štvrtok, 18. februára 2016

Alice in Puzzle-land a Hintikkov paradox

Z neporiadku na polici nad mojím pracovným stolom spadla knižka Raymonda Smullyana, Alice in Puzzle-land. Útla knižka ostala na mojom stole ležať stranami nadol otvorená na tejto pasáži:

"Well," said Humpty Dumpty, "would you believe if I told you I had a baby?"
"Why not?" said Alice.
"And would you believe it if I told you that everybody loves my baby?"
"Why not?" said Alice.
"And would you also believe it if I told you that my baby loves only me?"
"I don't see why not," replied Alice.
"Ah!" said Humpty Dumpty, "if you believed all those things, then you'd be inconsistent!"
"Why?" asked Alice.
"Or at least you would be driven to a very absurd conlusion: You don't believe I'm my own baby, do you?"
"Of course not!" replied Alice.
"Well, you'd have to if you believed all those other things!"
"Why?" asked Alice, who was very puzzled.
"It's just simple logic, that's all. Look, suppose those other things were true. Since everybody loves my baby, then my baby also loves my baby."
"Oh, I hadn't thought of that!" said Alice.
"Of course not, but you should have, you know. You should always think of everything."
"I can't think of everything!" replied Alice.
"I never said you could," replied Humpty Dumpty, "I merely said you should."
"But is it reasonable to say that I should do something that I cannot do?" asked Alice.
"That is an interesting problem in Moral Philosophy," he replied, "but that would take us too far afield. Coming back to this problem,..."

...a záver si vyskúšajte domyslieť - ako z troch Humptyho tvrdení vyplýva, že je sám svojím dieťaťom?

Je krásne, keď jednému skvelému matematikovi píše úvod do knihy jeho kamoš, ďalší skvelý matematik. Úvod k Smullyanovej knihe napísal Martin Gardner. Bez jeho komentáru by som nezistil, že v tomto texte Smullyan naráža na v tých časoch (1982) populárny Hintikkov paradox z morálnej filozofie. Fínsky filozof Jaakko Hintikka tvrdí, že je morálne nesprávne pokúšať sa o nemožné. A takto pôvabne vysvetľuje prečo:


1. Doing something that cannot be done without something wrong being done would in itself be wrong.

2. Something that cannot be done at all cannot be done either with or without something wrong being done. So, for example, if X is impossible and Y is wrong, it is not possible to do either (X and Y) or (X and (not Y)).

3. Assume that Y is wrong. We have shown in the previous step that (X and (not Y)) is impossible. In other words, it is impossible to do X without something wrong (Y) being done. By step 1, X must be wrong.

4. Therefore, if it is impossible to do something, it is wrong to do it.

3 komentáre:

rasťo povedal(a)...

SPOILER - riešenie hádanky:

"...since my baby loves himself and also loves only me, it would follow that I am my own baby! Therefore, not everything I told you can be true."

Charon ME povedal(a)...

nie je ten hintikkov paradox iba jednoduchy dosledok ex falso quodlibet? ved tvrdenie ze niekto urobi(l) nieco co je nemozne urobit je kontradikcia, takze z nej sa da odvodit cokolvek, aj ze urobit nieco nemozne je nemoralne (aj ze je to moralny imperativ, aj cokolvek ine, napr. ze zem je plocha)

inak podla mna pokusat sa urobit nieco nemoralne nemusi byt nutne tiez nemoralne, ved jednotlive cleny nejakeho radu mozu mat nejaku vlastnost ktoru nema limita toho radu (alebo naopak)

rasťo povedal(a)...

@charon ME:
Hej, odhliadnuc od toho, ze tiez v tom argumente nevidim viac, nez (A and nonA)->(H), kde H je Hocico, hned ma napadlo niekolko intuicii, ktore tomu zaveru odporuju. Alebo som ho mozno len nepochopil.

Napriklad, citim ako spravne bojovat so smrtelnou chorobou do posledneho dychu, pripadne branit svojim telom vlastne dieta proti atomovej bombe a podobne. Alebo subtilnejsie - ktovie, ci ma zivot zmysel (v nejakom univerzalnom zmysle), ci existuje Boh, ci nas k niecomu zavazuje, ci nase subjektivne prezivanie "bytia" nie je len iluzia, ci mame nadej na nejaku vecnu existenciu atd. To vsetko vyzeraju byt zatial neriesitelne otazky. Pozerajuc sa na rozne postoje mudrych ludi k tymto otazkam ma naplna obava, ze ich mozno sam nikdy nerozlusknem. Je to uplne mimo toho Hintikkovho argumentu, alebo konam nemoralne, ak sa ich rozlusknut pokusam?

Este sa mi sem hodi tento vytrhnuty Ecov text (Foucaltovo kyvadlo), v niecom to ma "podobneho ducha":
But now I have come to believe that the whole world is an enigma, a harmless enigma that is made terrible by our own mad attempt to interpret it as though it had an underlying truth.