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There is usually the notion the we don't require certainty for knowledge. This usually comes through an assessment of probabilities. This is entailed in induction(which are probabilistic), including inference to the best explanation(the most likely explanation).

But to me this would entail a closed-off, certain base. To say, for example, 1/2 or 1/50, entails the 2 or the 50 to be fixed and certain. Even ranges where it is not fixed but certain and known requires this sort of "containment" of the variables. But how can that be justified? All of this, including the framing seems wildly subjective.

Let's say that every day during 10 years the mailman comes around the corner. We can make an inference that the likelihood that the mailman doesn't come this day is 1/3650 or something of that sort. But this assumes the framing is closed, that the proper, objective "measurement" for inference is the days. Maybe, the mailman didn't come because he got sick, so beyond the 1/3650, we would need to include the likelihood of him having a "can't go to work" sick day. Maybe he was battling terminal cancer, and so the likelihood of him dying would have been far greater than the 1/3,650.

This assumes that our everyday understanding of reality and hence our framing of its local conditions for our analysis can be used to determine things. In short, it bakes in a determination upon which the analysis is built. But how can that determination, which ought to be objective, be determined as such objectively and contained? What if frogs start raining, atoms decompose, what if an unknown cosmic anomaly destroys our planet or our Universe? Our model of reality is contained within as a subset within the limits of our imagination, and the possibilities of reality could far outstrip our imagination, including the possibilities within reality that destroy our determination?

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  • "To say, for example, 1/2 or 1/50..." a better Bayesian practice would be to have a prior and posterior distribution over the probability, rather than a point value. This indicates that you don't know it's "true value", in which case the problem of the 2 or the 50 being entailed to be fixed and certain goes away. e.g. the probability that the mailman won't come today is a beta distribution (perhaps using the Laplace correction) that is sharply peaked at zero, but has some non-neglible density for small values. Then integrate out this distribution when making decisions.
    – user6527
    Commented Jul 9 at 12:25
  • "But how can that determination, which ought to be objective" says who?
    – user6527
    Commented Jul 9 at 13:01
  • Indeed there're various kinds of uncertainty in reality and we usually use credible interval or confidence interval to quantify uncertainty after we infer some point estimate of your concerned probabilistic model's parameter, or if you stay with the posterior distribution then there're still many statistical metrics applied to empirically validated representative tests such as divergence, distance, error rate, MSE, etc to quantify such gap corresponding to reality...
    – Double Knot
    Commented Jul 10 at 5:27
  • @DoubleKnot Thank you for the response, but I guess I am still not understanding how can we justify the confidence in such tools. If we take them as created tools, they would be contingent upon our access to reality as such and for reality as such to be in such a way to correspond confidently with those tools. But how can we justify that?
    – Sismetic
    Commented Jul 11 at 0:37
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    @DoubleKnot I work at home on the computer and have no life :D
    – Sismetic
    Commented Jul 13 at 20:31

2 Answers 2

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Probability is a means of dealing with situations where we don't have full knowledge (say of initial conditions, or the exact specification of the problem) by treating the uncertainty as if it were due to randomness. It isn't clear whether anything in the real world is truly random, Bell's experiment does not quite rule out the quantum world being deterministic, so in the majority of cases (e.g. flipping a coin, rolling a die) the "randomness" is illusory - the system is completely deterministic.

So if we are talking about probabilities, we are not talking about reality, we are talking about a model of reality that we have constructed. GEP Box wrote

"All models are wrong, but some are useful"

By "wrong" he meant all models are necessarily simplifications of reality, we need the simplification for the model to be tractable. A model of the universe that is as complicated as the universe would give us a perfect simulation of the real universe, but it would be of no use in understanding the real universe as it would be no easier to understand the model than understanding reality itself.

By "but some are useful" he meant that in some cases as simplified model is a good tool for understanding some aspect of reality, or predicting it's behaviour with useful accuracy.

SO it depends on how accurate you want your model of the mailman to be. You could have a very simple probabilistic model, starting from a uniform distribution on the probability before you have met them, and updating that every day, using Bayes rule, according to whether they turned up or not. Or you could make a computer simulation of the mailman (c.f. "The Matrix") and their environment down to the atomic/quantum level. That would probably be overkill, so something in the middle perhaps?

"But how can that determination, which ought to be objective"

Define what you mean by "objective"? Probability is used to encode a state of knowledge about something. In that situation the meaning of "objective" is somewhat nuanced, and is likely to have a technical/jargon meaning.

