추론（논리）집합

1. 추론（논리）집합 • 추론이란 무엇인가? • 어째서 어떤 추론은 여러분이 수긍할수 있고 다른 것은 궤변이라고 생각되는가? • 기준은 무엇인가? • 철학자, 논리학자, 수학자, 과학자, 경제학자, 사회학자, 인문학자, 문학가의 논리는 다 각각 다른가? 정치가, 위정자, 선동가의 논리는 무엇인가?

2. 소크라테스, 플라톤 • 추론은 자신이 무엇을 정의하고어떻게 사용했는지 모르면서 때로는 진행하고 있다. • 이러한 점을 어떻게 모든사람이 수긍할수 있는 방법으로 바꾸는가? • 이러한 점에서 현대나 고대 그리스나 어떠한 차이가 있는가? 또는 발전이 있었는가? • 다음은 소크라테스의 방법을 소개한다.

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.

7. 아리스토텔레스의 3단 논법syllogism • SaP: All S is P, SeP: No S is P, SiP: Some S is P, SoP: Some S is not P • MaP, SaM -> SaP • (I) aaa, eae, aii, eio (II) eae, aee, eio, aoo(III) aai, iai, aii, eao, oao, eio(IV) aai, aee, iai, eao, eio • 더줄이면　(I) aaa, eae, aii, eio (II) aoo, (III) aai, eao, oao (e, i는　주어　술어　바꾸어도　됨）

8. Venn diagram • P S M

9. George Boole (1815-1864) • 사고의 법칙 • 불 대수 x + y = y+x, xy=yx(x+y)+z = x+(y+z), x(yz) = (xy)z,x(y+z) = xy + xz, x+0= x, 1x = x, 2x = x+x = x, xx= x • 0은 공집합 1은 전체집합을 말한다. • x에　속하지　않는　집합　1-x

10. 불대수의 활용 • SaP: s(1-p)=0, SeP: sp=0, SiP: sp0,SoP: s(1-p)0 • 아리스토텔레스의 오류 aai, eao(2000년간발견안됨) MaP, MaS -> SiP (책１０１）MeP, MaS -> SoP: mp=0, m(1-s)=0, s(1-p) 0

11. 명제논리학(propositional logic) • 기호 p, q, , ∧,∨, ∼를 이용한다. p∧q=q∧p, p∨q=q∨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∧T=p, p∧F=F, p∨T=T, p∨F=p,~(p∧q)= (~p)∨(~q), ~(p∨q)=(~p) ∧(~q), ~~p=p, p q= (~p)∨q

12. 진리표 • http://sciris.shu.edu/~borowski/Truth/

13. 술어논리학(predicate logic) • ∀,∃사용 • ∀x, x 는 사람이다 -> x는 잠잔다. • ∃x, x 는 사람이다 ∧ ~(x는 잠잔다). • 법칙 ~(∀x: P(x)) = ∃x: ~P(x)모든사람이 자는것은 아니다 = 잠을 자자않는 사람이 존재한다.

14. 정수의 공리화 (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.

15. 토의 • 소크라테스의 방법은 아직도 유효하다. 그이유는 무엇일까?