Ockham's Razor

[vhawk01]

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A correct statement of Occam's razor is, "The simplest explanation that fits the data is the most likely to be correct.[/b]



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A number of respondents have said something like this. As I understand it, Occam's razor is not about which theory is more likely to be 'correct'. Occam's razor has nothing to do with how likely a theory is to be true, but instead is a principle that directs us how to choose among theories, on non-empirical grounds, that are equally likely to be true given the evidence.

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I couldn't disagree more. This doesn't even make sense. If the simpler explanation were not more likely to be true, what is the justification for the razor at all? The very point is that they are NOT equally likely to be true given the evidence. Hence the razor.

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I don't think thats quite right. There is really no reason to think any theory, X, is more likely to be correct than another theory, X+invisible blue goblins. Its just that there are an infinite number of more complicated theories, and we couldn't ever have ANY meaningful consensus or discussion about any theory if we just accepted any of the infinite as 'equally good.' They are still equally likely, I think, whatever that means. They just aren't as...easy to talk about? To think about, maybe.

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This is silly. They are certainly all not just as likely to be correct. That is the principle the razor embodies.

If I can't find my keys, and it were REALLY just as likely that invisible blue goblins stole them and altered my memory so that I don't remember where I left them as it is that I just forgot where I put them, and hence an infinite number of other theories, then it would LITERALLY be the case the the chances that I just forgot where I put them would be 0%, when obviously it is near 100%. This is patently ridiculous. The only way this is avoided is if the simple explanations is MORE likely than alternative explanations that invoke extraneous ad hoc hypotheticals.

I repeat, if the simpler explanation were not more likely to be correct, then parsimony would be a useless concept.

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That is a misapplication of the concept. To stick with your keys scenario, the two (or infinite) competing theories are:

You forgot where you put your keys
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You forgot where you put your keys and invisible blue goblins watched you do it.

Both of these are equally likely. There is absolutely no difference in explanatory power. Its just the second one involves a whole bunch of unnecessary information. Your scenario is different because there are real differences in outcome or explanatory power to the two theories.

[kerowo]

It sounds like you think all theories are equally valid which is not true, despite what schools are teaching kids these days. Some theories are stupid and don't deserve the same weight as other theories. "Blue goblins" falls into that camp. A first pass at determining if a theory is stupid or not is given by OR.

[vhawk01]

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It sounds like you think all theories are equally valid which is not true, despite what schools are teaching kids these days. Some theories are stupid and don't deserve the same weight as other theories. "Blue goblins" falls into that camp. A first pass at determining if a theory is stupid or not is given by OR.

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Not equally valid, perhaps. But only because of things like OR. What possible measure can you use to tell me which of the two theories I mentioned above has a higher probability of being true? I guess you can say OR, but thats just question begging.

[Borodog]

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A correct statement of Occam's razor is, "The simplest explanation that fits the data is the most likely to be correct.[/b]



[/ QUOTE ]

A number of respondents have said something like this. As I understand it, Occam's razor is not about which theory is more likely to be 'correct'. Occam's razor has nothing to do with how likely a theory is to be true, but instead is a principle that directs us how to choose among theories, on non-empirical grounds, that are equally likely to be true given the evidence.

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I couldn't disagree more. This doesn't even make sense. If the simpler explanation were not more likely to be true, what is the justification for the razor at all? The very point is that they are NOT equally likely to be true given the evidence. Hence the razor.

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I don't think thats quite right. There is really no reason to think any theory, X, is more likely to be correct than another theory, X+invisible blue goblins. Its just that there are an infinite number of more complicated theories, and we couldn't ever have ANY meaningful consensus or discussion about any theory if we just accepted any of the infinite as 'equally good.' They are still equally likely, I think, whatever that means. They just aren't as...easy to talk about? To think about, maybe.

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This is silly. They are certainly all not just as likely to be correct. That is the principle the razor embodies.

