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Author Topic:   Induction and Science
Modulous
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Posts: 7801
From: Manchester, UK
Joined: 05-01-2005


Message 4 of 744 (283935)
02-04-2006 2:55 PM
Reply to: Message 1 by nwr
02-04-2006 2:36 PM


Induction
  • Yesterday, I bumped into Betty Crowe. She was wearing black shoes.
  • Two weeks ago, I was introduced to John Crowe. I happened to notice that he was wearing black shoes.
  • Bob Crowe was one of my high school friends. As I recall, he wore black shoes.
    Tentative conclusion: all Crowes are wearing black shoes.
    Test: Find more Crowes and see if they are wearing black shoes.
    The more Crowes we find with black shoes the stronger our conclusion
    Falsification: If we find one Crowe with non-black shoes
  • For every action there is a an equal and opposite reaction.
    Can we be sure that this will apply tommorrow? Or that it applies to all things that happen in Alpha Centauri?

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    Modulous
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    Posts: 7801
    From: Manchester, UK
    Joined: 05-01-2005


    Message 7 of 744 (283939)
    02-04-2006 3:06 PM
    Reply to: Message 1 by nwr
    02-04-2006 2:36 PM


    Another thing that science does with this kind of logic is explore whether it is reasonable to make the inductive leap. Is it reasonable to consider that all Crowes wear exclusively black footwear? If we had some theory as to why they might all wear black footwear, then we can make the induction.
    In this case, it is not particulary reasonable to make that leap. We have never seen a family-name being linked 100% with a fashion, so we cannot make the inductive leap that family-names and fashion tastes are linked somehow.

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    Modulous
    Member
    Posts: 7801
    From: Manchester, UK
    Joined: 05-01-2005


    Message 11 of 744 (283947)
    02-04-2006 3:41 PM
    Reply to: Message 8 by nwr
    02-04-2006 3:26 PM


    Re: Response to messages in older thread.
    If we change the inductive conclusion to "All crows are black, excepting those which are not black", then I grant the correctness of the conclusion. But it is no longer induction, it is tautology.
    The conclusion isn't a certainty. Its tentative. The conclusion is that 'all crows are black, but we might change our mind in the future should any non-black crows turn up'. That's scientific induction.
    The logic there is impeccable. The problem is with one of the premises.
    Right, and the problem with the first problem was that we had only observed black crows. You piped up with "Are you saying we have never seen an albino crow?". That's not the point, there is no need to take the statement "We have observed only black crows" literally.
    Not so. It also leaves empirical methodology, and that is the heart of science.
    Yes, but what is empirical methodology. Doesn't the methodology include making inductions? We observe a small subset of events and make general conclusions about all events that share the same properties.

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    Modulous
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    Posts: 7801
    From: Manchester, UK
    Joined: 05-01-2005


    Message 12 of 744 (283949)
    02-04-2006 3:44 PM
    Reply to: Message 9 by nwr
    02-04-2006 3:34 PM


    Re: Is it reasonable?
    That was Nelson Goodman's explanation of his "grue" paradox. But it cannot explain science. If science depends on induction, but you only use inductions of the type that have worked before, then there is no way to get started and no way to get started in a new branch of science.
    You seem to think that the position is that science is ONLY based on induction. Not so. Induction is used, deduction is used.
    No, it isn't reasonable. But why not? Isn't that something philosophers, the self-appointed experts on reason, should have investigated?
    I said why not:
    quote:
    We have never seen a family-name being linked 100% with a fashion, so we cannot make the inductive leap that family-names and fashion tastes are linked somehow.

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    Modulous
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    Posts: 7801
    From: Manchester, UK
    Joined: 05-01-2005


    Message 14 of 744 (283953)
    02-04-2006 4:04 PM
    Reply to: Message 13 by nwr
    02-04-2006 3:56 PM


    Re: The irony of it all
    Clint is a chimp.
    His DNA is 96% to the sampled human DNA
    Observation: When we look at a species' DNA, they tend to have such similarities that we can consider them the same.
    Induction: All chimpanzee DNA is 96% similar to all human DNA.
    Ironic, science isn't it. Its almost like it insists that it can never arrive at definite conclusions about anything. Its almost like tentativity and falsification are practically built into the concept of science.
    Personally, I think the reason for tentativeness of science is because it makes inductive general statements about the world and the universe, based on a small subset of observations.
    Perhaps you can show me how induction isn't made by science?

