Here, I try to analyze the notion of epistemic possibility.* [* Based on: “Epistemic Possibility,” Synthese 156 (2007): 119-42.] 1. The Idea of Epistemic Possibility According to philosophers, there are multiple different kinds of “possibility”, including metaphysical possibility, which might be distinct from logical possibility; physical possibility; and epistemic possibility.
Nov 19, 2022·edited Nov 19, 2022Liked by Michael Huemer
The Unconscious Sam case is a weird one. I'm not sure how to apply (actual, non-idealized) epistemic possibility to unconscious reasoners. Since they can't actually reason, there's a lot of strange things that can be going on: for example, they could hold contradictory beliefs with no way of deriving a contradiction from them. Perhaps we should not attribute them beliefs at all.
In that case, it's true that ~[Sam believes Sam is unconscious]. If Sam believed ~[Sam believes Sam is unconscious]. then he would know it. Given your intention of capturing "knowledge is justified true Gettier-proof belief", your conditions 2 & 3 should be satisfied. Then it's epistemically impossible for Sam to believe that he's unconscious, but it's possible that he is.
I originally intended for this to be a counterexample, but it actually seems insightful. Still, this is weird. Honestly, I'd rather reject the concept of epistemic possibility applied to unconscious reasoners, as they're not really reasoners at the referenced point of time.
By Kolmogorov axioms, given that the proof is in fact correct and Sam did not misread it, its probability ought to be 1 just like for any tautology. Of course, in real life Sam can always misread an invalid proof as a valid one, but we can stipulate that away.
In general, Bayesianism assumes logical omniscience. There are attempts to weaken that requirement, such as logical induction: https://arxiv.org/abs/1609.03543 . They weaken the Dutch book criteria: the reasoner should not be bookable by a computationally limited adversary. Perhaps they are the correct theory of probability for imperfect reasoners.
I am supposed to be working right now (don't tell my boss), so I just skimmed this. But here is my understanding of epistemic possibility. When I look at the post more carefully, I will see if you have already rejected this. Suppose Elizarraraz (I am so sick of Smith and Jones) has hidden a peanut under one of three shells. Under which one I do not know (obviously). Now define possible world #1 as comprising all state of affairs in the actual world -- EXCEPT what is the case with regard to what is under the three shells, AND the peanut is under shell #1. Possible world #2 comprises all states of affairs in the actual world -- EXCEPT what is the case under shell #2, AND the peanut is under shell #2. Possible world #3 comprises all states of affairs in the actual world -- EXCEPT what is the case under shell #3, AND the peanut is under shell #3. To say it is epistemically possible the peanut is under shell #1 is to say that there is nothing I know that would rule out the identity of possible world #1 with the actual world. Ditto for the possibility that the peanut is under shell #2, and for the possibility it is under shell #3. -- Okay, I got it out here even I am supposed to be working. Now it's your turn to show me what obvious thing I am missing.
Amy comes out of a store and goes to the parking lot looking for her car. She knows she drove to the store, and she knows she parked in that lot. When she gets to the area she recalls parking in, she doesn't find her car. She widens the scope of her search, and finally decides that her car is not in the lot at all. She deduces that it has been stolen, and she calls the police.
Is it epistemically possible for Amy that her car is exactly where she last parked it?
I think it odd to say that that's epistemically possible for her. She knows that she drove to this store and she knows she parked in this lot. She knows that she hasn't moved her car since then, and there is no one who would have her permission to take her car without asking her first. She does not remember being asked, and knows she would have objected if they'd asked while she was in the store.
She seems to me to be in a situation similar to that of Sam in the Landing scenario, and you in your lost wallet scenario (it can't be at the theatre because you purchased gas since you were at the theatre). The context provides what seems to be sufficient evidence that her car has been taken away by someone else (probably stolen).
And yet, in this scenario the car is exactly where she last parked it, and so by your account it is epistemically possible for her that it is right where she left it.
