Comments

  • "What is truth? said jesting Pilate; and would not stay for an answer."
    ↪Michael


    Yeah there you go.
  • "What is truth? said jesting Pilate; and would not stay for an answer."
    So she believed that it was on the nightstand, but that belief wasn’t available to her? That just seems very farfetched. — Michael

    Is every belief you hold present to mind all the time? No. Are all of your beliefs available to you on demand? I don't think so. There's plenty of reason to think we have beliefs that are strictly unavailable to us, that are unconscious. Even for beliefs that are in principle available to us, we sometimes cannot call them to mind. I see nothing farfetched about any of this.

    I think it far more sensible to say that, at the time, she didn’t believe that it was on the nightstand, and so didn’t know that it was on the nightstand. Further prompting then elicited the memory, and from that spawned the belief and the knowledge. — Michael

    "Spawned"?

    So B went from (1) a state of knowing that she herself put the book on A's nightstand, to (2) a state of not knowing that, and then, by *remembering* that she did, to (3) a state of knowing again.

    So what's up with the memory? Did she, between (1) and (3), have a memory that she put the book on the nightstand while somehow not knowing that she did? Or did she not have the memory while it wasn't present to mind? But she has to have the memory or she can't get from (2) to (3). How do you propose she did that? And what was going on with her between (1) and (3)?

    You’re saying that at the time that I believed that the pint was mine I knew that the pint was Jane’s? I knew something that I believed was false? — Michael

    Yes. You held, for a moment, a belief that was false and inconsistent with your knowledge. It happens.
  • "What is truth? said jesting Pilate; and would not stay for an answer."
    ↪Michael


    Nevertheless. B knew where the book was, but that knowledge was unavailable to her for the moment. It seems clear that the belief was unavailable as well. In my scenario, I didn't suggest B formed the belief that it was not on A's nightstand, but she might have. She seems to have formed the *incorrect* belief that she never touched the book. Our total knowledge must be consistent, but our total beliefs needn't.
  • "What is truth? said jesting Pilate; and would not stay for an answer."
    Unless you want to say that she knew all along, despite not have the relevant justified true belief? — Michael

    Yes. I am saying exactly that.

    Are you claiming she *discovered* that she herself put A's book on A's nightstand? That she *inferred* it from the evidence of her memory?
  • "What is truth? said jesting Pilate; and would not stay for an answer."
    ↪Michael


    Here’s an example, a sort of cartoon version of Hume:

    Hume argued directly that reasoning about matters of fact is merely probable. He didn’t argue that what people mean when they say “I know that ...” is “I think it highly probable that ...” As far as I can tell, he assumed people meant that they know, and he believed that in all such cases they are actually wrong, that what they do know is only that something is probable, not that it’s fact.
  • "What is truth? said jesting Pilate; and would not stay for an answer."
    They were right, but does it then follow that they knew? — Michael

    It doesn’t follow, but it was implicitly stipulated in my scenario. That was the point of having B suddenly remember that she moved the book; A suggested that her book would have been in the way, and B then remembered that it was in the way and she moved it.

    I know but I could be wrong? I was the one saying that last time and you spent days telling me that was nonsense. — Michael

    But here I’m talking about what someone might say, not about the fact of their knowing that P being consistent with ~P.

    What does "but I'm not certain" actually mean? It might be that when we tease this out we are confronted with the conclusion that "I'm not certain" actually means "I don't know". — Michael

    But we’re not just interested in what people mean by what they say.

    From “I’m certain that Trump won,” we can’t infer that Trump won. We can’t infer that you know that Trump won. We can’t even infer that you are certain that Trump won. It’s a thing you are saying. What it means, what you mean by it, what you mean by saying it, all that might be interesting, but is not the same as addressing the question of whether knowing that P is equivalent to being certain that P, or if there’s some other relation or what.
  • "What is truth? said jesting Pilate; and would not stay for an answer."
    it still needs to be explained what "I'm not certain" actually means, as it may very well lead to the same conclusion above; that "I'm not certain" means "I don't know". — Michael

    And even if it is used, on some occasion, with that intention, what does that tell you?

    I’ve already presented a case in which someone flatly denies having knowledge that they do in fact have. It’s not so odd. (And it’s another reminder that from someone asserting P, you can’t deduce P.) I gave my intuitions about whether and when we should say they are certain. Unless we intend to define certainty or knowledge, that’s about all we’ve got so far. Can we improve that situation? Does certainty at least entail something else we could check for?

    I’ll give another example: people sometimes downgrade their claims to knowledge for non-epistemic reasons. (Women on this forum are no doubt familiar with this maneuver.) “I know the answer! — At least, I think I do. I could be wrong.” That could be a genuine expression of uncertainty, or a political move. It can’t help us explain the connection between knowledge and certainty.
  • "What is truth? said jesting Pilate; and would not stay for an answer."
    The problem I see with the possible worlds scenario, is that if we assume possible worlds, and we want to assign "actual world" to one of them, then we need some principles to support the "actual world" as distinct from the others. Then, the actual world is a special world, and cannot be one of the possible worlds, because it has that special status which sets it apart as distinct. — Metaphysician Undercover

    So if I have a stack of boxes and put an X on one of them with a Sharpie, it’s no longer a box. Cool. Nice job.

    Or maybe your argument is that if I have a stack of boxes and a toaster, then the toaster is not a box. That is certainly a stronger argument.
  • "What is truth? said jesting Pilate; and would not stay for an answer."
    ↪Michael


    Your argument is that if there’s something odd about saying “I know that p but I am not certain,” then (“perhaps”) knowledge requires certainty.

