= 27d567bc2d48d9f40e9ccc20ea370b15)
CronoDAS comments on Right for the Wrong Reasons - Less Wrong
You are viewing a comment permalink. View the original post to see all comments and the full post content.
= 783df68a0f980790206b9ea87794c5b6)
Loading…= b715d02e85f7b3b4ae65ca3d3e450868)
Subscribe to RSS Feed
Powered by Reddit
= f037147d6e6c911a85753b9abdedda8d)
You are viewing a comment permalink. View the original post to see all comments and the full post content.
Comments (66)
That suggests a question.
If I flip a fair coin, and it comes up heads, what is the probability of that coin flip, which I already made, having instead been tails? (Approximately) 0, because we've already seen that the coin didn't come up tails, or (approximately) 50%, because it's a fair coin and we have no way of knowing the outcome in advance?
As Jaynes suggested, it's best to view all probabilities as conditional. P(coin came up heads | what i know now) = 1, P(coin came up heads | what i knew before flipping it) = 0.5.
The way I look at it is that before the coin flip you obtain a probability from information you have at the time and you predict ~50%. After the coin flip, you have obtained new information, so the probability that the last coin flip came up tails becomes ~100% (because it did), and the new information also gives you a tiny bit of data that says "maybe the coin comes up heads more often", so you also update to ~50.005% heads for the next one (or whatever). So, yes, the probability that the coin came up tails last try becomes ~100%, you just couldn't estimate it from the information you had and with just your brain beforehand (an AGI would've probably immediately seen how much force is going into the flip and calculated it all out and seen ~100% probability).
Although if you have an event that's heavily influenced by quantum magic, which a coin flip is not, you might need to consider that maybe it did have true 50% probability (that is, no amount of information and processing power would improve the prediction), and you just lost half your world's measure.
If you define "probability" as something that exists in a mind then it's perfectly reasonable that you_then.prob != you_now.prob.
If you're defining "probability" in some other way, please explain what you mean.
The relevant number for the purpose of judging the "correctness" of predictions is the probability you should have had at the time of the prediction (ie. the epistemically correct prior). Whether the outcome of the coin flip is heads or tails, the correct prior odds are 1:1, because you had no evidence either way.
If royf bets that katydee will win a fencing bout, and in fact they lose fourteen touches in a row, only to win by forfeit, we should update towards suspecting that royf miscounted the evidence, since such a bad athlete should not have much strong evidence predicting their winning. We should believe that the correct prior probability of katydee winning (from royf's point of view) is lower than royf thought it was.
Does this answer your question?
Not really.
Let me elaborate:
In a book of his, Daniel Dennett appropriates the word "actualism" to mean "the belief that only things that have actually happened, or will happen, are possible." In other words, all statements that are false are not only false, but also impossible: If the coin flip comes up heads, it was never possible for the coin flip to have come up tails. He considers this rather silly, says there are good reasons for dismissing it that aren't relevant to the current discussion, and proceeds as though the matter is solved. This strikes me as one of those philosophical positions that seem obviously absurd but very difficult to refute in practice. (It also strikes me as splitting hairs over words, so maybe it's just a wrong question in the first place?)
Well, assuming a strict definition of "possible", it's just determinism; if God's playing dice then "actualism" is false, and if he's not then it's true.
Assuming a useful definition of possible, then it's trivially false.
Looks like yet another argument over definitions.
On LessWrong, we generally use 'possible,' 'necessary,' 'probable,' etc. epistemically. Epistemic actualism, the doctrine that all events that occur have epistemic probability 1 (or approaching 1), is clearly absurd, since it requires that I be mistaken about nothing, and have perfect epistemic access to all facts in the universe. (But, of course, by 'actualism' no one ever means 'epistemic actualism'.)
On the other hand, metaphysical actualism seems quite reasonable; indeed, thee metaphysical non-actualist has a lot of ground to cover in establishing what s/he even means by 'metaphysically non-actual events'. Are non-actual 'worlds' abstract, for instance? Concrete? Neither? Both? Actually existent as non-actuals? Actually non-existent as non-actuals? Meinongian? And how do we gain any epistemic access to these mysterious possibilia? Even if you aren't a Lewisian modal realist, asserting anything but actualism (or, equivalently, necessitarianism) with respect to metaphysical modality seems... spooky.
We can epistemically access possible but non actual worlds by noting that they are not against known laws of nature...what is not impossible is possible.
