• 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.
  • "What is truth? said jesting Pilate; and would not stay for an answer."
    In our world, time passes, and things change as time passes. — Metaphysician Undercover

    For instance, if there were so many coins in the jar that I would die before I could finish counting them, then I would have to pass this sacred duty on to my son, and no doubt him to his daughter, and now we're writing a Kafka short story, not doing philosophy.

    The issue here is not all of metaphysics but a simple conditional: if they can be counted -- if -- then there must be a specific number of coins in the jar right now. All of these other issues are different ways of saying that as a matter of fact they can't be counted. (And that doesn't tell us whether the jar has a specific number of coins or not.)

    I say the conditional is true. Do you say it is false?
  • "What is truth? said jesting Pilate; and would not stay for an answer."
    if a pointer is measured to be pointing North along the North-South axis, then what direction is it pointing along the West-East axis? — Andrew M

    I feel like I'm doing something wrong because I keep wanting to refute the examples. (Also, it reminds of my first my earliest experiences in philosophy, when I kept thinking that old-timey philosophers just didn't know enough math.) I'll try to think of an example after I do this one.

    In this example, since you're only interested in direction from a point, defining that relative to a pair of orthogonal axes is at best an intermediate step (if you defined a location first and then converted it). What you ought to be saying is that the pointer is 0° off North. For jollies, you can throw in that it's 270° off East and 90° off West, but why bother? The extra axis adds nothing.

    You didn't even have to align your direction right on the North-South axis to get here: if it were pointing exactly Northeast (45° off North), or, you know, almost anywhere, it's not aligned on either of your canonical axes! Oh my god! Its direction is undefined!

    The only measurement always available is how far off a given axis it is. So just start there, and only use the half-axis from origin to North. Or take that direction as the default, define it as 0° and do other directions relative to that, whatever, but why would you define more than one axis in the first place? (Put this way, East-West is, to begin with, defined as passing through 90° off North and 270° off North, or 90° off South, defined as 180° from North.)

    I think it's presented as pointing exactly North to support the illusion than some measurements could be made and some couldn't. But that's not what's happening here. We have a system that is useless for measuring anything but one or maybe two directions, which means we're not measuring at all, we're classifying directions as "North" (and maybe as "South") and "not North". That's not measuring.

    I'm doing all this because it looks like this was a purely verbal conundrum. It seems to present a genuine problem (like the lap) but does not, and one way you know it doesn't is that it doesn't even do properly what it was pretending to do. The suggestion seems to be that directions generally have a North-South component and an East-West component, except for the degenerate case where you're actually on one of the axes, and then the other value doesn't go to zero but is suddenly undefined and maybe can have any value at all! Horrors! But the system supposedly breaking down only works for the case of pointing exactly North or, I guess, exactly South. This wasn't a genuine question but an intuition pump.
  • "What is truth? said jesting Pilate; and would not stay for an answer."
    What I said, is that your logic is not valid without a premise of temporal continuity. That a coin might disappear without one noticing, is just a simple example as to why such a premise is necessary. — Metaphysician Undercover

    If you mean that my argument is only valid in a world very much like ours, I agree. If you wanted to discuss jars of coins in a hypothetical world in which coins randomly appear and disappear, that's rather different from the discussion I believed we were having. I understood you to be making a point about the necessity of a free human judgment that assigns a number to the coins, but it appears I was mistaken.

    To return to the issue at hand: I consider my arguments valid in worlds very much like this one. In worlds like this, if the number of coins in a jar can be determined by counting them, then you can know, without counting, that there is a specific number of coins in the jar.

    Do you agree?
  • "What is truth? said jesting Pilate; and would not stay for an answer."
    for the agent, there would be a potential (but not actual) number of coins in the jar that is only actualized in the counting of the coins. — Andrew M

    I think the mathematical vocabulary is clearer: if they can be counted, then the cardinality of the set of coins in the jar exists and is unique, though we do not know its value until we count.

