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Geoffrey Hunter, Metalogic. An Introduction to the Metatheory of Standard First Order Logic, Berkeley and Los Angeles: University of California Press, 1996, pp. 3-6. (1) truths of logic(2) sentences used to express truths of logicNotably, (1) and (2) are not the same; for two different sentences, e.g. one in French, one in English, might be used to express the same truths of logic.Keeping the ab..

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..

2023-2 Modal Logic (Segment 3) Q) Describe in some detail the different approaches to understanding possible worlds—e.g., out in Lycan’s discussion in “The Trouble with Possible Worlds”. What is the problem of how we know we are actual”? What are some main difficulties of and attempt at a combinatorial approach to possible worlds? What sense of “possible” seems more amenable to a combinatorial a..

2023-2 Modal Logic (Segment 2) Q) Evaluate the following wffs in the B-semantics + inclusion requirement and determine in what systems, K, T, S4, β, S5 (if any) they are valid. 1. (∃y)LM(ϕy ⊃ (∀x)ϕx) 2. L(∃x)(Lϕx ∨ ψy) ⊃ (∃x)L(Lϕx ∨ ψy) 3. L(M(∃x)ϕx ⊃ (∃x)Mϕx) 4. L(∃x)ϕx ⊃ (∃x)Lϕx

2023-2 Modal Logic (Segment 3) Q) Use the tableau method (which involves non-normal world idea) to determine whether the following are valid in Lewis’ systems S2, S3:1. Lp ⊃ LLp2. L( M(p ∧ q) ⊃ Mp)3. L(L(p ⊃ q ) ⊃ L(Lp ⊃ Lq))

2023-2 Modal Logic (Segment 3) Q) How might one use relevant logic to interpret C. I. Lewis’ strict implication as relevant entailment where we have: Give proofs of the wffs K and T in Lewis’s S1, i.e., prove: 1. L(p ⊃ q) : ⊃: Lp ⊃ Lq 2. Lp ⊃ p

2023-2 Modal Logic (Segment 3) Q) Routley-Meyer Semantics for Relevant Logic has this: Prove (using the semantics) the following: 1. A & B .–▶. A v B 2. ¬¬A ◀– –▶ A 3. ¬(A & B) ◀– –▶. ¬A v ¬B 4. ¬A –▶ B .–▶. ¬B –▶ A

2023-2 Modal Logic (Segment 3) Q) Explain why that (∀x)Roox yields (∀x)Roxo and collapses Relevent logic into classical logic. If is sufficient (for the present purposes) to just prove something that doesn’t hold in Relevant Logic, e.g., ¬A ∧ (A ∨ B) .–Ȝ. B. Why does it seem not to be viable to take relevant logic to be a universal logic (a logic that can capture all others?) #2) Generally speak..

2023-2 Modal Logic (Segment 1)① Determine whether the following valid in the systems indicated by the semantic tableauL(Lp ⊃ Lq) ∨ L(Lq ⊃ Lp)ML(p ⊃ LMp)② Determine which of the following are valid in K, D, T, S4, S5, B by tableaux.L(p ∨ Lq) .⊃. Lq ∨ LpM(p⊃p)Mp ⊃ LMMpLp ∧ M(q ⊃ r) :⊃: L(p⊃q) ⊃ M(p ∧ r)

2023-2 Modal Logic (Segment 1) Q) Prove the following by Translation into quantification theory (you may use conditional proof). Trans(R) & Symm(R) ├ Mp ∧ Mq .⊃. M(p ∧ Mq) Trans(R)├ M(Lp ⊃ Mq) ⊃ M(p ⊃ q) Symm(R) ├ p ⊃ LMp