Class notes on Modal Logic

(Originally written December 8, 2006 in Book 9)

Class note

Modal Logic

(W⊃T) 'if today is Wednesday then I need to take out the trash
(S⊃F) 'if this figure is a square then it has four sides

The second statement is necessarily true. The first statement is contingently true.

Modal logic acknowledges that some statements are just plain true (they are actual) and that there are necessary truths.

Modal Logic
True - Actual
True - Necessary
True - Possible
False - Actual
False - impossible, necessarily false
False - possible

A statement that is necessarily rue has something in front of the well formed formula.
□(S⊃F)

But a possible truth has something in front of the well formed formula as well
◊(R⊃T)

□ - necessarily so
◊ - possibly so

~□(F⊃S) - It is not necessarily the case that a four-sided object is a square

◊~(F⊃S) - It is possible that a four-sided object is not a square

□ & ◊ are modal operators

True:
Actual - P
Necessary - □P
Possibly - ◊P

False:
Actual - ~P
Not necessarily true - ~□P
Impossible - ~◊P

Problem with modal logic is ◊□P ≡ □P

Modal logic deals with possible worlds.

Possible statements must be true in at least one possible world.

Necessary statements must be true in all possible worlds.

W.V.O. Quine flat out rejected modal logic because it entails essences.

Alvin Plantinga asserts that there are essences and therefore modal logic is a good system.

In modal logic a possible world cannot contradict the essence of the object of the actual world.