    Except that’s not an argument. From S asserting “I know that p,” it does not follow that S knows that p; from S asserting “I am uncertain,” it does not follow that S is uncertain; we can’t infer that if S were to assert the problematic sentence then S would have to be in a problematic mental state.

    But we can argue directly.

    You suspect that S knows that P entails S is certain that P. (No one is claiming the converse.) That’s not implausible; I just don’t think there’s been any argument for it yet. And I find the contrapositive dubious.

    Here’s another example, A and B fighting about a book of A’s that she can’t find:
    B: I swear, I don’t know where it is, I never touched your book!!!
    A: I might have left it in the kitchen.
    B: We’re in the kitchen, and I don’t see it, so you left it somewhere else.
    A: It would have been in the way when you were bringing in the groceries.
    B: Oh. Right. Yes. I put it on your nightstand.

    In this case, B flatly denies knowing where the book is. (Note this construction: it’s knowing-what rather than knowing-that.) As it turns out, B does know where the book is, because B herself put it there. What do we say about B’s certainty in such a case?

    B is certain that her mental state is not that of knowing where the book is — and she’s wrong — but we’re not interested in that. What is B’s certainty with respect to “where the book is”? B is certain that that location, whatever it is, is not a member of “in the kitchen”! Still not what we want. (B is probably also convinced that A knows — but can’t recall — or should know where the book is, because she is responsible for its current location, not B.)

    We want B’s attitude toward the proposition “The book is on A’s nightstand.” This is a proposition that B knows, as it turns out, but cannot at the moment produce. If asked, that might be enough to jog B’s memory, so she might assent to the proposition. Might not. But certainty? Would you say B is certain that the book is on A’s nightstand?

    I suspect certainty that the book is on A’s nightstand attaches the moment B remembers putting it there. Before that? I don’t know.

    Maybe your conception of certainty is different from mine, but I always think of it as a more or less fleeting psychological state, so it’s only in evidence when what you’re certain about is present to mind. That’s clearly not the case with knowledge.

    Maybe you have a better or a different conception of certainty.
  • "What is truth? said jesting Pilate; and would not stay for an answer."
    My belief is that if we pretend that something said, which says nothing about the real world, actually does say something about the real world, this is deception. — Metaphysician Undercover

    This has occurred to me. It might be simpler to call a spade a spade here.

    An assumption H for the purposes of hypothetical reasoning picks out a set of possible worlds at which H is true. That set may or may not include the actual world. We may or may not know whether it does.

    The goal then would be to discharge the hypothetical assumption in a true counterfactual conditional, which may be degenerate in the sense of having an antecedent that is true at the actual world. I understand those are tricky to deal with, but oh well.

    For example, the hypothetical assumption “Suppose I have lost my copy of Lewis 1973” picks out a set of possible worlds at which I have indeed lost my copy of Lewis 1973. If I determine that in any such world (or only in nearby worlds, or in sufficiently similar worlds, etc., whatever the appropriate restriction is) I would be a miserable cuss, and I would prefer not to be, then I can discharge the assumption by concluding, for example, “If I were to lose my copy of Lewis 1973, I would have to replace it.”

    Pretending is a very interesting subject, but the sorts of hypotheticals we’re interested in around here are probably best analyzed in the obvious way, as counterfactuals.

    (IIRC, Frank Ramsey scratched his head over hypotheticals in a footnote somewhere, suggesting that entertaining a hypothetical was like “temporarily” adding it to your set of beliefs — I always wondered how he imagined we did such a thing.)
  • "What is truth? said jesting Pilate; and would not stay for an answer."
    ↪Michael


    I’ve written and deleted screens of analysis of your problematic sentence. I doubt you (or anyone else) are all that interested.

    Let me ask you this: are you interested in this sentence because you think it tells us something important about knowledge? If so, I doubt it, but you’ll have to provide more analysis than “This sounds wrong.” Do you, for instance, think that such a sentence is necessarily false?

    Or are you interested in this sentence because it strikes you as a bit peculiar, and you’re curious what makes it strike you as peculiar. I think there is no simple answer to that, but I’ll point out that saying either “I know that 7 x 9 is 63” or “I am uncertain that Topeka is the capital of Kansas” is already peculiar. Its peculiarity may not bear on its truth-value.

    Addendum:

    This is much like Moorean sentences. — Michael

    The upshot of which was all about assertion. There’s nothing to learn about the nature of belief from Moore’s paradox.
  • "What is truth? said jesting Pilate; and would not stay for an answer."
    Do you have any good links that would clarify the differences? — Andrew M

    No, sorry. I’m reading his book, Knowledge and Its Limits.

    There’s a whole lot I don’t know yet, but my understanding is that a number of problems in epistemology present somewhat differently if you take knowledge seriously. One of the best-known claims of the book is known as “E = K,” that is, your total evidence is your total knowledge. When it comes to rational belief formation, for instance, it is your knowledge you rely on in deciding what to believe. There’s a similar transformation with assertibility, because we can specify the maxim as “Do not assert what you do not know,” rather than something about honest belief, evidence, justification, warrant, all that business.

    on Williamson’s account, is truth defined in terms of knowledge? — Banno

    Not to my knowledge. I have no idea what Williamson’s views on truth are.

    So how do we make sense of "I know that p but I'm not certain"? — Michael

    The cases I was talking about were ones where a subject who does know is unwilling to assert that they know because of their uncertainty; your case starts with “I know that p.” It is so common as to be unremarkable for people to say, “I think I know ...” so people evidently do recognize that knowledge and uncertainty about their own state are compatible. People also recognize that the bald claim to know implicates something about their knowledge of their own state of knowing, and can cancel that implication: “I know how to fix this — at least, I think I do.” Your case is a little odd to my ear, but not substantially different from these, I think.