    If that's what's meant by "potential but not actual," then cool. MU's position is that there is no number "associated with" the cardinality of the set of coins in the jar until they have been counted, because no one has made a judgment assigning a number to the set; my position is that if they can be counted, then there must be a specific number of them, though we do not know that number. If the counting procedure can be followed, but will not yield a result, that can only be because it will not terminate, and that can only be because there is an infinite number of coins in the jar, and then indeed there is no natural number equal to the cardinality of the set of coins in the jar. Whether we call aleph-null a number I did not address. Whether a jar can hold an infinite number of coins, I did not address.

    There's modal language all over this, and I'm fine with that. In part, that's simply because MU agreed that they can be counted, and if they were to be counted, then we would know how many coins are in the jar. I was simply working within a counterfactual framework already accepted. A possible world in which coins appear and disappear at random is not a world in which coins can be counted, so it is not, as we might say, salient for this case. A possible world in which coins sometimes disappear after I've touched them is a world in which I can count coins, but my count cannot be verified, and in such a world my count applies only to the past, to the coins that were in the jar in its initial state.

    To use a macroscopic analogy, an interpretation which rejects counterfactual definiteness views measuring the position as akin to asking where in a room a person is located, while measuring the momentum is akin to asking whether the person's lap is empty or has something on it. If the person's position has changed by making him or her stand rather than sit, then that person has no lap and neither the statement "the person's lap is empty" nor "there is something on the person's lap" is true. Any statistical calculation based on values where the person is standing at some place in the room and simultaneously has a lap as if sitting would be meaningless. — Same wiki article on counterfactuals in QM

    A person who has no lap has nothing in their lap. Russell's analysis of definite descriptions works just fine here, but physicists don't read Bertrand Russell. It's also tempting here to give a counterfactual analysis: if a standing person holding nothing were to sit, they would have an empty lap; if a standing person holding a child on their back and nothing else were to sit, they would have an empty lap, until another child scrambled onto it; if a standing person holding a child against their chest were to sit and loosen their grip upon the child even a little, they would have a child in their lap, and they would sigh with relief.

    Quantum mechanics may have some specific prohibitions on the use of counterfactual values in calculations, but it is, for me anyway, inconceivable (!) that we could get along without counterfactuals. They're hiding absolutely everywhere.
  • Do the past and future exist?
    Could I christen yesterday at 10:30 pm "now"? — Tate

    In a sense, yes, though I'm not sure it helps with the question at hand.

    i think we have three options:
    (1) Tensed language centered on our notional now (most common);
    (2) Untensed language with "timestamps" or times as parameters (common among scientists and not too uncommon among philosophers);
    (3) Tensed language centered on some other time than our notional now (pretty uncommon except for the historical present -- the option you asked about).

    You can, to some degree, use these three strategies interchangeably and just translate among them. I think they aren't entirely equivalent though, and it shows up not in the content of propositions but in our attitudes toward them. We do not remember the future, for instance, under any scheme. And speaking yesterday of the rock as it is today was future-tense speculation, but for us, looking at it in the present, it's merely fact. I think there's more to all that, but again I'm not sure it helps at all.
  • "What is truth? said jesting Pilate; and would not stay for an answer."
    I think this is just too vague.
    — Srap Tasmaner

    Just trying to capture the essential idea here! Apparently not successfully...     — Andrew M

    Wasn't trying to lay that at your feet!

    I think the other issue is that standards can vary according to context. For example, Alice might know that it's raining outside, having looked. But when challenged with the possibility of Bob hosing the window, making that possibility salient, she might doubt it and go and look more carefully. — Andrew M

    I'll have to read the rest of Lewis paper to see what he was getting up to. I think I get the intent of this example, but it feels like we're screwing around with justification and I don't know why anyone would think that road leads to knowledge. It leads to high-quality beliefs, that's it. Maybe Lewis has something up his sleeve...
  • "What is truth? said jesting Pilate; and would not stay for an answer."
    ↪Metaphysician Undercover


    I addressed in my posts a single issue you raised: must the coins in a jar actually be counted, by you, me, God, or anyone, to know that there is a specific number of coins in such a jar?

    That question I answered as clearly as I could, and even provided informal proofs to support my position.

