Tal's epistemology (and DCP's)

[NorthboundZax]

I think a sensible explanation for why you might not have got where I'm coming from is that I was mis-respresenting you.
I guess I was worried that the only reason you were really going for Popper's juggular (or at least appeared to be) is to 'get one over' some apologist who may have used Popper (or some other philosopher) as a defense to trash some theory they didn't like

---Ah. Well, no one needs to resort to Karl Popper to "get one over" on someone who thinks that the creator of the universe is directing earring wear. You know? And that's leaving aside the fact that, say, Book of Abraham defenders must also believe that the sun "receives its power through the medium of Kli-flos-is-es, or Hah-ko-kau-beam, the stars represented by numbers 22 and 23, receiving light from the revolutions of Kolob." (Lovely.)

Popper only came up because there is a strange habit - or perhaps not-so-strange given the necessity of defending propositions like "Solar Kolobian-Light- Borrowing Theory" - of apologists enlisting skepticism as a basis on which to construct faith. I think this might have been started by Nibley (figures), and it's just a version of the same argument used by young earth creationists, alien-made crop circle enthusiasts, and every other crank. It goes something like this:

"Scientists used to believe X; they now know that X is wrong; therefore, science ain't all that; therefore, beliefs I have should not be denied credibility on grounds that scientific investigation, or even pure logic, finds them baseless or false".

(And of course, they never admit that the only reason they now know that "X" isn't actually true, is precisely because of science itself, which is nothing if not inherently structured so as to facilitate correction - unlike, say, religious authoritarianism).

So, I guess it is no wonder that Kuhn's paradigms, for example, themselves the product of a profound skepticism about science and knowledge, should be found so attractive by religious apologists struggling to defend what appears increasingly indefensible. His paradigms appear to destroy any rational basis for a hierarchy of credibility. (That only means that Kuhnianism is itself a paragon of irrationality, which again would only explain its attraction to the likes of certain Mopos. Sad).

About your comment on "choosing": If you mean by that, that I "chose" to believe that Joseph Smith didn't tell the truth about his experiences, I wouldn't put it that way myself. I feel I "chose" to believe that, as little as I feel I "chose" to believe David Irving isn't a reliable source of information about World War II. I felt, in a word, that I didn't HAVE a choice after a while. When you lay out all the inconsistencies and contradictions on the table - even apart from all the physical evidence - I just don't know how I could have said, "Hmmm...well........I choose to believe it's true". I don't think, for me, that is possible.

The way I see it is, just because he may have expressed something to an extreme that I wouldn't nessesarily accept, it doesn't mean that the underlying point he's making isn't valid.

If by "underlying point" you mean, our understandings are fallible, well then sure; the problem is that Karl ends up doing all sorts of other way-out things, like trying to construct a theory of theory preference, entirely without recourse to any inductive reasoning, so twisting himself into pretzels trying to avoid admitting that the basic criterion of preference, to not be irrational, must have reference to some theory of truth probability, or just that hierarchy of credibility which Kuhn assaults. (I mean, really - how in the world could empiricism and induction be detached?).

...you wanna put Popper in with people who 'fall victim to confidence tricks', and 'belief in the supernatural without evidence'?
As you wish. Personally, I think he deserves better than that! :D

---Popper wasn't like that personally, that I know of; I do think his philosophy of science, as he himself expresses it in book after book, denies the invalidity and existence of the main engine of human rationality, induction, which in turn precludes things like the rational predicting of a six for the 1001st toss, after the previous 1000 straight tosses of the die all ended in six.

About blood theory vs. sand theory - it was Popper who said that "scientists can never know if their findings are true", and said it in about a million different ways over fifty years. My own view is that at some point, you kind of have to take a guy at his word. If you "can't know it's true" that it's blood circulating through our veins...then...you "can't know it's true", can you? And if you don't know it's true, you're forced to admit that it might not be blood. Perhaps I got that one wrong, but I'm not really sure how, given Popper's consistently extreme language.

Anyway, nice to hear from you on this, I hear where you're coming from.

P.S. Tarski keeps asking me now to justify induction. Any ideas?