    Do you recognize that #2, the hypothetical itself "if it is raining, we won't be able to go for a walk", is an assumption — Metaphysician Undercover

    Not sure where you’re going with this. As a bit of reasoning, it’s a little compressed — there are a lot of steps between antecedent and consequent, mostly background knowledge, which you could certainly characterize as assumptions. (That if it rains people get wet, that people don’t want to get wet, and a dozen others).

    Still not sure what point you’re making though.
  • "What is truth? said jesting Pilate; and would not stay for an answer."
    ↪Andrew M


    The claim is that knowledge is a first-class mental state, distinct from belief, not a particular variety of belief. If S knows that p, that also entails that S believes that p, and entails that p, but for all that, believing that p is not a component of knowing that p and neither is p being true. It’s Timothy Williamson’s “knowledge first” program, and I find it pretty persuasive, though I haven’t gotten through all the technical stuff yet. On his account, knowledge has no such components, and cannot be analyzed into, say, justified true belief.

    It’s a position also associated with Oxford dons of yore like Cook Wilson and H. A. Prichard. For Williamson, it’s largely a straightforward extension of an externalist approach to mental content.
  • "What is truth? said jesting Pilate; and would not stay for an answer."
    "I know that p but I am not certain" could be seen to be something of a Moorean sentence. — Michael

    I really don’t think so, but I wouldn’t base that entirely on what people say, their reports. We can say of the shy schoolboy or the forgetful grandfather that he does know something, even though we would not classify them as highly confident that they know. If, with a little goosing and a little encouragement, they can come up with the right bit of info, then they did know, but thought maybe they didn’t. And indeed there’s nothing so unusual about people expressing doubts about whether they know something, rather than what they know. “I think I remember locking the door” can be said in a case where you do remember locking the door, but you’ve done it so many times, you’re not sure you’re recalling the right event. Especially under emotional stress people may flatly deny, in all honesty, that they know something they do: “I swear, I have no idea where your book is, I never touched it!” “But it would have been in your way when you were putting the groceries away.” “Oh. Right. I put it on your nightstand.”

    But Andrew was saying that the hypothetical shows what follows "when it is actually raining in the real world". And that's what I argued against, because it really only shows what follows from the assumption that it is raining, as you agree with me here. — Metaphysician Undercover

    I’m sure I don’t agree with you.

    There are ambiguities here we could try to clear up:

    (1) If I, in the course of my daily life, assume that it’s raining, that’s to say I honestly hold the belief that it is raining, without having gone to a great deal of trouble to find out.

    (2) If, for the sake of a hypothetical bit of reasoning, and with some concern about the weather but no access at the moment to a weather report, suggest that if it is raining, we won’t be able to go for a walk, I hold no belief either way about whether it is raining; I only mean to suggest how we should act if it turns out (that is, if at a later time we actually know) that it’s raining. Quite different from (1), in which the “assumption” is what I honestly believe. That’s simply not the case here. NB: these are the sort of assumptions that must be discharged; it’s just the terminology of natural deduction.

    (3) If I make an assumption of any kind, the word “assumption” does multiple duty: (a) it can describe my mental action, somewhat like “assuming”, of taking an attitude toward a proposition; (b) it can denote the object of my mental attitude, the proposition itself, what I assumed; (c) it can be used just to mark the status of the proposition and my relation to it — “But that’s just an assumption!“

    The subject we were discussing is the issue with the use of "true", in the formulation of "knowledge" as justified true belief. — Metaphysician Undercover

    Which I for one have not defended, and would not defend, but @Andrew M has said some things along those lines. I claim only that knowledge entails truth, not that truth is a component of knowledge. Make of that what you will.

    If "true" here means what is actually the case, then when it turns out that what appeared to be known is actually not the case, then we must say that it was not knowledge. So, I suggested that "true" is better defined in relation to honesty, what one honestly believes. — Metaphysician Undercover

    You may of course do as you like, but the rest of us have not invented some special usage for “know” or for “true”; I’m using them exactly the way everyone I know uses them, this being the population that is also perfectly comfortable saying “I could have sworn I knew where I left it, but it’s not there, so I guess I was wrong.”

    Here, I’ll give you a good one. When I was a kid, I was taught, and I learned, that there are nine planets. That is no longer true, but it was true at the time, because there is a specific body of astronomers who make the “official” determination of whether a solar object is a planet. In such a case, I might be able to say I used to know that there were 9 planets, but now I know that there are 8. Note that I have made no mistake and have no reason to retract my knowledge claim. But suppose it was a couple weeks before I heard that Pluto had been demoted; during that time I might get into a heated argument with someone I think a fool because he says there are only 8 planets. At this point I will be wrong; I will be in the position of thinking that I know how many planets there are, and I will be wrong about that. Once he points out to me that there was a change in Pluto’s status, I will readily admit that I thought I knew, but that he was right.
  • "What is truth? said jesting Pilate; and would not stay for an answer."
    ↪Moliere


    Proof is in the pudding. There are lots of linguists doing lots of fieldwork. Maybe they'll find something, maybe they won't. Arguments that they must, or that they cannot, hang in the air exactly the way a brick doesn't.

    I don't think it would be the end of linguistics if there were no universal grammar but several kinds of language, but we all came from the same place and probably had language before we left, so it's a reasonable expectation that there is some unique capacity for language (since evolution *usually* but not always solves problems once).
  • "What is truth? said jesting Pilate; and would not stay for an answer."
    I really do suspect there is no such thing as a language, in these terms of rules and such — Moliere

    Which is a perfectly good prior. What do you do next?