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  • I think that the very idea of a random(in my lay understanding) reality is just nonsensical(by definition). But the problem persists, in my view, and although there are ways to work around the issue, it remains an issue. As I understand your answer, you are implying that the conceptualization of reality needs not match reality as such but that some sense can be derived of it, namely some idea of reality or utility, but that is what I'm problematizing. The issue is not the complexity or simplicity, but the reliability. A pragmatic approach assumes its own axioms and its own truth.
    – Sismetic
    Commented Jul 9 at 22:19
  • I accept the view that the models can be a simplification, but are they reliable? Those are different questions. And assuming reliability due to usefulness already does assume usefulness, justification that is being problematized. > Define what you mean by "objective"? I see. With this I merely mean "corresponding" with reality, even if imperfectly, or analogously(as per your simplification modeling). If I determine X, then X needs to be determined. Even if I determine quasy-X(X-like), then X-like is determined in reality in order for my model to correspond to reality.
    – Sismetic
    Commented Jul 9 at 22:22
  • "As I understand your answer, you are implying that the conceptualization of reality needs not match reality" the point is that we fundamentally cannot conceptualise reality in all of it's detail - firstly because our (even collective) brains are finite and because some of the required information is not available to us (e.g. what is inside a black hole). All we can do is to understand it as best we can at some level of abstraction.
    – user6527
    Commented Jul 10 at 9:04
  • What do you mean by "reliability"? Whether a probabilistic model is reliable will vary from model to model and depends on the problems the model is intended to address. There will always be irreducible uncertainty, whether that makes the model unreliable is not something that you can make blanket statements about. At the end of the day, you have to rely on the best model(s) (understanding(s)) you have, and be aware of the uncertainties involved, there is nothing else you can do,
    – user6527
    Commented Jul 10 at 9:07
  • The degree to which a model is "objective" in the sense you have explained again will vary from model to model and will depend on how it is constructed and on what knowledge/evidence was available from which to construct it. I don't think you can make useful generalisations about it.
    – user6527
    Commented Jul 10 at 9:09
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What if frogs start raining

It is not about imagination, of course in some sense everything is possible: it is about trusting the uniformity/regularity/rationality of Cosmos as a whole, and that it is not just playing tricks on us. And the point, put simply, is: such a trust, aka an inductive attitude, is the only attitude that actually makes sense... (for us, see the last paragraph.)

Indeed, induction (as in inductive reasoning, not as in mathematical induction) is not probabilistic reasoning, which itself is just yet another mode of deduction. As for a "justification of induction", the last two chapters of P.F. Strawson, Introduction to Logical Theory, are exactly about what "inductive reasoning" actually is, how asking for a "justification" is in fact senseless, and even how all other modes of reasoning are actually founded on induction.

Also, relevant for a properly philosophical but also sociological perspective: D.C. Williams, The Evils of Inductive Skepticism.

That said, for an even broader context, I shall mention that a "problem of induction" is especially pertinent to western philosophy (and culture and society) and the specific form in our culture taken by the primality of reason as a tool for understanding. Via Socrates we inherit from eastern traditions the way (to liberation and wisdom) of the mind, as opposed to the way of the heart or the way of the body (see e.g. the three forms of Yoga). Later Socrates is "rejected", in practice we progressively lose the holistic and (immanently) spiritual connections, which is the beginning of an era of "separation", where "(the problem of) induction" is the modern name for the specific "problem/mode" of a specific way of understanding and action, the western way essentially, at the stage at which it happens to be. -- In my understanding: anyway hoping this gives some more coordinates.

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  • > it is about trusting the uniformity/regularity/rationality of Cosmos as a whole But what justifies this trust? As it stands, this seems like an existentialist approach of faith(postulating the existential requirement of hope, or a correspondence between Absolute or reality as such and the individual despite the human finitude). Will look for the Strawson book. As per williams article, I found it really interesting, thank you, but I think it fails
    – Sismetic
    Commented Jul 9 at 22:23
  • The reason why I think it fails(at resolving my doubts) is that, as I understand it(and correct me if I'm wrong), beyond the rhetoric(which I don't object to), is a question begging assertion that the loss of induction leads to absurdity. Of course, this is already an inducted reasoning and so question begs. But beyond this question begging, hides maybe the issue that the autonomous process of reason is self-undermining. Williams does not seem to provide the ground other than say a lack of ground is untenable. Which I can agree with but doesn't resolve the issue as to the nature of it.
    – Sismetic
    Commented Jul 9 at 22:26
  • In some sense, it reminds me of the notion that undermining ethics leads to a loss of the political and similar arguing from the consequences. Which, of course does not address the issue of grounding ethics or how to ground ethics or what does this condition tells us of ethics(or induction). But there's another pressing issue: even if we were to grant induction in the general, we still need to justify EACH specific induction as justified and we cannot do so by appealing to a general justification. Yet this problem also remains unsolved as far as I can tell
    – Sismetic
    Commented Jul 9 at 22:30
  • It is not unsolved, it is indeed a false problem and you are talking cheap nonsense. But of course, if we have a right, beside that of polluting and appropriating, it's the right to talk nonsense... Indeed, good luck with that, you too, and EOD.
    – Julio Di Egidio
    Commented Jul 11 at 4:58

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