This Is Metaphysics by Kris McDaniel

Author:Kris McDaniel [McDaniel, Kris]
Language: eng
Format: epub
ISBN: 9781118400784
Publisher: Wiley
Published: 2020-05-14T00:00:00+00:00

4.6 An Alternative Theory of Possible Worlds: Propositions First

4.77 The first alternative to Lewis’s theory says that propositions form an ontological category and builds possible worlds out of propositions. Remember that Lewis does not have propositions as an ontological category. Rather, for Lewis, propositions are sets of worlds. But, on this alternative theory, which I will call the Propositions First Theory, worlds are sets of propositions.

4.78 Ok, but is every set of propositions a possible world? No, because some sets of propositions are not maximally opinionated in the way that possible worlds must be maximally opinionated. Remember that we discussed the metaphor that possible worlds are maximally opinionated in Section 4.3. What we meant there was that, for any proposition P and possible world w, either P is true at w or P is false at w. A possible world has an opinion on whether P is true by either having P as a member or by having the negation of P as a member. If possible, worlds are sets of propositions, then a set of propositions is a possible world only if that set is maximal in the following sense: for any proposition P, either P or not‐P is a member of that set of propositions.

4.79 Moreover, not every maximal set of propositions is a possible world. Consider a maximal set that includes every proposition and that proposition’s negation. This set is a maximally inconsistent set: its opinions are massively contradictory! This set is no possible world, since there is no possible situation in which contradictions are true! So, at the very least, we need to say that a set of propositions is a possible world only if that set is logically consistent, that is, the set contains no logically inconsistent items.

4.80 Can we say that a possible world just is a maximal and logically consistent set of propositions? Now we enter tricky territory. If every logically consistent set of propositions is absolutely possible, then we can. But if a set of propositions can be logically consistent and yet still impossible, then we can’t simply say that a possible world is a maximal and logically consistent set of propositions—because some of these maximal and logically consistent sets of propositions might still be collectively metaphysically impossible.

4.81 Not every formally logically consistent and maximal set of propositions is a possible world. Here’s an exercise to see this. Consider the following (admittedly not maximal) set of propositions: {1. Kris is a bachelor; 2. It’s not the case that Kris is a bachelor.} This is a logically inconsistent set of propositions: proposition 1 is of the form P and proposition 2 is of the form not‐P. Any set that contains propositions 1 and 2 is definitely not a possible world. But now consider the following (admittedly not maximal) set of propositions: {3. Kris is a bachelor; 4. Kris has a spouse}. This set is strictly not formally logically inconsistent: it’s not of the form P and not‐P. Proposition 3 is of the form P and proposition 4 is of the form Q.

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