    Maybe I'm just ignorant of its implications. — Moliere

    That would be one thing to do next. If the theory has entailments that are false, it's toast. But arguments for and against at this level of abstraction tend to be question-begging, so this is tricky. (I know I didn't find Derangement at all convincing, even though my sympathies then were different from what they are at the moment.)

    Perhaps the whole approach of specifying rules of interpretation is what's wrongheaded? — Moliere

    This would be the other thing to do next. Try specifying some rules and see how it goes.

    If it can't be done, that ought to become pretty clear at some point. Linguistics is littered with failed theories, even failed research programs, like any other science, but not all of them.
  • Two Questions about Logic/Reasoning
    ↪Moliere


    Dang. Should also have said that the rest of the mapping is that logic’s or is + (but you have to not double count where they overlap) and and is *, all of which is perfectly natural because logic is a kind of algebra. In logic, we deal with functions that map propositions to a discrete set {0, 1}, but with probability it’s a mapping to the entire interval [0, 1]. You can say that logic is a special case of probability, but it might be better to say that probability is a generalization of logic.

    We are already, sadly, approaching the limits of my knowledge here, but there are folks around that know this stuff much better than I do.
  • Two Questions about Logic/Reasoning
    ↪Moliere


    Should have said, the interesting stuff is with conditional probabilities, but it can be harder to wrap your head around at first.
  • Two Questions about Logic/Reasoning
    ↪Moliere


    We can do some stuff with validity in a way. It’s far more common, I think, to claim straight up that P ⊃ Q, but give a probability for P. Then you can reason from P being entirely contained within Q, and you get that pr(Q) is at least as great as pr(P) (because it might include some of ~P, the freebies). That makes ⊃ “probability conserving” in a sense, that you get out at least as much as you put in, you don’t lose anything, just as in logic we want inferences to be truth preserving. (For probabilities, the biconditional is just =, because each side is greater than or equal to the other.)
  • "What is truth? said jesting Pilate; and would not stay for an answer."
    This means that unless we are absolutely certain, we ought not call something "knowledge", because it could turn out not to be knowledge. — Metaphysician Undercover

    To me, certainty sounds like a psychological state, something like “maximal confidence,” and it’s irrelevant. It could turn out I was wrong even if I was certain. Would you like here to do the same thing you don’t like with the word “knowledge” and say that if that were to happen, then it must be that you weren’t really certain, but only thought you were?

    if there is a possibility that the thing which appears to be knowledge is not actually knowledge, then we ought not call it "knowledge"? — Metaphysician Undercover

    Knowledge is just actual knowledge, and knowledge of the actual. It doesn’t have to be necessary, and neither does the proposition known. What is cannot not be, but in many cases it might not have been. There are different sorts of necessity at work here. We can say that it is possible for something that is not to have been without denying that it is. “I know that it’s raining but maybe it isn’t” is incoherent; “I know that it’s raining but it might not have been” isn’t.

    The rewrite rules make this really clear. If you have a propositional attitude Φ toward a proposition P, Φ is factive just in case you can, with no change in truth-value, rewrite “S Φs P” as “P and S Φs that.”

    I know that it is raining = It’s raining and I know that
    Steve thinks that it is raining ≠ It’s raining and Steve thinks that

    The interesting thing people keep saying is that it might “turn out” that P isn’t or wasn’t the case, that I was right or wrong. No worries when we’re just dealing with belief, because that suggests that there is newly acquired evidence. No one bats an eye at “I thought she was at the store but it turns out she wasn’t.” For all I knew, she was at the store, but now I know more and my knowledge now includes that she wasn’t.

    No one seems to bring up, “I thought she was at the store and it turns out I was right.” Here the speaker is still not claiming to have known she was at the store, but to have had the belief, a belief which was true, without his knowing that.

    But “I knew that water freezes at 32°C but it turns out it doesn’t” is incoherent. Why? Because knowledge is factive, so something is entailed about the state of the world by what you know; water either freezes at 32°C or it doesn’t. If you know that water doesn’t freeze above 0°C, then it’s not your knowledge that rules out the possibility of water freezing at 32°C, but what is entailed by your knowledge.
  • "What is truth? said jesting Pilate; and would not stay for an answer."
    nothing less than deception — Metaphysician Undercover

    I for one would appreciate it if you stopped saying things like this. Andrew and Michael are clearly not trying to deceive you. If they are mistaken, then they are mistaken, but there’s no deception here.
  • "What is truth? said jesting Pilate; and would not stay for an answer."
    The hypothetical shows the logical consequences which follow from the assumption that it is actually raining in the real world. And, there is a very big difference in meaning between "it is actually raining in the real world", and "I assume it is actually raining in the real world". The latter recognizes the possibility that it is not raining in the real world. — Metaphysician Undercover

    Not necessarily. From the fact that it‘s raining, you can’t conclude that it might not be; for all you know, it might necessarily be raining.

    I don’t think any of that affects how a hypothetical works. It can be quite natural to construct a hypothetical with an assumption that is at least counterfactual, for explanatory purposes: if this thingy weren’t here, this other thingy would blah-blah-blah; if squirrels couldn’t climb trees so quickly, then cats would catch them easily.

    You can even do this with an assumption that is necessarily false, and that’s roughly how proof by reductio ad absurdum works. Must it be the case that a space with properties A, B, and C has property D? Assume A, B, C, and ~D and then derive a clear contradiction. That means the entire set of premises, taken as the conjunction A & B & C & ~D, is necessarily false.

