Tarski wrote: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.
I'm going to have to go read Popper and some secondary literature and mull things before I can really give an opinion on what I think Popper is really up to.
I once found a book that challenges the idea that any of our actions are done for "reasons" in the normal sense. The claim is that the reasons are generated afterward in order to justify actions to ourselves and to our our fellow humans. Pretty weird idea.
Tarski wrote: 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.
Oh. I was assuming it was a fair die. I've never even heard of a weighted die! Of course I realized the odds were impossible that a die would roll a six a thousand times in a row, but I figured we were dealing with hypotheticals and a hypothetically fair die. I'm fairly naïve, but I hope I would suspect foul play if I ever noticed a die rolling the same number too many times in a row.
Hmmm...now I know why Dawn always wins at Bunko! She's rolling weighted dice! ;)
Tarski wrote: 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.
Oh. I was assuming it was a fair die. I've never even heard of a weighted die! Of course I realized the odds were impossible that a die would roll a six a thousand times in a row, but I figured we were dealing with hypotheticals and a hypothetically fair die. I'm fairly naïve, but I hope I would suspect foul play if I ever noticed a die rolling the same number too many times in a row.
Hmmm...now I know why Dawn always wins at Bunko! She's rolling weighted dice! ;)
KA
I'm ready to take my kids to the pool, and they're on my case to leave, but I just thought of something that maybe doesn't make sense, but I'm posting it anyway, lol! (Not making sense has never stopped me before.)
Wouldn't Popper say that we wouldn't be justified in assuming a die were weighted just because it rolled six a thousand times? Wouldn't our prior beliefs about dice and how they work be irrelevant, according to Popper? I very well could be misunderstanding his philosophy, but from what I gather, he believes we're wrong in inferring anything from past results or experience.
Probably misunderstanding or misinformed but nevertheless curious,
KA
Last edited by Guest on Sun Jul 22, 2007 7:23 pm, edited 1 time in total.
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.
---Not sure if I can satisfy you here; all I mean by "probability" here is what Popper himself means - "likelihood" - when he declares that any estimate of the "probability", or likelihood, that a proposition is true has no rational basis. Popper does try to get round this in a variety of ways, but I'm hoping I don't need to dive into that whole mess. In a nutshell, Popper tries to construct a rational basis for "preferring" one theory to another which does not rely on some estimate - which would necessarily have to arise via inductive inference - of the likelihood of that theory actually being true.
About the connection between an estimation of a proposition's probable truth, and rationality, I'm not sure what to say here other than if we did not have a refined probability-gauging talent, that we should have all perished long ago. If we regard as equal the chances of surviving front-line combat and the chances of surviving a quiet walk on an isolated beach, then...how long would we last? Is it not more probable that we should be the victim of a crime in certain neighbourhoods of certain cities, versus others? I'm not sure what you're wanting here, or if I can really give it to you.
Our brains make estimates of probabilities constantly. Even walking to the front door involves numerous such estimates based on what our brains have logged - that is, based precisely on estimates about the unobserved from the already observed. Those inferences are not infallible, of course; but fortuntately, each prediction which we make, even unconsciously, which does not come true, is accounted for and serves in healthy minds to improve the calibration of our cognitive prediction mechanisms. That is what the best research indicates, anyway.
Maybe I'm not addressing what you want here, I don't know.
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.
---Okay Tarski - you sound like some sadistic professor who's torturing me as some kind of rite of passage...:P
You mentioned evolution, so let me make this point to you.
Our brains comprise around 2% of our body weight, but they consume about 20% of our energy. Given what kind of burden that consumption of energy puts on us, what do you think the chances are that hundreds of thousands of years of evolution would select for brains which make simple inferences, which however have no consistent relationship to probabilities as they actually exist in nature?
The point is to dare to question whether induction in and of itself abstracted away from our theoretical understandings and deductive deliberations is truly rational (but we need to clarify the meaning of rationality again).
---But where would "theoretical understandings" about the world even come from, if not from induction itself? If we say that a "theoretical understanding" is, or even can be, rational, then we must also say that the mode of reasoning which gives birth to it is, or can be. Know what I mean?
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.
---Even if that is so, how could pure deduction account for "our working assumptions about how dice work" See what I'm saying? How can there be any account of cognition, and our understanding about the world, which does not acknowledge a role, and even a very important role, for inductive reasoning?
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)
---Okay Herr Doktor Gedanken
I'm finding the wordings of your questions kind of tough to manage....for example, I'm not sure "what happens"...a few thoughts though.
