- The 'Equivalence of Things' (齐物论) chapter of the Zhuangzi (庄子) (c. 3rd c. B.C.E.)

Once upon a time I, Zhuang Zhou (庄周), dreamt I was a butterfly.
Flapping my wings in true butterfly fashion, I was happy as could be, and I knew nothing of any person named Zhuang Zhou.
But suddenly I awakened, astonished to be Zhuang Zhou.
I still don't know whether as Zhuang Zhou I was dreaming I was a butterfly or whether as a butterfly I was dreaming I was Zhuang Zhou.
There ought to be a difference between Zhuang Zhou and a butterfly, but this is called the transformation of things.
- David K. Jordan translation (adapted)

## Epistemic Logic

### Epistêmê is the Greek word for 'knowledge'

1. Epistemic logic is a branch of epistemology that is concerned with logical approaches to knowledge, belief, and related notions
2. Epistemic logic consists of a number of axioms that capture certain important features of knowledge, belief, and the interactions between the knowledge and belief modalities

 2 seminal works in the formal study of epistemic logic G. H. von Wright's (1951) An Essay in Modal Logic Jaako Hintikka's (1962) Knowledge & Belief

# Kap

Agent a knows that p

# Bap

Agent a believes that p

Axioms of epistemic logic:
Formal notation Translation
(T) Kap → p If Agent a knows that p, then p is true (truth or veridicality)
(K) Ka(p → q) → (Kap → Kaq) If Agent a knows that if p then q, then if she knows the antecedent p, she also knows the consequent (closure under implication)
Axiom K tells us that knowledge is closed under implication
(RN) ⊦p → ⊦Kap If p is a tautology, then it is always already logically true that Agent a knows that p (rule of necessitation)
(4) Kap → KaKap If Agent a knows that p, then she knows that she knows that p (positive introspection)
(5) ~Kap → Ka~Kap If Agent a does not know that p, then she knows that she does not know that p (negative introspection)
(KB1) Kap → Bap If Agent a knows that p, then she believes that p
Axiom KB1 is an interaction axiom that connects the modalities of belief and knowledge
(KB2) Bap → KaBap If Agent a believes that p, then she knows that she believes that p
Axiom KB2 is another interaction axiom that connects the modalities of belief and knowledge
(D) Bap → ~Ba~p If Agent a believes that p, then she does not believe that not-p
(D′) ~Ba Agent a's beliefs cannot be inconsistent

### ⋮

1. Epistemic logic is able to do the following:
2. Connect knowledge and belief to truth (Axioms T, D′)
3. Link the modalities of belief and knowledge with bridge principles (Axioms KB1 and KB2)
4. Capture the principled access that we have to our own mental states (Axioms 4 and 5)
5. Ensure the consistency of our knowledge and belief modalities (Axioms T, D, and D′)

1. However, the notion of justification is conspicuously absent in epistemic logic
2. The gap between epistemic logic (absence of the notion of justification) and mainstream epistemology (presence of the notion of justification) could be bridged by justification logic