1. Modality Necessity Possibility/impossibility Contingency Compare the following: 1)It is necessary that 7 + 5 = 12. 2)If all men are mortal and Socrates is a man, then, necessarily, Socrates is mortal. 3)It is possible for me to touch the ceiling. 4)It is impossible for me to jump over POT. 5)It is impossible that 2 + 1 ≠ 3. 6)It happens to the case that Lee Todd is president of UK.

2. Counterfactuals (α) If Gore had won the election in 2000, the US would not have invaded Iraq. Is (α) true? Is it false? Or is it meaningless? If it is either true or false, what makes it true? In virtue of what is it true? (β) If I were to drop this book, it would fall. Is this true?

3. Possible Worlds and Modal Discourse In the 1960s logicians found that they could give a clear sense to the notions of necessity and possibility by appropriating the Leibnizian idea of possible worlds. Propositions can have truth-values in different possible worlds. Modal discourse has validity over the totality of possible worlds. That’s why empiricists couldn’t account for it. So, Necessity: true in all possible worlds Possibility: true in some possible world Impossibility: true in no possible world Contingency: true in this (actual) world (but false in another world)

4. P is necessary = def. P is true in all possible worlds or x is necessary = def. x exists in all possible worlds F is essential to x = def. x is F in all possible worlds (in which x exists) P is contingent = def. P is true in some possible world, i.e. the actual world P is possible = def. P is true in some possible world F is accidental to x = def. x lacks F in some possible world (in which x exists) P is impossible = def. P is true in no possible world

5. But we should be clear: what we are talking about (logically) is quantifying over possible worlds. In other words, we are saying thing like this: For all worlds w, and propositions P, P is necessary iff P is true in w. Or, for an accidental property: There is a world w such that x is not F at w.

6. Chisholm, “Identity Through Possible Worlds” Guiding Question: Can an individual in one possible world be identical with an individual in another possible world? (149a) Provisional Answer: The only way is to appeal to some version of the doctrine that individual things have essential properties. (151a)

7. Chisholm’s Thought Experiment We go from possible world to possible world, keeping our fingers, so to speak, on the same entities, x and y, while subtly changing their properties. At a certain point, we could come to a world, W n, in which the properties of x and y have been switched. Question: how do we distinguish the two worlds?

8. Again, according to Chisholm, the only way that we can make sense of the idea of sameness over possible worlds is by invoking the idea of essential properties. “For every entity x, there are certain properties N and certain properties E such that: x has N in some possible worlds and x has non-N in others; but x has E in every possible world in which x exists; and, moreover, for every y, if y has E in any possible world, then y is identical with x.” (151a) But what is the procedure for finding out what the essential properties of a thing are? (151b)