More generally though, on this topic of the laws of nature not changing: that is not something we believe because of induction, but something we must believe to do induction. If we don’t assume that that’s the case, then there is no reason to expect patterns to continue as we have seen them do thus far. — Pfhorrest

I disagree: It seems obvious we believe in an invariant law-like nature because that is all we have ever experienced; that's induction in a nutshell. That's not even an arguable point as far as I am concerned. If there were not universal invariant patterns in nature science would be impossible; human life, any life, any stability at all, would be impossible. If you disagree with that, then I can only wonder what planet you've been living on.

So we can know that induction works (that we can extrapolate patterns into the future) because it always has before, so we can extrapolate that pattern into the future?

(If it's not clear, I'm pointing out that that's circular reasoning, which is the root of the problem of induction, and the post you're responding to is my solution to that problem).

Meh. You should keep in mind that circular arguments are perfectly valid.

In pointing to the problem of induction, Hume was just highlighting the fact that induction is not deduction; that there is nothing logically necessary about the laws of nature.

So we can know that induction works (that we can extrapolate patterns into the future) because it always has before, so we can extrapolate that pattern into the future? — Pfhorrest

So, this is where your thinking is going astray as I see it. Of course we don't know, in the sense of being deductively certain, that the laws as we have discovered them will not change, but, based on all our experience, we have confidence that they will not change.

The kettle will boil when I put it on the hotplate - unless something else happens, such as not turning the power on.

Denying induction is also irrational.

There is some scholarly disagreement about what exactly Hume's point was, but the widely-held interpretation is that it means that unless the problem of induction can be surmounted, induction does not provide any reason whatsoever to believe anything.

From the SEP article I just linked:

Hume’s argument is one of the most famous in philosophy. A number of philosophers have attempted solutions to the problem, but a significant number have embraced his conclusion that it is insoluble. There is also a wide spectrum of opinion on the significance of the problem. Some have argued that Hume’s argument does not establish any far-reaching skeptical conclusion, either because it was never intended to, or because the argument is in some way misformulated. Yet many have regarded it as one of the most profound philosophical challenges imaginable since it seems to call into question the justification of one of the most fundamental ways in which we form knowledge. Bertrand Russell, for example, expressed the view that if Hume’s problem cannot be solved, “there is no intellectual difference between sanity and insanity” — SEP

Denying induction is also irrational. — Banno

If you mean that there can be no reason to think one way or the other about induction, then I pretty much said exactly that at the end of the previous page:

These are things like the assumption of objectivity about which we could not possibly know one way or the other whether they are true, but which we cannot help but assume one way or the other through our actions, and without the assumption of which we could not possibly hope to ever know anything, thus pragmatically requiring us to always act as though they are true or else give up all hope of knowledge. — Pfhorrest

If you mean that there can be no reason to think one way or the other about induction... — Pfhorrest

No, I mean that induction as such works. You and I use it to make tea.

And that's the problem with this thread, and the OP. Explaining things that do not need explanation.

Explaining things that do not need explanation. — Banno

To people who already agree, sure. But what of those who disagree, like Hume does on induction? Just let their arguments go unaddressed, instead of refuting them?

I'd really like to take "this is obviously true" as a compliment, but people like you seem to want to make it an insult.

But what of those who disagree, like Hume does on induction? — Pfhorrest

Well, first off, Hume uses induction extensively in his writing. Funny, that, if he thought as you do.

And then...

If anyone said that information about the past could not convince him that something would happen in the future, I should not understand him. One might ask him: what do you expect to be told, then? What sort of information do you call a ground for such a belief? … If these are not grounds, then what are grounds?—If you say these are not grounds, then you must surely be able to state what must be the case for us to have the right to say that there are grounds for our assumption….

Every time I put the kettle on, the water boils. What more could you ask for, by way of 'addressing the argument'? What place has doubt here?

Your program wants to reduce induction to deduction. Why bother?

Your program wants to reduce induction to deduction. — Banno

It does not, and I have repeatedly said as much.

It just doesn't rely on induction for the task of differentiating between competing beliefs.

Induction is a fine way of coming up with beliefs. But induction on the same set of observations may come up with different beliefs. (And non-inductive processes may result in still other beliefs too). How then to choose between them? That's the issue at hand here.

Did you see this video I linked earlier?



Everyone there is using induction to come up with their hypotheses. All of their hypotheses are consistent with the data. But they're all different hypotheses. And they're all wrong, until someone finally catches on to try seeing what doesn't fit the data, and figures out the correct solution.

