Ockham's Razor

[wazz]

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.

[oe39]

[ QUOTE ]
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.

[/ QUOTE ]

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

[wazz]

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.

[Siegmund]

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.

[wazz]

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.

[jgodin]

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.

[oe39]

[ QUOTE ]
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.

[/ QUOTE ]

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

[Neuge]

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.

[pzhon]

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.

[EnderIII]

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.