There are two options for what you're trying to do here:
(1) You're trying to analyze away metaphysical-possibilityspeak in terms of metaphysical-lawspeak. I.e., there's nothing we could discover or learn that would disassociate these two concepts; one is simply an definitional analysis of the other. In which case, we can simply discard the idea of metaphysical possibility, to avoid miscommunication (since most people do not understand it in this way), and speak only of the laws of nature.
(2) You're leaving the concepts distinct, but explaining that it just is the case that 'what is lawful is possible, and what is "against the (natural) law" is impossible', even though this is not synonymous with saying 'what is possible is possible, and what is impossible is impossible'. That is, this is a substantive metaphysical thesis.
If you mean to be asserting (2), the metaphysical rather than semantic thesis (i.e., the non-trivial and interesting one), then I ask: What is your basis for this claim? What is your prior grasp on metaphysical possibility, such that you can be confident of its relationship to natural law? Are the laws of nature themselves contingent, or necessary? What evidence could we use to decide the matter one way or the other?
Because most people do understand it epistemically/subjectively? I think there are many kinds of possibility and many kinds of laws, and different kinds of possibility, and we make judgements about possibility based on lows. The nomologically possible is that which is allowed by the laws of nature, the logically possible is that which is not contradictory, which follows the law of non contradiction, and the epistemically possible is that which does not contradict anything I already know. So I think the kinds of possibility have a family resemblance, and there is no issue of dsicarding the other kinds in favour of epistemic possibility. (I am however happy to deflate a "possible world" into a "hypothetical state of affairs that is allowed by such-and-such laws"). into
No. Most English language speakers use modal terms both epistemically and metaphysically. My point was that most people, both lay- and academic, do not use 'p is (metaphysically) possible' to mean 'p is not ruled out by the laws of physics'. If they did, then they wouldn't understand anthropic arguments that presuppose the contingency of the physical laws themselves.
Then I don't know what claim you're making anymore. Taboo 'law'; what is it you're actually including in this 'law' category, potentially?
But you still haven't explained what a 'merely possible' thing is. If logical and nomological possibility are metaphysical, then you owe us an account of what kinds of beings or thingies these possibilia are. On the other hand, if you reduce logical and nomological possibility to epistemic possibility -- logical necessity is what I can infer from a certain set of logical axioms alone, logical possibility is what I can't infer the negation of from some set of axioms, nomological necessity is what I know given only a certain set of 'natural laws'.... but if we epistemologize these forms of necessity, then we collapse everything into the epistemic, and no longer owe any account of mysterious 'possible worlds' floating out there in the aether.
If that is meant to indicate there is some specific sense of possible that is used instead, I doubt that. Consider the following:
A: "Are perpertual motions machines possible?"
B: "I don;t see why not"
A: "Ah, but theyre against the laws of thermodynamics <explains them>"
B: "Ok, they.re impossible".
A: "But could the laws of phsyics have been different..?"
B: "I suppse so. I don't know what makes them thew way they are".
AFAICS, B has gone through as many of 3 different notions of possibility there.
I don't think there is "mere" possibility, if it means subtracting the X from "something is X-ly possible if it is allowed by X-ical laws".
What they are would depend on the value of X. Family resemblance.
Taboo "possible." My take: in the absence of real physical indeterminism (which I doubt exists), "possible" is basically an epistemic term meaning "my model does not rule this out." So actualism is wrong, on my view, because it projects the limitations of my mind onto the future causal evolution of the universe.
You may doubt that real physical indeterminism exists; others do not. The problem is that communication hinges on shared meanings, so if you change your meanings to reflect beliefs you have and others don't, confusion may ensue.
True; however, even granting physical indeterminism, in most cases we can say that what possibility there is is epistemic. For example, whether katydee wins her fencing match probably does not depend closely on the result of some quantum event. (Although there is an interesting resonance between the probability she assigns to winning, and her actual likelihood of winning - but that's a whole other kettle of worms.)
Or it might be better to use two different words. In fact, (courtesy of Popper IRC), we have "propensity" for objective probabilitty.
That is a well-chosen word.
Good answer.
This is perhaps not the best description of actualism, but I see your point. Actualists would disagree with this part of my comment:
on the grounds that those other universes don't exist.
But that was just a figure of speech. I don't actually need those other universes to argue against 0 and 1 as probabilities. And if Frequentists disbelieve in that, there's no place in Bayes Heaven for them.