Tal's epistemology (and DCP's)

[_Ren]

Well, I said I was going to wait, but I blatently lied!

Every inductive argument, he says, has an unstated, but no less crucial for that, premise. So, take the following inductive argument:

Premise 1: The sun has always risen in the morning;
Conclusion: The sun will rise tomorrow morning.

This argument should be recast, in Hume's view, as follows:

Premise 1: The sun has always risen in the morning;
Premise 2: Nature is uniform (I.e., these past observed sunrises are the result of physical laws which will never cease operation);

Conclusion: The sun will rise tomorrow morning.

I think I get the argument, and I'll take your word for it that - in Hume's view - it's all about reaching a conclusion that 'Nature is uniform' (do you have a direct quote from Hume on this point...? Not that it's central to anything, I'm just curious).
But for me, I don't' see the need to bring in the uniformity of nature as the 'reason' why we can't say - with 100% surety - that 'the sun will rise tomrrow'. Nor to question the principle of 'induction'.

Nature may well be uniform. But that still doesn't 'guarantee' that the sun will rise tomorrow. Nature could well be uniform, but the statement 'the sun will rise tomorrow' could still turn out to be false.
How would that be possible? Well - the possibilities are endless really. As endless as our imaginations.
It's always easy to 'blame it on the aliens', so I'll do just that! An alien race comes along, sees our star and - like a redneck who sees a deer - thinks 'Ohh - I'd like to shoot that'. And then - taking out their Death-Star, they blow the thing to smithereens.
I mean, forget the the fact that approx. 8 minutes later, us humans won't care one way or the other whether the sun rises tomorrow or not. Either way, the sun can no longer 'rise' over anything.

Is it gonna happen? Not a gnat in hell's chance. But that's the point. We still call it a 'chance'. Not a certainty, but a 'chance'.
If some betting shop were dumb enough to place odds on 'whether the sun will rise tomorrow' (that wasn't some trick based around whether it could be 'seen' to rise - cloud cover etc.), then of course I'd bet all I own in it. I'd dig into my life savings. I'd sell off everything I could. And put it ALL on that bet. And I'd collect. And feel very 'clever'.

So then that takes us to the question: 'What is the difference between saying "The sun WILL rise tomorrow", and saying "The sun is almost certainly going to rise tomorrow?"
Well - in practical terms - I'd argue there is no difference. Both people will act in the same way. Neither will spend anytime worrying about the 'possibility' that the sun won't rise tomorrow.

The only difference I'd note and identify is that one may well take the philosophy of science 'seriously'. And the other may well not. in my opinion.
But if it's reasonable to be convinced otherwise, I certainly hope I can be...

And in any case, even if the rejection of 'induction' to produce 'ultimate truth' is incorrect, I still can't see how it would lead to the conclusion 'We don't know any more now than we did 500 years ago..!'. Even if induction is rejected (at least to it's ultimate conclusion), I still don't see how that attitude ends up with that summary...

[_A Light in the Darkness]

I, for one, can't wait for Tal to solve the problem of induction.

[_A Light in the Darkness]

RoP -

Hume pointed out that Nature has to be stable in order to be able to infer from some observations a general rule. This means the past has to resemble the present, the laws of nature cannot change indiscriminately, and so on. Nature has to be uniform or, as we would say today, regular. Think about how you infer the Sun will probably rise tomorrow from the fact that it has in the past. That implicitly requires you to think that reality today will be like yesterday: that your experience of nature is a representative sample of how nature is. If the laws of physics were just as likely to be something else as they are what they are in a second, then you would have no basis to think the sun will probably rise tommorrow. Hume, correctly, pointed out there is no logical necessity that Nature is uniform. The present need not resemeble the past. And an inductive justification of this just trivially begs the question as the uniformity of nature already figures as a premise in any inductive argument. We have no justification that this is the case. So, therefore, induction itself remains unjustified. If necessary, I can come up with some concrete hypothetical conversations to help you understand this.

Hume wasn't a radical skeptic though. He plainly accepted induction even if he didn't solve the metaphysical problem. There has never been an adequate response to the problem of induction. This is widely accepted, but science hasn't ground to a hault.

The contemporary form you are likely to hear discussed is Goodman's "green and grue."

[_Ren]

Hume pointed out that Nature has to be stable in order to be able to infer from some observations a general rule. This means the past has to resemble the present, the laws of nature cannot change indiscriminately, and so on. Nature has to be uniform or, as we would say today, regular. Think about how you infer the Sun will probably rise tomorrow from the fact that it has in the past. That implicitly requires you to think that reality today will be like yesterday: that your experience of nature is a representative sample of how nature is. If the laws of physics were just as likely to be something else as they are what they are in a second, then you would have no basis to think the sun will probably rise tommorrow. Hume, correctly, pointed out there is no logical necessity that Nature is uniform. The present need not resemeble the past. And an inductive justification of this just trivially begs the question as the uniformity of nature already figures as a premise in any inductive argument. We have no justification that this is the case. So, therefore, induction itself remains unjustified. If necessary, I can come up with some concrete hypothetical conversations to help you understand this.

