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G.E. Hughes & M.J. Cresswell, A New Introduction to Modal Logic, London and New York: Routledge, 1996, pp. 41-43. (5) The System T ⓛ As we previously noted, Lp ⊃ p is not K-valid ② The System T K + T (Lp ⊃ p) ※ T is often called Axiom of Necessity ③ Translation into quantification theory ④ T1 p ⊃ Mp ⑤ T2 M(p ⊃ Lp) ⑥ p is not a rule of T If P were a rule of T, then from it and T2 we could derive ..

G.E. Hughes & M.J. Cresswell, A New Introduction to Modal Logic, London and New York: Routledge, 1996, pp. 33-36. (4) L and M ① K5 Lp ≡ ~M~p K5: Lp ≡ ~M~p Proof 1. p ≡ ~~p PC12 (DN) 2. Lp ≡ ~~Lp 1[Lp/p] 3. Lp ≡ ~~L~~p 2 × 1 × Eq 4. Lp ≡ ~M~P Def M Q. E. D. ※ Clearly K5, by Eq, will entitle us to replace L by ~M~ anywhere in a theorem; and by Def M we may replace M anywhere in a theorem by ~L~. ②..

G.E. Hughes & M.J. Cresswell, A New Introduction to Modal Logic, London and New York: Routledge, 1996, pp. 24-33. (2) The System K ① The system K is one which will turn out to have as its theorems precisely those modal formulae which are K-valid. ② The axioms of the system K consist of (a) all valid wff of PC (b) the single distinctively modal wff, K PC: If α is a valid wff of PC, then α is an a..

G.E. Hughes & M.J. Cresswell, A New Introduction to Modal Logic, London and New York: Routledge, 1996, pp. 23-24. (1) Systems of Modal Logic ① The axiomatic method: it allows us to define a class of wff without any reference to their meanings. ② An axiomatic basis for a logical system (a) a specification of the language in which the formulae of the system will be expressed - i.e. a list of primi..

G.E. Hughes & M.J. Cresswell, A New Introduction to Modal Logic, London and New York: Routledge, 1996, pp. 13-21. (9) Basic modal notions ① In modal logic, there are a number of non-truth-functional concepts. ② Modal Operator L (□) L: necessity operator "necessarily," "must be," "is bound to" Instead of writing "A is bound to be B," we can write "It is bound to be the case that A is B." Lp= Nece..

G.E. Hughes & M.J. Cresswell, A New Introduction to Modal Logic, London and New York: Routledge, 1996, pp. 3-13. (1) The Language of PC (Propositional Carculus) ① Primitive (or undefined) symbols of PC 1. A set of letters: p, q, r, . . . (with or without numerical subscripts). We suppose ourselves to have an unlimited number of these. 2. The following four symbols: ~, V, (, ). ※ Any symbol in th..

2023-1 사회철학연습 초월 논리의 또 다른 길 -칸트, 프레게, 그리고 비트겐슈타인- 1. 칸트와 논리학의 혁신 (1): 규준(Kanon)으로서의 논리 우리는 일반적으로 칸트를 독단론과 회의론이라는 스킬라와 카리브디스 사이(between Scylla and Charybdis)를 빠져나와 합리론과 경험론의 장점을 종합했던 철학자로 평가한다. 짧게 말해, ‘경험으로부터 떠나지 않는 합리주의 철학’이라는 기획은 이후 200년의 철학사를 지배했던 칸트의 유산이다. 그러나 한층 더 중요한 것은 그러한 기획이 어떻게 성립할 수 있었는지를 추적하고, 그 과정에서 남아 있던 문제들이 그간의 철학사 속에서 어떻게 전개되었는지를 파악하는 일일 것이다. 칸트는 그의 기획을 실현하기 위해 새로운 학문을 창조해야 했던바, ..