[2012-Jan-08] What is Beauty

[Stu]

I've seen the idea of "induction is impossible" used as the premise for jokes a few times now. I was wondering if anyone could explain this concept to me or point me to a source for reading up on it. Or, is it just a creation of Zach's?

MOD EDIT:
ANSWER ON PAGE 3

[Pitch Hitter]

When you induce something, you require something to induce from. However there is nothing to induce from because you must induce to it first.

It's like climbing a ladder except before climb a rung you must climb the rung before. There is no way to know the start of this ladder and also it's very expensive ladder.

[anon]

The problem of induction proper started with Hume, if you read An Enquiry Concerning Human Understanding it's in their. Also If you just google the problem of induction you'll find a ton of articles, it's a big question in epistemology. Or just google the stanford encyclopedia of philosophy and search induction, it sums up the debate well.

[ChaoticBrain]

and also it's very expensive ladder.

I would pay all the dollars to own an infinitely long ladder.

[Pitch Hitter]

well whoever sold you that ladder would be making a very bad deal, no matter how hard Ben Bernanke tries (some very topical humour there, I hope you appreciate it) there aren't infinite dollars.

[DonRetrasado]

An example of inductive reasoning (stolen from wiki) goes like such:

All of the swans that all living beings have ever seen are white
Therefore, all swans are white.

Of course, we know that this doesn't actually "prove" anything. No matter how many swans you see that are white, it's always possible that one day you will find a swan that is not white, meaning that our conclusion was incorrect. That's why science hinges on the belief that induction is real; even though the scientific method says that, with enough data, we should always get a predictable result, there's always the possibility that something comes up and smashes that to bits (which, as we know, happens quite frequently). Science and induction are extremely useful to us but they're not "real" or "truth" in the same way that, for instance, deductive reasoning is. (of course, many philosophers, like Descartes, argued that the number of "real" conclusions we could derive from deductive reasoning is actually quite limited)

[Quintushalls]

LESS PHILOSOPHY JOKES!!! MORE DICK JOKES!!!

[Danny Boy (London Derriere)]

Induction has (generally) worked so far. So I guess it will continue to.

[gforce121]

I think that Karl Popper actually addressed the problem of induction in his work "The Logic of Scientific Discovery". His idea of science/knowledge was that it was created by conjecture and refutation, in his words the criterion of falsifiability. Science isn't, or doesn't have to be based upon logical induction.

[abb3w]

What axiom gives the basis for a (poset? ordering?) relationship of "highest" over the set of use choices?

[abb3w]

Oh, for a hideously mathematical justification of induction (in the philosophical sense) as a basis for probabilistic inference, see "Minimum Description Length Induction, Bayesianism, and Kolmogorov Complexity" by Vitanyi and Li (doi:10.1109/18.825807). The principle therein can be extended to higher (non-zero) ordinals of Turing hypercomputer model, rather than just Recursively Enumerable complexity (the 0 case). It depends on the existence of such an ordinal and on the standard axioms of ZF (and thus, the axiom of infinity), but not on the Axiom of Choice. It also doesn't guarantee better than "most probably".

One can alternately Refute rather than Assert the existence of such an ordinal as one's axiom. In which case, you can go look up Ramsey's Theorem, and find that any sized island of "order" inevitably must result within a sufficiently large sea of chaos, and ergo no prospect for induction under that axiom.

[DonRetrasado]

i know like five of those words

[Mr Kang]

Induction has (generally) worked so far. So I guess it will continue to.

I'm afraid induction has been in doubt since Hume, and dead since Popper. We do not derive knowledege by induction from observation, rather we invent theories about the world and then test them with observations. Eventually an observation is incompatible with the current theory and a better/modified one is sought. To quote Popper: ``All knowledge is theory-laden''.

Science = fallibilism + conjecture + critisicm.

[Mr Kang]

I think that Karl Popper actually addressed the problem of induction in his work "The Logic of Scientific Discovery". His idea of science/knowledge was that it was created by conjecture and refutation, in his words the criterion of falsifiability. Science isn't, or doesn't have to be based upon logical induction.

Correct. Sorry, didn't see you there...

[abb3w]

i know like five of those words

Wikipedia can help with that, if you like.