Induction and Science

And I debunked it in Message 9:

Which I responded to in Message 12: 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

If I had listed 1000 encounter with Crowes, would that make it any more persuasive? I am questioning whether science depends on "true regularities", and even whether there are such things.

Maybe I explained my point poorly.I was not suggesting irony in the way that ToE arose. Rather, I was pointing to such discoveries as that homo sapiens can find a viable niche on this planet, apparently without using induction in that process of discovery.

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Rather, I was pointing to such discoveries as that homo sapiens can find a viable niche on this planet, apparently without using induction in that process of discovery.

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Because we are not discussing how a species finds a viable niche, nor how people live their day-to-day lives, nor how I find my house keys when I have misplaced them. We are discussing how scientists practice science.

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"Intellectually, scientifically, even artistically, fundamentalism -- biblical literalism -- is a road to nowhere, because it insists on fidelity to revealed truths that are not true." -- Katha Pollitt

In Message 1, I gave an induction regarding Crowes (people named Crowe).

In Message 241, Modulous quoted wiki on a traditional induction regarding crows (the birds).

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What is the difference between these cases?

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Modulous attempted to explain the difference in Message 9 Message 7. IMO his explanation does not work.

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Here is the difference as I see it:

The assignment of a name such as "Crowe" to people is pretty much arbitrary.

The assignment of a name such as "crow" to birds is a result of using systematic methodology.

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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.

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In summary, it is systematicity, not induction, that is important to science.

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(edit: corrected message reference)

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This message has been edited by nwr, 02-04-2006 06:51 PM

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By contrast, the people named "Crowe" are expected to be relatively inhomogeneous, and thus we would not expect interpolation or extrapolation to be useful.

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But the fact that all of the Crowes observed wear black shoes seems to suggest that Crowes are somewhat homogenous after all.

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"Intellectually, scientifically, even artistically, fundamentalism -- biblical literalism -- is a road to nowhere, because it insists on fidelity to revealed truths that are not true." -- Katha Pollitt

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. Which is what I said:

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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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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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If I had listed 1000 encounter with Crowes, would that make it any more persuasive?

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Doesn't this all depend on how many Crowe's we think exist? Therefore, the degree of certainty to which our inductive generalization is supported depends on how general our hypothesis is. This is similar to Hempel's solution to the "Paradox of the Ravens."() Whatever confirms a hypothesis also confirms a logically equivalent one() A generalization of the form “All F are G” is confirmed by its positive instances-i.e., by cases of F that have been found to be G.(p) All ravens are black(p*) All non-black things are non-ravenAccording to (), a non-black non-raven will support (p*); according to (), any observation that supports (p*) will support (p). Therefore, a non-black non-raven will support (p). A red apple will support the proposition that “All ravens are black.”Hempel’s solution is that both a black raven and a non-black non-raven support the proposition that “All ravens are black,” but they do so to different degrees. The non-black non-raven supports (p) to a much smaller degree than a black raven would. In order to understand this, imagine the similar proposition that “All coins in this container are pennies” and imagine that we know there are 100 coins in the container. Now imagine Joe checks one coin and discovers it is a penny. Jack then checks 99 coins in the container and they are also all pennies. According to (), both these positive instances support the original proposition. Yet, would not Jack have much more confidence in the proposition than Joe? Is it reasonable to say that they supported the proposition to varying degrees? The answer seems to be yes.To model it mathematically, if the claim is that “All F are G,” then the degree of confirmation (assuming there are no negative instances) is the ratio of the number of positive instances (F+) to the number of (F)s:Degree of Confirmation (DoC) = [ (F+)/F]A degree of confirmation of 1 would represent absolute confirmation. In the penny example, Jack would have a degree of confirmation of .99, whereas Joe would only have a degree of confirmation of .01.
Bringing this back to the “Paradox of the Ravens,” let us use this formula to get a feel for the different degrees with which a black raven and a non-black non-raven would support (p). In both cases the numerator would be 1. The difference comes in the denominator. The set of all non-black things in the universe is gigantic. Therefore, the non-black non-raven would confirm (p*) only to an infinitesimally small degree. Since the degree of confirmation is the same for two logically equivalent statements (), a non-black non-raven would support (p) as much as it supports (p*), which is practically zero. On the other hand, the set of black ravens in the universe is much smaller than the set of non-black things. The DoC associated with observing a black raven would therefore be much higher than the DoC associated with observing a non-black non-raven.So, the degree to which we accept a hypothesis would depend on its DoC. I know this is kind of hard to think about in terms of major generalizations (e.g., all mass is correlated with curved spacetime), but as long as there are no counter-instances you have to accept the generatlization with the highest DoC, imo.

Ha ha ha. I love Hempel's Paradox. I bring it into the Math Concepts class that I teach when we do symbolic logic.In my opinion, that is exactly the essential difference between crows and Crowes. Assuming, for the sake of argument, that we have never seen a non-black crow, then we can assume that, over recorded history, we have seen a significant fraction of crows -- enough to come to a definite conclusion that crows are black.On the other hand, without knowing how many Crowes there are, the fact that all the Crowes we have seen were wearing black shoes could be due to the statistically small sample that we have observed.Added by edit:By small, I mean not only the small number of Crowes relative to the total number of Crowes, but the small fraction of the lives of each one where we have seen them wearing anything at all.This message has been edited by Chiroptera, 04-Feb-2006 11:41 PM

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"Intellectually, scientifically, even artistically, fundamentalism -- biblical literalism -- is a road to nowhere, because it insists on fidelity to revealed truths that are not true." -- Katha Pollitt

Perhaps it could be said to hint at some homogeneity. Still, scientists would not jump to an induction. Rather, they would investigate to look for a common cause.

Apologies on the incorrect reference. I have now edited my earlier message to correct that.You assert that there are no important differences.
Then you assert that there is a difference, important enough that induction would work. Seems contradictory. 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. Of course it is silly. That's why I picked it as an example.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.

In the often presented example of crows, the standard literature does not suggest that you need to know how many crows exist.

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. 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. 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?

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.