Of course, to anyone reading this little puzzle it is epistemically possible that the car is where she last parked it -- the set up and context make it pretty much mandatory that it be so. But she's not reading this story; she's living it.
So it strikes me as wrong that anything that is true is epistemically possible for everyone. Sometimes people have quite rational beliefs that rule out certain possibilities, and so it's not rational for them to act on those possibilities. I'd say that your desire (expressed in the paper this post is based on) for your account to "[explain] the connection between rational actions and judgements of epistemic modality" you need to allow some exceptions to your principle (ii) -- meant to be observed "insofar as this is possible":
(ii) If it is [epistemically] impossible that P, then ~P.
Your suggested account incorporates (ii) wholesale, in that anything that is true is epistemically possible for everyone. I think this story is a counterexample to your suggested account.
Another route to reject definition 2 is simply to point out that (i) some propositions are epistemically possible that are either necessary or impossible (Goldbach's Conjecture, say) and (ii) we know some necessary truths (~(A&~A)). Since nothing impossible is consistent with anything necessary, it would become open whether or not Goldbach's conjecture was really epistemically possible. But it's not open (it definitely *is* epistemically possible). So definition 2 must be false.
I agree with Prado’s comment. Definition 5 states:
P is epistemically possible for S = The probability of P on S’s evidence is nonzero
The reader is told the proof is in fact correct. So, for the reader, the probability of the proof being correct is 1. Then the reader would assign the probability of the proof being false to zero, which, by definition 5, means it is not epistemically possible.
But this is not the case for Sam, who is yet to check the proof, knows he is prone to error, and so lacks the evidence to assign the probability of the proof being false to zero. From his perspective, he would assign this probability as nonzero.
Anyway, interesting subject and obviously it’s easy to lose track of whose epistemology is the one in question. Epistemology within epistemology?
Is the concept of epistemic possibility all that useful? Is there a theory or application where it gets used on a critical way?
I don’t quite think that Wittgenstein's “family resemblance” criticism quite applies, since I can’t quite swallow the idea that there is a family resemblance between things that are epistemically possible and what is meant changes depending on context. But it feels similar. We seek precision but it eludes us.
I think the concept of epistemic possibility is useful if explicated in terms of epistemically accessible possible worlds, as Fitelson does here: http://fitelson.org/125/accessibility.pdf . (Fitelson seems to be close to Definition 8.) We can use the different accessibility conditions to say meaningful things about different sorts of possibility. For example, it is epistemically possible that I can distinguish by taste a cup of black coffee from a cup to which I have added, one by one, n + 1 grains of sugar. even though I cannot distinguish the n + 1 cup from the n cup, nor the n cup from the n - 1 cup, and so on. Epistemic possibility is intransitive. Logical possibility by contrast is transitive.
"PWS [possibile world semanics] has applications not only in metaphysics and logic, but also in epistemology. We can talk about the relation of espistemic accessibility. A world w0 is epistemically accessible from w for an agent S (in w) iff S knows nothing that would rule out the hypothesis that w0 = w. Then, p is epistemically necessary (for S) iff p is true at all possible worlds that are epistemically accessible from w (for S). And, for instance, if we want to know whether epistemic necessity satisfies axiom (4), we can ask whether espistemic accessibility is transitive. If S knows nothing that rules out w0 = w, and S knows nothing that rules out w00 = w0, then does it follow that S knows nothing that rules out w00 = w? It seems not. After all, S may not be able to distinguish w from w0, and he may not be able to distinguish w0 from w00, but it does not follow that he cannot distinguish w from w00. Small, imperceptible differences can add up to big, perceptible ones. You may not be able to distinguish a cup of coffee with 1/2 a teaspoon of sugar from a black cup, and you may not be able to distinguish a cup with 1/2 a teaspoon of sugar from a cup with 1 teaspoon. But, you may, nonetheless, be able to distinguish a black cup from a cup with 1 teaspoon of sugar. These sorts of intransitivites in perception and knowledge are common."