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    Modulous
    Member
    Posts: 7801
    From: Manchester, UK
    Joined: 05-01-2005


    Message 17 of 744 (283959)
    02-04-2006 4:15 PM
    Reply to: Message 16 by nwr
    02-04-2006 4:12 PM


    Re: Is it reasonable?
    And I debunked it in Message 9:
    If science depends on induction, but you only use inductions of the type that have worked before, then there is no way to get started and no way to get started in a new branch of science.
    Which I responded to in Message 12:
    You seem to think that the position is that science is ONLY based on induction. Not so. Induction is used, deduction is used.
    AbE: In our case:
    We observe that there are family-names which are 100% tied to certain fashions. We observe that the Crowes that we have seen all wear black shoes. We make the reasonable induction that the Crowes are 100% tied to the black shoe fashion. We appreciate the conclusion is tentative, and will be falsified by observing a Crowe wearing non-black shoes. Let's go find some Crowes.
    This message has been edited by Modulous, Sat, 04-February-2006 09:18 PM

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    Modulous
    Member
    Posts: 7801
    From: Manchester, UK
    Joined: 05-01-2005


    Message 23 of 744 (283980)
    02-04-2006 6:11 PM
    Reply to: Message 21 by nwr
    02-04-2006 4:50 PM


    Re: Crowes and crows
    What is the difference between these cases?
    Modulous attempted to explain the difference in Message 9. IMO his explanation does not work.
    For two reasons you are wrong. First is that Message 9 is your post. Second I don't think there are any important differences between the two examples. The only difference is that with crows we have a reason to make the inductive leap.
    I am arguing that what is said to result from induction is actually the result of systematic methodology. Because the study of birds has been systematic, and the name "crow" assigned as a result of that systematic methodology, we can be assured that crows form a reasonably homogeneous group of birds. An inference on the color of crows is based on this homogeneity. In effect, it is a kind of interpolation or extrapolation over a continuum, based on the evidence of a few examples. By contrast, the people named "Crowe" are expected to be relatively inhomogeneous, and thus we would not expect interpolation or extrapolation to be useful.
    Which is what I said:
    quote:
    We have never seen a family-name being linked 100% with a fashion, so we cannot make the inductive leap that family-names and fashion tastes are linked somehow.
    We have no reason to make the inductive leap with regards to fashion and family names, so the induction is a bit silly and unfounded.

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    Modulous
    Member
    Posts: 7801
    From: Manchester, UK
    Joined: 05-01-2005


    Message 29 of 744 (284024)
    02-04-2006 8:28 PM
    Reply to: Message 27 by nwr
    02-04-2006 8:03 PM


    Re: Crowes and crows
    Then you assert that there is a difference, important enough that induction would work. Seems contradictory.
    Not that induction would work but that it would be the kind of induction that science would make. There is no real difference in the induction process itself, its just that one has an actual rationale behind making the induction.
    No, it isn't what you said. As a reason for a difference, you gave past experience. My reason was that the naming procedures for "crow" and "Crowe" are quite different, with one being systematic.
    I did not give past experience as a difference. I said that we have reason for making the induction with crows. That reason is as you have listed. We have no link between family name and fashion preference. The two have no percieved reason to be linked. However with crows we do have a link: genetics and observation.
    It would be reasonable to assume, after viewing an enormous amount of crows that all crows were black, but realize that it is tentative.
    It is not reasonable to assume that all Crowes wear black shoes unless we had previous reason to think that family names were somehow linked with fashion tastes. We don't have this reason, thus it is unreasonable, and unscientific.
    So yes, we name crows because of their characteristics, which might include black. It is reasonable to think that all crows share certain properties and it is reasonable to think (by induction) that all crows share the same colour.
    If we had a similar reason to think family names worked in the same way, it would be a more scientific induction, or perhaps some family names themselves have psychological effects. For example if we knew that everyone with the surname Robin wore red waistcoats, and other names had similar strange affects on psychology, we might make the induction that the surname Crowe is one of these names after a good amount of observations confirming it.
    If you read the literature on induction, and there is quite a bit of it, you won't find reference to a principle "you have to have a reason to make the inductive leap." The input to the induction is supposed to be reason enough.
    Right I know I won't. But science doesn't base its results purely on inductive reasoning, but it does use inductive reasoning as part of its arsenal to describe the world we live in.
    Incidentally, I have provided several examples of induction in science. Can you demonstrate why induction wasn't used, or show some other science that uses no induction whatsoever?