Suppose we've just emerged from a dark cave, which we've lived in forever, and we've never seen a die. We emerge, and a die is produced with six sides. For whatever reason, we guess that it will only ever turn up a six when tossed. It is then tossed ten thousand times, and every time it turns up a six. Our hypothesis might not have been the result of an inductive inference, but it will be, I daresay, not possible for us to avoid having increasing confidence that our guess is something like a true statement about this one little aspect of the world. To what sort of reasoning, if not inductive, would you attribute our increasing confidence? Likewise, if we had made no prediction at all until the 10,000th observed throw, that prediction I think could not be fairly described as purely deductive - as having had no basis in observation. Predictions might be the result of blind, pure guessing; or, they might be the result of some long chain of inductive inferences; but even in the first place, the prediction won't last long "untainted" by inductive reasoning.
Well, this is an interesting question. What do we actually mean by "inductively infer".
---Dude, you ought to write for FARMS or something! It's like "this depends on what we mean by terms like 'Native Americans', 'descendants', 'Israelites', 'ancestry'"...
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?
---I think so, yeah. Why wouldn't it? How else would it survive? How else could it track, hunt, survive in a pack?
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.
---Tarski, I don't understand why you should regard homeostatic capacities and inductive inferences as mutually exclusive. It may seem a stretch to regard your car as making actual inductive inferences, but it is unclear to me to what degree any aspect of the mind is not purely the result of mechanical operation. So, I am not certain what real difference there necessarily is between your car, and say, the body's ongoing decisions as to how most effiicently to process/store fuel. Our "cognitive unconscious", leaving aside for a moment our conscious minds, makes inferences all the time.
Let me mention one real example. Once when my second son was a toddler, he fell ill. His body temperature rose, but then started to rise very quickly. As a result, his body went into febrile seizure, leaving him unconscious - in a kind of sleeper mode. I suggest that this can be looked at as an example of innate homeostatic capacities, or perhaps better, his cognitive unconscious, in effect drawing an inference - making an estimate about the probability of something happening (experiencing body temperatures so high they would *probably* cause permanent damage) based on what had already happened (an extraordinary skyrocketing of temperature) - and then reacting to it. It might be asked how an inductive inference could ever have been made that permanent damage might be sustained, when no such damage had ever been sustained; I don't really know how to answer that other than the almost deux ex machina of selected-for mutations over generations. Or, that God created us that way.
Lastly - it seems unbelievable to some readers that Karl Popper could deny not just validity to inductive reasoning, but existence. This is notwithstanding the several quotes from Popper saying exactly that. So, here are a few new ones from his autobiography, "Unended Quest":
"The point is that there is no rule of inductive inference - inferences leading to theories or universal laws - ever proposed which can be taken seriously for even a minute...Sensible rules of inductive inference do not exist...Thus induction is a myth. No 'inductive logic' exists...nor is it to be regretted that induction does not exist: we seem to do quite well without it - with theories that are bold guesses...". (p. 169-171)
"Of course theories which we claim to be no more than conjectures or hypotheses need no justification (and least of all a justification by a nonexistent 'method of induction', of which nobody has ever given a sensible description)." (p. 89)
Here is Popper in the midst of yet another attempt at trying to describe how predictions could be made without recourse to probability estimates based on the past (notice also what he means by "corroboration"):
"I regarded (and still regard) the degree of corroboration of a theory merely as a critical report on the quality of past performance: it could not be used to predict future performance. (The theory [my note: that is, the 100% non-induction-derived wild guess], of course, may help us to predict future events)". (Italics in original. P. 117).
---By the way, I should like to know how past observations can NOT help us draw inferences of probability, but a completely wild guess could...
"This view made me reject the psychological theory of learning by induction, a theory to which Hume adhered even after he had rejected induction on logical grounds". (p. 55)
"This way of looking at knowledge made it possible for me to reformulate Hume's problem of induction...in this form, the problem of induction becomes soluble: there is no induction, because universal theories are not deducible from singular statements." (P. 96).
I hope this is all I ever have to say about Thomas Kuhn.
1.) His book contains an outrageous number of contradictions and equivocations (one careful critic, one Margaret Masterman, counted 21 different meanings employed by Kuhn for "paradigm" - in a book of only 200 pages);
2.) Many of his explanations of science would annihilate rational grounds for crediting discoveries made through the most rigourously applied scientific method above beliefs derived from things like astrology, Moonie-ism, or Mormonism;
3.) Not even Kuhn, in the end, seemed capable of defending his ideas. Steve Fuller, for one, amply demonstrates this in his bio of Kuhn.
Rather than a bunch of quotes, maybe just one will suffice here. Keep in mind that you're reading this on a computer, and that you rmother didn't die in childbirth delivering you because no one knew what a "germ" was:
"We may, to be more precise, have to relinquish the notion, explicit or implicit, that changes of paradigm carry scientists and those who learn from them closer and closer to the truth". ("Structure", p. 170).
