

Discover more from Just Emil Kirkegaard Things
No filter science
Over 5,000 subscribers
Continue reading
Similarity between PWS and predicate logic
It seems to me that the formulas:
1. ◊P
2. (∃x)(Fx)
and:
3. □P
4. (∀x)(Fx)
are quite similar, if we translate the modal propositional ones into PWS. Here is the result:
1*. (∃w)(Pw)
3*. (∀w)(Pw)
Translated into a formal-ish english language, they should be read as:
1*. There exists a possible world, w, such that P is the case in w.
2. There exists an x such that Fx.
3*. For all possible worlds, w, P is the case in w.
4. For all x, Fx.
The similarity becomes stronger when an interpretation is added to the predicate logic formula though I leave that up to the reader to do.