Ironic Modesty

1
??(??)??

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  ?? ???? ???, ???, ???? ??? ?????

2
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• ??? ?????? ??? ????.

3
Ironic Modesty

• Explaining his mission as a philosopher, Socrates
  reports an oracular message telling him that "No
  one is wiser than you." (Apology 21a) He then
  proceeds through a series of ironic descriptions
  of his efforts to disprove the oracle by
  conversing with notable Athenians who must surely
  be wiser. In each case, however, Socrates
  concludes that he has a kind of wisdom that each
  of them lacks namely, an open awareness of his
  own ignorance.

4
Questioning Habit

• The goal of Socratic interrogation, then, is to
  help individuals to achieve genuine
  self-knowledge, even if it often turns out to be
  negative in character. As his cross-examination
  of Meletus shows, Socrates means to turn the
  methods of the Sophists inside-out, using logical
  nit-picking to expose (rather than to create)
  illusions about reality. If the method rarely
  succeeds with interlocutors, it can nevertheless
  be effectively internalized as a dialectical mode
  of reasoning in an effort to understand
  everything.

5
Devotion to Truth

• Even after he has been convicted by the jury,
  Socrates declines to abandon his pursuit of the
  truth in all matters. Refusing to accept exile
  from Athens or a commitment to silence as his
  penalty, he maintains that public discussion of
  the great issues of life and virtue is a
  necessary part of any valuable human life. "The
  unexamined life is not worth living." (Apology
  38a) Socrates would rather die than give up
  philosophy, and the jury seems happy to grant him
  that wish.

6
Dispassionate Reason

• Even when the jury has sentenced him to death,
  Socrates calmly delivers his final public words,
  a speculation about what the future holds.
  Disclaiming any certainty about the fate of a
  human being after death, he nevertheless
  expresses a continued confidence in the power of
  reason, which he has exhibited (while the jury
  has not). Who really wins will remain unclear.

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???????? 3? ??syllogism

• SaP All S is P, SeP No S is P, SiP Some S is
  P, SoP Some S is not P
• MaP, SaM -gt SaP
• (I) aaa, eae, aii, eio (II) eae, aee, eio,
  aoo(III) aai, iai, aii, eao, oao, eio(IV) aai,
  aee, iai, eao, eio
• ???? (I) aaa, eae, aii, eio (II) aoo, (III) aai,
  eao, oao (e, i? ?? ?? ???? ?)

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Venn diagram
S

• P

M
9
George Boole (1815-1864)

• ??? ??
• ? ?? x y yx, xyyx(xy)z x(yz), x(yz)
  (xy)z,x(yz) xy xz, x0 x, 1x x, 2x
  xx x, xx x
• 0? ??? 1? ????? ???.
• x? ??? ?? ?? 1-x

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???? ??

• SaP s(1-p)0, SeP sp0, SiP sp?0,SoP
  s(1-p)?0
• ???????? ?? aai, eao(2000??????) MaP, MaS -gt SiP
  (?101)MeP, MaS -gt SoP mp0, m(1-s)0, s(1-p) ?0

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?????(propositional logic)

• ?? p, q, ?, ?,?, ? ????. p?qq?p, p?qq?p,
  p?(q?r)(p?q)?r, p?(q?r)(p?q)?r,p?(q?r)(p?q)?(
  p?r),p?(q?r)(p?q)?(p?r),p?Tp, p?FF, p?TT,
  p?Fp,(p?q) (p)?(q), (p?q)(p) ?(q),
  pp, p ?q (p)?q

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???

• http//sciris.shu.edu/borowski/Truth/

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?????(predicate logic)

• ?,???
• ?x, x ? ???? -gt x? ???.
• ?x, x ? ???? ? (x? ???).
• ?? (?x P(x)) ?x P(x)????? ???? ??? ??
  ???? ??? ????.

14
??? ??? (Peano Axioms)

• 1. Zero is a number.
• 2. If a is a number, the successor of a is a
  number.
• 3. zero is not the successor of a number.
• 4. Two numbers of which the successors are equal
  are themselves equal.
• 5. (induction axiom.) If a set S of numbers
  contains zero and also the successor of every
  number in S, then every number is in S.

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