Many propositions can be given event semantics, but with the caveat that events should still be parts of a space of possible worlds, so that “It’s Friday” is not an event (while “When it’s Friday, I try to check the mail” is).
Where do you think is the difference? I agree that there is a problem with indexical content, though this affects both examples. (“It’s (currently) Friday (where I live).”)
Even though it doesn’t solve all problems with indexicals, it’s probably better to not start with possible worlds but instead start with propositions directly, similar to propositional logic. Indeed this is what Richard Jeffrey does. Instead of starting with a set of possible worlds, he starts with a disjunction of two mutually exclusive propositions A and B:
U(A∨B)=P(A)U(A)+P(B)U(B)P(A)+P(B), if P(A∧B)=0,P(A∨B)≠0.
An indexical proposition doesn’t evaluate a possible world (in the sense of a maximally detailed world history), it evaluates a possible world together with a location or time or a subsystem (such as an agent/person) in it. But pointing to some location or subsystem that is already part of the world doesn’t affect the possible world itself, so it makes little sense to have preference that becomes different depending on which location or subsystem we are looking at (from outside the world), while the world remains completely the same. The events that should be objects of preference are made of worlds, not of (world, embedded subsystem) pairs.
Whether “It’s Friday” is not a property of a world, it’s a property of a world together with some admissible spacetime location. You can’t collect a set of possible world histories that centrally have the property of “It’s Friday”. On the other hand, “I try to make sure to check the mail on Fridays” is a property that does distinguish worlds where it’s centrally true (for a specific value of “I”). In general, many observations are indexical, they tell you where you are, which version of you is currently affecting the world, and a policy converts those indexical observations into an actual effect in the world that can be understood as an event, in the sense of a set of possible worlds.
I mean I agree, indexicals don’t really work with interpreting propositions simply as sets of possible worlds, but both sentences contain such indexicals, like “I”, implicitly or explicitly. “I” makes only sense for a specific person at a specific time. “It’s Friday (for me)”, relative to a person and a time, fixes a set of possible worlds where the statement is true. It’s the same for “I try to make sure to check the mail on Fridays”.
After you bundle the values of free variables into the proposition (make a closure), and “I” and such get assigned their specific referents, “It’s Friday” is still in trouble. Because if it gets the current time bundled in it, then it’s either true or false depending on the time, not depending on the world (in the maximally detailed world history sense), and so it’s either true about all worlds or none (“The worlds where it’s Friday on Tuesday”), there is no nontrivial set-of-worlds meaning. But with the mail proposition (or other propositions about policies) there is no problem like that.
I think one issue with the “person+time” context is that we may assume that once I know the time, I must know whether it is Friday or not. A more accurate assessment would be to say that an indexical proposition corresponds to a set of possible worlds together with a person moment, i.e. a complete mental state. The person moment replaces the “person + time” context. This makes it clear that “It’s Friday” is true in some possible worlds and false in others, depending on whether my person moment (my current mental state, including all the evidence I have from perception etc) is spatio-temporally located at a Friday in that possible world. This also makes intuitive sense, since I know my current mental state but that alone is not necessarily sufficient to determine the time of week, and I could be mistaken about whether it’s Friday or not.
A different case is “I am here now” or the classic “I exist”. Which would be true for any person moment and any possible world where that person moment exists. These are “synthetic a priori” propositions. Their truth can be ascertained from introspection alone (“a priori”), but they are “synthetic” rather than “analytic”, since they aren’t true in every possible world, i.e. in worlds were the person moment doesn’t exist. At least “I exist” is false at worlds where the associated person moment doesn’t exist, and arguably also “I am here now”.
Yet another variation would be “I’m hungry”, “I have a headache”, “I have the visual impression of a rose”, “I’m thinking about X”. These only state something about aspects of an internal state, so their truth value only depends on the person moment, not on what the world is like apart from it. So a proposition of this sort is either true in all possible worlds where that person moment exists, or false in all possible worlds where that person moment exists (depending on whether the sensation of hungriness etc is part of the person moment or not). Though I’m not sure which truth value they should be assigned in possible worlds where the person moment doesn’t exist. If “I’m thinking of a rose” is false when I don’t exist, is “I’m not thinking of a rose” also false when I don’t exist? Both presuppose that I exist. To avoid contradictions, this would apparently require a three-valued logic, with a third truth value for propositions like that in case the associated person moment doesn’t exist.
This makes it clear that “It’s Friday” is true in some possible worlds and false in others, depending on whether my person moment (my current mental state, including all the evidence I have from perception etc) is spatio-temporally located at a Friday in that possible world.
My point is that the choice of your person moment is not part of the data of a possible world, it’s something additional to the possible world. A world contains all sorts of person moments, for many people and at many times, all together. Specifying a world doesn’t specify which of the person moments we are looking at (or from). Whether “It’s Friday” or not is a property of a (world, person-moment) pair, but not of a world considered on its own.
Keeping this distinction in mind is crucial for decision theory, since decisions are shaping the content of the world, in particular multiple agents can together shape the same world. The states of the same agent at different times or from different instances (“person moments”) can coordinate such shaping of their shared world. So the data for preference should be about what matters for determining a world, but not necessarily other things such as world-together-with-one-of-its-person-moments.
