Why the "Problem of Induction" really isn't a problem. (And why theists don't even get it right)
What is Inductive Logic?
Gregory Lopez and Chris Smith
We can define any type of logic as a formal a priori system (axiomatic) that is usually employed in reasoning. In general, if we feed in true propositions, and follow the rules of the particular system, the logic will crank out true conclusions.
We can define 'induction" as a thought process that involves moving from particular observations of real world phenomena to general rules about all similar types of phenomena (a posteriori). We hold that these rules that we generate are probably, but not certainly, true, because such claims are not tautologies.
Inductive logic therefore, is a formal system that can be distinguished from deductive logic in that the premises we feed into these arguments are not categories or definitions or equalities, but observations of the real world - a posteriori world. Inductive logic therefore, is the reasoning we do every day while working in the real world - i.e. the probabilities that we deal with while making judgments about the world. We can think of it as learning from experience and
applying our prior experiences to new, but similar, situations.
History
Inductive logic is basically a form of probability. While human beings have used intuitive forms of inductive reasoning all throughout history, probably theory was first formalized in 1654 by the mathematicians Pascal and Fermat - during their correspondence over the game of dice! In their attempts to understand the game, they created a set of frequencies - or possibilities that described the likelihood for particular rolls of the dice. In doing this, they accidentally set down the basics of probability theory.
It was only a short time later, in 1748, that someone noticed a problem in probability theory - that it included the presumption that the future would be just like the past, yet this assumption could not in of itself provide a sufficient condition for justifying induction, seeing as there is no valid logical connection between a collection of past experiences and what will be the case in the future. Hume's Inquiry Concerning Human Understanding" is noted, even today, for pointing out this problem - the "problem of induction". However, few realize that a solution to the problem appeared only a few years later: In 1763, Thomas Bayes's presented a theorm that unaware to him, could be used to provide a logical connection between the past and the future in order to account for induction. More recently, Kolmogorv (1933) axiomized probability theory, which means that he gave probability theory an axiomatic foundation. Induction, therefore, while a probabilistic enterprise, is founded on a deduced system:
The three axioms of formalized probability theory:
1. The probability of any proposition falls between 1 and 0.
2. Certian propositions have a probability of 1
3. When there is no overlap, P(P or Q) = P(P) + P(Q)
and the definition of conditional probability:
P(P/Q) = P(P & Q)/P(Q)
If you accept these axioms, you must accept Bayes Theorem. It follows logically from the axioms.
These are the key points to the history of induction as far as the formal origins and formal supports for induction. I will cover these points in more detail below. But first, let's look at the different types of inductive logic.
Types of Inductive Logic
Let's do a brief review of some kinds of Inductive Logic
Argument from analogy . This occurs when we compare two phenomena based on traits that they share. For example, we might hold that Object 'A' shares the traits w, x and y, with with object 'B,' therefore, object A might also share other qualities of object B.
Statistical syllogism. This inductive logic is similar to the argument from analogy. The form of the logic follows: X% of "A" are "B", so the probability of "A' being "B" is X%
Example: 3% of smokers eventually contract lung cancer. John Doe is a smoker, therefore, he has a 3% chance of contracting lung cancer.
Generalization from sample to population The best example of this inductive logic would be a poll. Polls rely on random samples that are representative of a group by virture of their random selection (i.e. the fact that every person had the same chance of being chosen for the sample).
On my website, I will also discuss John Stuart Mill's Method of Causality. For now, let's return to the aformentioned "problem of induction" and take a deeper look both at the problem of induction, and some solutions for this problem.
The problem of induction
You've probably heard about Hume's famous 'problem of induction"
How do we know that the future will be like the past?
Or... more comedically
How do we know that the future will continue to be as it always has been?!
Consider the following example: we observe two billiard balls interact. From this, we observe that they appear to obey a physical law that could be presented in the formula: F=ma - Force = Mass X acceleration. From this observation, we then generate a general law of force. However, the problem then arises: how can we hold that this law will really apply to all similar situations in the future? How can we justify that this will always be the case?
If we argue that "we can know this, because the balls have always acted this way in the past" we are not really answering the question for the question asks how how we know that the balls will act this way in the future. Of course, we can then insist that the future will be just like the past, but this is the very question under consideration! We might then insist that there is a uniformity of nature that allows us to deduce our conclusion. But, how do we know that nature is uniform? Because in the past it always seemed so? Again, we are simply assuming what we seek to prove.
So, it turns out that this defense is circular... we assume what we seek to justify in the first place, that the past will be like the future. So this argument fails to provide a justification for induction.
But this in itself is not the whole story, in fact, if we stop here, we get the story all wrong. You see, the 'uniformity of nature' is in fact a necessary condition for induction but it could never be a sufficient justification of inductive inference anyway. The actual problem of induction is more than this: it is the claim that there is no valid logical "connection" between a collection of past experiences and what will be the case in the future. The classic "white swans" example serves: the fact that every swan you've seen in the past was white means simply that: every swan you've seen has been white. There is no logical "therefore" to bridge the connection "all the swans I've seen are white" to "all swans are white" or "the next swan I encounter will be white".
So, yes induction presupposes the uniformity of nature, but while this is a necessary condition for induction, the UN is not sufficient to justify inductive inferences epistemologically. So, any attempt to solve the problem by shoring up the 'uniformity of nature' will never work to begin with. When the next swan turns out to be black, it shows your statement "all swans are white" had no actual "knowledge" content. What you've done is presupposed nature to be uniform, but not in fact justified any particular inductive inference you may wish to make.
So,solving the 'problem' of induction is more than just trying to find a way out of the 'circle' of uniformity of nature/justifying induction. There is a problem that needs a solution. Interestingly, many critics seem to believe that the story ends here - that there simply is a problem, and that all solutions are merely circular. But this is untrue. There are responses to the problem.
Since it was Hume who first uncovered this problem, let's begin by looking at his response:
David Hume's Response: This assumption is a 'habit'
Hume's answer was that we had little choice but to assume that the future will be like the past..... in other words, it was a habit born of necessity - we'd starve without it! And, given that there was nothing contradictory, logically impossible or irrational to holding to the assumption, this utility of induction was seen to support the assumption on a pragmatic basis. This is a key point lost upon many people: there is nothing illogical or irrational about assuming that induction works, nor are there any rational grounds for holding that 'induction is untrustworthy'. The fact that I cannot be absolutely certain that the sun will rise tomorrow does
not give me any justification in holding that it will not rise tomorrow! This error is called the fallacy of arguing from inductive uncertainty.
But merely holding that an assumption is 'not irrational' is not a satisfying enough answer for many. Hume himself stated: "As an agent I am satisfied but as a philosopher I am still curious." So let's continue our search for an answer to the problem.
What is the Basis for Inductive Logic? - An examination of Probability Theory
Curiously, the axiomatic foundations for inductive logic only tell us how a probability behaves, not what it is. So let's begin our examination by first defining what we actually mean by saying the word "probability".
Three common definitions:
Classical - the classical definition describes probability as a set of possible occurrences where all possibilities are 'equally likely' - but a problem arises from this definition. For example, how do you define "possibility" in a univocal manner? Is an outcome 50/50 (either it happens or it does not) or is an outcome actually 1/10, 1/100? In many cases there are possible reasons for each choice. So let's look at another definition.
Frequentist - the 'frequency' is the probability for a given event, that is determined as you approach an infinite number of trials. For example, as with the central limit theorm, you could learn what a probability might be for the roll of a 7 on a pair of dice, after rolling them for a large number of trials. This is the most popular definition, including in science and medicine. This view is backed up by axiomatic deduced probability theory (based on infinite trials (like coin flips)) the law of large numbers. The frequency converges to the probability when we reach infinity. But there are problems here as well: does the limit actually exist? Do we ever really know a probability, since we can't do things infinitely? Also, this method gives us very counterintuitive interpretations. For example, consider a 95% confidence
interval - often this is read to mean that 1 out of every 20 such studies is in error. In
actuality, what this means is that if the experiment were repeated infinitely, you'd get the real mean 95% of the time. This is hardly what people think when they read a poll.
Finally, we can't apply this method to singular cases. 'One case probabilities' are "nonsense" to the frequentist. How do we work out the probability of the meteor that hit the earth to kill the dinosaurs?
We can't repeat this experiment infinitely! We can't repeat it once! We see the same problem with creationist arguments for our universe that attempt to assign a probability to the universe.
Subjective probability - Here, probability is held to be the degree of belief in an event, fact, or proposition. Look at the benefits of this model. 1) We can more carefully assign a probability to a given situation. 2) We can apply this to method 'one case events'. 3) This manner of defining probability gives us very natural and intuitive interpretations of events that fits with our use of the word "probably", circumventing the problems of frequentism.
MOST IMPORTANTLY: Allows us to rationally adjust our beliefs "inductively" by use of probability theory, which is a mathematically deduced theory, so we can latch on our beliefs onto a deductive axiomatic system. Here then, for many, is the solution to Hume's "problem" - induction is no longer merely "not irrational', but instead, can be seen as resting upon a firm deductive foundation.
How does it work?
How do you get a 'number' or probability, for subjective probability? Let's use the concept of wagering.... What would you consider to be a fair bet for a particular outcome? Is X more probable then getting Y heads in a row in your view? In brief, this is how the method works.
Subjective probability and frequency are linked by the "Principal Principle" (David Lewis) or Ian Hacking's "Frequency Principle" (his book cover appears at top). Subjective probablity is justified by a reductio argument: if your subjective probabilities don't match the frequency, and you know nothing else, you have no grounds for your belief.
A question may arise: How can we reason anything if probability's subjective? Well, it is true that you can just choose any starting ground you desire, HOWEVER, your choice must follow laws of probability, or else you're susceptible to 'Dutch Book Arguments' - what this means is that if your degrees of belief don't follow the laws of probability, you are being inconsistent and incoherent. You can choose to believe what you want, but at the risk of being incoherent. The beauty of this method is that a starting point is not necessarily very important: given differing
starting probabilities, based on different subjective evaluations, two very different people who are shown enough of the same evidence will have their probabilities converge to the same value (a LAW OF LARGE NUMBERS) by probability theory - beliefs will converge to a similar value!
Being a subjectivist who wants to use probability as a basis of induction leads us to focus on a certain way of doing things using, Bayes' Theorm
BAYES' THEOREM
The simplest form of Bayes' Theorem:
where:
H is is the hypothesis. This is a falsifiable claim you have about some phenomena in the real world
E is the evidence This it the reason or justification you have for holding to the
hypothesis. It is your grounds.
