NOTE:
I expect that working all this out is too difficult for me. I think in
My modal system - definitions
, I have indicated how my approach would go. I have insufficient training in logic and to work all this out
will take me a long time - if at all. I encourage anyone else interested to work on these ideas.
More Thoughts
For a universal point of view [S=God] there would be no difference from usual logics. I.e. B(God,t,p) iff p.
But for any other S, no new consequences would follow, as other S's need not be logical!
But I would point out it is still true:
(∀ x)(∀ y)((x = y) ⇒ B(S,t,...,x,...) ⇔ B(S,t,...,y...)) [ where x and y are in the same position.]
But that this position is for names and that 'Tully' ≠ 'Cicero' even if Tully = Cicero.
Preliminary Axioms
I am using
Blackwell's Guide to Philosophical Logic ed. Lou Goble as a guide.
- Axioms from Classical First Order Logic
- Φ⇒(Ψ⇒Φ)
- (Φ⇒Ψ)⇒((Φ⇒(Ψ⇒Χ))⇒(Ψ⇒Χ))