If I can't find my keys, and it were REALLY just as likely that invisible blue goblins stole them and altered my memory so that I don't remember where I left them as it is that I just forgot where I put them, and hence an infinite number of other theories, then it would LITERALLY be the case the the chances that I just forgot where I put them would be 0%, when obviously it is near 100%. This is patently ridiculous. The only way this is avoided is if the simple explanations is MORE likely than alternative explanations that invoke extraneous ad hoc hypotheticals.

I repeat, if the simpler explanation were not more likely to be correct, then parsimony would be a useless concept.

[/ QUOTE ]

That is a misapplication of the concept. To stick with your keys scenario, the two (or infinite) competing theories are:

You forgot where you put your keys
and
You forgot where you put your keys and invisible blue goblins watched you do it.

Both of these are equally likely.

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No, they aren't. You have totally sidestepped my entire argument. If this were actually true, then the chance that I simply forgot where I put my keys is literally 0%. The only way to avoid this farcical result is to conclude that the simplest explanation is literally more likely than the alternative explanations. That's the entire point of the principle of parsimony (Occam's Razor).

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There is absolutely no difference in explanatory power.

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I would argue that yes, there is a difference in explanatory power; that unneccesary ad hoc hypotheticals reduce the explanatory power, even if the theory accounts for all the evidence in question.

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Its just the second one involves a whole bunch of unnecessary information.

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Here's the crux: SO WHAT? If the one involving the unnecessary information is really just as likely, how is the unnecessary information "bad"? What exactly does it mean for the simplest explanation to be "better" in such a crazy world? That you have to type less to describe it, even though an infinite number of alternative theories are just as likely, and hence the odds of the simple theory being the correct one are 0%? Why think up any theory at all if it isn't more likely than any alternative? Such a premise would render science pointless, not to mention impossible.

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Your scenario is different because there are real differences in outcome or explanatory power to the two theories.

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How so? [img]/images/graemlins/confused.gif[/img]

[Borodog]

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It sounds like you think all theories are equally valid which is not true, despite what schools are teaching kids these days. Some theories are stupid and don't deserve the same weight as other theories. "Blue goblins" falls into that camp. A first pass at determining if a theory is stupid or not is given by OR.

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Not equally valid, perhaps. But only because of things like OR. What possible measure can you use to tell me which of the two theories I mentioned above has a higher probability of being true?

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Probability?

The probability that I forgot where I put my keys is F, where F is less than 1. The probability that invisible blue goblins watched me is B, where B is less than 1. Hence BF < F. Hence F is more likely than BF.

[Philo]

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A correct statement of Occam's razor is, "The simplest explanation that fits the data is the most likely to be correct.[/b]



[/ QUOTE ]

A number of respondents have said something like this. As I understand it, Occam's razor is not about which theory is more likely to be 'correct'. Occam's razor has nothing to do with how likely a theory is to be true, but instead is a principle that directs us how to choose among theories, on non-empirical grounds, that are equally likely to be true given the evidence.

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I couldn't disagree more. This doesn't even make sense. If the simpler explanation were not more likely to be true, what is the justification for the razor at all? The very point is that they are NOT equally likely to be true given the evidence. Hence the razor.

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No. If one theory is more likely to be true given the evidence, we don't need a heuristic principle like Occam's Razor in order to choose among theories. We can just go by the evidence in that case.

We apply Occam's Razor when we have competing theories each of which is empirically adequate. Since you can't choose among theories in that case based solely on the evidence, we need some other principle to guide theory choice, like Occam's Razor. Occam's Razor is not an empirical principle.

[Borodog]

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A correct statement of Occam's razor is, "The simplest explanation that fits the data is the most likely to be correct.[/b]



[/ QUOTE ]

A number of respondents have said something like this. As I understand it, Occam's razor is not about which theory is more likely to be 'correct'. Occam's razor has nothing to do with how likely a theory is to be true, but instead is a principle that directs us how to choose among theories, on non-empirical grounds, that are equally likely to be true given the evidence.

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I couldn't disagree more. This doesn't even make sense. If the simpler explanation were not more likely to be true, what is the justification for the razor at all? The very point is that they are NOT equally likely to be true given the evidence. Hence the razor.

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No. If one theory is more likely to be true given the evidence, we don't need a heuristic principle like Occam's Razor in order to choose among theories. We can just go by the evidence in that case.

