## § Motivation for modal logic

• possibly A -> necessarily (possibly A -> B) -> necessarily B
• this weakens the precondition A -> (A -> B) -> B by needing only possible Aand strengthens the postcondition by spitting out necessarily B.
• Key idea 1: if A is true in no world w, then possibly A that we have is false, and from this we derive explosion.
• Key idea 2: if A is true in some world wa, then suppose we are in some arbitrary world wr.
• Since A is true in wa, we have possibly A.
• Since necessarily (possibly A -> B) is true in all worlds, we have (possibly A -> B).
• Since we have both possibly A, and possibly A -> B, we derive B in wr.
• Since wr was arbitrary, we then have necessarily B since B holds in any arbitrary worlds.

#### § Use of this for Kant

• experience of objects is possible.
• it is necessarily the case that if experience is possible, then I must have some way to unite experience.
• thus, necessarily we have unity of experience.

#### § Use of this for descartes

• it is possible for me to be certain of something (ie, I think therefore I am)
• it is neecessarily the case that if I can be certain of something, I have clear and distinct perception.
• Therefore, it is necessary that I have clear and distinct perception.