    But in all these examples, the important thing about a hypothetical is that you must discharge your assumption. So the conclusion of a hypothetical is always, at least implicitly, a conditional. “Suppose I have a dollar bill and 2 quarters. Then I have $1.50 total,” is to be understood as “If I have a dollar bill and 2 quarters, then I have $1.50.”

    That’s the whole point of hypotheticals, to see what follows from the assumption, to see whether something in particular does, not to make a claim about whether the assumption holds or not, or even whether it’s possible or not. Sometimes in informal reasoning, people miss the step of discharging their assumptions, so they’ll end up claiming something like “But I just proved that I have $1.50!!!“ when all they‘ve proven is that if they had $1.50 then they’d have $1.50.

    Since I’ve cited Margaret Wise Brown, I’ll cite another of my favorite works of philosophy, Open House for Butterflies:
    If you’re pretending you’re a lion, it’s good to know if you’re pretending you’re really a lion. — Ruth Kraus
  • Two Questions about Logic/Reasoning
    suppose a friend were to say to us: "If you attend my party, you will receive a prize." Immediately, we would think, "If I don't attend the party, I won't receive a prize. But since I want a prize, I must attend the party." — MichaelJYoo

    Forgot to do this part!

    This is called “perfecting the conditional.” It’s a known thing, that in everyday conversation, conditionals are often taken to be biconditionals. This is a solid example. The standard one is “If you cut my grass, I’ll give you $10.” Maybe I’ll give you $10 even if you don’t cut my grass, but it’s taken to mean “If and only if you cut my grass, I’ll give you $10.”

    Works out better for the OP's point, that the conclusion is less likely than each initial premise — Moliere

    I think that’s probably true. I just worked the example given.

    Logic can be mapped onto probability somewhat naturally (Ramsey thought they were one thing), but there are some pitfalls. (Lewis has a famous result in “Probability of Conditionals and Conditional Probabilities,” for instance, showing that you can’t interpret pr(P ⊃ Q) as pr(Q | P).) The inferences are very similar, but I think there are objections — at least, interpretively — to taking truth as probability 1 and falsehood as probability 0. (Also: picking a real number, winning the lottery, the usual probability 0 stuff.) Formally, though, it does make some sense to think of logic as a special case of a more general calculus of probabilities.

    Not sure what vocabulary we should use for this sort of thing, but “validity” feels really out of place. Once you’re doing probabilities, that’s what you’re doing.
  • Two Questions about Logic/Reasoning
    while each premise individually considered is more likely to be true than their contraries, the chance (mathematically speaking, in this example) that both are true at the same time is 0.65 * 0.65, or 0.4225 (42.25%) — MichaelJYoo

    This isn’t right though, because the p → q and p are not independent. p → q is true in cases where p is false, or where both p and q are true. Since we’re doing p & p → q, we’re supposed to be interested only in the part where p and q are both true. The probability of that would be pr(p) * pr(q), but of course we don’t have a probability for q — that’s what we want to find. More importantly, we only have a probability for p → q.

    Suppose the only cases for P ⊃ Q are ~P & ~Q or P & Q. Then we would be getting 35% of our 65 from ~P and the remaining 30% from a Q entirely contained within P. That leaves about 54% of P unoccupied by Q. That sounds like it’s too high. Shouldn’t it be only 35%?

    Nope. P ⊃ Q intuitively says that P is contained within Q, but in this case, it’s only partially contained. 35% of the time we get P without Q, and that’s 35% of the total space, not of P.

    So now we have a low figure for pr(Q) of 0.30, worst case scenario where P ⊃ Q is more often true because P is false and Q is false.

    The biggest number for Q would be if it entirely contained ~P. (Taking all the cases where P ⊃ Q would have been true anyway because ~P.) That gets us, as before, 35% of the total space, and the same overlap as before where P & Q is another 30% of the total space. The high number then is pr(Q) = 0.65.

    Where we end up is that pr(Q) = 0.3 + x, where x is some value between 0 and 35. I think that’s as much as we can do.

    It might be noteworthy that we know P and Q are not disjoint, Q entirely contained in ~P, because that would leave only 35% for cases where ~P or Q, and that’s too small.

    And again, Q cannot entirely contain P, and that includes being the same as P, because then P ⊃ Q would climb to 100% (all of ~P and all of P with no overlap).

    It makes some intuitive sense that the max value for Q can’t exceed the max values for the premises, but could be even lower.

    That’s my take on it. Happy to be corrected.

    Oh, and this is a different thing:

    If F(65%) then G(65%)
    F(65%)
    Therefore, G(65%)     — Moliere

    We had a probability for the whole conditional, plus a second premise giving a probability for its antecedent, but no probability for the consequent. If we already knew that pr(G) = 0.65, why we would we bother trying to calculate it?
  • "What is truth? said jesting Pilate; and would not stay for an answer."
    revision theory — Banno

    Think I was otherwise occupied when you mentioned that. I'll take a look.
  • "What is truth? said jesting Pilate; and would not stay for an answer."
    ↪fdrake


    Back when I was a tournament chess player, it seemed to me that the style of play of serious players -- that is, who studied, practiced, and played a lot, regardless of talent -- was a generation or so behind what the world's top players were doing. This shows up in opening repertoire too: things current GMs aren't playing are still common in weekend tournaments among amateurs. Some of that is really a matter of knowledge and technique: GMs might avoid an opening as black because the current state-of-the-art for white forces a very favorable endgame. That's not the kind of advantage amateurs can reliably convert, and so it's not the kind of advantage they think about much or know much about.