P(E|H) is called the likelihood : it is also the probability of E given H. In other
words, it is the probability that the evidence would occur if the hypothesis were true.
P(H) is called the prior, or prior probability of H. It is the probability of the
hypothesis being true without taking additional evidence into consideration. In other words, it is an unconditional probability. When I call something, "the prior" without qualification, I mean this probability.
P(E) is called the prior , or prior probability of the evidence E. It is the probability of E occurring regardless of H being true. This probability can be broken down further into the partition , as explained below.
The denominator of Eqn. 1 can be broken down as:
where H is the compliment of H, AKA not-H, and S is the sum over all independent hypotheses. This is sometimes called the partition. The top form is used when one is only considering whether a hypothesis H is true or false. The bottom form is more general, and holds for several independent hypotheses.
Plugging these into Eqn. 1 yields either:
which is useful when considering one hypothesis, being either true or false - this denominator of the right side of the equation multiplies the probability of the hypothesis being true against the probability of the hypothesis being false.
or it yeilds:
which is useful when considering how some evidence supports several independent hypotheses.
This, in a nutshell, is a possible foundation for Inductive logic. For more on this concept, try Wikipedia's entry on Bayesian Inference
Some notes on Bayes' himself:
Rev. Bayes may have (but not definitely) disagreed with "subjective probability". He derived his equation in order to answer a weird problem, which is briefly (and IIRC - no resources with me right now) as follows: you have a pool table of a known size. You draw a line across it parallel to one of the edges (I forget if it's the long or short edge). But you don't know where along the pool table the line's drawn. Now, you place a billiard ball on the table "at random" (equal probabilities of it being anywhere on the table), and you get a yes or no answer to the following question each time you do it: "is the ball to the left of the line?". Repeat this process a few times. With this problem, Bayes derived his equation and used it to find the probability that the
line is drawn at distance X from one side of the table: i.e. the probability that the line is X away from one side of the table.
So, whiles Bayes' theorm can be called upon to solve the problem of induction, Bayes wasn't really concerned with induction. He laid the mathematical foundations, however, for it to be "solved" (many people still today say that Bayesianism isn't really a solution, but a circumvention, of the problem of induction - a very technical point, however. And some object to Bayesianism altogether). The mathematician Pierre Laplace was the one who took up subjective probability and ran with it: he calculated the probability of the mass of a planet with it, and even calculated the probability that the sun would in fact rise tomorrow. There were, however, fatal flaws in his argument which led subjective probability to be all but abandoned. The frequentists took up the ball, and ran with it, until the mathematician Bruno De
Finetti picked up Laplace's torch, leading to "Bayesianism" almost as we know it today.
Conclusion
Lopez believes that both classical and Bayesian statistics answer the problem of induction, as they are both founded on a priori deductive systems. Thus, he ultimately believes that the problem of induction is only a problem if one wishes to find certainty in a belief, and nothing more. It completely discounts degrees of belief.
Degrees of belief is most directly addressed by the Bayesian view. However, the frequentist interpretation still has some power against the problem of induction in my view as well.
Two Further notes:
As already stated above, Christian Presuppositionalists often state the Problem of Induction incorrectly, confusing it with the assumption of a Uniformity of Nature, an error made even more comical when one considers that there solution is an assumption of the Uniformity of "God"!
However, they commit yet another serious blunder: it is a mistake to hold that a failure to provide an adequate justification for induction leaves us without any grounds to rely on induction other than 'faith': The fact one cannot prove something to be correct doesn't imply that one cannot know that the system is correct. A child is unable to prove his name, does this mean he does not know it? Knowledge and proof are two different philosophical concepts. The Problem of Induction relates to philosophical justification.
In short - no matter how one ultimately slices it, the mathematics of probability and statistics ultimately does away with the problem of induction - Bayesian or not.
More Comments on the Problem
Quite frequently I encounter people who equate lack of certitude with giant inferential leaps. Science deals with probabilities, often quite high probabilities, but not certitudes. It is one of the strengths of the scientific method as it acknowledges a chance of error(while maintaining rigorous standards to establish provisional acceptance of propositions). "It is a mistake to believe that a science consists in nothing but conclusively proved propositions, and it is unjust to demand that it should It is a demand only made by those who feel a craving for authority in some form and a need to replace the religious catechism by something else, even if it be a scientific one. Science in its catechism has but few apodictic precepts; it consists mainly of statements which it has developed to varying degrees of probability. The capacity to be content with these approximations to certainty and the ability to carry on constructive work despite the lack of final confirmation are actually a mark of the scientific habit of mind." -- Sigmund Freud
Usually when people talk about how induction is "flawed," they mean that it's not
truth-preserving like deduction. You don't get certainty from true premises. I.e.: Holding an inductive claim as if it were a series of equivalencies is an error.
I think that the problem of induction is only a problem because: a) Some people look for certainty in it, and b)historically, the problem arose before probability theory was mature. If you don't look for certainty, and you know about modern probability and statistics, the problem of induction is not a problem at all. The whole (deductively-created) theory of probability and statistics is dedicated to telling us something about "populations" from "samples." It's made for induction.
Another possible solution: Can we assume that nature has a Uniformity?
As already mentioned previously, the assumption of a uniformity of nature is a necessary but not a sufficient condition for building inferences from the past to the future. So the assumption is not only circular, it fails to provide a justification for such inferences. In addition, Howson & Urbach point out, assuming a uniformity of nature is doubly a nonsolution, since it's a fairly empty assumption. For how is nature uniform? And what, really, are we talking about. What would really be needed are millions upon millions of uniformity assumptions for each item under discussion. We'd need one for the melting temperature of water, of iron, of nickel, etc, etc. For example "block of ice x will melt at 0 Celsius;" for these types of assumptions actually say something. Furthermore, the uniformity of nature assumptions fall prey to meta-uniformity issues - for how are we to know that nature will always be uniform? Well, we have to assume that too. And how do we know that the uniformity of nature is uniform? Ad infinitum. So, to "solve" the philosphical problem of justifying induction by uniformity of nature solutions doesn't really work.
"Hitler burned people like Anne Frank, for that we call him evil.
"God" burns Anne Frank eternally. For that, theists call him 'good.'
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I'm afraid I think you've
I'm afraid I think you've got it all wrong. I agree with you that demonstrating the uniformity of nature is not the crux of the problem of induction. The uniformity of nature issue looks at induction from the top down and picks holes in our assumptions. In fact the real issue is just a subset of the doubt Descartes acknowledged but unsuccessfully attempted to overcome. Rather than "how can we show the uniformity of nature?", the real question is "how can we gain knowledge of future events on the basis of past events?"
I think you have, however, misunderstood Bayes' Theorem. The theorem does not allow us to deduce the probabilities of future events on the basis of past events. It is not a recipie that we can use to cook up probabilities from events.It is a mathematical formula showing the relationship between a group of probabilities. If we know the probability of a certain event happening as well as the probability of another event happening, it is possible, in some cases, to use Bayes' Theorem to deduce the probability of another related event. Unfortunately, we're trying to find out what the probabilities are in the first place and Bayes' Theorem cannot tell us that; we need to know the probabilities to being with.
The frequentist interpretation adds nothing at all. It assumes that if a certain event has always happened with a certain probability in the past, we can know that it will happen with the same probability in the future. This assumes the uniormity of nature.
It would be interesting if you could give an examplke of how we may make a logical inference from past events. I do not believe it is possible without making unjustified assumptions.
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Would be interested to hear todangst's refutation to the above.
Topher
I would be more interested in why Jloll even made the above post. I mean, How did he KNOW when he hit the enter button we would be able to read his words? Why did he bother? Just because this forum existed earlier today, on what basis did he assume it would exist after he hit 'post'?
If induction is irrational then so is his participation here.
gregfl wrote: Topher
I don't rely on reason to know the truth.
LJoll wrote: gregfl
Care to share your truth finding methods and how you justify them? You mentioned "intuition" before. Care to justify why your intuition allows you to *know* the truth? Has it always, or even usually worked for you? If so, You are using induction to justify your intuition. Amazing.
gregfl wrote: LJoll
The fact that my intuition has worked in the past isn't using induction to justify my intuition because it isn't my justification. I don't have a rational justification, but I'm not claiming to be rational.
If you make no claim to
If you make no claim to rationality on what basis should I or anyone else reading this take anything you say seriously?
Just how do you justify using your intuition?
If past experience with your intuition is not how you justify its truth finding ability, then on what basis do you trust your intution?
<<<<<chirp>>>>>
<<<<<chirp>>>>>
gregfl wrote: If you make
I don't really care if you personally take me seriously. If you can't accept my argument without a rational justification it will be your own failling.
I do not try to justify the power of my intuition because I know that it works. Most of the things you believe are actually the basis of your intuition. You have simply confused yourself by trying to justify them on the basis of rationality.
LJoll wrote:
The question you keep avoiding is;
HOW DO YOU KNOW IT WORKS?
The answer is actually quite amusing (induction) but I don't suspect you will be admitting that anytime soon.
No, it is you that has confused yourself by using rationality to deny you are rational and by assuming "the power" of your intuition but refusing to acknowledge you do so based on past experience with its success (induction) . You deny induction but use it to post every word you have posted on this forum. Without it you couldn't justify your next breath.
You have committed yourself to an indefensable position and are holding to it dogmatically.
edit:
gregfl wrote: LJoll
I do not deny induction. I do not even doubt it. My knowledge of induction was not gained through any rational method however. There are lots of reasons why I trust my intuitions, however I cannot rationally show that they are correct.
LJoll wrote:I do not deny
This, pulled from the other induction thread, is your denial:
"I am arguing that induction is completely logically unfounded, so you have no excuse to pretend your knowledge is ultimately rational."
Since you now are saying you don't doubt induction but you have knowledge of induction working, could you please explain on what basis you have this knowledge? If you say 'intuition', explain how you can trust your intuition without invoking induction. If you can't, maybe this will help you see the philosophical corner you have backed yourself into.
gregfl wrote: LJoll
The fact that a belief in it is not rational does not mean it is untrue. I believe that the future will resemble the past, but not on the basis of reason. I don't have a rational reason why I trust my intuitions. I just do. I cannot show you that they're correct. You have to decide for youself whether you want to rely on intuitions, although you don't really have much choice.
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LJoll wrote: gregfl
Assuming that you were really relying on intuition to get you thru the day, then you would have a rational reason to rely on it or not. It would be the inductive process. If you intuition was letting you down more then it was working, then you would no longer trust it.
You deny this simple fact because it reductos your argument.
