Controversial formulas in Quantified Modal Logic

1.∀α′(∀α 𝜙α ⊃ 𝜙α′) ∀α′(∀α 𝜙α ⊃ 𝜙α′) forall α′(forall α 𝜙α → 𝜙α′)Universal Closure✹
2.∀α 𝜙α ⊃ 𝜙β ∀α 𝜙α ⊃ 𝜙β forall α 𝜙α → 𝜙βUniversal Instantiation✹
3.∀α𝜙α ⊃ ∃α𝜙α ∀α𝜙α ⊃ ∃α𝜙α forall α𝜙α → forsome existsα𝜙αsubalternation✹
4.∀α□𝜙α ⊃ □∀α𝜙α ∀α□𝜙α ⊃ □∀α𝜙α forall α□𝜙α → □forall α𝜙αBarcan formula✹
5.□∀α𝜙α ⊃ ∀α□𝜙α □∀α𝜙α ⊃ ∀α□𝜙α □forall α𝜙α → forall α□𝜙αconverse of Barcan formula✹
6.◇∀α𝜙α ⊃ ∀α ◇𝜙α ◇∀α𝜙α ⊃ ∀α ◇𝜙α ◇forall α𝜙α → forall α ◇𝜙αBuridan formula✹
7.∀α◇𝜙α ⊃ ◇∀α𝜙α ∀α◇𝜙α ⊃ ◇∀α𝜙α forall α◇𝜙α → ◇forall α𝜙αconverse of Buridan formula✹

تاربرگ‌های پیموده‌شده در این نشست: powerset ⟩ implication ⟩ Set theory ⟩ possible-world semantics ⟩ notion of existence ⟩ Introduction to Logic and to the Methodology of Deductive Sciences