    I think something similar happens with us. We advocate positions professionals consider to have nearly fatal flaws because we don't know that -- don't even know what counts as that sort of flaw -- and because the people we talk to don't know it either, don't know that there is such a case to be made or how to make it. Thus even when a discussion here lands right on such a point -- about as close to dispositive as philosophy gets -- no one knows this is enough to call the bout and move on.

    Philosophy and chess are similar in this sense, that they are driven by fashion, but fashion that is shaped by an arms race. Obviously not an infallible procedure for approaching truth, but also one that is easily misunderstood. Grandmasters will abandon a line in an opening because of one specific move (initiating a variation) available to their opponent. The technical details matter, and they are what drive the shifts in fashion. New ideas in old openings have surprise value (the Theoretical Novelty), but it also has to be a good idea. Sometimes a great player will refute a TN over the board, in real time.

    So I see professional philosophers in part as engaged in rather technical issues because it's how you push alternatives toward the possibility of decision. Absent such technical knowledge and expertise, our choices of fashion are somewhat arbitrary, and there are never any decisive encounters of one view with another.
  • Where Do The Profits Go?
    I am not an economist, but I suspect the principal use of profits is to create new debt.

    No doubt there is research on this sort of thing.
  • "What is truth? said jesting Pilate; and would not stay for an answer."
    You've discovered the attractor of philosophical discourse. — Isaac

    It's been done before, many, many times. (And whether I discovered it or invented it is exactly the debate.)

    I suspect it's really selection bias. Out of the entire population that might post here, the vast majority keep on walking, a small number are interested in academic philosophy, a tiny number of those become academic philosophers, an unknown number create an account here, a fraction of those read some of the site, and a fraction of those post. Certain interests, and certain sorts of arguments, seem to be over-represented in those who post, relative even to the population of those with an interest in academic philosophy.
  • "What is truth? said jesting Pilate; and would not stay for an answer."
    ↪fdrake


    Read through the whole discussion. It is the same discussion as this one. Every (philosophical) discussion on TPF becomes the same discussion, if it has enough time to get there. It’s kinda depressing, to be honest.
  • "What is truth? said jesting Pilate; and would not stay for an answer."
    A hypothetical doesn't provide us with the required knowledge. — Metaphysician Undercover

    A hypothetical is a conditional, isn’t it? “Suppose I give you a million dollars” is not me giving you squat.
  • "What is truth? said jesting Pilate; and would not stay for an answer."
    The boxes may operate in a well-defined (definite) way, but are instead able to input and output coins in an indefinite state. But that can't be directly confirmed since a coin is always measured to be in a definite state. — Andrew M

    So the reliance on counterfactual definiteness is here? That perhaps a coin was emitted in an indefinite state but we can’t observe indefinite states, only definite ones. This is like your grid-world example with the direction of the unobserved arrow.

    So the issue is that in some cases there might be no fact of the matter, no definite state, but if we take a measurement, we’ll always find that there is. And then counterfactual definiteness is specifically the claim that since our measurements always show definite states, then what we measure — or, more specifically, what we intend to measure or consider or imagine measuring, must always be in a definite state because indeed that’s what measuring it would show.
  • "What is truth? said jesting Pilate; and would not stay for an answer."
    ↪Andrew M

    Assuming the coin always has a definite heads or tails state, even when not measured, what definite state could it have had when it was between the two black boxes? It seems that the coin couldn't have had a definite state, contrary to assumption. — Andrew M

    Still not getting it, so I'll just ask.

    Is this the claim? If each coin left box 1 with a definite state, then it would enter box 2 with a definite state, and if all of the coins entered box 2 with a definite state, then we should see some coins not in their initial orientation? Since we don't, it must not be true that coins leave box 1 and enter box 2 with a definite state.

    What I don't get is that the behavior of the boxes is defined only for coins entering with a definite state, and as emitting coins only in a definite state. What are the boxes doing if not that? Isn't this a way of saying that the behavior of the boxes is not entirely definite?
  • "What is truth? said jesting Pilate; and would not stay for an answer."
    Before continuing with this, I want to point out that truth is very much the issue at stake in all of these apparent detours. Our customary way of explaining truth is by distinguishing it from knowledge: someone who guesses correctly how many coins are in a jar has put their finger on the truth, even though they do not know how many coins are in the jar, and even though they cannot know that their guess is correct (else it wouldn’t be a guess).

    We can describe a situation in which someone knows that the guess was correct, just not the person guessing, and so we presume that even if no one knew whether the guess was correct, there would be a “fact of the matter” about the quantity of coins, that some sentences about the quantity of coins would be true and some would be false, even if no one knew that, even if no one ever knew that, even if no one ever could know that.

    There was, I believe, a definite number of living spiders on my porch last night at 11 pm, but no one can ever know what that number was, because they weren’t counted and the opportunity to count them is gone forever. If I simply listed all the numbers between 0 and some implausibly high upper bound like 109, one of those numbers would be right, and all of the others wrong.

    Besides the intuitive plausibility of the distinction between truth and knowledge, there is the Church-Fitch argument, which shows that there must be truths (like the spiders on my porch) that are not only unknown by me, but unknowable by anyone, unless you're willing to say that everything that is the case is known. Which is just to say that there is no comfortable resting place partway between identifying truth with knowledge and not doing so.
  • "What is truth? said jesting Pilate; and would not stay for an answer."
    Perhaps this also says something about how the word "count" is used. — Andrew M

    Of course, and this is what I was trying to show in a roundabout away. It was moderately fun to do, and counterfactuals are interesting, but we don’t need any of that, all we need is this:

    (Card) If and only if there is a one-to-one correspondence between the coins in a jar and the set of natural numbers less than or equal to k, for some natural number k, then the number of coins in the jar is k and there is a definite number of coins in the jar.

