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2023-2 Modal Logic (Segment 2) Q)UG, MP. E! is primitive, ∼ , ∨ are primitive and we have the usual definitions. Sketch proofs of:① ├FL (∀x)( E!x ≡ (∃y)(x = y)).② ├FL (∀y) ((∀x) ϕx ⊃ ϕy).Now consider the system FL* which is just like the above except that (∀y) ((∀x) ϕx ⊃ ϕy) replaces axiom schemas 2 and 3, and E! is dropped as a primitive sign.Sketch proofs of:③ ├FL* (∀x) (∃y)(x = y)④ ├FL* (∀x)B..

2023-2 Modal Logic (Segment 3) Q) Explain the system S1. In what sense is it the case that the “unrestricted” rules of Necessitation does not hold in S1. Does pc tautology necessitation hold in S1 ? What is the Cresswell argument (See my SS1 paper) that S1 has no theorems of the form LL(p⊃ p)? Explain the semantic system for S2 and S3 and S4 where one introduces odd vs normal worlds. Note that b..

2023-2 Modal Logic (Segment 2) Q) Use tableaux to show the difference between what we have called the A semantics and the B semantics (+ inclusion requirement) and the C-semantics for quantified modal logic. Be sure to explain by reference to the question of the validity of the Carnap-Barcan Formula (BF) and its converse. Be sure to explain the situation withAx1 (∀x) (ϕx) ⊃ ϕy, where y is free f..

2023-2 Modal Logic (Segment 1) Q) Use the technique of Modal Conjunctive Normal form to test the follow for S5 Validity and if Valid construct a proof using the technique.ML(p ⊃ LMp)M(Lp ⊃Mq)⊃ M(p⊃ q)L(p ∨ Lq) .⊃. Lp ∨ LqLMLp ⊃ Lp

2023-2 Modal Logic (Segment 1) ① Give a recipe justifying the following derived rule: ├K p ∨ q ⇒ ├K Lp ∨ Mq ② Some Drived Rules

2023-2 Modal Logic (Segment 2) Q) Quantification theory may be formalized this way: Prove the following in the systems indicated.1. ├ L(∀x)ϕx . ⊃. (∀x)Lϕx2. ├ β (∀x)Lϕx . ⊃. L(∀x)ϕx (Recall that system β is T + p ⊃ LMp. )3. ├ M(∃x)ϕx . ⊃. (∃x)Mϕx (The system is QML + (∀x)Lϕx . ⊃. L(∀x)ϕx)4. ├ (∀x)Lα ⊃ L(∀x)α (The system is QML+ (∀x)L(α ⊃ β) .⊃. L((∀x)α ⊃ (∀x)β)

2023-2 Modal Logic (Segment 1)Q) Give a proof of the following in the systems indicated:├S5 Mp ∧ Mq .⊃. M(p ∧ Mq)├B MLp ⊃ LMp├S5 Lp ⊃ LLp├S5 p ⊃ LMp├S5 L(p ∨ Lq) .⊃. Lp ∨ Lq├S4 M(p ∧ Mq) .⊃. Mp ∧ Mq

2023-2 Modal Logic (Segment 1)① Check to see which of the following are S4 valid or S5 only valid and give a proof in S4 if it is S4 valid and give a proof in S5 if it is S5 only valid:MMLMp ⊃ MpLp ⊃ LLMLpLLMLp ⊃ Lp② Give a proof of the following in the systems indicated:├K L(p ∨ q) .⊃. Lp ∨ Mq├S4 Lp ∨ Lq .⊃. L(p ∨ Lq)├T M(p ⊃Mp )

2023.12.21 - [Research/Publications] - 전기 비트겐슈타인의 내재적 비판철학 : 스테니우스의 칸트적 해석에 관한 비판적 고찰 전기 비트겐슈타인의 내재적 비판철학 : 스테니우스의 칸트적 해석에 관한 비판적 고찰김현균. ｢전기 비트겐슈타인의 내재적 비판철학 : 스테니우스의 칸트적 해석에 관한 비판적 고찰｣. 건국대학교 일반대학원 석사학위논문. 2022.georgia15.tistory.com 2022 석사논문 제2장 제3절 전기 비트겐슈타인의 근본 사상과 논리의 본성 잘 알려져 있듯이, 러셀은 그의 분석의 핵심 도구로 삼았던 논리의 지위에 관한 문제를 해결하는 데 어려움을 겪었다. 특히, 비트겐슈타인의 비판처럼, 논리 상항(logical constant)의 본성과 그것의 인식론적 ..

2024-2 Frege and Russell Midterm Exam#1) What is special about those functions that Frege calls concepts. Explain the role of truth-values, the True and the False in Frege notion of a concept. Explain how it is that concepts can play the role of what mathematicians nowadays call “characteristic functions.” Could Frege identify the True with, say 0 and identify the False with 1? Would this be met..