[_KimberlyAnn]

Heh - I think a sensible explanation for why you might not have got where I'm coming from is that I was mis-respresenting you.
I guess I was worried that the only reason you were really going for Popper's juggular (or at least appeared to be) is to 'get one over' some apologist who may have used Popper (or some other philosopher) as a defense to trash some theory they didn't like. That was my worry.

Nah. You weren't misrepresenting anyone. Perhaps there was a misunderstanding on your part or the message you were interpreting wasn't clear, but there's no way you are guilty of misrepresentation. That implies purposeful distortion, of which you certainly aren't guilty, RoP.

To me, it's clear that no matter what philosopher is conjured to the defense of Mormonism, Mormonism still doesn't stand up to reasonable scrutiny and should be determined fraudulent. It is interesting, however, or at least amusing, to witness such entertaining mental gymnastics. *evil grin*.

By the way, I was just at the grocery with my four year old daughter and she convinced me to buy her a Reese's. As I saw her clutching it in her hot little hand I had a vision of sorts of how you eat a Reese's. So here it is. How RenegadeofPhunk eats a Reese's:

Renegade of Phunk: UNWRAP SUCKA! BITE SUCKA! CHEW SUCKA! REPEAT SUCKA!

KA

[_Tarski]

I think a sensible explanation for why you might not have got where I'm coming

---Popper wasn't like that personally, that I know of; I do think his philosophy of science, as he himself expresses it in book after book, denies the invalidity and existence of the main engine of human rationality, induction, which in turn precludes things like the rational predicting of a six for the 1001st toss, after the previous 1000 straight tosses of the die all ended in six.

There is something about this example that I don't like. The fact that something specific happened in 1000 straight tosses is not by itself the grounds for scientific conclusions. In fact, it is information that is useless without other facts and prior theoretical commitments. We are using the fact that the die has six sides and the belief that an unweighted die has an equiprobable (or uniform) probability distribution (this in turn is based on things like appeal to symmetry etc). We actualy reason in a vaguely deductive manner about the situation.
(A dog expecting a bone delivered on the 1001st press of a button is not the same.)

Suppose we take a black box with a button and we press the button 1000 times and everytime it displays a six on an LED. Most of us would expect a six on 1001st time. But it doesn't seem like much is going on with that "induction". It certainly isn't science. Science needs theoretical structures within which to make deductions and trace implications to be tested.

Indeed, it turns out that the black box was timing device that merely told the hour of the day and the first 1000 presses of the button took place between 5:30 and 5:59! It read a seven on the 1001st press of the button.

Another similar example is the situation of an earth crossing asteroid. The mere observation of its passing without harm the first 100 times is a fact that, without a theoreticla background, gives us only the barest information about the 101st time. In fact, a colision with the earth on the 101st time might actually count as "proof" of the science of Newtonian mechanics if it were the case that a collision was calculated to occur on the 101st time.

I think Popper is challenging us to abstract the induction component away from the deductive and theoretical part and see what we really have left.

By the way, its hard to see how induction was a major player in transition from Newtonian gravity to general relativity. Essential every obsevation relavant supported newtonian gravity and this is includes countless everyday observations about gravity. Einstien was lead to General Relativity without be guided by (or maybe even aware of) a single negative experiment about gravity per se that would motivate it.

By the way, I have to ask myself, which biological organisms use inductive "reasoning"? Humans? Apes? Dogs? Spiders? ladybugs?, amoebae? viruses?
Without the ability to represent theoretical structures and reason about interconnections and mutual implications, what do we really have?

[_Gadianton]

But, I might just as well have recommended Stanford philosopher Peter Godfrey-Smith's book "Theory and Reality", which also mentions Popper's irrationalism, or Simon Blackburn's "Truth"

What can I say other than those would have been better recommendations. :) I guess Tal, I'm not entirely sure at this point where my disagreements are with you. If you just want to say you hold to Godfrey-Smith's assessment of Popper I'd say that's good enough for me.