I think your argument fails somewhere in your definition of rational. Rationality does not require absolute certainty it merely means the ability to think using and embracing reason. Your very survival, today, depends on your ability to make rational choices. When you deny you are rational, you deny the very essence of who and what you are as a human.
I am bailing on this thread because if you cannot agree you are capable of rationality, we cannot talk in any meaningfull way. Thank you for the polite exchange.
gregfl wrote: Assuming
What could I possibly change to if my intuition was getting it wrong all the time? I'd simply have to hope my intuitions adapt, which they would. When you act emotionally and intuitively you can still react and adapt to outside events.
What do you consider makes an actiona rational? How can I disthinguish a rational act from an irrational act?
If you do not want to reply to this post, thank you too.
This may be just my own
This may be just my own failing to comprehend the topic, but I don't see how probability solves the issue. Making a statement about probability is a claim of certainty itself isn't it? To say that something "has a 95% probability" is equivalent in certitude to saying that "all men are mortal", because although what the probability points to is not an absolute statement, the probability statement itself is. The only way to avoid that would be to say that it probably has a probability of 95%. But that just pushes the problem one step back, ad infinitum.
I tend to agree.
The article doesn't really explain much. For example, imagine that we are on an island and we have deduced from the number of swan guano that there are probably 100 swan. We then go outside every morning and observe the swan we see. The first morning we observe 5 white swan on the lake. The next morning we observe 7 white swan on the lake. The next day we observe 6 white swan on the lake. The next morning we observe 5 white swan on the lake. What is the probability that all swan on the island are white? Apparently Bayesians think they can calculate this probability, but I'm not so sure. I'd like to see it done.
For the record, I don't agree that induction makes valid inferences.
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"The church at the time of Galileo was much more faithful to reason than Galileo himself, and also took into consideration the ethical and social consequences of Galileo's doctrine. Its verdict against Galileo was rational and just, and revisionism can be legitimized solely for motives of political opportunism." -Paul Feyerabend
"Let me just anticipate that nobody to date has found a demarcation criteria according to which Darwin can be described as scientific, but this is exactly what we are looking for." -Imre Lakatos
Phil E wrote:This may be
No, it short-circuits the problem.
I can see what you are trying to point out, but if you adopt that particular approach consistently to all statements, you have no way to express a degree of confidence in ANY statement, deductive or inductive, whatever value you feel is appropriate, including 0% and 100%.
So it requires that each statement be assigned simply an estimate of the confidence we feel it warrants, based on whatever relevant evidence we have. If that is all we were doing, your objection might be valid.
What Bayesian analysis allows us to do is combine these estimates in a rigorous manner to show what overall confidence we are justified in placing in the conclusion, given those estimates for each element.
That is no different from any statement of deductive logic, in that all such a statement can say is that IF the axioms and specific input propositions are true, THEN this conclusion is true.
Bayesian analysis using probabilities simply extends this in a rigorous manner: IF we assign all a particular set of estimates of confidence to the raw data, THEN x% is the implied degree of confidence that we are justified in having about the conclusion, to allow us to see how uncertainty in any or all input data propagates through to the conclusion.
It can also allow us to identify which inputs have most effect on the conclusion, ie which ones we need to check most carefully.
Hope this helps.
Favorite oxymorons: Gospel Truth, Rational Supernaturalist, Business Ethics, Christian Morality
"Theology is now little more than a branch of human ignorance. Indeed, it is ignorance with wings." - Sam Harris
The path to Truth lies via careful study of reality, not the dreams of our fallible minds - me
From the sublime to the ridiculous: Science -> Philosophy -> Theology
BobSpence1 wrote:Phil E
So really all you're doing is measuring the level of belief in any particular scientific theory?
Even without the Bayesian system you can assign probability to items. For example, we can safely conclude that the probability that a heavier object will always fall faster than a lighter one to be zero. For practical terms we could consider that theory to be falsified.
To me, induction seems much less reliable than induction because not only do you have the normal problems with deductions (your initial assumptions) but you have the problem that even if all the inputs are correct the output may be wrong.
Perhaps we're just not understanding well. Take a scenario:
You are on an island and you have reason to believe there are 100 swans there (due to droppings). You have received a grant for scientific research and you successfully trap, photograph, and tag 60 swans, all of which are white. Then you run out of funding. What probability could be assigned to the theory that all swans on the island are white?
How does this tie in with the pool table thing above?
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"The church at the time of Galileo was much more faithful to reason than Galileo himself, and also took into consideration the ethical and social consequences of Galileo's doctrine. Its verdict against Galileo was rational and just, and revisionism can be legitimized solely for motives of political opportunism." -Paul Feyerabend
"Let me just anticipate that nobody to date has found a demarcation criteria according to which Darwin can be described as scientific, but this is exactly what we are looking for." -Imre Lakatos
XaosPeru wrote:BobSpence1
It certainly would not be 100%.We are not measuring belief, we are estimating error ranges.
Your thing about inputs being 'wrong' etc is a completely inaccurate way to describe the 'problem'. Bayes assures us that our output confidence accurately reflects the confidence we assign to each input. It makes no sense to apply "right" and "wrong" to inputs in this context.
If you had absolutely no background information, such as the amount of variability of plumage colour observed among closely related bird species in general, you would be fully and logically justified in saying that the remaining birds are most likely also white, but you really could not put a tighter figure on it, without more data.
Imagine you had a portable DNA sequencer. If the DNA in the droppings showed they were all very closely related, you could be more confident in putting it in stronger terms.
Bayesian analysis is only really useful when you have a lot of more-or-less separate observations.
Whatever, you would still be perfectly justified in assuming, in the absense of further observation, that the remaining swans were also white.
Bayes, and probability theory and statistics, would be very useful if, for example, you then observed one black swan, and wanted to estimate the number of black swans likely to be in the remaining birds yet to be observed.
it is all about the scientific approach, where nothing is ultimately proved in a strict sense. We make initial assumptions on available data, calculate the consequences under various assumptions, and see if we can come up with possible observations or experiments to test the various hypotheses. And even try different sets of initial assumptions if our tests and observations suggest we are 'way off'.
When our estimates of particular input confidence are themselves very uncertain, we express this typically by giving a range of values, eg 20-50%.
To repeat, these input assessments are assumptions, IOW the minimum requirement for ANY type of argument.
Is a statement like "I am 100% certain that I have no idea what the 'correct' value is in this case" an expression of certainty or uncertainty? Neither - and both. Depending how you read it.
The simplistic assignment to a statement of a single figure is only appropriate for a certain category of simple assertions.
Induction, as applied in science, is a major enhancement to older systems of analysing reality, designed to cope with the uncertainties and 'error-bars' of real-world study.
The 'problem' is a reflection of the iimitations of purely deductive, binary logic systems.
Favorite oxymorons: Gospel Truth, Rational Supernaturalist, Business Ethics, Christian Morality
"Theology is now little more than a branch of human ignorance. Indeed, it is ignorance with wings." - Sam Harris
The path to Truth lies via careful study of reality, not the dreams of our fallible minds - me
From the sublime to the ridiculous: Science -> Philosophy -> Theology
BobSpence1 wrote:It
First of all, in many animal species DNA does not control the color. Highly inbred mice, with identical DNA among them, still end up with varying colors.
That being said, the crux of the argument was that Bayesian statistics can 'solve' the problem of induction. So far I am long on assurances, and short on actual details of how that works or why I should believe it. You say that it's not applicable to the swan situation. Accordingly, I can only assume that it does nothing towards the problem of induction.
I guess we'll have to take the assumption that all swans on the island are white as 'just a theory.' Of course that phrase must rankle you a bit. I'm sure if I said evolution was just a theory or some other pet belief of yours, I'd have half the board jumping on me. Still, I don't see how it can be classified in any other way. Perhaps you can guide me ... ?
Really, though, it was a trick question. I had planned to reveal to you that in the hypothetical example that 67% of the swans are white (and diurnal) whereas 33% of the swans were black (and nocturnal). You see, the pool table example ASSUMES that all drops of the cue ball on the table are random. Yet how can we be assured in the real world that our samples of (let's say) the law of gravity are random samples? Really most of our experience with gravity is in the last 200 years and only on this planet and those nearby.
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"The church at the time of Galileo was much more faithful to reason than Galileo himself, and also took into consideration the ethical and social consequences of Galileo's doctrine. Its verdict against Galileo was rational and just, and revisionism can be legitimized solely for motives of political opportunism." -Paul Feyerabend
"Let me just anticipate that nobody to date has found a demarcation criteria according to which Darwin can be described as scientific, but this is exactly what we are looking for." -Imre Lakatos
XaosPeru wrote:BobSpence1
There is no problem to solve, except for how to get through to you that you completely misunderstand the reality here.
Bayesian analysis just allows us to make the inductive process more rigorous in complex cases.
And yes , environment can contribute to color determination as well. Not really relevant to the argument.
"All swans on the island are white" is arguably 'just a theory', but you don't need to call it anything more than a working assumption. It is a perfectly reasonable assumption until further evidence turns up - eg seeing a black swan. It is quite simple, really.
That phrase just makes me take you even less seriously.
Actually, it would be more accurate to call it a hypothesis than a theory, since we have insufficient evidence to positively demonstrate that ALL the swans on the island are white.
We don't need to rely on "random samples" of gravity. That doesn't even make sense.
You only revert to 'random sampling' when the situation is too complex to allow more systematic tests, where there is a risk of missing some conditions.
Every astronomical object body that we have observed moves consistently with the Law of Gravity.
Every test on Earth is consistent with it.
It allows us to predict the path of our satellites and other space-craft.
That is all that is logically required to treat it as a sufficiently accurate model of reality to rely on, until we find something behaving in a manner inconsistent with it.
We have already seen that, when the orbit of Mercury was found to be not quite consistent with Newton's formulation. This is is one of the observations that led to Einstein's General Relativity, which accurately accounted for the anomalies, and so supersedes Newtons version, at least where maximum accuracy is required.
Favorite oxymorons: Gospel Truth, Rational Supernaturalist, Business Ethics, Christian Morality
"Theology is now little more than a branch of human ignorance. Indeed, it is ignorance with wings." - Sam Harris
The path to Truth lies via careful study of reality, not the dreams of our fallible minds - me
From the sublime to the ridiculous: Science -> Philosophy -> Theology
Well, I guess I'll have to
Well, I guess I'll have to agree with you that I definitely don't understand. Considering that no one has presented a logical reason for concluding that the past is a good guide to the future all the observations that you have made about gravity really don't mean anything to me. I was led to believe that Bayesian statistics was a solution in that it presented a logical and/or mathematical reason for believing that the past was a good guide to the future. I'm all ears, but I'm not hearing anything other than, "Trust me ... it works."