    That’s just the definition of cardinality for finite sets plus existential generalization. We don’t need counterfactuals for that, and we don’t need them for this:

    (Count) If and only if a jar contains k coins, then counting the coins in the jar yields the value k.

    This definition of cardinality for finite sets might as well be a description of counting; there’s almost nothing else to say.

    *

    I’ll check out the Rovelli. My path suggested that the necessity of mathematical truth is the tipoff; if you go backwards and collect the sorts of things you can know a priori and that are true across any set of possible worlds, the first things you’d find would be what we’ve been calling mathematics, and the rest would be disciplines that aspire to be like mathematics. That’s why math is special, that’s why math is what you can count on, that’s why problems and theories should be formalized mathematically. (If it’s not math, it’s just stamp collecting.)

    *

    I see how your coins and boxes are analogous to photons and interferometers, but I’m still not getting the point here.

    But! I think I have thought of the perfect example, because it also involves making calculations based on values that you should not be using: the two envelopes problem.

    Refresher: The only right way to do this is to treat the envelopes as X and 2X; you don’t know which one you got, so you stand to gain X or to lose X by switching, and the expected value of switching is 0. But if instead, you call whatever you got Y, and then reason that if it’s the bigger the other is Y/2, and if it’s the smaller then the other is 2Y, then the expected value of switching is Y/4.

    It could be that exactly what’s wrong with this analysis is that it relies on counterfactual definiteness. (Oddly, like the black boxes and the interferometers, there are points in the defense of this analysis that rely on the principle of indifference giving equal chances to events, and then relying on those chances as if they were real values. Among many many other issues.)

    I’m still not sure it hooks up with the sort of counterfactuals I’m used to thinking about.

    Talk of switching in either the X or the Y analysis is counterfactual. Why does one of them work and the other not?
  • "What is truth? said jesting Pilate; and would not stay for an answer."
    Deductive inferences if valid are certain, so they do constitute proof. — Janus

    You meant “don‘t constitute evidence” right?
  • "What is truth? said jesting Pilate; and would not stay for an answer."
    ↪Andrew M


    Preamble

    Well, this is humbling. I wrote a rambling, exploratory post last night that I thought ended in a pretty good place, a really interesting place, but with a problem, one I've been interested in for a long time. Then this morning it occurred to me that there might be a sort of solution suggested by how I arrived at the problem, so I wrote an addendum to last night's post. And not until I was actually writing the words this morning did it occur to me what I've been talking about for days.

    TL;DR

    What I have been claiming about the number of coins in a jar is simply that we can know a priori that if they can be counted then there is already a specific number of coins in the jar; we can only know a posteriori what that number is.

    I do not think I have ever had occasion to make a claim to knowledge that so clearly fits the definition of a priori. Whaddya know.

    Archive
    But an arrow is only ever observed pointing along one of the grid lines. Thus raising the question of which direction the arrow is actually pointing (if it has a definite direction at all) when not observed. — Andrew M

    Does it? Your QM example gets there, I guess, but I've got nothing to say about that.

    What isn't clear in your grid world example is what would motivate this question. If you sometimes observe an arrow pointing North and never observe anything else, what would make you think that it exists the whole time but the rest of the time it's pointing somewhere you can't observe? As you say, we don't seem to be able to distinguish pointing somewhere else from not pointing at all, or, as I put it before, we're really talking not about measuring but about two classes, North and not-North, which would also include just not pointing at all.

    You must have some reason for positing that the arrow is pointing non-northwards when unobserved, right? But by stipulation, you don't. So I'm still at a loss. If the point is just exactly this, that if you, in essence, only imagine a situation, then you can't make measurements, that seems indisputable. You had a pithy quote to that effect.

    ---- Enough of that. I think I have better answers below, toward the end, or part of an answer anyway. ----

    My claim, as you know, was not that I could figure out how many coins are in a jar by imagining counting them. That's clearly false. It was a claim about the nature of counting, that it does not "create" the cardinality of the set, that the cardinality of a set does not fail to exist until its members are counted, but that counting (to borrow a phrase from the wiki you linked) reveals a pre-existing unknown value.

    What I have imagined happening here is, roughly, the mathematization of a physical problem: counting in the real world is a physical process, taking time, consuming energy and so on, but the result -- well, I suppose I can't really finish that sentence the way I want, because clearly what we're talking about now is information. I want to say that there is an aspect of what's going on that it is mathematical, and thus non-physical and non-temporal, but information is after all physical. Yuck. But there is also a mathematics of information, so maybe I come out okay. Gonna leave that alone for the moment.

    What I'm trying to say is that if the math didn't work the way it does, then the physical process of counting could not work the way it does. It's not that the mathematics constrains your actions, but it does constrain the results. Performing a physical task such as counting or measuring or dividing, all this business and much more, in a way that doesn't respect the mathematics won't reliably produce the right result. (Hence engineering.) And therefore the mathematics can give you some insight into what the right procedure must be.

    And that seems right. Philosophy and mathematics are old friends. Plato will refer to this cluster of disciplines -- philosophy, mathematics, music, astronomy -- as if it's perfectly obvious why they go together, and indeed it is, if you think this way. The impulse to mathematize a problem is sound. It's what we do.

