Critique of this Approach to Modal Logic
by Dennis J. Darland
April 20, 2008
Last revised 20.04.2008 22.20 time
Copyright © 2008 Dennis J. Darland
Points on Modal Logic
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It seems to me that the Barcan formula:
∀xLΦx ⇒ L∀xΦx [Goble, p. 150]
is not true.
" This objection depends on the assumption that in various possible worlds, not merely might objects have different properties
from those they have in the actual world, but there might even be objects which do not exist in the actual world at all. It looks
as though the semantics given above for modal predicate logic implicitly denies this assumption since each model has only a single
domain of individuals, the same for each world. That is what yields the validity of the Barcan formula. This suggests that one might
obtain a semantics which does not validate this formula by admitting models in which different domains are associated with different
worlds. ", M. J. Cresswell, "Modal Logic" in The Blackwell Guide to Philosophical Logic, ed. Lou Goble, p. 150.
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In Whitehead's metaphysics [which is closest to mine], not only could different worlds contain different individuals, but the same
world would at different times.
In fact, the world consists of what Whitehead calls "actual entities", all of which except one [God] are "actual
occasions", which only occur once.
- The "actual occasions" themselves are usually not named. People [and ordinary physical objects and even, probably,
the elementary particles of physics] would be what Whitehead calls "societies" of actual occasions. Though one could
name them through definite descriptions [as abbreviations(and such definitions could not guarantee their existence)].
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It would seem that "truth" would only exist as an application of symbols to portions of the world.
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