    If you have no rebuttal besides "maybe coins spontaneously appear and disappear," then we're done here.
  • Cracks in the Matrix
    ↪Sam26


    I wasn't convinced either but it was a really interesting discussion. I'm grateful you brought us your arguments and gave us the opportunity to deal with some really interesting issues.
  • Cracks in the Matrix
    ↪Xtrix


    I'm none too solid on the statistics but I think in many cases the mistake people are making is really just exactly a statistical mistake.

    Every piece of evidence should move the needle; the mistake people make is thinking a single piece of evidence moves the needle more than it does. (The classic example is doctors misjudging the chances of breast cancer given a positive test.)
  • Cracks in the Matrix
    ↪fdrake


    Agreed. And I just invoked your name in post about Sam's central focus, the evidentiary value of eyewitness accounts. Freaking kismet.
  • Cracks in the Matrix
    The reason for not believing in these claims is the same for everything else: extraordinary claims require extraordinary evidence. Carl Sagan was right. — Xtrix

    And David Hume.

    That maxim is not by itself dispositive though. If an eyewitness account comes from someone you are inclined to consider trustworthy, unlikely to be mistaken, and with no reason to lie, that has to count for something. @fdrake could fill in the details much better than I, but the point can be made in Bayesian terms: the chances of Reliable Ron making such a claim, given that it's true, are higher than the chances of him making such a claim given that it's false. If you believe your boyfriend is visiting his parents, but a good friend tells you she saw him at a bar last night, you're going to take that seriously, and it's going to move your prior.
  • Cracks in the Matrix
    ↪fdrake


    We remember that discussion differently then.
  • "What is truth? said jesting Pilate; and would not stay for an answer."
    That we "exclude the possibility of mistake" is not a condition of knowledge, as ordinarily defined and used. — Andrew M

    I think this is just too vague.

    If S knows that p, then S is incapable of knowing that ~p. But S is still capable of mistakenly believing that ~p in various ways: S may have forgotten for the moment that they know that p and have reason at the time to believe that ~p; there may be some subtlety they have failed to reason through, may believe some q that would support ~p without realizing that p excludes q, and so on. Our knowledge must be consistent, but our beliefs show no such discipline. I think.

    The trouble is not our knowledge, but our beliefs, and around here it's our beliefs that we know that p, which clearly can be mistaken even though our knowledge cannot.

    And I think there are at least two senses of "fallibility." One is when you hold only partial belief, so you can consistently say "I think he's in the office, but he could be elsewhere." The other is when you are willing to endorse your individual beliefs taken singly, in sensu diviso, but hold something like partial belief with regard to your total beliefs, taken altogether, in sensu composito, that is, when you hold that some subset of your beliefs may be mistaken -- which you are also willing to say of many individual beliefs -- or that some subset of your beliefs is mistaken.

    That latter is a little paradoxical, but defensible. (Your belief in sensu composito doesn't entail the corresponding set of beliefs in sensu diviso. You can fall to make an inference, be lacking some connective knowledge, etc.)

    It's also possible that generally people only believe that they're probably wrong about something, and that's as much "fallibility" as they're committed to.

    ++++

    One more note: I think people sometimes reason *from* what they take to be reasonable doubt that they're right about *everything*, *to* the conclusion that they should treat each of their beliefs with a certain amount of suspicion. The thinking is, if I'm probably wrong in at least one of my beliefs, some small part of that probability should attach to each and every one of my beliefs. Even though the original claim was that my beliefs are overwhelmingly right, I have the epistemic problem of not knowing which are the good ones and which the bad. (But attaching a modicum of doubt to all your beliefs is so ham-fisted, I don't think anyone actually does it or can do it.)
  • "What is truth? said jesting Pilate; and would not stay for an answer."
    We must premise a temporal continuity of the quantity in order to conclude that the quantity at the time prior to being counted was the same as the quantity at the later time of being counted — Metaphysician Undercover

    I see. No, we needn't take that as a premise. We can argue for it.

    But to say that there will be one number, after being counted, out of a present infinite number of possibilities, is not the same as saying that there is one number presently. — Metaphysician Undercover

    Suppose a jar containing some coins at a time t0. We agree that we can count the coins by removing them one at a time, and that doing so would result in a unique natural number m, at some time tm, after t0.

