s Paradox
• Cantor’s Paradox
PARADOXES IN SCIENCE
• How wonderful that we have met with a paradox. Now we have some hope of
making progress. (Niels Bohr)
• The paradox is really the pathos of intellectual life and just as only great souls are
exposed to passions it is only the great thinker who is exposed to what I call
paradoxes which are nothing else than grandiose thoughts in embryo. (
Kierkegaard)
HOW TO APPROACH PARADOXES
• Chuang-Tzu: the word life only have a meaning in
front of the word death.
• Octavio Paz: (about cuerpo y no-cuerpo) They don’t
have any meaning except to express a relation of
contradiction.
PROOF BY CONTRADICTION
Aristotle’s proof for square root of two
Euclid’s proof for infinity of prime numbers
SELF-REFERENTIAL SENTENCES
True: This sentence has one verb.
False: This sentence has two verbs.
Paradoxical: This sentence is false
True with true opposite: This sentence has five words. This sentence does not have five
words.
True with false opposite: This sentence has at least one verb. This sentence has no
verb.
False with true opposite: This sentence has two words. This sentence does not have
two words.
False with false opposite. This sentence has seven word. This sentence does not have
seven words.
GÖDEL'S INCOMPLETENESS THEOREM
If a system only create true statements and allows the
construction of the sentence A: This statement can’t be
proved in the system.
By definition it is true, so A is true and can’t be proved.