Many propositions can be given event semantics, but with the caveat that events should still be parts of a space of possible worlds, so that “It’s Friday” is not an event (while “When it’s Friday, I try to check the mail” is).
Where do you think is the difference? I agree that there is a problem with indexical content, though this affects both examples. (“It’s (currently) Friday (where I live).”)
Even though it doesn’t solve all problems with indexicals, it’s probably better to not start with possible worlds but instead start with propositions directly, similar to propositional logic. Indeed this is what Richard Jeffrey does. Instead of starting with a set of possible worlds, he starts with a disjunction of two mutually exclusive propositions A and B:
U(A∨B)=P(A)U(A)+P(B)U(B)P(A)+P(B), if P(A∧B)=0,P(A∨B)≠0.
An indexical proposition doesn’t evaluate a possible world (in the sense of a maximally detailed world history), it evaluates a possible world together with a location or time or a subsystem (such as an agent/person) in it. But pointing to some location or subsystem that is already part of the world doesn’t affect the possible world itself, so it makes little sense to have preference that becomes different depending on which location or subsystem we are looking at (from outside the world), while the world remains completely the same. The events that should be objects of preference are made of worlds, not of (world, embedded subsystem) pairs.
Whether “It’s Friday” is not a property of a world, it’s a property of a world together with some admissible spacetime location. You can’t collect a set of possible world histories that centrally have the property of “It’s Friday”. On the other hand, “I try to make sure to check the mail on Fridays” is a property that does distinguish worlds where it’s centrally true (for a specific value of “I”). In general, many observations are indexical, they tell you where you are, which version of you is currently affecting the world, and a policy converts those indexical observations into an actual effect in the world that can be understood as an event, in the sense of a set of possible worlds.
I mean I agree, indexicals don’t really work with interpreting propositions simply as sets of possible worlds, but both sentences contain such indexicals, like “I”, implicitly or explicitly. “I” makes only sense for a specific person at a specific time. “It’s Friday (for me)”, relative to a person and a time, fixes a set of possible worlds where the statement is true. It’s the same for “I try to make sure to check the mail on Fridays”.
After you bundle the values of free variables into the proposition (make a closure), and “I” and such get assigned their specific referents, “It’s Friday” is still in trouble. Because if it gets the current time bundled in it, then it’s either true or false depending on the time, not depending on the world (in the maximally detailed world history sense), and so it’s either true about all worlds or none (“The worlds where it’s Friday on Tuesday”), there is no nontrivial set-of-worlds meaning. But with the mail proposition (or other propositions about policies) there is no problem like that.
I think one issue with the “person+time” context is that we may assume that once I know the time, I must know whether it is Friday or not. A more accurate assessment would be to say that an indexical proposition corresponds to a set of possible worlds together with a person moment, i.e. a complete mental state. The person moment replaces the “person + time” context. This makes it clear that “It’s Friday” is true in some possible worlds and false in others, depending on whether my person moment (my current mental state, including all the evidence I have from perception etc) is spatio-temporally located at a Friday in that possible world. This also makes intuitive sense, since I know my current mental state but that alone is not necessarily sufficient to determine the time of week, and I could be mistaken about whether it’s Friday or not.
A different case is “I am here now” or the classic “I exist”. Which would be true for any person moment and any possible world where that person moment exists. These are “synthetic a priori” propositions. Their truth can be ascertained from introspection alone (“a priori”), but they are “synthetic” rather than “analytic”, since they aren’t true in every possible world, i.e. in worlds were the person moment doesn’t exist. At least “I exist” is false at worlds where the associated person moment doesn’t exist, and arguably also “I am here now”.
Yet another variation would be “I’m hungry”, “I have a headache”, “I have the visual impression of a rose”, “I’m thinking about X”. These only state something about aspects of an internal state, so their truth value only depends on the person moment, not on what the world is like apart from it. So a proposition of this sort is either true in all possible worlds where that person moment exists, or false in all possible worlds where that person moment exists (depending on whether the sensation of hungriness etc is part of the person moment or not). Though I’m not sure which truth value they should be assigned in possible worlds where the person moment doesn’t exist. If “I’m thinking of a rose” is false when I don’t exist, is “I’m not thinking of a rose” also false when I don’t exist? Both presuppose that I exist. To avoid contradictions, this would apparently require a three-valued logic, with a third truth value for propositions like that in case the associated person moment doesn’t exist.
My point is that the choice of your person moment is not part of the data of a possible world, it’s something additional to the possible world. A world contains all sorts of person moments, for many people and at many times, all together. Specifying a world doesn’t specify which of the person moments we are looking at (or from). Whether “It’s Friday” or not is a property of a (world, person-moment) pair, but not of a world considered on its own.
Keeping this distinction in mind is crucial for decision theory, since decisions are shaping the content of the world, in particular multiple agents can together shape the same world. The states of the same agent at different times or from different instances (“person moments”) can coordinate such shaping of their shared world. So the data for preference should be about what matters for determining a world, but not necessarily other things such as world-together-with-one-of-its-person-moments.