Hume wasn't a radical skeptic though. He plainly accepted induction even if he didn't solve the metaphysical problem. There has never been an adequate response to the problem of induction. This is widely accepted, but science hasn't ground to a hault.

The contemporary form you are likely to hear discussed is Goodman's "green and grue."

Well, perhaps I'm being nieve, but I'm pretty sure I understand what you've just been talking about.
I get the point that Hume is making. The assumption that nature is 'regular', and that the future resembles the past etc. etc.
And I agree that it is an assumption.

My only point was that - even if somehow, in some unimaginable way, you were able to logically 'prove' that nature was regular (I have no idea what this proof could possibly look like, but go with the hypothetical for now...) - that still wouldn't mean that you would be justified in making a claim like 'I can say, with 100% certainty - that the sun will rise tomorrow'.
I wouldn't matter if it was logical 'fact' that nature is - in fact - regular. To make that statement, you would still need to know - at the very least - the exact state of all energy and matter within a 24-hour light-cone around the sun. Otherwise, how would you rule out aliens / some black hole on a collision course / whatever other zany possibility? All of which would be perfectly consistent with a 'regular' universe...

It's possible I'm moving off onto a seperate topic. Is the problem of not being assured of having all the nessesary information / data / parameters a problem related to induction? I thought it was - but I could be wrong. But either way, I still see it as relavent to the 'problem' of making the decleration that it is KNOWN that the sun will rise tomorrow.

I suppose to summarise, I don't see why the ability to predict the future with 100% certainly is being related to the idea that we 'know more now than we do 500 years go'. This is where it was stated we are heading - after all...

As far as 'solving the problem of induction', well - I'm personally satisfied with Poppers ideas here. From my understanding, thinking of induction as something to be 'solved' is not the point. Induction is 'helpful', in the sense that it allows us to have increased confidence in theories over time. And that's all well and good. As I understand Popper's viewpoint, the problem comes if you think that induction leads to some kind of 'conclusion'. I think Popper's argument was that this is a fallacy. Induction gives us increased confidence in theories / ideas / facts / whatever, but it never actually 'proves' anything.
You can only 'disprove' theories. You can't prove them. And as you narrow down possibilities, THAT's the way that knowledge is actually increased - in practise.

OK - but just a sanity check before I go too much further. Am I making any sense at all? Or should I just give up now? :)

[_A Light in the Darkness]

My only point was that - even if somehow, in some unimaginable way, you were able to logically 'prove' that nature was regular (I have no idea what this proof could possibly look like, but go with the hypothetical for now...) - that still wouldn't mean that you would be justified in making a claim like 'I can say, with 100% certainty - that the sun will rise tomorrow'.

Sure. Induction is probabilistic by its very nature. I fail to see the broader point of this. This is just a truism.

As far as 'solving the problem of induction', well - I'm personally satisfied with Poppers ideas here

.

I am not. To say the least. Nor is the philosophical community at large. Popper deflects the problem by ignoring induction in preference for falsificationism. But, without getting into why, his falsificiationism is a failed project.

I think Popper's argument was that this is a fallacy. Induction gives us increased confidence in theories / ideas / facts / whatever, but it never actually 'proves' anything.
You can only 'disprove' theories. You can't prove them. And as you narrow down possibilities, THAT's the way that knowledge is actually increased - in practise.

Huh? I suppose this is your broader point. The problem of induction isn't that induction can't provide certainty. It's that this process of "increased confidence" in an inference's truth is not really justified in any concievable way. And Popper again is jettisoning induction because of the problem of induction. He isn't attempting to provide an account of it. In this view, theories do not receive increasing inductive confidence from observation. You don't actually use induction to show anything more likely to be true. Instead, there just exist theories that have been disproven and those yet to be so: those that are false and those that are as of yet, not shown to be false. (One of the natural problems with this is that any theory can be insulated from being falsified by attaching auxillary ad hocs theories to it, but that is a side issue.)

[Guest]

Sure. Induction is probabilistic by its very nature. I fail to see the broader point of this. This is just a truism.

Sure. I guess this is where I'm more talking to Tal than you. Perhaps...

I am not. To say the least. Nor is the philosophical community at large. Popper deflects the problem by ignoring induction in preference for falsificationism. But, without getting into why, his falsificiationism is a failed project.

Hmmm. I guess I can see why you've chosen to use the term 'ignores' induction. Not sure I agree with this, but - let's continue...

It's that this process of "increased confidence" in an inference's truth is not really justified in any concievable way.

Ahh - I see. Yeah, I guess this comes back to this problem of the 'regularity' of nature, and the fact that the concept of 'induction' technically involved circular reasoning.
OK - I get that.

OK - right. So let me relay back to you how it appears to me YOU see Popper's arguments, and in that way we can see how far we are talking past each-other...

Your point is that Popper doesn't actually 'deal' with the problem of induction. He simply 'side-steps' it by placing the emphasis on falsification. And the way he tries to justify 'increasing confidence' in a theory has really nothing to do with induction, because he's not giving any better explination for it's vadility than anybody else. (And to my knowledge, he made no attempt to).
Instead, he questions it's 'nessesity' in the first place - by using falsification as the judging factor.