How is that different from the old line, "Trust me ... the Bible is 100% inerrantly true."
The problem with all of your "body of knowledge" is that the scientific method is based on a logical fallacy. You theorize that gravity works in a certain way. Then you observe some things that are consistent with your view of gravity and you erroneously think that you have confirmation, but you have nothing. It's the same kind of confirmation that a true believer in Noah's flood thinks he gets every time he sees a fish or whale fossil on dry land. He is more and more convinced of his theory. The only thing he is doing is affirming the consequent.
This is why the logical solution to the problems of the scientific method is the one proposed by Karl Popper - that is, Popperian falsification.
Simply applying this test to the theory of gravity reveals worrysome results. Either 95% of the universe is composed of dark "voodoo" matter or the law of gravity needs to be rewritten (that's where MOND comes in). Both of these theories have serious problems. So in the face of all of that, I'm supposed to think that you have it covered because Bayesian statistics can measure the amount of subjective belief you have in the theories and thus "...make the inductive process more rigorous in complex cases"?
To the extent that science is inductive, it is worthless.
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"The church at the time of Galileo was much more faithful to reason than Galileo himself, and also took into consideration the ethical and social consequences of Galileo's doctrine. Its verdict against Galileo was rational and just, and revisionism can be legitimized solely for motives of political opportunism." -Paul Feyerabend
"Let me just anticipate that nobody to date has found a demarcation criteria according to which Darwin can be described as scientific, but this is exactly what we are looking for." -Imre Lakatos
XaosPeru wrote:Well, I guess
The past is our only guide to the future.
The FACT that part of our data is precisely that is has been a good guide for all of living memory.
It would be pathologically insane to say that it is perfectly reasonable to assume it will not arbitrarily change in the future, which is all I am saying, and all we can rationally and logically do.
A 'good guide' does not require 100% proof. That would require the expression to be a 'perfect guide'. So expressing it in terms of probabilities, it IS logically and mathematically valid to assign a high degree of confidence to the assumption that things will not suddenly change.
The alternative is to say ALL knowledge is useless. Which actually would be the logical implication if an omnipotent sentient being existed - that would logically imply that everything really could change at any time at the whim of such an entity.
Read up on Bayesian analysis. I described it accurately, AFAICS, after checking back on some representative sites.
I am NOT asking you to trust me.
If something has been valid for a million years, it would be batshit crazy to assume there is a significant probability that it will be not-valid tomorrow, in the absence of any indication of an imminent massive disruption in reality. We are not asserting that we know, or can prove, that it will remain valid, just that the assumption is entirely reasonable.
Rigorous demonstration of the accuracy of a theory requires us, wherever possible, as per Popper, to devise experiments or observations that would give clearly different results if any aspects of the hypothesis were not consistent with reality. Why did you present such a 'straw-man', casual picture of how science is done??
If it passes all the tests we can devise, we are logically justified in using it as our current working model. That is not a fallacy.
When every observation we can devise is consistent with the postulated Law of Gravity, of course that doesn't prove it is true, but it DOES prove that it is a valid model within the limits of precision of our observations, over the domain of observation.
There are observations that suggest that at extremely small and large scales, gravity departs from the distance/mass/force relationship that applies at 'normal' scales. This does not change the FACT that it still works more than adequately over a vast range of scales away from those extremes.
Your example of dark matter observations suggesting a necessary revision of our model is a repeat of what already happened with the observations of anomalies in the orbital motion of Mercury, and that whole process is part of Science.
Bayesian statistics DO NOT "measure the amount of subjective belief" we have in some conclusion. That is absolutely a misunderstanding/misrepresentation.
It "measures" nothing. It provides a mathematically rigorous way to show the implications of any uncertainty in our input data, whether due to the need to make educated guesses when there are gaps in our data, or due to lack of precision in our measurements, on the range of possible error in our conclusions.
Your example of the believer in the Flood is not employing the scientific process.
Do you study philosophy, by any chance? That would explain your massive misconceptions.
The deductive approach to 'knowledge', as practiced by the most prominent Greek philosophers, has a long record of mostly error - trumped by people like Copernicus and Galileo.
Induction is not perfect, but deduction on its own is useless.
If you believe in God, you are logically required to doubt the value of induction, it is true, since such a being could indeed change things arbitrarily at any instant, but in the real world, the actual practice of induction being continually applied to 'reality', ie empiricism, becomes self-justifying, in that as we get ever more complex models of reality that still keep working, our justifiable confidence in the whole process grows.
Because we are continually monitoring 'reality' any changes from historical values will be detected, and simply become part of the input data, to be hypothesised about and investigated.
Perhaps your problem is you don't grasp the implications of an iterative process, that we are not dealing with a simple linear progression of observation/hypothesis/theory in one shot.
Just wondering, how the hell do you think such a useless process allowed people to design your computer, which does appear to work....
Science WORKS, bitch!!
Favorite oxymorons: Gospel Truth, Rational Supernaturalist, Business Ethics, Christian Morality
"Theology is now little more than a branch of human ignorance. Indeed, it is ignorance with wings." - Sam Harris
The path to Truth lies via careful study of reality, not the dreams of our fallible minds - me
From the sublime to the ridiculous: Science -> Philosophy -> Theology
Well, with such a shotgun
Well, with such a shotgun approach to defending your philosophy, it's hard to know where to start, but I guess I'll start at the bottom and work my way up.
Science WORKS, bitch!!
You mean you assume science works because it appears to work at least some of the time. Here in Peru we have a history of curanderos - what you might call witch doctors. They promise to do amarres which literally means bindings. You would call it a love spell. You collect the hair of the victim, some of his personal possessions, etc., etc., and the shaman of your choice does the appropriate ritual to ensure that this person will fall madly in love with you. I could easily find thousands of people who have engaged in these types of rituals that will swear up and down that they work.
Witchcraft WORKS, bitch!!
Well, I'm an open-minded kinda guy. Maybe it DOES work, but simplistic logic like that fails to convince me. You have a computer ergo science is infallible. No sale here, bub.
As for your claim that "deduction on its own is useless" ... do you ever use mathematics? What do you think that's based on?
Basically the argument you've presented for induction is called the naive justification for induction. The past is a good guide to the future because it has worked well in the past ... and will therefore work well in the future. This is circular logic. It's called begging the question. How is that any different from saying, "The Bible is true because the Bible says so."
I don't believe in the napkin religion, either. Sorry.
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On what basis do you assume that the universe is uniform? How can you say that observations made regarding gravity here on earth were valid on the other side of the universe 4 billion years ago? Even assuming the universe is orderly, isn't it possible that the law of gravity changes in an orderly, predictible fashion every 1 billion years? How can you rule that out?
Finally, the last thing is your strange historically-revisionist look at Galileo. Bluntly put, every observation made at the time of Galileo cast serious doubt on his theory. Stellar parallax should have been observed if the earth were really moving around the sun. Multiple attempts to find this parallax failed. Even the claim that the model was simpler because it eliminated epicycles is wrong - the moon still needed an epicycle to account for its motion.
From http://www.scientus.org/Copernicus-Stellar-Parallax.html
"No one in Galileo's time or for almost 200 years after his death was able to demonstrate this necessary effect of earth's motion around the sun. Stellar parallax was finally observed in 1838 by Friedrich Bessel, a German scientist. But it is not Bessel that is credited with finally proving that the earth moved around the earth. In 1725, James Bradley, while searching for the elusive stellar parallax, detected motion of the stars over the course of the year which did not fit the pattern of stellar parallax. He had discovered stellar aberration, which is also related to the motion of the earth. Regardless, proof of the earth's motion was not available in the seventeenth century and those arguing for it's motion had no answer for why stellar parallax could not be observed. If there is a necessary consequence of a theory and that consequence cannot be observed that is a huge problem for any scientific proposition. It is enough to keep a hypothesis from being accepted as a proven theory, regardless of the number of positive arguments in its favor. This applies to science today and it also applied in the seventeeth century.
While this criticism of a sun-centered solar-system may have been scientifically valid at the time it does illustrate a kink in the scientific approach which exists even today. These scientists were correct that if there was a moving earth then there must be stellar parallax. They were also correct that this parallax could not be observed. However, their rejection of the hypothesis was based on more than this; it was also based on the assumption that the stars were millions of miles away. These stars were billions of miles away. Given the instrumentation of the day, one could expect to detect stellar parallax if the stars were millions of miles away but not if they were billions of miles away.
The difficulty of eliminating assumptions in testing theories exists as much today as it did four centuries ago. It even has a name; the Duhem-Quine thesis. It was originally proposed by the great philosopher of science, Pierre Duhem. Simply put, this thesis states that in practice it is difficult to ever test a theory independently of other theories or assumptions. This means that when an experiment 'proves' a theory false it is really just proving the collection of theories and assumptions false, not necessarily the theory itself. This has implications for important themes in the modern philosophy of science, especially falsification. Interestingly, Pierre Duhem is the same person who as a historian discovered that there were important scientific advances in the middle ages, largely attributable to church scientists (see Duhem and the DaVinci Code). Duhem was also one of the most prominent victims of academic censorship in the twentieth century largely due to his historical work."
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"The church at the time of Galileo was much more faithful to reason than Galileo himself, and also took into consideration the ethical and social consequences of Galileo's doctrine. Its verdict against Galileo was rational and just, and revisionism can be legitimized solely for motives of political opportunism." -Paul Feyerabend
"Let me just anticipate that nobody to date has found a demarcation criteria according to which Darwin can be described as scientific, but this is exactly what we are looking for." -Imre Lakatos
Saying "Science works" is
Saying "Science works" is NOT claiming that science is infallible!!
The 'shotgun' effect is due to the fact that there are so many ways to show how your position is a fallacy or a misunderstanding or worse.
That is your problem, you keep arguing in terms of true/false, proof/disproof.
Galilieo's position was based on observations of the moons of Jupiter, which specifically demonstrated that not all heavenly bodies revolved around the Earth.
Other observations he made with the help of his telescope, such as the phases of Venus, also were even stronger demonstrations of heliocentrism.
The failure to observe stellar parallax was certainly not disproof of heliocentrism.
Speculation about the possibility that the 'constants' may be different in different parts of the Universe, or at different stages in its history, have always been an active part of science.
The simple assumption that we treat things which appear to be constants on all initial tests as constant until we have evidence of variation is a perfectly valid and reasonable one, closely related to Occam's Razor.
The justification of the scientific, empirical, inductive approach is NOT based simply on the success or failure of individual experiments or observations, it is massively helped by the correlations which show up across different areas of investigation and between whole disciplines - results from one area frequently find application in unexpected areas.