We apply Occam's Razor when we have competing theories each of which is empirically adequate. Since you can't choose among theories in that case based solely on the evidence, we need some other principle to guide theory choice, like Occam's Razor. Occam's Razor is not an empirical principle.

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The bolded part is an incorrect interpolation by you of my statement. You make it seem like I am saying some piece of evidence exists which points to the simpler theory being more likely than the other. That's not what I'm saying. I'm saying that given the same evidence, a simpler theory that adequately explains all that evidence is LITERALLY more likely to be correct than less simple alternatives tha adequately explain that same evidence. This is why parsimony and Occam's Razor are useful in the first place.

I repeat, if the simpler explanation is NOT more likely to be correct, WHAT IS THE JUSTIFICATION OF OCCAM'S RAZOR IN THE FIRST PLACE? The simpler theory requires fewer keystrokes?

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[Philo]

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The bolded part is an incorrect interpolation by you of my statement. You make it seem like I am saying some piece of evidence exists which points to the simpler theory being more likely than the other. That's not what I'm saying. I'm saying that given the same evidence, a simpler theory that adequately explains all that evidence is LITERALLY more likely to be correct than less simple alternatives tha adequately explain that same evidence. This is why parsimony and Occam's Razor are useful in the first place.

I repeat, if the simpler explanation is NOT more likely to be correct, WHAT IS THE JUSTIFICATION OF OCCAM'S RAZOR IN THE FIRST PLACE? The simpler theory requires fewer keystrokes?

[img]/images/graemlins/confused.gif[/img]

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Perhaps this will help, from http://en.wikipedia.org/wiki/Occam's_Razor

"Empirical justification

One way a theory or a principle could be justified is empirically; that is to say, if simpler theories were to have a better record of turning out to be correct than more complex ones, that would corroborate Occam's razor. However, this type of justification has several complications.

First of all, even assuming that simpler theories have been more successful, this observation provides little insight into exactly why this is, and thus leaves open the possibility that the factor behind the success of these theories was not their simplicity but rather something that causally correlates with it (see Correlation vs. Causation). Second, Occam's Razor is not a theory; it is a heuristic maxim for choosing among theories, and attempting to choose between it and some alternative as if they were theories of the regular sort invokes circular logic. We rely on the razor when we justify induction; by attempting to in turn rely on induction when we justify the razor, we are begging the question.

There are many different ways of making inductive inferences from past data concerning the success of different theories throughout the history of science; inferring that "simpler theories are, other things being equal, generally better than more complex ones" is just one way of many, and only seems more plausible to us because we are already assuming the razor to be true (see e.g. Swinburne 1997). Inductive justification for Occam's razor being a dead-end game, we have the choice of either accepting it as an article of faith based on pragmatist considerations or attempting deductive justification."

I posted one such deductive justification earlier, here it is again, by Jerrold Katz:

"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."

[wazz]

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The bolded part is an incorrect interpolation by you of my statement. You make it seem like I am saying some piece of evidence exists which points to the simpler theory being more likely than the other. That's not what I'm saying. I'm saying that given the same evidence, a simpler theory that adequately explains all that evidence is LITERALLY more likely to be correct than less simple alternatives tha adequately explain that same evidence. This is why parsimony and Occam's Razor are useful in the first place.

I repeat, if the simpler explanation is NOT more likely to be correct, WHAT IS THE JUSTIFICATION OF OCCAM'S RAZOR IN THE FIRST PLACE? The simpler theory requires fewer keystrokes?

[img]/images/graemlins/confused.gif[/img]

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Perhaps this will help, from http://en.wikipedia.org/wiki/Occam's_Razor

"Empirical justification

One way a theory or a principle could be justified is empirically; that is to say, if simpler theories were to have a better record of turning out to be correct than more complex ones, that would corroborate Occam's razor. However, this type of justification has several complications.