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    Modulous
    Member
    Posts: 7801
    From: Manchester, UK
    Joined: 05-01-2005


    Message 38 of 744 (284107)
    02-05-2006 8:56 AM
    Reply to: Message 30 by nwr
    02-04-2006 10:04 PM


    Induction is not science, science is not induction
    Okay. But then you are relying on a different meaning for "induction."
    The usual account talks of the "logic of induction." If it is logic, then it is operation on symbols. Questions such as "an actual rationale" do not arise if induction is taken as a logic operation.
    I am using induction to mean
    quote:
    The process of deriving general principles from particular facts or instances.
    Science doesn't exclusively use induction, it uses induction as one of its tools. Using induction doesn't mean you are being scientific.

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    Modulous
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    Posts: 7801
    From: Manchester, UK
    Joined: 05-01-2005


    Message 50 of 744 (284187)
    02-05-2006 4:24 PM
    Reply to: Message 48 by nwr
    02-05-2006 4:09 PM


    All Boeing 737 passenger aircraft have arrived safely at their destination. By induction, all such aircraft will arrive safely. Oops, one of them crashed, so the induction has failed.
    Yes, the hypothesis that aircraft will arrive safely has been falsified. It was induction, but it was not scientific induction.
    We actually learn a lot from work by groups such as the NTSB. We make scientific advances by investigating apparent induction failures.
    We find that there was a hairline fracture in the jet engine. We know by experiment that hairline fractures can lead to weaknesses in jet engines.
    We make the inductive leap that the experiments on jet engines are applicable to the jet engine on the plane that crashed. (We derive a general principle from particular facts). The inductive leap has a reasoned argument behind making it. This is science.

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    Modulous
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    Posts: 7801
    From: Manchester, UK
    Joined: 05-01-2005


    Message 51 of 744 (284190)
    02-05-2006 4:29 PM
    Reply to: Message 45 by nwr
    02-05-2006 3:50 PM


    Re: Induction is not science, science is not induction
    I am arguing that it is often the other way around. That is, we start with general principles, and use those to enable us to find particular facts.
    Indeed, we can apply science to find particular facts. Scientific theories are massively inductive in nature...they are the epitome of deriving general principles from particular facts.
    The frequency of it being the other way around is not important just yet, the concession that some frequency of induction is involved in science is a good start.
    This message has been edited by Modulous, Sun, 05-February-2006 09:33 PM

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    Modulous
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    Posts: 7801
    From: Manchester, UK
    Joined: 05-01-2005


    Message 78 of 744 (285452)
    02-10-2006 9:16 AM


    Reasoning
    Deductive reasoning: If the premises are true then conclusion is true.
    Inductive reasoning: If the premises are true, the conclusion follows with some degree of probability.
    Abductive reasoning: Inference to the best explanation (aka science).
    Charles S. Peirce writes:
    Abduction having suggested a theory, we employ deduction to deduce from that ideal theory a promiscuous variety of consequences to the effect that if we perform certain acts, we shall find ourselves confronted with certain experiences. We then proceed to try these experiments, and if the predictions of the theory are verified, we have a proportionate confidence that the experiments that remain to be tried will confirm the theory [Peirce previously refers to this as induction]. I say that these three are the only elementary modes of reasoning there are.
    I think that basically sums up what I've been trying to say on this thread. Science uses induction, but not exclusively, it uses other tools also.