Also, you get that I'm not arguing against induction at all? The bit of my past post I just quoted ended, in case you didn't read to the end:

...pragmatically requiring us to always act as though they [things like induction] are true or else give up all hope of knowledge — Pfhorrest

Did you see this video I linked earlier? — Pfhorrest

Sure. There's a whole literature around rule following that derives from PI, and then again from Kripkenstein, that makes a related point.

Notice, though, that in your example there is a single correct answer - that chosen by your pundit. That's an unusual case. More often there is more than one answer that gets us to where we want to be, and the choice is rather arbitrary.

Sure looking for contradictions is a neat way to refine your beliefs.

But it ain't the whole story.

Come back to the basic point; Polly put the kettle on in order to make tea. She did not put it on in order to test an hypothesis. There was no doubt that putting the kettle on the heat would boil the water. Nor should there have been.

Come back to the basic point; Polly put the kettle on in order to make tea. She did not put it on in order to test an hypothesis. — Banno

I addressed exactly that difference in the last paragraph of the OP:

In general, I hold, we should tentatively adopt more specific and so risky beliefs when we can afford to risk being wrong, but when we cannot afford that risk, we should act in accordance with those beliefs that have the greatest probability of being true. — Pfhorrest

So sure if you're just trying to make tea, not test a hypothesis, then roll with the belief that's more probably correct, so you don't mess up your tea, even though you might possibly learn something by messing up your tea.

I addressed exactly that difference in the last paragraph of the OP: — Pfhorrest

Yeah, no, that does not address the issue. Polly's belief was not at all tentative.

Polly's belief was not at all tentative. — Banno

So she is not at all open to the possibility that it could be wrong, if she should see something that would show it wrong? She believes that dogmatically? Because the contrary to that is precisely what "tentative" means in that context: not dogmatic.

In any case, the "tentative" there wasn't even in reference to the "safe" beliefs like Polly's, but to the "risky" beliefs of someone who was testing a hypothesis rather than making tea. Can you not read more than half a sentence at one?

It can be amusing to watch someone defending their theory against obvious falsification.

So she is not at all open to the possibility that it could be wrong... — Pfhorrest

Did she contemplate the kettle sitting on the heat and yet not boiling? What do you think?

She believes that dogmatically? — Pfhorrest

Well, yes; and indeed, she was correct to do so, as evidenced by the need for Sukey to take the kettle off again.

Again, it would have been irrational, unreasonable, improper, even crazy, for her to doubt that the kettle would boil.

Yet you would make such doubt the cornerstone of epistemology.

It can be amusing to watch someone defending their theory against obvious falsification. — Banno

I wish I could say it was amusing to watch someone selectively read and willfully misinterpret so as to score cheap internet points instead of having an honest conversation, but reality it’s just petty and irritating.

For instance:

Again, it would have been irrational, unreasonable, improper, even crazy, for her to doubt that the kettle would boil.

Yet you would make such doubt the cornerstone of epistemology. — Banno

If you actually read anything in this thread at all, you would see that fully half of my point is against the same greedy skepticism you’re arguing against here.

I didn’t ask if she doubted it, and I didn’t say she should. I asked if she would have been open to revising her belief had there counterfactually turned out to be evidence against it. Because that’s all that “tentative” means, and “dogmatic” is the opposite of that.

You are conflating dogmatism with what I call “liberalism”, and also conflating “critical” skepticism with “cynical”skepticism, exactly as I said opponents to the OP would mistakenly do.

You put up a theory for critique - and when it is critiqued, cry foul.

No pleasing some folk.

And that strategy of claiming that you have already addressed the issues raised - might work were you a philosopher of note. But that you ain't.

You put up a variation on Popper. I put up the very arguments that undermined his philosophy: Feyerabend, Wittgenstein, Strawson. You haven't addressed them.

I had thought you might be interesting. But no. OK, I'll go back to ignoring your posts.

Addenda - twenty odd years ago I would pretty much have agreed with you. But I was wrong.

I have addressed everything put forth. Me being of note or not is of no relevance. And just because other have come after and disagreed with Popper doesn’t make him conclusively refuted.

I have no problem with actual criticism of my position, if you've actually got something new to add that I haven't already accounted for. And I have absolutely no problem with people being unpersuaded by my arguments; I generally don't expect anyone to ever be persuaded by anyone.