    If we remove a coin from the jar, then there is some time t1, after t0 and after we have removed one coin but before we have removed another. If the jar is empty at t1, then the initial state of the jar at t0 was that it contained 1 coin, and 1 is a natural number. If the jar is not empty at t1, we go again. If we remove another coin, then there is a time t2, after t1 and after we have removed another coin but before removing any others (if there are any). If the jar is empty at t2, then it contained 1 coin at t1, and 2 coins at t0, and 2 is a natural number. If the jar is not empty at t2, we go again.

    For any step of the counting process, there is a time tk, after we have removed k coins from the jar but before we have removed another (if we can), and at tk the jar is empty or the jar still has some coins in it. If the jar is empty, then the initial state of the jar at t0 was that it had k coins in it, k a natural number. (If the jar is empty at tk, then at t1, the jar had k - 1 coins in it; at t2, it had k - 2 coins in it; and so on, up to time tk.)

    If there is no natural number n such that the jar is empty at time tn, then the process never terminates and the coins in the jar cannot be counted (except by Zeus).
  • "What is truth? said jesting Pilate; and would not stay for an answer."
    Retroactively, after counting, we can now employ a premise about temporal continuity, to conclude that this was the number before counting. — Metaphysician Undercover

    The temporal continuity of what? I don't understand the point you're making here.

    prior to counting, we have to admit numerous possibilities. — Metaphysician Undercover

    The procedure I described, if it terminates at all, yields a unique value. It cannot do otherwise unless the procedure is undermined by other premises. Did you have such a premise in mind?

    I agree, that prior to counting, we can truthfully say that we might count the coins, apply logic, and say how many coins are in the jar now. But that does not mean that the coins in the jar have a number now. — Metaphysician Undercover

    Suppose a jar contains some coins, but for no natural number n is it the case that the jar contains n coins. Then for no natural number n is it the case that removing exactly n coins from the jar would leave the jar empty. If the number of coins in the jar could be determined by counting to be some natural number k, then removing exactly k coins from the jar would leave the jar empty; therefore the number of coins in the jar cannot be determined by counting to be any natural number k.
  • Do the past and future exist?
    ↪hypericin


    I think it's a perfectly good question.

    Our experience seems to suggest to many that there is something special, something unique about the present moment, about now, and it is tempting to think that the universe is continuously changing from one instantaneous state into another and exists only as it is in such an instantaneous state.

    There are, I understand, weighty arguments against such a view, but it is how we seem to experience things.
  • Do the past and future exist?
    In your sense, fairies on mars exist as much as my nose.
    — hypericin

    Yep. Both may be the. subject of a predicate.     — Banno

    ?

    "All the fairies on Mars like rice pudding" appears to predicate of these martian fairies but doesn't entail that any exist.
  • "What is truth? said jesting Pilate; and would not stay for an answer."
    The truth of the phrase "the number of coins in the jar" implies that there is one specific number attached to, associated with, or related to, the quantity of coins in the jar. Can you agree with that? Now do you honestly believe that a particular number has already been singled out, and related to the quantity of coins in the jar, prior to them being counted? How is that possible? — Metaphysician Undercover

    A jar of coins either has no coins in it, or some coins in it. For the moment only, assume there is no other possible state for a jar. (We need neither claim nor stipulate that the number of coins in an empty jar is 0.) If a jar has no coins in it, we cannot remove a coin from it; if a jar has some coins in it, we can remove a coin from it, and If we were to remove one coin, then again the jar would have in it either no coins or some coins. This we know because a jar must have no coins in it or some coins in it. We count, from 1, as we remove coins from the jar, stopping when there are no coins in the jar; if the procedure does not terminate, then there is no number of coins in the jar. If the procedure terminates, then the number we have reached is the number of coins that were in the jar before we started counting.