Something important you said,

Popper's philosophy is an inadvertently irrationalist

This is important. Let's say I hold a particular view on morality. And let's say it has some blindspots and a critic rightfully demonstrated that if my view X is true, then it follows that we should torture animals for fun. I see the problem, I reconsider, my new position Y fixes things a little but then new leaks spring up, and ultimately I'm not able to offer a clear, consistent, and desirable moral theory.

That would be different than if I were to directly argue that we should torture animals for fun and then contradict myself, confuse issues and so on, finding stretched justifications to support my belief. It would be, unrecognizably different.

I also think some of the criticisms are stretching it and begging the question...the probability stuff etc.

My remaining questions would still be how to understand Popper et. all in context with what a proper philosophy of science should be.

[_Tal Bachman]

There is something about this example that I don't like. The fact that something specific happened in 1000 straight tosses is not by itself the grounds for scientific conclusions.

---Tarski

Let me restate my point for clarity's sake. Read closely and tell me what I've gotten wrong.

Forget "scientific conclusions" for a moment; after all, my loaded die example wasn't meant to illustrate anything about "scientific conclusions" - only something about probability and rationality.

Popper denies that an estimation of truth probability can be rational. I think I have shown that in a few quotes on this very thread. For example:

Second Amendment.) "My theory of preference has nothing to do with a preference for the 'more probable' hypothesis...every probabilistic theory of preference (and therefore every probabilistic theory of induction) is absurd". (OK, 18)

Since, evidently, Popper's own words are too incredible to be believed by some readers, here is one exegete, philosopher of science Barry Gower, who is actually quite gentle with Popper overall:

"Popper's claim about inductive reasoning is crucial to an understanding of his methodology. Such reasoning cannot and should not, he said, be part of any rational decision-making process in science, for inductive reasoning is fallacious reasoning...(According to Popper), we cannot deduce the truth of theories, hypotheses, and laws that are used in science from the observations and experiments that we think, though wrongly, provide inductive support for them. And since inductive reasoning must be abandoned, we cannot deduce, either, their probable truth."

The point of my die example was to suggest, through it, that inductive arguments, contrary to Popper, not only exist, but can be rational; for while it may not be any "scientific conclusion" (whatever we intend that to mean) at all to state that the next toss will produce a six, I think very few people would deny it is rational. Let me exaggerate the example so as to further prove my point.

Die A has not been cast yet;

Die A has now been cast 10 times;

Die A has now been cast 100 times;

Die A has now been cast 1000 times;

and

Die A has now been cast one MILLION times.

Each toss has only ever turned up a six, and now suppose, at some point, we have to bet on very next toss.

Is it not rational that our belief in a subsequent six, increases as the number of the observed tossed sixes increased? Do we not have greater reason to believe in our prediction of 6, after watching one million sixes, than we had prior to any toss at all? Popper, I submit, says no; for he says (amongst many examples), "there is no argument or reason which permits an inference from one case to another, however similar the conditions may be; and I completely agree with (Hume) in this respect". (OK, 96).

I submit that if is irrational to have more confidence in our prediction of 6 after watching one million sixes turn up, than we did prior to seeing a single toss, that the words rational and irrational don't really have any meaning. If we say we can't have absolute knowledge, and we say ALSO that we don't have any reason to believe in the probability of any proposition, then we might as well be rocks. We could do without the first one perhaps; but the second? That something is probable, not certain, doesn't mean it's "useless". It just means it's probable. It's better than a guess, but not as good as absolute knowledge. Could that really be controversial?

In fact, it is information that is useless without other facts and prior theoretical commitments. We are using the fact that the die has six sides and the belief that an unweighted die has an equiprobable (or uniform) probability distribution (this in turn is based on things like appeal to symmetry etc). We actualy reason in a vaguely deductive manner about the situation. (A dog expecting a bone delivered on the 1001st press of a button is not the same.)

---Not sure why it should matter to any of my points if we reason in this case in a "vaguely deductive manner"; it is only Popper who insists that reasoning is 100% deductive at all times. By the way, would you explain why you think a dog expecting a bone on the 1001st press of a button is not the same, or is not an example of inductive inference?