The only thing I’m getting tired of is people attacking positions I don’t hold as though they were disagreeing with me, often by using points I already agree with myself. And when I point out that that’s not my position they’re attacking, and that I already agree with the points they have against that strawman, I’m accused of “digging in my heels”, “reiterating the same claims with no further argument”, “not addressing counter arguments”, etc. I generally feel like I'm faced with people seemingly offended that I’m not persuaded by their arguments to abandon the position that I never held in the first place, in favor of their position that I already agreed with.

TL;DR: I'm not bothered that anyone disagrees with me. I'm bothered that people seem bothered that I (they think) I disagree with them. Like the only thing that would make them happy is if I just said "ok you're right" and shut up, no responses allowed.

You’re the only one bringing up any belief about being able to predict the future perfectly. That’s not anything I’m talking about at all. — Pfhorrest

Except that...

I’m saying that if you see something and think “whoa a black swan, I didn’t think those were possible...” — Pfhorrest

is exactly that, a prediction about the future - that there would be no observations of black swans in it.

If instead you see the same thing and think “oh look, somebody painted that swan black...” then you don’t have to revise any beliefs because a fake black swan is what your background beliefs initially lead you to perceive and that doesn’t contradict any other beliefs such as that all swans are white. — Pfhorrest

Again, you're ignoring the effect of states of uncertainty. I know you keep saying that you've included uncertainty by attaching the word 'probably' to your original theses, but tacking on the word 'probably' doesn't even begin to address the complexities of adding probability and uncertainty (or it's opposite) to the understanding of beliefs. What I think just about every other person involved in this thread is trying to tell you (in one way or another) is that situations where we are in no doubt (such as @Banno is pointing out), and how we resolve uncertainty when we are in doubt (such as @Janus and @Srap Tasmaner are discussing), are key to understanding beliefs.

You treat them as if we can innumerate and resolve them one at a time (again, despite your protestations to the contrary, you keep coming back to simple examples as if they encapsulated a principle which applied more widely). In the situation regarding the observation of a black swan - if you isolate the observer from all social connections, all linguistics, all embodiment and all cognitive context - it may just be the case that he would simply choose between the two options you describe. But there are no such people, and in reality the situation is vastly more complex to a point where this simple algorithm is next to useless.

...Not that it matters now, but

I’m saying that if P(A) is small and P(B) is small then P(A)*P(B) is small. “P(A)*P(B)” is the probabilistic equivalent of “A and B” in the same way that “P(A|B)” is the probabilistic equivalent of “A if B”. — Pfhorrest

...is exactly what I said you were doing (incorrectly), so that paragraph shouldn't start with "No", it should start with "Yes" followed by an explanation of why you're doing that when A and B are not independent variables and you were supposed to be explaining how such matters were resolved using Bayes.

is exactly that, a prediction about the future - that there would be no observations of black swans in it. — Isaac

So you think that nobody holds any categorical beliefs like that, even defeasibly, such that they could find out that such beliefs were wrong when they observed something that was unexpected according to such a belief? Nobody can ever be wrong, because nobody ever has any expectations of how the future will turn out?

Again, you're ignoring the effect of states of uncertainty. I know you keep saying that you've included uncertainty by attaching the word 'probably' to your original theses, but tacking on the word 'probably' doesn't even begin to address the complexities of adding probability and uncertainty (or it's opposite) to the understanding of beliefs. — Isaac

I never said that just tacking on the word “probably” solved everything, that’s just the natural way of casually conveying in normal language the gist of the actual statistical math that needs to be done on the ground. What else besides “If A is true then B is probably true” would be a natural-language way of conveying the meaning of something like “P(B|A) is close to 1”?

You treat them as if we can innumerate and resolve them one at a time (again, despite your protestations to the contrary, you keep coming back to simple examples as if they encapsulated a principle which applied more widely). In the situation regarding the observation of a black swan - if you isolate the observer from all social connections, all linguistics, all embodiment and all cognitive context - it may just be the case that he would simply choose between the two options you describe. But there are no such people, and in reality the situation is vastly more complex to a point where this simple algorithm is next to useless. — Isaac

You’re ignoring that one of those two options is the extremely broad “or something else that I’m assuming, which leads me to believe this is a black swan I’m seeing, is false”. There are lots of (perhaps infinitely many) possibilities embedded in there. All the complexity you say I’m ignoring is in there.

The point is simply that if all your beliefs tell you that you’re seeing something that’s impossible (or improbable), then that combination of beliefs is impossible (or improbable), so you should (probably) change those beliefs, somehow. I’m not saying here how exactly you should, just that you should.