The Unconscious Sam case is a weird one. I'm not sure how to apply (actual, non-idealized) epistemic possibility to unconscious reasoners. Since they can't actually reason, there's a lot of strange things that can be going on: for example, they could hold contradictory beliefs with no way of deriving a contradiction from them. Perhaps we should not attribute them beliefs at all.
In that case, it's true that ~[Sam believes Sam is unconscious]. If Sam believed ~[Sam believes Sam is unconscious]. then he would know it. Given your intention of capturing "knowledge is justified true Gettier-proof belief", your conditions 2 & 3 should be satisfied. Then it's epistemically impossible for Sam to believe that he's unconscious, but it's possible that he is.
I originally intended for this to be a counterexample, but it actually seems insightful. Still, this is weird. Honestly, I'd rather reject the concept of epistemic possibility applied to unconscious reasoners, as they're not really reasoners at the referenced point of time.
“According to standard probability theory, given that the proof is in fact correct, the probability of its conclusion would be 1.“
The evidential probability of the conclusion, given Sam’s knowledge of having made mistakes in the past, is not 1.
By Kolmogorov axioms, given that the proof is in fact correct and Sam did not misread it, its probability ought to be 1 just like for any tautology. Of course, in real life Sam can always misread an invalid proof as a valid one, but we can stipulate that away.
In general, Bayesianism assumes logical omniscience. There are attempts to weaken that requirement, such as logical induction: https://arxiv.org/abs/1609.03543 . They weaken the Dutch book criteria: the reasoner should not be bookable by a computationally limited adversary. Perhaps they are the correct theory of probability for imperfect reasoners.
I am supposed to be working right now (don't tell my boss), so I just skimmed this. But here is my understanding of epistemic possibility. When I look at the post more carefully, I will see if you have already rejected this. Suppose Elizarraraz (I am so sick of Smith and Jones) has hidden a peanut under one of three shells. Under which one I do not know (obviously). Now define possible world #1 as comprising all state of affairs in the actual world -- EXCEPT what is the case with regard to what is under the three shells, AND the peanut is under shell #1. Possible world #2 comprises all states of affairs in the actual world -- EXCEPT what is the case under shell #2, AND the peanut is under shell #2. Possible world #3 comprises all states of affairs in the actual world -- EXCEPT what is the case under shell #3, AND the peanut is under shell #3. To say it is epistemically possible the peanut is under shell #1 is to say that there is nothing I know that would rule out the identity of possible world #1 with the actual world. Ditto for the possibility that the peanut is under shell #2, and for the possibility it is under shell #3. -- Okay, I got it out here even I am supposed to be working. Now it's your turn to show me what obvious thing I am missing.
Consider this example.
Amy comes out of a store and goes to the parking lot looking for her car. She knows she drove to the store, and she knows she parked in that lot. When she gets to the area she recalls parking in, she doesn't find her car. She widens the scope of her search, and finally decides that her car is not in the lot at all. She deduces that it has been stolen, and she calls the police.
Is it epistemically possible for Amy that her car is exactly where she last parked it?
I think it odd to say that that's epistemically possible for her. She knows that she drove to this store and she knows she parked in this lot. She knows that she hasn't moved her car since then, and there is no one who would have her permission to take her car without asking her first. She does not remember being asked, and knows she would have objected if they'd asked while she was in the store.
She seems to me to be in a situation similar to that of Sam in the Landing scenario, and you in your lost wallet scenario (it can't be at the theatre because you purchased gas since you were at the theatre). The context provides what seems to be sufficient evidence that her car has been taken away by someone else (probably stolen).
And yet, in this scenario the car is exactly where she last parked it, and so by your account it is epistemically possible for her that it is right where she left it.