And the fact that science and scientists are not perfect, with no questionable procedures or assumptions, is fully recognized by science, which is why independent replication, peer review, and many such mechanisms have been set up explicitly to address the issues you raise.
Most of which do not in any way address your issue of the 'problem of induction'.
As to your initial story, a scientist could respond "Placebo works, bitch!".
You keep bringing these strawman examples, which are utterly irrelevant to how actual science is conducted.
Of course if you do sloppy, casual, biased investigation, or none at all, at least none that would remotely qualify as publishable science, as with informal 'confirmation' of witchcraft, you are going to get highly unreliable results. D'uh!
Favorite oxymorons: Gospel Truth, Rational Supernaturalist, Business Ethics, Christian Morality
"Theology is now little more than a branch of human ignorance. Indeed, it is ignorance with wings." - Sam Harris
The path to Truth lies via careful study of reality, not the dreams of our fallible minds - me
From the sublime to the ridiculous: Science -> Philosophy -> Theology
Mathematics, and Logic, are
Mathematics, and Logic, are based on a set of basic axioms.
Logic uses the Law of Identity, and the Law of Non-Contradiction, which are about as basic as you can get to perceive a coherent universe, so they are reasonable starting points.
Math uses a series of axioms, progressively adding them for different areas.
All math or a logic argument says, is that IF X THEN Y.
The results are only as accurate as the starting assumptions.
Math results are only useful to the degree that the math formula accurately match the empirical data and reality.
For example, Euclid's axiom about parallel lines is only valid in a 'flat' space. We do not inhabit such a space, although away from massive stellar bodies, it is close enough to flat for ordinary purposes that it doesn't matter.
Math and logic are essential TOOLS of empirical/inductive investigation - they do not generate new KNOWLEDGE about external reality, no purely deductive process can. It requires extrapolation, which is essentially induction. Deduction is more like linear interpolation.
If we want to advance our understanding beyond what we can strictly see and/or touch induction is ESSENTIAL.
Obviously, constant error checking is also extremely important - that's the important thing science added to induction which makes it self-correcting. If some assumed constant is not in fact constant, the only way this will be detected is by the process of science itself. The errors that arise due to any such faulty assumption are what will eventually lead to new hypothesis, as with Einstein and the discrepancies in the orbital motion of Mercury, and a refinememt to explain or allow for the new data.
Any non-uniformity is just that: new data to be revealed and incorporated into the next generation of theories, just like any other kind of data. That is another of your misunderstandings -
Favorite oxymorons: Gospel Truth, Rational Supernaturalist, Business Ethics, Christian Morality
"Theology is now little more than a branch of human ignorance. Indeed, it is ignorance with wings." - Sam Harris
The path to Truth lies via careful study of reality, not the dreams of our fallible minds - me
From the sublime to the ridiculous: Science -> Philosophy -> Theology
To refer right back to the
To refer right back to the swans thing, if we observed 60 white swans, and had evidence that there were 100 swans on the island, then we could say with 100% confidence that the chance that any random sighting of an individual swan was white was at least 60%. Do you have a problem with that?
Obviously going beyond that would not be justified in the absence of more evidence.
Favorite oxymorons: Gospel Truth, Rational Supernaturalist, Business Ethics, Christian Morality
"Theology is now little more than a branch of human ignorance. Indeed, it is ignorance with wings." - Sam Harris
The path to Truth lies via careful study of reality, not the dreams of our fallible minds - me
From the sublime to the ridiculous: Science -> Philosophy -> Theology
BobSpence1 wrote:Saying
Here's hoping you had a good weekend.
The "shotgun effect" is due to the fact that you have no idea how to respond to the criticisms. Probably you don't even understand the problem of induction since you can so glibly assure us all that it's not a problem.
As you've already admitted, there's no way of knowing that any of science's pet theories of the day are true. Accordingly there's no way of demonstrating that scientific induction is superior to flipping a coin. The advantages of coin flipping over the scientific method are clear: It's a lot cheaper.
As for Galileo and your revisionist attempt at history, we need to go back to the Greeks to understand why the Earth was considered to be the center of the universe.
The Greeks knew that things don't go on moving forever. That would require a perpetual motion machine. Accordingly they postulated that an impetus was what moved objects. An object is pushed, generating an impetus, and when the impetus ran out, the object stopped moving. Now when an object is pushed, and you are on it, you feel the push. Since no one on earth felt any pushing, it was obvious that the earth didn't move. Most other heavenly bodies had an orderly motion - the stars wheeled around the earth in a big circle.
The problem were the wanderers. In fact, that's what the word planets means. Aristotle theorized that they also moved in circles, but with certain other circular epicycles. Soon a system of prediction was worked out that could tell you where the planets would be at any given time or place. The science (or rather, natural philosophy) was settled.
Now Copernicus published, on his death bed, his proposed revision of the solar system. It had only one advantage: It was simpler. It still required epicycles, but it didn't require as many epicycles as the tried and true Aristotle system. In addition, since no parallax was observed, it was inconsistent with the observations of the time.
Later on Galileo (who was not a scientist) started making some observations. He got a telescope and looked at Jupiter and appeared to observe 4 moons going round it. In no way was this observation a threat to the Aristotle system, which was based on the idea of impetus. Furthermore the phases of Venus proved little either, since Venus orbitting the sun and having phases was not in any way inconsistent with the impetus contention and the lack of pushing being felt.
Nor were any of Galileo's observations rejected. Initially the scientists were unable to replicate his experiments. Most of them couldn't build his telescope and when they did, and looked through it, they saw nothing but blurry headache-causing nonsense. Galileo was unable to explain why his telescope worked. Additionally, since Galileo wasn't a scientist, he was low in the pecking order. He could safely be ignored. He was nothing more than a mathematician and (as you've already pointed out) math and logic really don't prove much of anything. It is induction that was seen as the saviour of the day.
Jesuit priests eventually managed to get a working telescope and they confirmed all of Galileo's observations around Jupiter. The Bible was in no way disproved because it says nothing about Jupiter or having moons or anything like that.
Galileo, however, made the mistake of sidestepping the university system and getting a private post. Then he used his sarcastic wit to ridicule the scientists. Once they had had enough, they found it easy to demolish Galileo scientifically (lack of parallax). The only advantage Galileo had was that his system was simpler - an appeal to Ockham's Razor (the principle of parsimony). However, there is no rational reason to assume that simpler solutions are better.
Galileo wisely decided to plead guilty to a minor charge against him, he was placed under house arrest for the remainder of his days, and science won out over the upstart mathematician.
Nowadays in revisionist history science likes to sweep its role in his trial and punishment under the rug. Why it was the Christians who accused him of heresy and locked him up! We swear!
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Then, of course, you bring up the peer review system. That is, in fact, the very system that prevented Galileo's theories from getting a fair shake. But it's not just him. A simple look at http://amasci.com/weird/vindac.html#j1 will show a long list of now-accepted scientific discoveries that were ridiculed and attacked by science from the get-go. Chladni is my favorite. Have a look.
There is no rational basis for believing that the past is a good guide to the future. Simply seeing a woman walk down the same street at the same time every day in no way increases the likelihood that she will do so tomorrow. Hundreds of examples could be given (in and out of science) of induction coming up with a wonderful, and completely wrong conclusion.
Only Popperian falsification resolves the conflict by eliminating induction altogether.
Of course most scientists aren't interested in accepting that, considring that the existence of dark matter is not falsifiable. How can we prove that invisible matter doesn't exist? Impossible. Ditto for the theory of natural selection.
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"The church at the time of Galileo was much more faithful to reason than Galileo himself, and also took into consideration the ethical and social consequences of Galileo's doctrine. Its verdict against Galileo was rational and just, and revisionism can be legitimized solely for motives of political opportunism." -Paul Feyerabend
"Let me just anticipate that nobody to date has found a demarcation criteria according to which Darwin can be described as scientific, but this is exactly what we are looking for." -Imre Lakatos
BobSpence1 wrote:To refer
That's the point, really ... a random sighting of an individual swan being white must be at least 60 percent. But how can you be certain that your sighting is random? As I pointed out, the scenario was designed as a trick question. On the hypothetical island, black swans are nocturnal. Whether you postulate that God made them black to be well adapted to the night, or made them nocturnal to have their blackness be useful, or that Darwinian (or another evolutionary method) resulted in either black feathers or noctural habits is irrelevant.
Walking out the front door, on a bright sunny day, and seeing some white swans is what would be expected. Such a method is not a random sighting.
How do we know that the scientific observations we make about gravity, natural selection, fossils, electromagnetism, whatever, are random sightings?
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"The church at the time of Galileo was much more faithful to reason than Galileo himself, and also took into consideration the ethical and social consequences of Galileo's doctrine. Its verdict against Galileo was rational and just, and revisionism can be legitimized solely for motives of political opportunism." -Paul Feyerabend
"Let me just anticipate that nobody to date has found a demarcation criteria according to which Darwin can be described as scientific, but this is exactly what we are looking for." -Imre Lakatos
XaosPeru wrote:BobSpence1
You still don't get it. We do have all kinds of ways of assessing which theories are most accurate, which is all anyone can know, and all that is needed.
The Greeks assumed "that things don't go on moving forever". They were wrong.
The Greeks were grossly mistaken about almost everything.
What you describe in that paragraph are indeed the ideas held at the time, and are absolutely wrong in every detail, which Galileo eventually showed experimentally.
Things do keep moving 'for ever' unless they encounter some force to change their state of motion. See Isaac Newton.
Are you a troll?
How can anyone claiming to have some modern education regurgitate this medieval nonsense as if were to be taken seriously??
The point about the moons of Jupiter is that they showed astronomical objects going around a body other than the earth - the 'impetus' theory had nothing to do with it.
The problem was not with the Bible, which did not say anything about Jupiter having moons, although it was aware of Jupiter, it is one of the classic stars, which include the five planets which are easily visible without a telescope.
The phases of Venus showed that it was at different times on opposite sides of the sun relative to the Earth, which they were unable to fit into a coherent picture with the assumed motions of all the bodies.
Absence of parallax observable with the instruments of the time did not disprove heliocentrism, but it meant that the stars had to be much further away than was believed at the time. It is NOT inconsistent with it, since they had no way to measure the distance to the stars until the instruments become sufficiently accurate to measure the actual parallax that we can now measure very accurately.
Copernicus theory still required epicycles, because he still assumed that all heavenly bodies moved in combinations of perfect circles. It was not till Kepler showed that they actaull moved in ellipses, that it all became much simpler, and laid the groundwork for Newton, since elliptical orbits are perfectly consistent with his Law of Gravitation.