    The only difficulty we face is determining what it means for a coin to be in the jar. If the jar is quite full, so that some coins rest on other coins but above the lip of the jar -- that is, outside the space we think of as bounded by the jar -- shall we count those as in the jar or not? If a coin is partially within the space bounded by the jar and partially outside that space, shall we say the coin is in the jar or not? If our jar of coins is in such a problematic state, then our counting procedure is of no use until we agree which coins will be considered to be in the jar. If we cannot agree which coins to count, there is no point in counting them. Similar considerations apply to what is a coin.

    But if we do agree what to count as a coin and which coins to count, we know there is a procedure available, and that we will be able to determine the number of coins currently in the jar, even if we have not yet made that determination.

    Proof that such a procedure, if it yields an answer, must yield a unique answer, is left to the reader.
  • "What is truth? said jesting Pilate; and would not stay for an answer."
    Infallibility isn't a condition of knowledge, as ordinarily defined and used. — Andrew M

    I'm not proposing that possessing knowledge means that one knows one is infallibly correct, but that the knowledge we possess, if it is to be knowledge, must be infallible. — Janus

    If S's knowledge that p is infallible, then S "cannot be wrong" that p. If that's just to say it is not possible that S knows that p and yet ~p, sure, that's impossible.

    If S knows that p, and if we consider only possible worlds consistent with S's total knowledge, then p is true at all of those. p is, for S, epistemically necessary. But that's not to say that p is metaphysically necessary, which means there's a sort of odd gap. Any ~p-worlds that might exist are just epistemically inaccessible to S.

    And that strikes me as curious. My knowledge that p creates in me an incapacity -- I become unable to know that ~p. Which is as it should be, but imagine reversing the analysis: suppose I do not know that p, and suppose further that I am, for whatever reason, utterly incapable of knowing that ~p. Then p-worlds are, ceteris paribus, consistent with my total knowledge, and only ~p-worlds at which I do not know that ~p. (At none of those will I know p either, because ~p.) This inability to be epistemically committed to ~p seems to greatly increase the likelihood of my landing at a p-world and knowing it. An inability to be wrong doesn't guarantee that you will be right -- you may never come even to hold a belief regarding p either way, much less know the truth -- but it surely helps.

    (It's also curious that because we're interested in the complement, the weaker the commitment to ~p you are unable to make, the better for your chances of knowing that p: excluding worlds at which you only believe that ~p would be better; excluding worlds at which you take seriously ~p but are undecided, better still; excluding worlds at which you merely entertain the notion that ~p, better still.)

    David Lewis has a paper that addresses infallibility. I've not read it yet.

    ++++

    Dots I forgot to connect.

    There's nothing particularly interesting about being right when you're right. Being right means really, really not being wrong.

    But when Roman Catholics say that the pope is infallible with regard to certain, though not all, matters, what they mean is not only that whatever he has said is right, but that whatever he will say is right. He is unable to be wrong in these matters.

    So the point I was making above is that when you're right, you pick up -- for free -- that inability to be wrong on this matter, and that feels like it's in the neighborhood of infallibility, though it's really just what being right is.

    And that's why the reverse is interesting. An inability to speak ungrammatically doesn't mean you produce every grammatical sentence, but that every sentence you produce is grammatical. If you were unable to make faulty inferences, you wouldn't have every reasonable belief, but every belief you had would be reasonable, given your total evidence.

    Maybe that's not much to get excited about though. Sounds a bit like playing not to lose, which is a notoriously bad strategy.
  • "What is truth? said jesting Pilate; and would not stay for an answer."
    More ellipsis. — Banno

    I just don't see the point of being gnomic when doing philosophy, but you do you.

    For instance, as you note,

    sometimes we use propositions. — Banno

    and you yourself intend someday to tell a story that begins "Once upon a time there was an entity with a neural network,..." and ends "And they used propositions happily ever after."

    If you don't know the middle bit yet, that's understandable. I suppose people waiting for the next installment would like some reassurance that there will be a middle bit. "Blah blah blah, the end" is not a good story.
  • "What is truth? said jesting Pilate; and would not stay for an answer."
    But there are no propositions present in neural nets. — Banno

    There is somewhere that propositions are present?
  • "What is truth? said jesting Pilate; and would not stay for an answer."
    ↪Banno


    Do you want to keep truth functions?
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