Ockham's Razor

[soon2bepro]

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This doesn't prove Ockham's Razor, but it's a start.

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It's nowhere near anything resembling proof

[kerowo]

I'm sure a large part of the appeal of Ockham's Razor lies in it's focus on simplicity. Scientists and Mathematicians are usually trying to find elegant solutions to problems, so a solution that has x-5 (or whatever) steps is considered better than a solution that has x steps.

This gets translated into other fields as things like K.I.S.S and 'don't look for zebras when you hear huff beats.' It also goes hand in hand with 'extraordinary theories need extraordinary proof' because it is much more likely that someone is experiencing a false memory or is hallucinating than to think Elvis is an alien.

[pzhon]

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Suppose there is only one correct theory, and theories correspond to finite strings of letters. There are only finitely many incorrect theories that are shorter than the correct theory, but there are infinitely many incorrect theories which are longer than the correct theory.

This doesn't prove Ockham's Razor, but it's a start.

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It's nowhere near anything resembling proof

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As I stated, it is not a proof. It is the key idea behind many much longer justifications of Ockham's razor. Feel free to read those if you can't flesh out the argument from the above paragraph.

[Borodog]

I use Occam's razor because it's far simpler than the alternative.

[Andy Ross]

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I use Occam's razor because it's far simpler than the alternative.

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[Philo]

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I'm curious as to whether there's some sort of logical proof for this.

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I don't think there is any such thing as a logical proof for Occam's razor, since it is generally understood as a heuristic principle or a principle of parsimony, and so is not the kind of thing that admits of logical proof.

There is this:

"Jerrold Katz has outlined a deductive justification of Occam's razor:

"If a hypothesis, H, explains the same evidence as a hypothesis G, but does so by postulating more entities than G, then, other things being equal, the evidence has to bear greater weight in the case of H than in the case of G, and hence the amount of support it gives H is proportionately less than it gives G."

From http://en.wikipedia.org/wiki/Occam's_Razor

[oldbookguy]

Here is a simple, non math answer.

Two gals are gossiping;

Gal 1. Mary went out with Bill last night.
Gal. 2. Mary went out with Bill last night to make Bob mad.

Statement number 1 is fact, statement 2 is extranious and adds nothing to making number 1 any more or less correct, only adding more gossip.

Another way of looking at it, a prosecutor need only prove a crime, not a crime and a motive.

Thus Ockum's Razor.

obg

[tessarji]

The mutilated and incorrect statement of Ockham's Razor is that 'the simplest explanation is the correct one'. It should take all of about a minute to think of a counter-example.

The best statement of Ockham's Razor is simply, 'a smaller model is more useful than a larger model, if both make sufficiently accurate predictions for your purposes'.

This isn't a really a mind-blowing insight, thus Ockham's Razor is hugely overrated.

[Metric]

In the context of computer science, there are principles resembling Ockham's razor (simpler explanation which fits the data is best) which are mathematically well-defined.

http://en.wikipedia.org/wiki/Minimum_description_length

[MaxWeiss]

In fact it is somewhat of a proof. If I run over glass and then park, go somewhere, and come back to my car to find a glass shard in it (and it's flat) I could conclude an infinite number possibilities, including one that involved David S. and Brandi following me and stabbing glass into my tire in order to send a message to 2+2ers at large. The evidence given to me certainly does not negate that possibility, but there is no reason think that likely. Given the small amount of evidence I have, the most probable option is the simplest and easiest. As I get more data I can exclude more theories, although I can still come up with an infinite number. But mathematically, I approach the limit of just one theory, and with all available evidence, it is reasonable to assume what the limit is approaching is the right choice, until I find other evidence that suggests another theory is more likely. When you average out all the unavailable evidence, the simplest theory is easily the most probable choice.