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    Modulous
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    Posts: 7801
    From: Manchester, UK
    Joined: 05-01-2005


    Message 82 of 744 (285802)
    02-11-2006 5:49 AM
    Reply to: Message 80 by nwr
    02-10-2006 11:59 PM


    Re: Reasoning
    At first glance, abductive reasoning seems to better describe what science does. However as far as I can tell
    * no inference procedure is given;
    * there is no guarantee that there is a best explanation;
    * even if there is a best explanation, that might not be the one that science comes up with.
    I think that the reasoning process isn't necessarily a rigidly logical one, and that some 'creativity' is there. As for the second two, I believe you've summed up tentativity.

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    Modulous
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    Posts: 7801
    From: Manchester, UK
    Joined: 05-01-2005


    Message 180 of 744 (590835)
    11-10-2010 3:30 AM
    Reply to: Message 165 by nwr
    11-09-2010 8:45 PM


    Re: Induction And Science
    There are natural phenomena. Gravity is a natural phenomenon. But the laws of gravity are not part of nature. They are human constructs that we use as part of our system for representing/describing what happens in nature.
    Correction: they are human constructs that we use to describe what has happened in nature according to our limited set of observations. If you want to say 'happens' then you are using induction.
    I'm saying that Newtonian physics is not simply a matter of induction.
    No. But relying on Newtonian physics in novel situations would be induction.

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    Modulous
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    Posts: 7801
    From: Manchester, UK
    Joined: 05-01-2005


    Message 200 of 744 (590939)
    11-10-2010 4:50 PM
    Reply to: Message 189 by nwr
    11-10-2010 12:14 PM


    Induction And statistical reasoning
    I take induction to be making a truth claim. It might be an uncertain truth claim, but it is still a truth claim.
    Indeed. And if you say it is true that it is not certain, but probably true that gravity will be functioning next week, that your chair will exert an 'opposite force' to keep you falling on your ass, and that your car won't accelerate to light speed when you press the accelerator - then you are making an induction.
    When you say
    quote:
    I would call that "statistical reasoning" rather than "inductive logic."
    I have already agree that we use statistical reasoning
    you are saying that you accept induction. This article on inductive logic is almost entirely composed of statistical reasoning. It is very concerned with how confident we can be of our inductions using statistical reasoning.
    quote:
    An inductive logic is a system of reasoning that extends deductive logic to less-than-certain inferences. In a valid deductive argument the premises logically entail the conclusion, where such entailment means that the truth of the premises provides a guarantee of the truth of the conclusion. Similarly, in a good inductive argument the premises should provide some degree of support for the conclusion, where such support means that the truth of the premises indicates with some degree of strength that the conclusion is true. Presumably, if the logic of good inductive arguments is to be of any real value, the measure of support it articulates should meet the following condition:
    Criterion of Adequacy (CoA):
    As evidence accumulates, the degree to which the collection of true evidence statements comes to support a hypothesis, as measured by the logic, should tend to indicate that false hypotheses are probably false and that true hypotheses are probably true.
    {Several sections later...}
    The versions of Bayes' Theorem provided by Equations 9-11 show that for probabilistic inductive logic the influence of empirical evidence on posterior probabilities of hypotheses is completely captured by the ratios of likelihoods, P[en | hjbcn] / P[en | hibcn]. The evidence (cnen) influences the posterior probabilities in no other way. So, the following Law is a consequence of the inductive logic of support functions.
    General Law of Likelihood:
    Given any pair of incompatible hypotheses hi and hj, whenever the likelihoods Pα[en | hjbcn] and Pα[en | hibcn] are defined, the evidence (cnen) supports hi over hj, given b, if and only if Pα[en | hibcn] > Pα[en | hjbcn]. The ratio of likelihoods Pα[en | hibcn] / Pα[en | hjbcn] measures the strength of the evidence for hi over hj given b.
    Two features of this law require some explanation. As stated, the General Law of Likelihood does not presuppose that likelihoods of form Pα[en | hjbcn] and Pα[en | hibcn] are always defined. This qualification is introduced to accommodate a conception of evidential support called Likelihoodism, which is especially influential among statisticians. Also, the likelihoods in the law are expressed with the subscript α attached to indicate that the law holds for each inductive support function Pα, even when the values of the likelihoods are not objective or agreed on by all agents in a given scientific community.
    emphasis in original (definitions of most of the symbols are laid out in unquoted reams of text - making it difficult to quote)
    Edited by Modulous, : No reason given.

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