I'm sorry, I see no point into even trying to address the rest of that post, which is either irrelevant or incorrect.
Favorite oxymorons: Gospel Truth, Rational Supernaturalist, Business Ethics, Christian Morality
"Theology is now little more than a branch of human ignorance. Indeed, it is ignorance with wings." - Sam Harris
The path to Truth lies via careful study of reality, not the dreams of our fallible minds - me
From the sublime to the ridiculous: Science -> Philosophy -> Theology
XaosPeru wrote:BobSpence1
We DONT know that any given sighting is random. That is missing the point. You have it backwards - I am just making the plain statement that IF the sighting was random, and at least 60 of the swans were white, THEN we would expect to see white ones 60% of the time.
Of course such possible differences in behaviour would change the actual observed probability, but it is irrelevant to the basic proposition, which simply states the probability IF color is the only variable. If the situation you describe were real, then if we never saw black swans during the day, then that would be interpreted as indicating that either there no black swans, or that if there were they have different habits in where and when they appear. It would then require more observations, such as more exhaustive searches of the island, including ones at different times.
To avoid the distraction of complications of two variety of birds on an island with possible differences in behavior, we usually give much simpler examples.
A common one is pulling a ball out of a bag blindly. If we have seen 60 balls place in the bag, and we know there are a total of 100, but we didn't see the others, then we would expect at least a 60% chance of pulling a white ball out after they had been adequately shaken up.
That is all I am saying. We do not require that our observations of what you list are 'random', it doesn;t always make sense, but any differences in the context of the observations which conceivably might be relevant to the conclusions would be taken into account by any competent investigator. If anyone else could make a case that something other factor had been ignored or overlooked, they would have to be responded to, and if necessary, further observation/experiments devised to test for them. That is how science is carried out. In some situations, randomised observations are indeed applied.
Favorite oxymorons: Gospel Truth, Rational Supernaturalist, Business Ethics, Christian Morality
"Theology is now little more than a branch of human ignorance. Indeed, it is ignorance with wings." - Sam Harris
The path to Truth lies via careful study of reality, not the dreams of our fallible minds - me
From the sublime to the ridiculous: Science -> Philosophy -> Theology
BobSpence1 wrote:You still
Yes, I know that you claim there are "...all kinds of ways of assessing which theories are most accurate, which is all anyone can know, and all that is needed." and that's why I came here from http://www.rationalresponders.com/why_the_problem_of_induction_really_isnt_a_problem_and_why_theists_dont_even_get_it_right - to see what the proposed solution is. I'm still waiting to hear it.
You said that the Greeks assumed that everything moved forever and they were wrong. I completely agree - but how did they arrive at those conclusions? Why they looked at the world around them and used induction to draw conclusions. Accordingly, we shouldn't be that surprised that the conclusions were wrong! Induction, as you see, has a problem and a very serious one at that. Philosophers have struggled for centuries to try to resolve it and, so far, unsuccessfully.
"..., which Galileo eventually showed experimentally." Again, wrong. The credit for proving the earth moves goes to James Bradley for discovering stellar aberration... long after Galileo was dead.
As for the phases of Venus, those easily fit into Tycho Brahe's model of the universe, which had the sun moving around the earth and the rest of the planets moving around the sun, and had no problem with moons moving around Jupiter.
And no, I'm not a troll.
As for Kepler, he showed no such thing about planets moving in elipses. He theorized as much based largely on his belief in the occult and his astrological leanings, believing that the planets should fit into a sort of a "musical harmony" which is why Newton was so reluctant to accept his theories (he being a fundamentalist Christian... most of Kepler's writings smacked of heresy and witchcraft to him). Kepler's beliefs about astrology are well documented at http://www.skyscript.co.uk/kepler2.html
So I'm sorry to burst your bubble about how science has steadily moved forward through the centuries using the scientific method to conquor error, Christianity, and ignorance. Science has stumbled around in circles like a drunken man for centuries and its current theories of how the solar system work are based on the musical symphonies of a self-proclaimed astrologer and the faith in the Christian God that Newton used as the basis for his theory of hypothetico-deductivism what you now proclaim to be the "scientific method."
I shall now read your other post, but really arguing about the minute details of history really doesn't interest me. I just want to know how it is that you think that you can "[assess] which theories are most accurate..."
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"The church at the time of Galileo was much more faithful to reason than Galileo himself, and also took into consideration the ethical and social consequences of Galileo's doctrine. Its verdict against Galileo was rational and just, and revisionism can be legitimized solely for motives of political opportunism." -Paul Feyerabend
"Let me just anticipate that nobody to date has found a demarcation criteria according to which Darwin can be described as scientific, but this is exactly what we are looking for." -Imre Lakatos
BobSpence1 wrote:We DONT
Most of this is a moot point because it was based on my understanding of how you were using Bayesian statistics to resolve the problem of induction... which I concluded was a bad understanding more than a week ago.
Look, let's make it simple. Let us postulate two things: 1) John is a man and 2) All men are mortal. Using standard (that is, deductive) logic we can conclude that John is mortal.
The problem I have is when Christina shows up and you say, "Since Christina is mortal, she is a man." This is a logical fallacy, which I haven't hesitated to point out several times. It is this very logical fallacy that is at the heart of the "scientific method" (hypothetico-deductivism).
To which you respond, "Yes, we haven't proved that Christina is a man, but it's pretty likely based on the evidence we have at hand." Or later you say, "Admittedly, we don't and can't know she's a man, but it's a good working model." Or you've seemed to imply that you can use Bayesian statistics to calculate the probability that Christina is a man. I'm all ears.
I side very strongly with Karl Popper when I say that Christina being mortal is neutral to the theory that Christina is a man. It neither proves nor disproves the theory. Similarly if we discover that Christina eats food, drinks water, sleeps 8 hours a night, can speak, likes going to pubs, and is a huge fan of Manchester United... it still does not increase the chance of her being a man in the slightest... pool tables, billiard balls, and drawn lines notwithstanding.
Now perhaps I'm completely wrong. With that in mind, I'm very interested in hearing the solution to the problem - Bayesian or otherwise.
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"The church at the time of Galileo was much more faithful to reason than Galileo himself, and also took into consideration the ethical and social consequences of Galileo's doctrine. Its verdict against Galileo was rational and just, and revisionism can be legitimized solely for motives of political opportunism." -Paul Feyerabend
"Let me just anticipate that nobody to date has found a demarcation criteria according to which Darwin can be described as scientific, but this is exactly what we are looking for." -Imre Lakatos
XaosPeru wrote:BobSpence1
Just where was induction involved there? Simply making observations and drawing conclusions applies to anything - it does not define 'induction'. Induction involves extrapolation beyond what is directly observed, and may be valid or invalid depending on the specific reasoning involved. Induction from empirical data and some kind of probability analysis is what makes 'proper' inductive analysis.
The Greeks got it wrong because they used intuiton and 'pure reason', and didn't do much actual empirical experiment and/or observation, which would have shown that they were wrong.
Not so much to do with induction either way.
The reference to Galileo there referring to the laws of motion vs the 'impetus' idea of Aristotle, not so much the Helio vs Geo centrism thing..
Galileo's astronomical problem was that his observations of the motions of the moons of Jupiter threatened the idea of strict geocentrism, with the Earth as the center of the Universe, with everything rotating around it.
Detection of the phases of Venus was important since:
That last system is becoming geometrically correct, if you express all astronomical motion relative to the Earth.
But again, this not really connected with the 'problem of induction', it was initially a matter of intuition, based on naive observation, without adequate testing and verification. Naive strict geocentrism, which was based on intuitive ideas of astronomical motion taking place in a perfect realm beyond the orbit of the moon and all motion being in simple pure circles, the circle being seen as the 'ideal' perfect Platonic 'form'.
As more detailed observations were made, more empirical data gathered, more problems showed up, and this simplistic model was forced to evolve into Tycho's system.
I have no intention of denying that Kepler got caught up in Astrology, and his 'laws' regarding the spacing of the planetary orbits were based on strange mystical beliefs about the 'perfect' shapes etc.
But he did discover that the orbital paths were best described by ellipses:
Carry on...
Don't worry, no chance of you upsetting my ideas about how science has developed progressively more accurate models of how things work, by minimizing the errors due to faulty observation, instrumental and human error, and conscious or unconscious bias in individual researchers.
The ideas of science, the hypotheses, have been inspired by even more fanciful things than you suggest, but the verification phase applied to any resultant theory is driven by harnessing the competitive nature of humanity seeking to be the first to establish a new paradigm, or just a new theory, and receive the adulation of his peers.
Science is never perfectly correct, occasionally mistaken, but largely self-correcting, whereas Christianity (and other religions) are permanently wrong, and self-reinforcing, dishonestly twisting and re-interpreting disconfirming observations, or simply ignoring them.
I have described at length how we assess the relative accuracy of various theories - probability math, including Bayesian analysis, correlation across different fields of investigation,etc.
Favorite oxymorons: Gospel Truth, Rational Supernaturalist, Business Ethics, Christian Morality
"Theology is now little more than a branch of human ignorance. Indeed, it is ignorance with wings." - Sam Harris
The path to Truth lies via careful study of reality, not the dreams of our fallible minds - me
From the sublime to the ridiculous: Science -> Philosophy -> Theology
XaosPeru wrote:BobSpence1
That is YOUR misunderstanding, since I was not using Bayesian analysis to 'resolve the problem of induction', merely to show how it could be made more rigorous.
Of course you are completely wrong!
Identifying induction with a classic logic fallacy is either disengenuous or genuinely dumb.
What you discuss is utterly irrelevant to induction.
Neither 1) or 2) are relevant.
If there was a proposition that 3) all mortals that we have observed are men, then you could start to discuss induction.
Then we observe another person. If there are no difference that seem to be beyond the range we have previously observed in mortals, which is pretty much what we base our assumption that the person is mortal, then we are logically justified in assuming this person is a man. If someone can demonstrate that this new person is sufficiently different in some ways to deserve to be put in a new category (woman), then we need to find out if these difference affect whether this person is mortal or not. If we have valid tests for this, and 'she' passes, then we can say that both categories, man and woman, are mortal.
Now what is your problem with this, if any?
There is no "problem of induction", there is only the inability of dumb philosophers to move beyond binary logic into probability-based arguments that is a problem.
Because you demonstrate such a complete misunderstanding of so many basic points, I have been consistently responding by simply explaining the basic process of scientifically analysing a problem or scenario with different examples.