Of course, to anyone reading this little puzzle it is epistemically possible that the car is where she last parked it -- the set up and context make it pretty much mandatory that it be so. But she's not reading this story; she's living it.
So it strikes me as wrong that anything that is true is epistemically possible for everyone. Sometimes people have quite rational beliefs that rule out certain possibilities, and so it's not rational for them to act on those possibilities. I'd say that your desire (expressed in the paper this post is based on) for your account to "[explain] the connection between rational actions and judgements of epistemic modality" you need to allow some exceptions to your principle (ii) -- meant to be observed "insofar as this is possible":
(ii) If it is [epistemically] impossible that P, then ~P.
Your suggested account incorporates (ii) wholesale, in that anything that is true is epistemically possible for everyone. I think this story is a counterexample to your suggested account.
Another route to reject definition 2 is simply to point out that (i) some propositions are epistemically possible that are either necessary or impossible (Goldbach's Conjecture, say) and (ii) we know some necessary truths (~(A&~A)). Since nothing impossible is consistent with anything necessary, it would become open whether or not Goldbach's conjecture was really epistemically possible. But it's not open (it definitely *is* epistemically possible). So definition 2 must be false.
I agree with Prado’s comment. Definition 5 states:
P is epistemically possible for S = The probability of P on S’s evidence is nonzero
The reader is told the proof is in fact correct. So, for the reader, the probability of the proof being correct is 1. Then the reader would assign the probability of the proof being false to zero, which, by definition 5, means it is not epistemically possible.
But this is not the case for Sam, who is yet to check the proof, knows he is prone to error, and so lacks the evidence to assign the probability of the proof being false to zero. From his perspective, he would assign this probability as nonzero.
Anyway, interesting subject and obviously it’s easy to lose track of whose epistemology is the one in question. Epistemology within epistemology?
Is the concept of epistemic possibility all that useful? Is there a theory or application where it gets used on a critical way?
I don’t quite think that Wittgenstein's “family resemblance” criticism quite applies, since I can’t quite swallow the idea that there is a family resemblance between things that are epistemically possible and what is meant changes depending on context. But it feels similar. We seek precision but it eludes us.
I think the concept of epistemic possibility is useful if explicated in terms of epistemically accessible possible worlds, as Fitelson does here: http://fitelson.org/125/accessibility.pdf . (Fitelson seems to be close to Definition 8.) We can use the different accessibility conditions to say meaningful things about different sorts of possibility. For example, it is epistemically possible that I can distinguish by taste a cup of black coffee from a cup to which I have added, one by one, n + 1 grains of sugar. even though I cannot distinguish the n + 1 cup from the n cup, nor the n cup from the n - 1 cup, and so on. Epistemic possibility is intransitive. Logical possibility by contrast is transitive.
"PWS [possibile world semanics] has applications not only in metaphysics and logic, but also in epistemology. We can talk about the relation of espistemic accessibility. A world w0 is epistemically accessible from w for an agent S (in w) iff S knows nothing that would rule out the hypothesis that w0 = w. Then, p is epistemically necessary (for S) iff p is true at all possible worlds that are epistemically accessible from w (for S). And, for instance, if we want to know whether epistemic necessity satisfies axiom (4), we can ask whether espistemic accessibility is transitive. If S knows nothing that rules out w0 = w, and S knows nothing that rules out w00 = w0, then does it follow that S knows nothing that rules out w00 = w? It seems not. After all, S may not be able to distinguish w from w0, and he may not be able to distinguish w0 from w00, but it does not follow that he cannot distinguish w from w00. Small, imperceptible differences can add up to big, perceptible ones. You may not be able to distinguish a cup of coffee with 1/2 a teaspoon of sugar from a black cup, and you may not be able to distinguish a cup with 1/2 a teaspoon of sugar from a cup with 1 teaspoon. But, you may, nonetheless, be able to distinguish a black cup from a cup with 1 teaspoon of sugar. These sorts of intransitivites in perception and knowledge are common."