Suppose we take a black box with a button and we press the button 1000 times and everytime it displays a six on an LED. Most of us would expect a six on 1001st time. But it doesn't seem like much is going on with that "induction". It certainly isn't science. Science needs theoretical structures within which to make deductions and trace implications to be tested.

---Perhaps, but the question is, is it rational? Further, why do you believe that this inductive inference has no relationship to science, or scientific thinking? How do you think we lcould earn about the world without the help of induction?

Indeed, it turns out that the black box was timing device that merely told the hour of the day and the first 1000 presses of the button took place between 5:30 and 5:59! It read a seven on the 1001st press of the button.

---Tarski - does the fact that a new theory emerges with greater predictive power, mean that the old one had nothing to do with science? What's your point here?

By the way, its hard to see how induction was a major player in transition from Newtonian gravity to general relativity. Essential every obsevation relavant supported newtonian gravity and this is includes countless everyday observations about gravity. Einstien was lead to General Relativity without be guided by (or maybe even aware of) a single negative experiment about gravity per se that would motivate it.

---I'm glad you mentioned that. I don't believe that there is any reason to insist that all guesses, conjectures, hypotheses, theories, or whatever we want to call a proposition about how the world is, all fall into either Category Induction, or Category Deduction. Popper, in one of his books, offers the example of ancient Greeks proposing theories which couldn't conceivably have been prompted by anything they could have observed - for example, the "wild" idea that the world might be round. (Incidentally, this seems to speak against his other frequent claims that "all knowledge is a modification of pre-existing knowledge"). (He uses this example to argue that the sources of theories are deeply mysterious, and that they can have (sigh) nothing to do with inductive inferences from past observations). As far as I can tell, and as Popper's example suggests, ideas may very well seem to come out of nowhere (just as well as out of sustained observation). But that is no strike against anything I've said; it is only Popper who rules out one kind of idea, and that only because of his pre-commitment to very dubious premises.

By the way, I have to ask myself, which biological organisms use inductive "reasoning"? Humans? Apes? Dogs? Spiders? ladybugs?, amoebae? viruses?
Without the ability to represent theoretical structures and reason about interconnections and mutual implications, what do we really have?

---Well, if you're asking me, as far as I can discern, I don't even know what "cognition" could mean without the ability to inductively infer things. My, uh, conjecture is that to inductively infer is built directly into brains. I mean, if we agree that a man, or an ape, or a dog, made deaf and blind and strapped into a chair for the first five years of life, yet kept alive intravenously, say, would NOT know as much about the world than a counterpart raised normally for the same period of time - that is, if we agree that we can't know as much about the world through pure reason as through experience (if we credit empiricism) - then I don't know how we can deny the reality or power of inductive reasoning.

I propose that the brain itself is an inductive inference machine (though not exclusively so, of course). No wonder Popper spins himself round so furiously trying to avoid admitting it. His "corroboration" and "verisimilitude" and "propensity" and "logical probability" theories are all just evasion attempts, from what I can see.

[Guest]

KimberlyAnn,

but there's no way you are guilty of misrepresentation. That implies purposeful distortion, of which you certainly aren't guilty, RoP.

Cheers! Seems like you get where I'm coming from. Thanks...

To me, it's clear that no matter what philosopher is conjured to the defense of Mormonism, Mormonism still doesn't stand up to reasonable scrutiny and should be determined fraudulent. It is interesting, however, or at least amusing, to witness such entertaining mental gymnastics. *evil grin*.

For myself, I agree with you.
The only trouble is, I still have a mum, and a sister, and a brother, and a few cousins and aunts and uncles etc. etc. who would be offended by the conclusion. And I think the world of them.
So the furthest I'm willing to go is: "It no longer makes any sense to me"

Everybody else is free to make up their own mind.

By the way, I was just at the grocery with my four year old daughter and she convinced me to buy her a Reese's. As I saw her clutching it in her hot little hand I had a vision of sorts of how you eat a Reese's. So here it is. How RenegadeofPhunk eats a Reese's:

Renegade of Phunk: UNWRAP SUCKA! BITE SUCKA! CHEW SUCKA! REPEAT SUCKA!