Your program wants to reduce induction to deduction. — Banno


It does not, and I have repeatedly said as much.

It just doesn't rely on induction for the task of differentiating between competing beliefs. — Pfhorrest

Yes, but it does use an extensive interrelated network of inductively derived beliefs without which it would be operating in a vacuum, and be unable to confirm or dis-confirm any hypothesis. So, given that, it doesn't make sense to minimize the role of induction, and claim that is is really just falsification doing all the work.

So we can know that induction works (that we can extrapolate patterns into the future) because it always has before, so we can extrapolate that pattern into the future?

(If it's not clear, I'm pointing out that that's circular reasoning, which is the root of the problem of induction, and the post you're responding to is my solution to that problem). — Pfhorrest

This response shows again that you are trying to apply the criteria for valid deduction to inductive reasoning. It puzzles me that you apparently can't see that.

More generally though, on this topic of the laws of nature not changing: that is not something we believe because of induction, but something we must believe to do induction. If we don’t assume that that’s the case, then there is no reason to expect patterns to continue as we have seen them do thus far. — Pfhorrest

This again shows that you are not acknowledging the role of induction. The general regularities of nature that we all observe, and never consistently observe any counterexamples to, and are thus induced (induction) to believe in must persist, because otherwise there would be no science, no human life, no life at all, and thus certainly no falsification.

Yes, but it does use an extensive interrelated network of inductively derived beliefs without which it would be operating in a vacuum, and be unable to confirm or dis-confirm any hypothesis. So, given that, it doesn't make sense to minimize the role of induction, and claim that is is really just falsification doing all the work. — Janus

It operates ON that network of beliefs, or any other network of beliefs formed in any other way; it doesn’t at all depend on the network of beliefs being formed by induction.

I was just thinking earlier today that even as much as I dislike Feyerabend overall, my principle of “liberalism” is actually most of the way to his “epistemic anarchism”, in that it says that any method for coming up with beliefs is fine, there is no prescribed method that you have to follow in order to be initially permitted to hold a belief. But on my account there is still the requirement that you be open to revising any beliefs, however you formed them, and not hold any of them beyond all question.

I’m not super well versed on Feyerabend, so I might be wrong about this, but I suspect he would agree with that last caveat as obvious and not at all against his point, which makes me now wonder if his whole point wasn’t just basically the same as my “liberalism”, and maybe I should give him another more charitable reading.

This response shows again that you are trying to apply the criteria for valid deduction to inductive reasoning. It puzzles me that you apparently can't see that. — Janus

I’m not using deduction there at all. Induction has seemed to work many times in the past, so inductively that should give us some (but not deductively certain) reason to think that induction will always work. If that not your argument? Does not that argument rely on already accepting that inductive reasoning gives some reason to believe something, in order to show that inductive reasoning gives some reason to believe something? Is that not circular, even though no deduction is involved?

This again shows that you are not acknowledging the role of induction. The general regularities of nature that we all observe, and never consistently observe any counterexamples to, and are thus induced (induction) to believe in must persist, because otherwise there would be no science, no human life, no life at all, and thus certainly no falsification. — Janus

I agree that we have to assume the universe obeys regular laws in order to get anything done, but I think that that practical reason is enough to justify assuming that, even if we hadn’t yet noticed any particular lawlike patterns yet. That assumption is in turn necessary to do induction — which is the whole Humean problem of induction, because he shows that it can’t be inductively proven without circularity and it can’t be deductively proven. I think the solution to that problem is that it can be pragmatically “proven”. You on the other hand just run around one circle of Hume’s fork.

It operates ON that network of beliefs, or any other network of beliefs formed in any other way; it doesn’t at all depend on the network of beliefs being formed by induction. — Pfhorrest

Without that network of beliefs there would be nothing to operate upon. Even when a creative leap of the imagination is involved in coming up with novel hypotheses, that is only possible on the background of the general inter-subjective inductively derived network of knowledge that we accept as established.

Does not that argument rely on already accepting that inductive reasoning gives some reason to believe something, in order to show that inductive reasoning gives some reason to believe something? Is that not circular, even though no deduction is involved? — Pfhorrest

Sure, it looks circular, but it's not really because the premises (what you invariably observe) don't assume the conclusions (what you generalize from those observations), You don't have to believe that the laws of nature will not suddenly change, but you do have good reason not worry about such a seemingly small (given the totality of human experience) possibility.The problem with circular deduction is that it tells you nothing. Induction however, tells you everything you know (or believe, if you prefer) about the world.