You seem to see this as not providing 'proof' that induction works.
I have been providing examples of the scientific empirical/inductive method, and I ask you to point out where it 'goes of the rails', what unreasonable assumptions are being made.
Favorite oxymorons: Gospel Truth, Rational Supernaturalist, Business Ethics, Christian Morality
"Theology is now little more than a branch of human ignorance. Indeed, it is ignorance with wings." - Sam Harris
The path to Truth lies via careful study of reality, not the dreams of our fallible minds - me
From the sublime to the ridiculous: Science -> Philosophy -> Theology
Um, okay.Suppose that we
Um, okay.
Suppose that we have an entity named Christina, but we don't know anything else about it. It is at least possible that Christina is a man since men are entities.
Next, if we find out that Christina is a human, then it is more likely that Christina is a man than before since man is a larger subset of humans than of entities.
Would you agree with that?
Our revels now are ended. These our actors, | As I foretold you, were all spirits, and | Are melted into air, into thin air; | And, like the baseless fabric of this vision, | The cloud-capped towers, the gorgeous palaces, | The solemn temples, the great globe itself, - Yea, all which it inherit, shall dissolve, | And, like this insubstantial pageant faded, | Leave not a rack behind. We are such stuff | As dreams are made on, and our little life | Is rounded with a sleep. - Shakespeare
I think hypothetico-deductivism
is the issue and I guess we have to assume Xaos is an anti-realist of some kind. It's a head bending area arguing about inductive reasoning but the core element to me is that science works and for science to be successful there must be more to it than just the endless affirmings of the consequent that Xaos seems to be suggesting here. Most of us would agree that epistemic realism carries assumptions of truth. This truth is based on actual consequences our senses tell us about in this particular reality - the sense data we gather - but the anti-realist would claim this is question begging. Anti-realism, in a very odd way, demands stricter standards of philosophy than it demands of science tho' how that can possibly work is beyond me.
It's interesting that anti-realism itself depends on hypthetico-deductivism when accepting the empirical adequacy of a particular truth. This applies to Popper in reality, if not in theory. You have to think that if realists are guilty of a fallacy when explaining science, so is everybody else. Induction skeptics all employ induction and the only way to avoid the so-called problem of induction is to stop doing science completely. I like Popper's thinking but I think we are bound to inductive reasoning as we feel our way through the unknown. I don't think holding up things like dark matter annuls the profound depth and growth of scientific knowledge using inductive reasoning in the first instance.
In any case, Bob is not claiming inductive reasoning always works. He's saying it represents a best position in a given moment, with new data expected soon. This is the honest position. There are areas of understanding that use H-D processes as a form of abductive reasoning - or inference to best explanation. Such reasoning applies when the antecedent is the best explanation, given the truth of the consequent. For instance: Theory T predicts that we will observe E/Experimental observation shows E/Therefore theory T is true.
Pretty obviously, not all science is carried out in this way but it's exceedingly useful when we are at the limits of our ability to comprehend reality - weird stuff like the big bang, the existence of quarks, the maybe-Higgs Boson, the true nature of Bert Newton's face lift and so on. As long as the frailties of this sort of reasoning are acknowledged, inductive/abductive reasoning is useful to the overall process of attempting to gather knowledge. It's only when you insist H-D processes represent absolute truth that you run into trouble.
No one is doing that here.
"Experiments are the only means of knowledge at our disposal. The rest is poetry, imagination." Max Planck
First of all, let's just
First of all, let's just start and take it as a starting assumption (on faith, if you will) that induction works.
We can then move to the next step: Is induction falsifiable? I believe that it is, and therefore induction is a matter of scientific inquiry.
Accordingly I can ask what kind of things could I observe that would lead me to believe that induction has been falsified. Personally I think that watching people use induction and coming to the wrong conclusion would falsify induction.
As we seem to have already agreed, the Greeks used induction to come to the conclusion that no object moves forever. This is because Greeks had no experience with frictionless environments like those we believe to exist beyond the atmosphere of the Earth. As such, the Greeks used induction and came up with the wrong idea.
That alone should be enough to falsify the theory of induction, but other examples abound. People buying property believing that it will go up (based on the past) and being wrong. The hype over Psychic Octopus Paul (see http://www.telegraph.co.uk/sport/football/teams/spain/7881110/World-Cup-final-Paul-the-psychic-octopus-predicts-Spain-will-beat-Ho... ). Let's you and I agree that there are no psychic octopi and that all of the hubbub over the late psychic octopus is rubbish. But how did they arrive at that conclusion? Was it not through induction?
Ok so moving past that it seems that you basically agree with me that induction doesn't always work but you seem to feel that it works often enough to be worthwhile. Let us start out by agreeing that if induction works only 50% of the time that it is no better than flipping a coin. Additionally if it works only 50.4% of the time, then that 0.4% is not statistically significant.
So I'm asking you to demonstrate that induction works a statistically-significant percentage more often than flipping a coin. If you feel that's unreasonable for some reason, then let me know.
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"The church at the time of Galileo was much more faithful to reason than Galileo himself, and also took into consideration the ethical and social consequences of Galileo's doctrine. Its verdict against Galileo was rational and just, and revisionism can be legitimized solely for motives of political opportunism." -Paul Feyerabend
"Let me just anticipate that nobody to date has found a demarcation criteria according to which Darwin can be described as scientific, but this is exactly what we are looking for." -Imre Lakatos
butterbattle wrote:Um,
The thing is, I don't think it's possible to know that object X is a Y. We can look at an animal and decide that since it has four legs, non-cloven hooves, chews its cud, neighs, and is wearing a bridle that it is a horse. Really, however, we are just looking at aspects of the creature - those things that are physically observable and measurable. That it *is* a horse is impossible to state for certain. It might be a zebra, unicorn, zorse, or some completely new species of something.
Now I will certainly agree that if we *knew* that Christina was a human being that she becomes much more likely to be male. In fact, we can probably safely conclude that she's got a 48%ish chance of being a male (seeing as women are slightly more prevalent).
But I think by doing that we are getting away from the scientific method. Let's apply the scientific method to Christina.
(For those who are not familiar with the scientific method, I include http://www.sciencebuddies.org/science-fair-projects/project_scientific_method.shtml ) but I imagine this is unnecessary.
First I observe that Christina is bipedal and can speak. I note that she speaks English. I hypothesize that she is a man. Now I want to test this hypothesis by doing an experiment. So I place some catnip near here and she doesn't react. This tends to confirm the idea that she is a man (and certainly that she is not a cat). To ensure that it's not just an accident, I place catnip near her several times. The same response.
So now we figure that maybe Christina is hungry. So we put some tasty clover near her and a pizza. She prefers the pizza. After a few more tries we conclude that Christina doesn't like clover. We then conclude that this tends to confirm the hypothesis.
But does any of this really confirm the hypothesis? From the above website we read: "Your experiment tests whether your hypothesis is true or false. It is important for your experiment to be a fair test. You conduct a fair test by making sure that you change only one factor at a time while keeping all other conditions the same.You should also repeat your experiments several times to make sure that the first results weren't just an accident."
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Is it really true that these tests are determining whether the hypotehsis is true or false? I, personally, doubt it.
Falsification style, it's rather easier. We start out expressly to falsify the idea that Christina is a man. Men have penises and when we determine that Christina doesn't have one, we conclude that Christina is NOT a man. We have no idea what she is, but we do know what she is NOT.
Why, therefore, is Bayesian methodology superior to Popperian falsification?
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"The church at the time of Galileo was much more faithful to reason than Galileo himself, and also took into consideration the ethical and social consequences of Galileo's doctrine. Its verdict against Galileo was rational and just, and revisionism can be legitimized solely for motives of political opportunism." -Paul Feyerabend
"Let me just anticipate that nobody to date has found a demarcation criteria according to which Darwin can be described as scientific, but this is exactly what we are looking for." -Imre Lakatos
Atheistextremist wrote:is
Thank you for joining the conversation.
If I understand the purpose of this thread (based on the initial post) it is that Bayesian statistics enables one to calculate the probability of theory X being true. I should like to have an example, that's all.
I don't consider myself an anti-realist, rather an espistemological nihilist. I am not certain that truth exists. Assuming that it does exist, I don't see any way of knowing what that truth is. I believe that Popperian falsification can lead someone to know that something is definitely NOT true. This, however, has its limitations since most of the claims made in the world (e.g., God exists and created the universe) are not falsifiable.
You have made the claim that science works, but I don't know how you can claim to know that.
First of all, most of science fails due to an infinite regress problem of empiricism. If I wish to know, for example, that Alpha Centauri is the closest star to the sun, I will be unable to do that without eventually just taking someone's word for something. Even assuming that we rented a nice place in the Atacama desert and observed the star intensely for several days exactly six months apart (relying on parallax to tell us its distance) we would still be stymied by various things. First, we'd need to calculate our distance from the sun... the earth's orbit... we know that people claim it's 4.3 light years away so we'd need to calculate that distance ...that would require us to measure the speed of light in a vacuum ... in short, at some point, we'd just have to break down and look some of the information up and take the people's word for it. All of this, however, is beyond the scope of this thread, which is about induction and Bayesian statistics.
Now I note that a new thread has been created marked debate about induction. I plan to visit that thread later today (I've already read it and mentally formulated replies, but typing them is another matter ... I have to work once in awhile). Alternatively we could construct a new thread or take it private.
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"The church at the time of Galileo was much more faithful to reason than Galileo himself, and also took into consideration the ethical and social consequences of Galileo's doctrine. Its verdict against Galileo was rational and just, and revisionism can be legitimized solely for motives of political opportunism." -Paul Feyerabend
"Let me just anticipate that nobody to date has found a demarcation criteria according to which Darwin can be described as scientific, but this is exactly what we are looking for." -Imre Lakatos
XaosPeru wrote:So I'm asking
This is goofy. You do realize that statistics was derived using induction? It was all about determining if experimental results were important or not - see
I suppose if I had a lot (LOT) of time, I could come up with some sort of numbers as to how significant statistically the induction logic is. But I don't have that kind of time. Let's go with some examples.
You get up in the morning, hit the light switch and - "let there be light!" Yep, the induced laws of electromagnetism hold for yet another day. If the lights don't come on there is a reason - squirrels or lightning hit a power station or transformer, the lines are down, or you didn't pay your bill. You go to the john, and it flushes! Again! Amazing, the induced theoretical gravitational forces still work, the induced laws of flow and pressure still work, and the induced biological processes in your body are still functioning. Just like yesterday. If it doesn't flush, it is because it is plugged or you didn't pay your water bill. Did the sun come up in the east? Yep, induced cosmology is still true. No miracles today.
