From: Skouteris Dimitris (dimitris(@)impact.dyn.unipg.it)
Date: Τετ 07 Μαΐ 2003 - 12:27:27 EEST
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Agaphtoi sullistoi,
kat' arxhn, mallon ofeilw mia suggnwmh giati to provlhma, an kai logika 3eka0aro, einai anoixto se polles parermhneies logw ths 'an0rwpomorfikhs' domhs pou pairnei (ntopios, episkepths, ippotes, paliatsoi, akriveies klp.).
Gia tous pio 'ma0hmatikous' ths listas, para0etw to idio provlhma sto telos tou email alla se afhrhmenh, sumvolikh morfh.
Gia na doume...
O ntopios exei pei ston episkepth :
'De 0a pisteyeis pote pws eimai ippoths.'
PROVLHMA 1 : O episkepths skeptetai :
'Estw oti einai paliatsos. Ara eipe yemata, dhladh kapoia stigmh 0a pisteyw pws einai ippoths. Auto omws einai adunaton, giati egw de mporei pote na pisteyw kati esfalmeno. Ara exoume atopo, kata sunepeia den einai paliatsos. Einai ippoths. Opote eipe thn alh0eia, dhladh de 0a pisteyw pote pws einai ippoths.'
(Edw vlepoume thn parafrosunh sthn opoia odhgeitai o ptwxos episkepths, afou pisteuei pws o ntopios einai ippoths, alla sugxronws pisteuei pws DEN to pisteuei. Auto omws den ephreazei to provlhma mas.)
Kai o ntopios ti einai ; Afou en telei o episkepths pisteye pws o ntopios einai ippoths, auto shmainei pws o ntopios eipe yemata, ara einai paliatsos.
Apanthsh : O ntopios einai paliatsos kai o episkepths pisteuei pws einai ippoths.
PROVLHMA 2 : Estw oti o ntopios einai paliatsos. Ara leei yemata, kai o episkepths 0a pisteyei kapoia stigmh pws einai ippoths. Auto omws einai adunaton, giati o episkepths mas einai panta akrivhs kai den pisteuei pote kati esfalmeno. Ara exoume atopo kai o ntopios den einai paliatsos, alla ippoths.
Ara eipe thn alh0eia. O episkepths de 0a pisteyei pote pws einai ippoths. Alla oute kai to anti0eto 0a pisteyei giati tote 0a pisteue kati esfalmeno.
Apanthsh : O ntopios einai ippoths kai o episkepths menei 'gia panta anapofasistos' (e3 ou kai o titlos tou vivliou) ws pros thn tautothta tou.
Epituxwn :
George Papargiris (ton opoio euxaristw gia mia apo tis pio endiaferouses allhlografies pou eixa !)
Kala na pernate,
Dimitris
AFHRHMENH MORFH TOU PROVLHMATOS :
~ : Arnhsh & : Suzeu3h (KAI) V : Diazeu3h (H)
=> : Sunepagetai
<=> : Isodunamei
Genikes upo0eseis :
- Estw oti apo ka0e logikh protash p mporoume na ftia3oume mia allh, thn Bp (kai apo authn thn B(Bp) kai outw ka0e3hs...).
- Estw oti, gia oles tis tautologies p isxuei h Bp. (Tautologia=Mia protash kat' anagkh alh0hs MONO apo th logikh kai OXI apo alles upo0eseis, p.x. h (A & B) => A ).
- Estw oti, an isxuoun oi Bp kai B(p => q) tote isxuei kai h Bq gia opoiesdhpote protaseis p, q.
- Estw mia SUGKEKRIMENH protash k gia thn opoia isxuei k <=> ~Bk, ka0ws kai B(k <=> ~Bk).
Provlhma 1 :
- Estw oti, gia ka0e protash p, isxuei oti B(Bp => p).
Apodei3te oti B(~Bk), oti Bk kai oti ~k.
Provlhma 2 :
- Estw oti, gia ka0e protash p, isxuei oti Bp => p.
Apodei3te oti k, ~Bk kai ~B(~k).
--
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