One wasn't enough? Fine then:
"But nothing that has been or will be said makes (the developmental process of science) a process of evolution toward anything. Inevitably that lacuna will have disturbed many readers. We are all deeply accustomed to seeing science as the one enterprise that draws constantly nearer to some goal set by nature in advance. But need there be any such goal?...Does it really help to imagine that there is some one full, objective, true account of nature and that the proper measure of scientific achievement is the extent to which it brings us closer to that ultimate goal?" (p. 171)
---Perhaps Kuhn supporters would be so kind as to explain what the goal of science is, or should be, if not "the extent to which it brings us closer" to a full understanding of nature...
Give the views already expresed here, it can be no wonder that Kuhn would go on to say that "the notion of a match between the ontology of a theory and it's 'real' counterpart in nature now seems to me illusive in principle..." (note that's "IL-lusive", as in "illusory", not "elusive"); or that he would, seemingly to put the finest point possible on it, say that while he regards - in some mysterious way - Newton's mechanics as an "improvement" over Aristotle's, and Einstein's an "improvement" over Newton's, that he can still "see in their succession no coherent direction of ontological development...". Then, as is his wont, immediately after denying that this view really qualifies as relativism, he say, however, that "if the position be relativism, I cannot see that the relativist loses anything needed to account for the nature and development of the sciences". (Structure, pp. 206-207).
Still need more? What of Kuhn's "not altogether inappropriate" comparison of scientists to the totally brainwashed citizens in Orwell's 1984? (p. 167), or his suggestion that knowledge is not discovered, but "created" (see p. 210) (and typically, after writing the most influential argument for the social construction of knowledge of the 2oth century, he saw no problem in denying in subsequent interviews he was a social constructionist. Isn't that like Jimi Hendrix denying he's a bohemian?).
More?
What about his assertion that there is "no shared metric is available to compare our assertions about force and motion with Aristotle's, and thus to provide a basis for a claim that ours (or, for that matter, his) are closer to the truth”? Or his comparisons of theory adoption to religious conversion - an act thought by most critical thinkers to be the example par excellence of the irrational act? Or his claim that a paradigm “cannot be made logically or even probabilistically compelling for those who refuse to step into the circle”...(my God, this is a total horror!).
Can anyone seriously maintain that Kuhn's philosophy, denying as it does that science is progressing towards a fuller understanding of nature, gives any kind of coherent account of the state of our understanding of nature now, versus that of 100, 1000, or 10,000 years ago?
I conclude with a remark of Kuhn's which will hopefully trigger groans, at this point, in all those who've been reading through my posts on this thread (and which illustrates point 3 above). In a 1977 interview, Kuhn responded to a query about how to reconcile his incredulist views of science with science's history of developing techniques for prediction and control, by confessing that “to that question, unfortunately, I have no answer at all; but that is only another way of saying that I make no claim to have solved the problem of induction”.
I just typed about three pages of reply to Tal and when I hit submit it asked me to login again and when I did the whole thing was gone!
I was feeling pretty good about it too.
$F#k@$#@$D&$@$#S
Last edited by W3C [Validator] on Mon Jul 23, 2007 1:55 am, edited 1 time in total.
I just type about three pages of reply to tal and when I hit submit it asked me to login again and when I did the whole thing was gone! I was feeling pretty good about it too.
$F#k@$#@$D&$@$#S
Ah yes I can relate. It took me numerous times, much more than twice, to catch on to copying every post before I send it. I don't paste it, just copy and at least if the connection has timed out I still have it in the copy file.
I just type about three pages of reply to tal and when I hit submit it asked me to login again and when I did the whole thing was gone! I was feeling pretty good about it too.
$F#k@$#@$D&$@$#S
Ah yes I can relate. It took me numerous times, much more than twice, to catch on to copying every post before I send it. I don't paste it, just copy and at least if the connection has timed out I still have it in the copy file.
That's what I do, too. I copy everything and then I can paste it if I lose my connection or my post otherwise disappears. If I'm typing out a really long post or reply, I usually type it into Word and then copy/paste.
Sorry you lost your post, Tarski. That's so frustrating. Like Marg, I lost way too many posts before I started copying them, so I can relate to your "NNoooooooooo...". I've said it tons of times myself.
I just type about three pages of reply to tal and when I hit submit it asked me to login again and when I did the whole thing was gone! I was feeling pretty good about it too.
$F#k@$#@$D&$@$#S
Ah yes I can relate. It took me numerous times, much more than twice, to catch on to copying every post before I send it. I don't paste it, just copy and at least if the connection has timed out I still have it in the copy file.
That's what I do, too. I copy everything and then I can paste it if I lose my connection or my post otherwise disappears. If I'm typing out a really long post or reply, I usually type it into Word and then copy/paste.
Sorry you lost your post, Tarski. That's so frustrating. Like Marg, I lost way too many posts before I started copying them, so I can relate to your "NNoooooooooo...". I've said it tons of times myself.
KA
There is just no way I am going to try to reproduce it--at least not tonight.
That's what happened to me the other day. I think there is a glitch on this site; it seems like your first log in doesn't actually work, and you have to do it again.