    To come back to our issue -- I suppose I think of the physical counting of the coins as counterfactual, but mathematics, after all, is what it is at all possible worlds, and is never counterfactual. That's why it seems so clear to me that I am entitled before counting to make only the claims about an unperformed count that mathematics would entitle me to make, that the result I will get exists and is unique, though I do not know its value. If I follow an incorrect procedure, that's not true. If I cannot follow the correct procedure, that's not true. But I can know what a correct procedure is and what result it must produce if it can be followed. And that claim is based on the mathematics, so not counterfactual.

    What remains -- and it's too big for me -- is some explanation of how mathematics (non-physical, non-temporal) is implicated in the performance of a physical task in the actual world.

    Does this make any sense? I could go back and edit, but maybe it's clearer if you can watch me stumbling toward figuring out what I want to say...

    +++

    The last problem mentioned --- roughly, idealization, the function of ideals in our thinking, and so on --- does have a possible solution here, of a sort.

    I suggested that I can know some things about counting a set of objects without counting them because there is mathematics that constrains how counting works, and I can know the mathematics because, unlike the counting itself, it is never counterfactual.

    The little puzzle here, of what this mathematics is and how it connects to physical processes like counting coins, could be dissolved by reversing my description above: suppose instead we say first that there are things I can know about counting objects, without doing any counting, because they must be so (and thus are not counterfactual). And this sort of knowledge --- of just those aspects of a situation or process that must be so --- is more or less what we call mathematics.

    If that's defensible, then we may be able to find our way back around to questions about truth, because truth appears to come in varieties, which is slightly disconcerting, and I've been presenting an analysis that relies precisely on a distinction between a priori and a posteriori knowledge, and have offered a half-baked suggestion for how you might get the former out of the latter (thus perhaps re-linking some sorts of truth, if not quite re-unifying them).
  • Cracks in the Matrix
    Do we really need to be nuanced about these things? — Xtrix

    Not about what those people believe -- that's their problem. But we can afford to be nuanced about what we believe, and why we find what they believe (insofar as we understand it) incompatible with that. It is okay, for instance, for a paleontologist to describe the truly mind-boggling degree to which evolution by natural selection is supported by the fossil record while shying away from the word "proven."

    those who say there are witches are deluded — Xtrix

    Heavy word. Not saying it's never appropriate, but why that word instead of "wrong" or "mistaken" or "misinformed"?

    Anyhow, I've said my piece. Carry on.
  • Cracks in the Matrix
    ↪Xtrix


    Above my paygrade, but statistical mechanics is a thing. I think I learned about it from a book I never got very far into -- but will someday! -- called (in English) Laws of the Game by Manfred Eigen.

    Probabilities are central to That Branch of Physics That Shall Not Be Named. Evolution is almost entirely a matter of statistics (and game theory).

    And it's not like what we mean by "the laws of nature" is a simple matter, devoid of interest and controversy alike.

    I'm not advocating giving magical thinking a seat at the table, just a little nuance in how and why we reject it.

    Torches and pitchforks are for witches, and since we found that there don't seem to be any of those, they've been rusting in the barn. You seem to want to haul them back out for people who say there are witches; I'm not down for that, anymore than I am for some believers in witches hauling theirs out for an anti-witch crusade. (I have been present when an evangelical dad reminded his son that witches are an article of faith, mentioned in the Bible. His son had forgotten for a moment that they're not just superstition. And so it goes.)
  • Cracks in the Matrix
    I think the simple fact is that we don't notice just how large the sample size is. If our story is some "Middle aged woman in Utah in 1932 had a psychic experience..." we can be sure that there have been a huge number of middle aged women and not only in Utah every year when the astonishing consequence of events hasn't happened. — ssu

    This is very close to what I was saying. People fail to consider the baseline, overestimate how much a single observation should move their prior, all that.

    But if the laws of nature are in fact statistical, then being an outlier is not the same as "violating the laws of the nature"; it's just being several standard deviations away from the norm. Maybe it happened, maybe not, but statistical regularity marches on either way.

    It is true that a theorized mechanism intended to explain the statistical regularity may be unable to account for a peculiar observation, but we don't throw out observations because they don't match the theory; it's the other way around. That we don't drop a theory when a single observation is surprising is because we expect there to be confounding variables, and -- possibly -- because all we're really doing is statistics.

    I just don't see much justification for reaching for this "physics says that's impossible" line.
  • "What is truth? said jesting Pilate; and would not stay for an answer."
    For those of you losing patience with all this, I'll jump to the end. What I provided was a sketch of an algorithm, an algorithm that could be instantiated in a machine, and at no point in the machine's operation is human judgment required to "assign" a number to anything. Coin counters are quite real and there's probably one at the front of your local supermarket. They claim, correctly, to represent the value of the coins in your jar before you dumped them in.

    But didn't a human being have to design the machine, so isn't it just an embodiment of human judgment? Since we designed the coins and what values they represent, we have to design the machine to, you might say, take that into account; but you could also say that we design the machine to factor out (not in) complications we have added to the process of counting, to keep them from interfering. We tell the machine that objects of roughly the same size and weight are to be counted as the same thing so that it can count without the need for it to make such a judgment. (The machine, for instance, tallies only the nominal value of the coins, and won't notice if a rare coin worth a thousand dollars was mixed in with the dimes.)

    I count money using a machine every day I go to work; the machine is easily fooled, and its mistakes are sometimes interesting. (A roll of nickels that is a little over, IIRC, is very close in weight to a roll of dollar coins, but a $23 difference in value. This has caused some head-scratching in the cash room now and then.) But it is easily fooled because all it does is count, and counting doesn't require -- so the machine doesn't offer -- judgment.
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