First of all, even assuming that simpler theories have been more successful, this observation provides little insight into exactly why this is, and thus leaves open the possibility that the factor behind the success of these theories was not their simplicity but rather something that causally correlates with it (see Correlation vs. Causation). Second, Occam's Razor is not a theory; it is a heuristic maxim for choosing among theories, and attempting to choose between it and some alternative as if they were theories of the regular sort invokes circular logic. We rely on the razor when we justify induction; by attempting to in turn rely on induction when we justify the razor, we are begging the question.

There are many different ways of making inductive inferences from past data concerning the success of different theories throughout the history of science; inferring that "simpler theories are, other things being equal, generally better than more complex ones" is just one way of many, and only seems more plausible to us because we are already assuming the razor to be true (see e.g. Swinburne 1997). Inductive justification for Occam's razor being a dead-end game, we have the choice of either accepting it as an article of faith based on pragmatist considerations or attempting deductive justification."

I posted one such deductive justification earlier, here it is again, by Jerrold Katz:

"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."

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This ALL seems wrong. Firstly, an empirical justification is of no use or interest of me, as per my OP; secondly, like i said earlier, one could posit the alternatives to OR and easily find examples that support each; thirdly, induction does not need justification by OR, it stands up (as far as induction will stand up) by itself, and I don't see how it would be possible to justify OR without induction; fourthly, with regards to Katz's deductive justification, the fact that we give more weighting to the evidence of a simpler theory does not mean that the simpler theory is more likely to be true.

[Philo]

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The bolded part is an incorrect interpolation by you of my statement. You make it seem like I am saying some piece of evidence exists which points to the simpler theory being more likely than the other. That's not what I'm saying. I'm saying that given the same evidence, a simpler theory that adequately explains all that evidence is LITERALLY more likely to be correct than less simple alternatives tha adequately explain that same evidence. This is why parsimony and Occam's Razor are useful in the first place.

I repeat, if the simpler explanation is NOT more likely to be correct, WHAT IS THE JUSTIFICATION OF OCCAM'S RAZOR IN THE FIRST PLACE? The simpler theory requires fewer keystrokes?

[img]/images/graemlins/confused.gif[/img]

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Perhaps this will help, from http://en.wikipedia.org/wiki/Occam's_Razor

"Empirical justification

One way a theory or a principle could be justified is empirically; that is to say, if simpler theories were to have a better record of turning out to be correct than more complex ones, that would corroborate Occam's razor. However, this type of justification has several complications.

First of all, even assuming that simpler theories have been more successful, this observation provides little insight into exactly why this is, and thus leaves open the possibility that the factor behind the success of these theories was not their simplicity but rather something that causally correlates with it (see Correlation vs. Causation). Second, Occam's Razor is not a theory; it is a heuristic maxim for choosing among theories, and attempting to choose between it and some alternative as if they were theories of the regular sort invokes circular logic. We rely on the razor when we justify induction; by attempting to in turn rely on induction when we justify the razor, we are begging the question.

There are many different ways of making inductive inferences from past data concerning the success of different theories throughout the history of science; inferring that "simpler theories are, other things being equal, generally better than more complex ones" is just one way of many, and only seems more plausible to us because we are already assuming the razor to be true (see e.g. Swinburne 1997). Inductive justification for Occam's razor being a dead-end game, we have the choice of either accepting it as an article of faith based on pragmatist considerations or attempting deductive justification."

I posted one such deductive justification earlier, here it is again, by Jerrold Katz:

"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."

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This ALL seems wrong. Firstly, an empirical justification is of no use or interest of me, as per my OP; secondly, like i said earlier, one could posit the alternatives to OR and easily find examples that support each; thirdly, induction does not need justification by OR, it stands up (as far as induction will stand up) by itself, and I don't see how it would be possible to justify OR without induction; fourthly, with regards to Katz's deductive justification, the fact that we give more weighting to the evidence of a simpler theory does not mean that the simpler theory is more likely to be true.

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Firstly, I was responding to Boro, not to your OP. I already responded to that. In fact, I responded with Katz's attempt at a deductive justification, which is probably the closest thing you can get to a 'proof' of OR.

Fourthly, Katz's deductive justification is not meant to show that the simpler theory is more likely to be true. That's the whole point in giving a deductive justification rather than an empirical one.