HAHA! :)
...I have a 5 year-old niece, and that kinda made me think of her!
Cheers KA - you've made my day! :D

Tal,

"Scientists used to believe X; they now know that X is wrong; therefore, science ain't all that; therefore, beliefs I have should not be denied credibility on grounds that scientific investigation, or even pure logic, finds them baseless or false".

Exactly! This is exactly the kind of stuff that I had in mind.
And yes - the irony is they accept the latest scientific finding even though they haven't thought through the basis on which they accept it.
In short - their opinion is worthless. Some people take scientific progress for granted - unfortunately...

About your comment on "choosing": If you mean by that, that I "chose" to believe that Joseph Smith didn't tell the truth about his experiences, I wouldn't put it that way myself. I feel I "chose" to believe that, as little as I feel I "chose" to believe David Irving isn't a reliable source of information about World War II. I felt, in a word, that I didn't HAVE a choice after a while. When you lay out all the inconsistencies and contradictions on the table - even apart from all the physical evidence - I just don't know how I could have said, "Hmmm...well........I choose to believe it's true". I don't think, for me, that is possible.

I agree with you. I meant 'choose' in the sense of 'live a lie', or 'don't live a lie'.
What I believe has never been up for debate, or up for discussion. But I could have 'sucked it all up' in order to just keep life the way I understood it.

But I didn't. And I haven't looked back since.

So, I guess it is no wonder that Kuhn's paradigms, for example, themselves the product of a profound skepticism about science and knowledge, should be found so attractive by religious apologists struggling to defend what appears increasingly indefensible.

Perhaps. I do see why those wishing to push a certain view might latch on to Kuhn.
But back on page 2, I also explained why I have quite a bit of time for Kuhn. So, if your planning a big 'Here's why Kuhn got it wrong' expose - then, well - I'll be sure to add my own commentry.

The fact is that only people who advocate fundemental science are immune to hijacking from the religious and the irrational. And to me, the term 'fundemental science' is a misnomer. So I'm not interested in it.
In the end, science can be hijacked by the religious. And you know what? I'm really not that fussed. I'd rather have that than turn science into the fundementalism of the 21st century...

(I mean, really - how in the world could empiricism and induction be detached?).

In a way, I completely agree with you. On a certain level, induction is simply 'obvious'.
But on another level, I see 'induction' as deceptive. It can trick you. It can cover up the 'real' truth. It can make you think reality is 'simple', when there is actually ellusive complexity to be discovered - if only you realised it was there to be discovered...

---Popper wasn't like that personally, that I know of; I do think his philosophy of science, as he himself expresses it in book after book, denies the invalidity and existence of the main engine of human rationality, induction, which in turn precludes things like the rational predicting of a six for the 1001st toss, after the previous 1000 straight tosses of the die all ended in six.

Tarksi's post in response to this comment kinda says what I had in mind.
Simply relying on repetition without real understanding of what is going on 'under the hood' doesn't seem - to me - a particularly satisfying espimology. I do accept that it should give us some cause for confidence in the future, but it certainly doesn't point us directly towards any kind of underlying nature...

Tarski,

By the way, its hard to see how induction was a major player in transition from Newtonian gravity to general relativity. Essential every obsevation relavant supported newtonian gravity and this is includes countless everyday observations about gravity. Einstien was lead to General Relativity without be guided by (or maybe even aware of) a single negative experiment about gravity per se that would motivate it.

Indeed. What you said a while back about Einstien being influenced by specific mathematical models and concepts of reality really added weight to the Kuhnian view - in my mind.
You could provide all the new data you liked. But if nobody was willing to look at the world with a 'fresh set of eyes', it would seemingly make no difference to the 'status-quo' of Newtonian thought.

By the way, I have to ask myself, which biological organisms use inductive "reasoning"?

Well, isn't the essense of induction trusting future events based on the results of past events?
...if so, how can it be said that most life on this entire planet doesn't rely on inductive principles? (Whether rationally or not?)

[_Tarski]

[size=14][color=darkblue]

There is something about this example that I don't like. The fact that something specific happened in 1000 straight tosses is not by itself the grounds for scientific conclusions.