My point is that we do, and must, accept inductive reasons to believe things. You said earlier that Hume has refuted induction, but as @Banno noted he uses inductive reasoning in his writings; cf. A Treatise of Hum(e)an Nature :wink: ; just think about what that title implies.

That assumption is in turn necessary to do induction — which is the whole Humean problem of induction, because he shows that it can’t be inductively proven without circularity and it can’t be deductively proven. I think the solution to that problem is that it can be pragmatically “proven”. — Pfhorrest

Right it can't be deductively proven, but circularity is not a problem for inductive reasoning, because it is based on observation and experience which is not merely a matter of the premises assuming the conclusion. We accept experience and observation because we must; there simply is no other way to gain the material from which we can extrapolate our hypotheses about the way the world is and works.

It makes no sense to say that anything can be pragmatically proven, not if you are thinking of "proof" in the deductive sense at least, because none of nature's invariances are logically entailed by anything. Although having said that, and as I said earlier, without the regularities of nature there would be no network of beliefs or hypotheses, no human life, no life at all, and that we are here living, believing, hypothesizing does entail those regularities, but that entailment is material, not logical.

Without that network of beliefs there would be nothing to operate upon. — Janus

Sure, I never disputed that.

Sure, it's circular, but that doesn't matter for inductive purposes, The problem with circular deduction is that it tells you nothing. Induction however, tells you everything you know (or believe, if you prefer) about the world. — Janus

IF induction works, which you would have us believe on the grounds that “it aways has worked”, which would only be reason to believe induction worked if you already believed indiction worked.

I am not rejecting induction here, I have my own solution to the problem of induction I’ve already given, I’m just pointing out that your solution doesn’t work as an argument. If you were to argue to someone who doesn’t believe in induction that it always has worked so we should expect it to keep working, they would only be persuaded by that if they ALREADY believed in induction, which they don’t. That’s the heart of the circularity: it’s not convincing to someone who doesn’t already agree.

You said earlier that Hume has refuted induction — Janus

No I didn’t, I said that he presented the Problem of Induction, which needs to be addressed. I think it can be, and I think I know how. It seems like Hume must have figured there must be some way, because he like everyone acts like induction works, but didn’t know how exactly to give reason to think it would.

We accept experience and observation because we must; there simply is no other way to gain the material from which we can extrapolate our hypotheses about the way the world is and works. — Janus

This is a pragmatic argument much like my own, not a circularly inductive one.

It makes no sense to say that anything can be pragmatically proven — Janus

That’s why I put “proven” in scare quotes. Hume talks about “demonstrative” (deductive) and “probable” (inductive) arguments, and shows how neither kind can give reason to believe in induction (e.g. to convince someone who doesn’t already believe in it). I instead give, and above you seem to give, a pragmatic argument, a reason why we must act on the assumption, even though it’s not possible to prove it either way, because to do otherwise would simply be to give up.

But none of that has anything to do with anything I’m talking about in the OP.

IF induction works, which you would have us believe on the grounds that “it aways has worked”, which would only be reason to believe induction worked if you already believed indiction worked. — Pfhorrest

Induction obviously does work; to give us all our beliefs and understandings of the world. So, there is no need to provide an argument for that. Are you denying that induction has worked, or what? The problem is that it is not at all clear just what you want to argue. Every time someone critiques what they think you are claiming, you say 'no, it's not that', and yet you seem to be incapable of explaining what else it is you are trying to convey.

I said that he presented the Problem of Induction, which needs to be addressed. — Pfhorrest

Yes, and the problem of induction as I understand it, according to Hume, is that it cannot deliver deductive certainties. if we don't erroneously expect it to do that, the problem dissolves. So you are falling into the trap of thinking that induction is some kind of problem; presumably because it cannot deliver deductive certainty. If you have some other reason for thinking it a problem, you are yet to present it.

Induction obviously does work; to give us all our beliefs and understandings of the world. So, there is no need to provide an argument for that. — Janus

"It's obvious" is not an argument, and you do need an argument if you want to convince anyone who doesn't agree with you to change their minds.

Are you denying that induction has worked, or what? — Janus

No, I've been saying all along that induction is just fine, it simply has nothing to do with the point of this thread. I was never arguing against induction as a means of coming to our beliefs, only that by itself it doesn't give us a way of choosing between competing beliefs, and that it's not necessarily the only way of coming to believe things either. (And for my purposes it doesn't matter whether it is or isn't the only way, because my methodology is okay with any ways of coming to believe things, so long as you leave them open to falsification).