Whether he got even close to justifing that stance is a different matter. What I'm interested in right now is working out if I understand your viewpoint correctly...

[_Tarski]

This is getting good. So far everyones input is pretty good and Tal's exposition is entertaining and clear (so far).
I too wonder if Tal is going to attempt to solve the problem of induction.

Just a couple thoughts.

1. I am not so sure that the statement that nature is uniform is completely clear in content nor is is completely obvious. The reason for this is that when I consider in what ways nature is uniform I become worried. There are a lot of ideas in cosmology that paint a picture of the history of the universe in the large that is quite dynamic with regard to things that one might have formerly expected to be uniform "laws of nature". Also, what of the ideas that the laws of physics might be reset each time there is a "big bang" in the brane scenario version of cyclic cosmology. Of course now one might say that we have to reformulate what counts as a law. Are the basic laws expressable by equations at least in principle what if the equations have time as a parameter?

More abstractly, what if it were just the case that the laws of nature as we now think of them (and how is that??!!), do change over time but usually do so only slowly and without sudden changes (principle of continuity) ?

I also find myself a bit exercised about the fact that general and special relativity create problems for ordinary notions of past and present (we still have notions of absolute past and present with respect to a single event of choice but that is not what we normally think of when we discuss what the laws of physics might have been "yesterday".
In order to know what counts as past or present for the universe one must choose a frame (or better, a set of spacetime coordinates). Shall we use the CMB rest frame when we formulate a cosmic version of the principal of uniformity? Or shall we think in terms of an "atemporal" block spacetime universe and then say something about a kind of uniformity accross that manifold? It certainly isn't uniform in curvature from event-location to event-location.
2. It seems to me that induction is an informal principle that is about probabilities and expectations. One is free to "go against it" if one has good reasons. For example, that the sun will rise tomorrow is a good assumption unless one sees an earth size body on a collision course with earth. Of course, this is not really supposed to be a violation of a principle of induction but then what should be the bulletproof formulation?

[Guest]

More abstractly, what if it were just the case that the laws of nature as we now think of them (and how is that??!!), do change over time but usually do so only slowly and without sudden changes (principle of continuity) ?

They would have to do some in some regular fashion. It doesn't matter if the laws of physics change so long as the change is not arbitrary. In order to predict the behavior of some object from past observations of that object, the observed object's properties (its "nature") need to be the same so you can reasonably think the object will be observed the same in the future. It doesn't matter if this works on a meta-level. In other words, the objects properties are free to change so long as there is some stable meta-property guiding this. That's because that meta-property is still part of the object's properties. There just needs to be some uniformity at the bottom of all of this.

Hume's problem of induction is simply that induction itself isn't justified. Hume concludes it is just in our very nature to reason this way and sees no solution to the problem. Induction is a function of our psychology and we are stuck with it. It's not rational, but it is irresistable. Contrary to what Tal has said/implied, Hume was not an radical skeptic. And I don't think he'd deny progress in knowledge.

Goodman's "grue" problem is a little different, though it is part of the problem of induction. It attempts to show that a given set of observations no more confirms one theory than it does infinitely many others. It also is a sticky problem.

[_Tarski]

More abstractly, what if it were just the case that the laws of nature as we now think of them (and how is that??!!), do change over time but usually do so only slowly and without sudden changes (principle of continuity) ?

They would have to do some in some regular fashion. It doesn't matter if the laws of physics change so long as the change is not arbitrary. In order to predict the behavior of some object from past observations of that object, the observed object's properties (its "nature") need to be the same so you can reasonably think the object will be observed the the same. It doesn't matter if this works on a meta-level. In other words, the objects properties are free to change so long as there is some stable meta-property guiding this. That's because that meta-property is still part of the object's properties. There just needs to be some uniformity at the bottom of all of this.

Right. But what kind of uniformity and what is "the bottom" of it all? If cosmology has taught us anything it is that we cannot take on an explicit version as an axiom. We must always hold out the possibility that we must jump to a new meta-level.

Also, did you catch my question about time? Do you think that the uniformity is to always be understood as something about how the laws of physics do or don't change over time? Is it always about past and future?

[_A Light in the Darkness]

Your point is that Popper doesn't actually 'deal' with the problem of induction. He simply 'side-steps' it by placing the emphasis on falsification.

Popper specifically thinks the problem of induction is devastating and concludes "...that rationally, or logically, no amount of observed instances can have the slightest bearing upon unobserved instances." His "solution" to it is to accept its force.

http://dieoff.org/page126.ht

And the way he tries to justify 'increasing confidence' in a theory has really nothing to do with induction, because he's not giving any better explination for it's vadility than anybody else. (And to my knowledge, he made no attempt to).
Instead, he questions it's 'nessesity' in the first place - by using falsification as the judging factor.

He doesn't justify increasing confidence in a theory at all. He doesn't think scientific ideas can be shown likely true. He doesn't think amassing observations builds a better and better case that some theory is likely to be true. That is the nature of induction. He thinks theories can be shown false or, as of yet, not false.