---Tarski

Let me restate my point for clarity's sake. Read closely and tell me what I've gotten wrong.

Forget "scientific conclusions" for a moment; after all, my loaded die example wasn't meant to illustrate anything about "scientific conclusions" - only something about probability and rationality.

Popper denies that an estimation of truth probability can be rational. I think I have shown that in a few quotes on this very thread. For example:

Second Amendment.) "My theory of preference has nothing to do with a preference for the 'more probable' hypothesis...every probabilistic theory of preference (and therefore every probabilistic theory of induction) is absurd". (OK, 18)

Can we please clarify exactly what a probability is? This will help as far as assessing its connection to rationality. Do you hold to a species of frequentism? Or, do you go for Bayesian interpretation? Push comes to shove when we consider an infinite number of possible outcomes. The classical N(A)/N definition of probability works well for situations with only a finite number of equally-likely outcomes. Even there the issue of whether the set of outcomes really is equally likely is a problem when we wish to provide a foundation for probability theory. In mathematical probability theory one assumes that there is a so called measure space (of total measure one) and a so called measure. From that point its all formal mathematics--complexity but no philosophical worries.

The point of my die example was to suggest, through it, that inductive arguments, contrary to Popper, not only exist, but can be rational; for while it may not be any "scientific conclusion" (whatever we intend that to mean) at all to state that the next toss will produce a six, I think very few people would deny it is rational. Let me exaggerate the example so as to further prove my point.

Die A has not been cast yet;

Die A has now been cast 10 times;

Die A has now been cast 100 times;

Die A has now been cast 1000 times;

and

Die A has now been cast one MILLION times.

Each toss has only ever turned up a six, and now suppose, at some point, we have to bet on very next toss.

Is it not rational that our belief in a subsequent six, increases as the number of the observed tossed sixes increased?

It is a fact that (for normal people) our belief in a subsequent six, increases as the number of the observed tossed sixes increases. Evidently, evolution has filtered out those who don't think (or react) that way.
But wherein lies the rationality? I am tempted to be a jerk for the sake of argument and ask how can we assess that until we have a working definition of rationality.

---Tarski - does the fact that a new theory emerges with greater predictive power, mean that the old one had nothing to do with science? What's your point here?

The point is to dare to question whether induction in and of itself abstracted away from our theoretical understandings and deductive deliberations is truely rational (but we need to clarify the meaning of rationality again).

In the case of the die toss I feel like most of the rationality rested in deductive inferences based on our working assumptions about how dice work and on the physics etc.

Question: What happens if we say that the expectation is not based on a general inductive principle but rather on a working hypothesis about dice behavior that has not been falsified?
(This isn't my position but is rather a gedanken experiment)

---Well, if you're asking me, as far as I can discern, I don't even know what "cognition" could mean without the ability to inductively infer things. My, uh, conjecture is that to inductively infer is built directly into brains. I mean, if we agree that a man, or an ape, or a dog, made deaf and blind and strapped into a chair for the first five years of life, yet kept alive intravenously, say, would NOT know as much about the world than a counterpart raised normally for the same period of time - that is, if we agree that we can't know as much about the world through pure reason as through experience (if we credit empiricism) - then I don't know how we can deny the reality or power of inductive reasoning.

Well, this is an interesting question. What do we actually mean by "inductively infer". Must the biological or mechanical system internally apply GOFAI symbolic manipulations and instantiate actual logical manuevers? Does a dog actually make probability calculations and make inferences that obey a consistent probability calculus?
Suppose I design a car (my analogy for an organism) that drives around but I don't want it to drive too fast in crowded terrain. Now what if I design it so that after each crash a signal is sent to a controller that simply slows the car down (reduces it maximum speed). Is it learning to be careful? yes in a sense. If it doesn't crash for a long while it might be designed to increase its speed slightly. This is a kind of basic homeostasis. To me it is not clear what is the dividing line between neurally implimented homeostasis on the one hand and the ability to do logical inference based on a principle of induction on the other.