Every time someone critiques what they think you are claiming, you say 'no, it's not that', and yet you seem to be incapable of explaining what else it is you are trying to convey. — Janus

I think it's because I'm really saying very little at all here, and everyone seems to think I'm saying much more than I am.

I'm saying first of all that within some very broad limits, anything is okay. Those limits are:

- don't demand absolute proof of anything before allowing yourself (or others) to believe it, go ahead and believe things for whatever reason you're inclined to (induction or whatever else);

- so long as everything you believe, you believe tentatively, fallibly, non-dogmatically, in a way such that you would discard that belief if you came across reason to do so.

(I expected that on a philosophy forum, philosophy being traditionally a reason-centric enterprise, everyone would take the latter as a given, except maybe some religious folks; and the former would be the point of contention, from self-identified "rational skeptics" who don't realize that that methodology applied consistently would leave nobody able to ever learn anything at all).

And then I'm saying as a consequence of that broad approach, hypothetico-deductive confirmationism has no legs to stand on, because:

- just seeing an expected consequence of your belief can't give you any more justification than you already had to continue believing it (because you were already perfectly well-justified in believing it, for whatever reasons you already did);

- and it doesn't necessarily rule out any of the alternatives (and in the cases where it does, that's falsification right there, so the only the cases where such confirmationism works are the cases where it's indistinguishable from falsificationism).

the problem of induction as I understand it, according to Hume, is that it cannot deliver deductive certainties. — Janus

As I understand it, the problem is not only that it can't deliver certainty, but that there's no good reason to think it would deliver any support at all, even merely probabilistic support.

We all naturally act like it does, Hume included, but Hume noted that if we really question whether we should or shouldn't act like that, there's no way of presenting an argument that we should, because that argument would either have to rely on us already thinking that we should (in relying on an inductive argument to argue for relying on inductive arguments), or else require that its negation be self-contradictory (which it's just not). That doesn't (even supposedly) prove that induction doesn't work, only (supposedly) that there can be no good explanation as to why we should expect it to work.

You, like I, have been arguing that we pragmatically have to expect it to work (or rather, in my case, why we should expect the universe to behave in a lawlike way, which is a prerequisite for induction working), or else we can't get any kind of science done. Elsewhere I've fleshed out a more rigorous version of that kind of argument, and I think that that's a fine reason to expect the universe to behave in a lawlike way. I don't know why you think a circular argument for induction that relies on induction is even necessary, given such practical lines of argument, never mind how you don't see why they don't work.

"It's obvious" is not an argument, and you do need an argument if you want to convince anyone who doesn't agree with you to change their minds. — Pfhorrest

But it is obvious that induction has worked; there is no more need of argument for that than there is to justify saying the sun has always risen on earthly life.

No, I've been saying all along that induction is just fine, it simply has nothing to do with the point of this thread. I was never arguing against induction as a means of coming to our beliefs, only that by itself it doesn't give us a way of choosing between competing beliefs, and that it's not necessarily the only way of coming to believe things either. — Pfhorrest

Can you give an account of any other means of arriving at confirmable/ dis-confirmable beliefs than induction? You haven't so far. Can you give an example of two competing beliefs, and explain how induction would not be at all involved in deciding between them. Just one example will suffice.

- don't demand absolute proof of anything before allowing yourself (or others) to believe it, go ahead and believe things for whatever reason you're inclined to (induction or whatever else);

- so long as everything you believe, you believe tentatively, fallibly, non-dogmatically, in a way such that you would discard that belief if you came across reason to do so. — Pfhorrest

Yes, of course we shouldn't demand absolute proof of anything before believing it; that is very the nature of induction, that is just how it differs from deduction. There cannot be any absolute proof of any belief about empirical matters.

It is only in relation to empirically induced beliefs that any inter-subjectively corroborable reasons to discard the belief can be encountered. Other kinds of belief; aesthetical, ethical or metaphysical are discarded, if they are, for personal reasons; there can be no inter-subjectively definitive reasons in those cases. By that I mean there can be no reasons that a suitably educated unbiased observer would be bound to accept.

As I understand it, the problem is not only that it can't deliver certainty, but that there's no good reason to think it would deliver any support at all, even merely probabilistic support. — Pfhorrest

That's where we definitely do disagree. I think that the constantly observed regularities of nature and the complete lack of observed counterexamples, give us every reason to think that belief in those regularities and their highly likely continuance is justified; in fact there simply couldn't ever be any better reason than that.