Ockham\'s Razor
 

I'm curious as to whether there's some sort of logical proof for this. While I'm reasonably mathematically and philosophically educated (to a small degree - two dropped-out ones, to be precise), I wouldn't have any idea as to how to go about the problem.

Re: Ockham\'s Razor
 

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I'm curious as to whether there's some sort of logical proof for this. While I'm reasonably mathematically and philosophically educated (to a small degree - two dropped-out ones, to be precise), I wouldn't have any idea as to how to go about the problem.

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how could there be a proof? it's not even really well-defined.

Re: Ockham\'s Razor
 

Well the way I understand it (I know it was originally defined differently) was that in absence of other information, the simpler explanation for a phenomenon is more likely to be true. I've seen it explained that this is not a 'theory', in the sense that it is merely a rule to choose between theories, but this strikes me as wrong given you could choose the alternative theory (given no more information) that the more complicated theory is likely to be true, or even that the simplicity or complexity of a theory has no bearing on its truth-value.

Given that information can be quantified, would it not be possible to construct a continuous 'theory-space' whereby different theories are compared, then some prior probability criterion applied and compared to the results of applying ockham's razor? I guess that would be an analytic way of doing it, and that may well be the only way, if logical methods are out of the window.

I'm sorry if this question is a little too silly/abstract or badly worded, or even absurd - I'm out of practise, please humour me.

Re: Ockham\'s Razor
 

The only thing similar to it that I can think of is the likelihood ratio test to compare "full" and "reduced" models in statistics - adding an extra explanatory variable always gives you a better fit even if the extra variable is meaningless, so you have to prove the extra variable has improved the fit more than would be expected by chance.

Re: Ockham\'s Razor
 

I have no understanding of full and reduced models in statistics, but what you've said sounds both right and wrong, if you see what I mean - right in that it sounds analagous, wrong in that the extra information is making the proposition likelier rather than less likely.

Re: Ockham\'s Razor
 

What, if any, is the relationship between Ockham's Razor and Sklansky's "Coincidence Theory"?

I found the two to be quite similar in nature.

Re: Ockham\'s Razor
 

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Well the way I understand it (I know it was originally defined differently) was that in absence of other information, the simpler explanation for a phenomenon is more likely to be true. I've seen it explained that this is not a 'theory', in the sense that it is merely a rule to choose between theories, but this strikes me as wrong given you could choose the alternative theory (given no more information) that the more complicated theory is likely to be true, or even that the simplicity or complexity of a theory has no bearing on its truth-value.

Given that information can be quantified, would it not be possible to construct a continuous 'theory-space' whereby different theories are compared, then some prior probability criterion applied and compared to the results of applying ockham's razor? I guess that would be an analytic way of doing it, and that may well be the only way, if logical methods are out of the window.

I'm sorry if this question is a little too silly/abstract or badly worded, or even absurd - I'm out of practise, please humour me.

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i think this has gotten a little past the point of making sense... think about what you are asking for!

Re: Ockham\'s Razor
 

Ockham's Razor has for centuries been put into layman's terms as "the simpler explanation is the correct one," but that's not really what it's for. A more accurate scientific view of the postulate is "don't add any extraneous information." Basically (a largely exaggerated version), Newton comes up with his theory of gravitation. He finds that the force is proportional to the two masses and inversely proportional to the distance between said objects squared. It's a fine theory and fits empirical observation extremely well (until Einstein LDO).

Now what if he had postulated that the force is proportional to mass, yada yada yada... AND that this force was due to green aliens? That's obviously absurd, but such is the point of Ockham's Razor. If you have a working theory of an empirically observable phenomena, it's not necessary to add anything to it. It's always theoretically possible to find something "simpler" with fewer variables, but that rarely happens in scientific practice.

Re: Ockham\'s Razor
 

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.

Re: Ockham\'s Razor
 

Kevin Kelly's Research

Here is a link to a guy that works on this stuff. It may well be too heavy on the math for casual consumption, but just thought i'd toss it out there.

Re: Ockham\'s Razor
 

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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

Re: Ockham\'s Razor
 

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.

Re: Ockham\'s Razor
 

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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.

Re: Ockham\'s Razor
 

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

Re: Ockham\'s Razor
 

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

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Re: Ockham\'s Razor
 

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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

Re: Ockham\'s Razor
 

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

Re: Ockham\'s Razor
 

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.

Re: Ockham\'s Razor
 

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

Re: Ockham\'s Razor
 

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.

Re: Ockham\'s Razor
 

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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.

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Right. It was obviously witchcraft.

PairTheBoard

Re: Ockham\'s Razor
 

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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.

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I think this is wrong. The empirical justification of a theory does not work with mathematical precision. There are always an indefinite number of theories that are empirically adequate (i.e., that are consistent with all of the available evidence). There is no such thing as 'approaching the right' choice if by that you mean eliminating all but one theory based on the evidence.

Hence the need for Occam's razor. It is not an empirical principle but a heuristic one, which gives us some principled reason for choosing among equally empirically adequate theories.

Re: Ockham\'s Razor
 

Thanks for all the input, guys. I'm understanding this a bit better.

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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.

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Why isn't it a mind-blowing insight? I never suggested it was but am curious as to why you find this so trivial and don't find any use in Ockham's Razor.

Your first statement bears no relation to the rest of this thread, I feel.

Re: Ockham\'s Razor
 

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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'.

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I don't think either one of these is a correct statement of Occam's Razor. 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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This isn't a really a mind-blowing insight, thus Ockham's Razor is hugely overrated.

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I think it would be an incredibly mind-blowing insight for the people that don't actually understand it, which is the majority of people. Occam's razor informs my entire world view. In my opinion it's practically impossible to overrate it.

Re: Ockham\'s Razor
 

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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.

Re: Ockham\'s Razor
 

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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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Yep, thats a better way to put it. In practice we don't really care how likely to be capital T true the explanation is. Thats probably entirely impossible to determine for anything you'd apply the razor to. We just care about selecting one of the infinite explanations that fits the bill. Since you can only go UP infinitely, and cannot go down past some real minimum, we prefer the 'simplest' as a convention.

And I'm with Boro, this is probably the most important concept that exists, for me, and I think its really difficult to overrate it. Its amazing how the two most important, powerful concepts (this and evolution) both seem so ridiculous self-evident and simple, when you finally understand them.

Re: Ockham\'s Razor
 

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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.

Re: Ockham\'s Razor
 

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And I'm with Boro, this is probably the most important concept that exists, for me, and I think its really difficult to overrate it. Its amazing how the two most important, powerful concepts (this and evolution) both seem so ridiculous self-evident and simple, when you finally understand them.

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Well, they are related, so getting one opens the door to the other.

luckyme

Re: Ockham\'s Razor
 

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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.

Re: Ockham\'s Razor
 

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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.

Re: Ockham\'s Razor
 

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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.

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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
and
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.

Re: Ockham\'s Razor
 

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.

Re: Ockham\'s Razor
 

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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.

Re: Ockham\'s Razor
 

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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.

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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
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]

Re: Ockham\'s Razor
 

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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.

Re: Ockham\'s Razor
 

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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.

Re: Ockham\'s Razor
 

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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?

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

Re: Ockham\'s Razor
 

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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."

Re: Ockham\'s Razor
 

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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.

Re: Ockham\'s Razor
 

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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]

[/ QUOTE ]

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."

[/ QUOTE ]

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.