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

VERIDICAL PARADOX

EXAMPLES OF PARADOXES

• The Liar’s Paradox

• Curry‘s and Löb’s Paradox A:A implies B

• Russel’s Paradox

• Cantor’s Paradox

PARADOXES AS ART

AMBIGRAMS

VISUAL PARADOXES

Istvan Orosz

VISUAL PARADOXES AS A GAME: ECHOCHROME

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)

AMES ROOM

THE USE OF PARADOXES IN SCIENCES

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

THE PLACE OF PARADOXES IN NARRATIVES AND THE PRINCIPLE OF SUPERPOSITION

APPLICATIONS IN NARRATIVES

APPLICATIONS IN NARRATIVES

APPLICATIONS IN NARRATIVES

CHRIS WARE

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.

FUZZY LOGIC

Lofti A. SadehJan Lukasiewicz

ALfred Tarski

THEOLOGY

PARADOXES IN HUMORISTIC FUNCTIONS

KOANS

HOMEWORK

Prove this theorem to be unprovable

Félix Lambert

edomite@hotmail.com