[_KimberlyAnn]

[

The point of my die example was to suggest, through it, that inductive arguments, contrary to Popper, not only exist, but can be rational; for while it may not be any "scientific conclusion" (whatever we intend that to mean) at all to state that the next toss will produce a six, I think very few people would deny it is rational. Let me exaggerate the example so as to further prove my point.

Die A has not been cast yet;

Die A has now been cast 10 times;

Die A has now been cast 100 times;

Die A has now been cast 1000 times;

and

Die A has now been cast one MILLION times.

Each toss has only ever turned up a six, and now suppose, at some point, we have to bet on very next toss.

Is it not rational that our belief in a subsequent six, increases as the number of the observed tossed sixes increased?

It is a fact that (for normal people) our belief in a subsequent six, increases as the number of the observed tossed sixes increases. Evidently, evolution has filtered out those who don't think (or react) that way.
But wherein lies the rationality? I am tempted to be a jerk for the sake of argument and ask how can we assess that until we have a working definition of rationality.

In my very limited understanding, rationality is distinguished from experience, so, it seems to me no more rational to believe the millionth cast of the die should result in any more probability of the die turning up a six than the first cast of the die. The chances remain mathematically the same. So, using a strict definition of rationality which does not rely on experience, it is irrational to believe that the chances for a six increase with each subsequent six. Pragmatically, I imagine we'd all place our bets on the next cast of the die to result in a six, but it wouldn't be strictly rational.

I may be completely off, but that's my take on the matter unless I learn something new that changes my mind. Or my take is falsified. :)

KA

[_Ren]

It is a fact that (for normal people) our belief in a subsequent six, increases as the number of the observed tossed sixes increases. Evidently, evolution has filtered out those who don't think (or react) that way.
But wherein lies the rationality? I am tempted to be a jerk for the sake of argument and ask how can we assess that until we have a working definition of rationality.

But wasn't Popper going further than just questioning the 'rationality' of induction?
...he seemed to be going further than that, and effectively arguing that induction doesn't even really exist at all!
We don't even do it 'instinctively', or 'nievely'.

That's what really throws me on this point.

[_Tarski]

[

The point of my die example was to suggest, through it, that inductive arguments, contrary to Popper, not only exist, but can be rational; for while it may not be any "scientific conclusion" (whatever we intend that to mean) at all to state that the next toss will produce a six, I think very few people would deny it is rational. Let me exaggerate the example so as to further prove my point.

Die A has not been cast yet;

Die A has now been cast 10 times;

Die A has now been cast 100 times;

Die A has now been cast 1000 times;

and

Die A has now been cast one MILLION times.

Each toss has only ever turned up a six, and now suppose, at some point, we have to bet on very next toss.

Is it not rational that our belief in a subsequent six, increases as the number of the observed tossed sixes increased?

It is a fact that (for normal people) our belief in a subsequent six, increases as the number of the observed tossed sixes increases. Evidently, evolution has filtered out those who don't think (or react) that way.
But wherein lies the rationality? I am tempted to be a jerk for the sake of argument and ask how can we assess that until we have a working definition of rationality.

In my very limited understanding, rationality is distinguished from experience, so, it seems to me no more rational to believe the millionth cast of the die should result in any more probability of the die turning up a six than the first cast of the die. The chances remain mathematically the same. So, using a strict definition of rationality which does not rely on experience, it is irrational to believe that the chances for a six increase with each subsequent six. Pragmatically, I imagine we'd all place our bets on the next cast of the die to result in a six, but it wouldn't be strictly rational.

I may be completely off, but that's my take on the matter unless I learn something new that changes my mind. Or my take is falsified. :)

KA

Well, the idea is that we aren't assuming that the die is a fair die. We bring to the table our assumptions about how fair die and weighted die behave (part of my point to Tal). Observing so many sixes constitutes evidence that the die is weighted toward a six. Then we make a prediction on the next roll based on that.

If we knew in advance, say by physical testing, that the die was fair then each roll has the same chances of giving a six as you say. On the other hand, after 1000 sixes I would suspect that something had happened to the die rendering it unfair.