Priest’s non-classical logic

First of all, I would like to thank Davidagler for providing a helpful guide to use Markdown to type logic.

The rules are as follows:

¬ $\neg$
→ $\rightarrow$
↔ $\leftrightarrow$
∨ $\vee$
∧ $\wedge$
⊢ $\vdash$
⊣ $\dashv$

Predicate Logic
∀ $\forall$
∃ $\exists$
∈ $\in$
⊨ $\models$

Modal Logic
□ $\Box$
◊ $\Diamond$

It is quite unfortunate, then, that the Markdown in Svbtle in fact does not support such feature. However, the symbols can be directly copied and pasted to the blog as you can see.

After a little researching on Internet I found another useful guide:
tlextrait](http://tlextrait.svbtle.com/equations-with-markdown-and-svbtle).

The tenet is that we can use embedded images in the post with sites that can make images out of equations. I shall try to use it for later convenience.

For now, I would like to discuss several trivial findings in Graham Priest’s .

1.Modal logic for moral necessity.

Priest says that □A ⊃ A is “notorious for not satisfying moral necessity”, for “people do not bring about what they morally ought to.”
It seemed dubious to me, in the first place, that whether A can refer to “What K do ” and □A can refer to “What K ought to do” at the same time. For the former a statement of “is” and later a statement of “ought”.

At the class, P-X explained that the □ in □A ⊃ A is quite different from the ones discussed before in the book. I am having a different take on this: it is not the □ that is different, (obviously □ cannot be different as it is a logical constant),but the interpretation.
For K-morality, the relation between worlds 2r1 exists if and only if 2 is the corresponding moral ideal world for 1. It then can be explained that K-morality does not satisfy rho (the rule of reflexivity). The existing world is definitely not the moral ideal world.
However, this also faces a difficulty: we normally think that for moral necessary statements and worlds, there exists such a correlation of 2r1 “because of” A is morally necessary in 1, as there are conditions in 1 that makes A possible and not just “because of” the given interpretation of K-morality. So when discussing another proposition B that is morally necessary in world 1, 2r1 might not exist at all in the sense that makes □B: for a world 3 , A might happen in it while B does not happen in it at all.It is still left in question whether normal modal logic can be a system that express moral necessary propositions.