Are you a poe or a philosophy major? Or is running around in circles chasing your butt your normal state?
-- I feel so much better since I stopped trying to believe.
"We are entitled to our own opinions. We're not entitled to our own facts"- Al Franken
"If death isn't sweet oblivion, I will be severely disappointed" - Ruth M.
XaosPeru wrote:Is it really
Look, that is the point of knowing how to choose your tests. Clover or pizza has nothing to do with testing for maleness. You want to know biologically? Examine the genes. You want to know culturally or sociologically? You have to observe his/her life style choices. You want to know personally? Ask Christina.
Take any field of science - the people doing the research have been doing it for years. First, as grad students mentored by an experienced scientist in the field. Then, collaborating with other scientists. They have learned through experience what tests will give them relevant answers. They already know asking a fruit fly if it likes clover or smashed fruit to eat will tell them doodly squat about how the HOC gene works.
-- I feel so much better since I stopped trying to believe.
"We are entitled to our own opinions. We're not entitled to our own facts"- Al Franken
"If death isn't sweet oblivion, I will be severely disappointed" - Ruth M.
XaosPeru wrote:First of all,
No, because induction is a part of scientific enquiry, and no system of analysis or reason can be self-justified, including logical deduction.
To falsify induction, you would need to show that people applying induction were more likely to come to the wrong conclusion than people using some other technique applied to the same observations, or perhaps just random guessing.
Remember that the conclusion of inductive reasoning may be that the result of some process has a 50% chance of being one of two cases. This would apply to inductive analysis of coin-flipping.
Induction would only be falsified by a single incorrect result if an inherent claim was that it would always produce a correct conclusion, which is most definitely NOT the case.
It claims only a probably correct conclusion, so it would require a statistical process based over a number of examples, the more examples in which it failed more often than it succeeded would give you increasing confidence that induction didn't work, but that would be an inductive conclusion....
The Greeks did not use induction to come to that conclusion, they used informal observation and intuition. It was the reliance on intuition rather than empirical observation that lead to the error.
Even if they arguably did use induction, that certainly would not falsify induction, unless you could show that the observations and any prior assumptions they based their conclusions on clearly pointed to a different conclusion. Otherwise, it may only be simply inadequate investigation.
Otherwise you would be equally justified in saying any mode of reasoning and/or analysis that didn't always come up with the 'correct' result had been 'falsified'.
Looking at what has happened in the past is a basic starting point for any valid decision making process.
While relying purely on historical evidence is certainly not guaranteed to lead to a good decision, ignoring previous history is highly likely to be associated with bad decisions.
If you do not have any other evidence to base your decision on, basing a necessary decision on historical evidence is the ONLY rational thing to do, even if not guaranteed to work out well, it would be insane to do otherwise, just as it would be crazy not use more direct information as well, if it is available.
Let me see.
Consider case 1: We only have historical data on which to base a decision. If we don't use that data, we are left with a coin flip.
Ironically, the expected outcomes of flipping a particular coin are only known by historical data, ideally 50% likelihood for each possible outcome.
So you are saying that using historical data is no more reliable than flipping a coin.
If we do use other data, that's where, ideally, Bayesian analysis comes in, in giving us a way to try and compare the relative reliability and relevance of the historical and non-historical data. So it is no longer pure induction.
You can substitute the idea of data gained under conditions significantly different from what is currently being considered, for 'historical'.
So you require me to demonstrate that a given system is more likely to behave the same as it has in the past, or in other conditions, than otherwise, given no indication to the contrary?
I suppose that is consistent with the idea that we have no guarantee that the laws of the Universe will not completely change in the next second.
Taking that seriously and basing our behaviour on that being a serious probability would paralyse us or lead to total chaos.
Is that how you are currently living?
It would be a logical implication of the existence of an all-powerful sentient being with access to our Universe, of course.
So if you don't actively base your every decision, or at least all important ones, on the assumption that things could arbitrarily change completely at any instant, you are effectively assuming induction is valid.
Favorite oxymorons: Gospel Truth, Rational Supernaturalist, Business Ethics, Christian Morality
"Theology is now little more than a branch of human ignorance. Indeed, it is ignorance with wings." - Sam Harris
The path to Truth lies via careful study of reality, not the dreams of our fallible minds - me
From the sublime to the ridiculous: Science -> Philosophy -> Theology
You misunderstand. You
You misunderstand. You assume that humans use induction as their primary decision making method. I disagree.
Let's take a simple example. Every night I drive home and pass a school. There is a stop sign near the school. I have passed there hundreds of times and there is never any cross traffic nor pedestrians (as I go by quite late and the school is closed). Nevertheless, I always come to a stop and then proceed. Why? Induction? No ... quite simply, I figure that the gain if I'm right (home 5 seconds faster) is offset by the loss if I'm wrong (accident, ticket, points on my license, higher insurance costs, etc.). I believe that people make the same decision process many thousands of times per day in differing situations.
Although there are aspects of mathematics that are unproven (and by extension, statistics) it is not true that statistics, generally speaking, is inductive in nature. If, for example, I am playing a game of bridge and playing in a specific suit (missing the king) I am leading towards a AQ combination. My left-hand opponent (LHO) produces the two and I am trying to figure out if I should play the Ace or the Queen. If my LHO has the King, the Queen will win. If, on the other hand, my RHO has the King then the Queen will fail. We observe that my LHO has 6 unknown cards (the 2 on the table is now known) while my RHO waiting for me to play has 7 unknown cards. As such, I can calculate the probability that my LHO has the King as 6/13 or about 46.154 percent. What's inductive about that?
Accordingly I disagree with you when you say, "Looking at what has happened in the past is a basic starting point for any valid decision making process." Neither of the above-mentioned decision making processes relied on looking at the past.
-----------------------------------
I note you said, "So if you don't actively base your every decision, or at least all important ones, on the assumption that things could arbitrarily change completely at any instant, you are effectively assuming induction is valid."
I disagree. Let's take the starting point the idea that the sun could go supernova at any second exterminating all life on earth. Bear with me for a moment, and think for a moment - how could we mitigate that possibility? We know of no action to take that would help us in that eventuality so why worry about it? One might as well adopt a fatalistic outlook.
On the other hand, let's assume that the stove(cooker) which I have used faithfully for so many nights in a row suddenly and unexpectedly goes bad on me and lights my house on fire. I am (at least partially) prepared for that eventuality because I have a fire extinguisher available to help me in that situation. Induction would lead me to believe that the fire extinguisher was unnecessary. This same sort of reasoning explains why we have smoke detectors and have fire drills.
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"The church at the time of Galileo was much more faithful to reason than Galileo himself, and also took into consideration the ethical and social consequences of Galileo's doctrine. Its verdict against Galileo was rational and just, and revisionism can be legitimized solely for motives of political opportunism." -Paul Feyerabend
"Let me just anticipate that nobody to date has found a demarcation criteria according to which Darwin can be described as scientific, but this is exactly what we are looking for." -Imre Lakatos
Ooohh, so you do understand
Ooohh, so you do understand and recognize that you use inductive reasoning. You just refuse to call it that.
You just pick logical fallacies and call them induction.
Our revels now are ended. These our actors, | As I foretold you, were all spirits, and | Are melted into air, into thin air; | And, like the baseless fabric of this vision, | The cloud-capped towers, the gorgeous palaces, | The solemn temples, the great globe itself, - Yea, all which it inherit, shall dissolve, | And, like this insubstantial pageant faded, | Leave not a rack behind. We are such stuff | As dreams are made on, and our little life | Is rounded with a sleep. - Shakespeare
Induction right there
There is a stop sign. People have been booked in the past, including me on my motorbike last Christmas day, for not coming to a complete stop with both feet on the ground at some other stop sign. If I ride through this stop sign I could be booked. I will stop.
Help, some one like Eloise. Isn't mathematical induction actually defined as deductive reasoning?
"Experiments are the only means of knowledge at our disposal. The rest is poetry, imagination." Max Planck
Atheistextremist
You are 100% right - mathematical induction is, indeed, deductive reasoning. It is a form of proof in which the formula is proved to work for number 1. Then the person proceeds to prove that for any number (n+1) the formula is true if (n) is also true. This is an effective proof for the whole number system. This should not be construed as inductive reasoning. It is deductive in nature as is all of mathematics.
You seem to be attempting to misconstrue the stop sign situation as an example of induction. Perhaps a clearer example will help you see that it is not.
Yesterday someone asked about my family. I told them they were all in excellent health. As I did so, I reached out to a nearby wooden door and knocked on it. Why did I do that? Because the cost of that action, if wrong, is basically zero. I knock on the door and no harm comes to my family regardless. The potential cost of not performing that action, if wrong, would be serious illness, harm, death, etc., whatever, to my family.
Now surely you wouldn't infer that in the past I observed someone who failed to knock on the door and his family were immediately stricken with horrible diseases because of his failure to perform the necessary, superstitious act, and that I have concluded because of that (or a variety of similar experiences) that failure to knock on the door resulted in horrible diseases on my family through induction... would you?
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"The church at the time of Galileo was much more faithful to reason than Galileo himself, and also took into consideration the ethical and social consequences of Galileo's doctrine. Its verdict against Galileo was rational and just, and revisionism can be legitimized solely for motives of political opportunism." -Paul Feyerabend
"Let me just anticipate that nobody to date has found a demarcation criteria according to which Darwin can be described as scientific, but this is exactly what we are looking for." -Imre Lakatos
XaosPeru wrote:Now surely
What I would conclude is that the superstitious dummy didn't remember all the times he had knocked on wood and his family were stricken horribly anyway. It's called confirmation bias. That is why peer review is so important in any scientific study. Scientists are human, too, and they like to avoid mistakes. So peer review helps them avoid confirmation bias. Blind studies - where the doctor doesn't know who gets the placebo and who gets the real experimental drug - is another way to overcome this bias. Which patient got what is not revealed to anyone. The patients are assigned a number and the results are analyzed without using names.
Same happens when people pray. They remember all the times they get what they prayed for and forget all the times they didn't get what they wanted. Or else, they rationalize with "it's god's will". Religion is the ultimate steady source of income for the preachers. When there were only shamen and other magic workers, they had to get results. Or they were disinvited from the job. Preachers can claim the good results as the result of their hard praying and claim "god's will" for all the times praying doesn't work. Easy money. Too bad I'm so ethical.
-- I feel so much better since I stopped trying to believe.
"We are entitled to our own opinions. We're not entitled to our own facts"- Al Franken
"If death isn't sweet oblivion, I will be severely disappointed" - Ruth M.