On Theories

[Dragar]

"Things should be made as simple as possible, but not any simpler."
- Albert Einstein

"Pluralitas non est ponenda sine necessitate."
-William of Ockham, 1300-1349

"We are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances."
-Isaac Newton

It seems quite clear to me that for any observations we care to make, there an infinite number of explanations, limited only by our imagination and the Law of Non-Contradiction (which is hardly a restriction we should worry about). What is worse is that there are an infinite number of theories which explain the observations and make precisely the same predictions.

We need some way of limiting those we consider.

The only way I can think to do so is by treating the one which makes the least assumptions as probably right. It appears easy enough to justify using induction, but sadly results in me begging the question.

If we don't do this, I see no way of distinguishing between Ptolomy's Epicycles (modified to account for new experiments) and a heilocentric solar system, between creationism and evolution, between atheism and theism, between a world where other humans exist and a world filled with cleverly crafted cyborgs, etc. In fact, I think we all do use this principle the majority of the time.

And yet, I have been challenged on this by very bright people. And I could provide little justification for this theory, other than that it was used to great sucess in science. Of course, I need to use this principle to show this principle was the one that worked....

So I ask: how is this justified? Or is it justified? Perhaps Ptolomy had a point after all...

[livius drusus]

Excellent question, Dragar, and for the record I'll state that I have no idea what the answer is. One problem springs to my mind, though: does evolution make fewer assumptions than creation? Is Ptolemy's universe "simpler" than Copernicus'? Because that geocentric thing got pretty complicated from what I've seen. Is the simpler explanation really more historically successful in science?

I have to run to work, but I'll be back, hopefully with something of substance to contribute. Thank you for starting this very interesting thread, Dragar. :thankee:

[Dragar]

It's not so much that heliocentricity is simpler than Ptolomy's picture. It's that Ptolomy, in order to keep everything in line with the facts, was forced to posit certain points (I believe he called them 'Divine Points' or some other nonsense) which the other planets wandered around, to explain why they didn't appear to quite go around the Earth. There was no reason to think they were there, other than to save the theory. Which is sometimes justifiable, but when another theory appears - one which makes only the assumption that the planets go around the sun, and explains all the other observations - I see no reason at all to stick with Ptolomy.

Not simplicity. Number of assumptions. More junk posited for no reason other than to maintain the theory in the face of new observations.

We find the same thing with evolution versus creationism (by which I mean God creating every species individually 6000 years ago...you know the one I mean). We only need a few assumptions with evolution - that our observations are accurate is one of them, and is shared by creationism. If you don't already believe in God, God's existence is an assumption all on its own. That he intervened is another assumption, that there's a conspiracy amongst scientists, that all fossils are frauds, that our dating techniques are flawed, and so on. The tricky part is now you're into two areas of observation - that of geology, biology, and all those other sciences, and the Bible.

Biblical innerency is another interesting one. It's a very, very untidy theory, because makes so many extra assumptions. "Oh, the author just didn't mention the other angel sat in Jesus' tomb. No, there's no contradiction! Judas hung himself and then the rope broke, so he fell and all his bowels fell out!"

All assumptions. Not observed; made up as an explanation. All of these are made simply to save the theory that the Bible contains no errors.

As for historically...I'm not sure. But even if it were, it doesn't help matters. There could be an infinite number of explanations that explain why this were the case (mass hallucinations, divine intervention, aliens...let your imagination go wild!). Can you justify picking the explanation that the simplest explanation is more frequently correct? Remember - saying it's simpler is just circular! :wink:

[Socratoad]

Can this not be sorta be boiled down to the difference between rational thought versus irrational thought? Every time I have become involved in such discussion with theists and other magical belief systems ie crystal power etc, I have been accused of just not being open-minded enough.

How does one refute or even discuss intelligently a concept or entity with someone who is starting from a whole different premise.

[livius drusus]

I don't really see how that's related, Toad. The question, I believe, is can Ockham's razor be justified without a circular argument. :scratch:

[Dragar]

I don't think it can, socratoad. For instance, there are very real examples in physics where such a preference for the least number of assumptions is made.

Quantum mechanics, for instance, usually denies all hidden-variables theories - that electrons (or photons or whatever) all have non-local (see Bell's theorem) variables we don't know about. The reason? We can do just as well without them!

And yet...I struggle to see any way to justify this. Despite the fact we all do this, despite that fact it seems to be the only way to distinguish between an infinite number of explanations, despite the fact that it's intuitive (though I have a very low opinion of intuition) I can find no way to demonstrate this is the correct thing to do.

I've been thinking of trying something with probabilities. After all, if there are an infinite number of assumptions available, the odds of any single assumption (plucked randomly from the air) being correct must be close to 0. That means that any theory is almost certainly wrong! But the ones which make the least assumptions are less likely to be wrong, as they are the ones which are least likely to contain a false assumption.

Hmm. Does that work?

[livius drusus]

I don't know, Dragar; there's still a basic element missing for me. Could we go back a little? I can see the advantage of not multiplying premises or assumptions, even just as a matter of getting things done, but how does it follow therefore that the theory with fewest assumptions is true?

[Socratoad]

Very interesting thread you have started. And yes it certainly does work for me. I will be monitoring this thread with interest, but sadly not offering much input as my mind has been so rejuvenated with a whole new project that I can barely focus on anything else ...... seriously.

Keep the great thought inducing stuff coming.

[Dragar]

I don't know, Dragar; there's still a basic element missing for me. Could we go back a little? I can see the advantage of not multiplying premises or assumptions, even just as a matter of getting things done, but how does it follow therefore that the theory with fewest assumptions is true?

You're right, it doesn't follow. But, that's not the conclusion I'm drawing.

There are an infinite number of assumptions we can make. There will be a finite number which are true. This means that if we select an assumption from our supply of infinite assumptions at random, it will almost certainly be false.

That's the first step. Any old assumption is almost certainly false. But it's not certain - it might be true. Laws of probability and all.

On that basis, we compare two explanations - one which contains two assumptions, and one which only contains one. The one with two assumptions is twice as likely to contain a false assumption, and thus more than twice as likely to be a false theory. On that basis, a theory with fewer assumptions is less likely to be false than a theory with more.

This seems very sketchy to me, though. I'm hoping it can be tidied up or found fallacious. It's not very good as it is.

Edit: And it ignores we may have reasons for preferring one assumption over another.

[livius drusus]

Ohh, I see now. While I squint at the screen and wrack my very puny brain to find what exactly it is about this that feels so off-kilter, hopefully some of the brilliant folk we have around here will step up to the plate.

[Socratoad]

I don't really see how that's related, Toad. The question, I believe, is can Ockham's razor be justified without a circular argument. :scratch:


Well ya liv, but as we both know I have been having a little problem with perceptions lately. :yup:

[livius drusus]

Oh yeah, that... :giggles: Nevermind, then. How about starting a thread in the Hole about your new project?

[godfry n. glad]

It's not just "minimal assumptions", it's the "most explanatory power with the least assumptions."

Now, I don't know as this actually clarifies anything. It's just that because a theory has fewer assumptions does not make it "more true". It must have adequate explanatory power.

Kick that around.

godfry

[Dragar]

Right. That's the other important bit. That's why the only point of this is to tell apart two theories which explain the same observations, and/or make the same predictions.

Of course, this is hairy too. We could argue we only need one assumption to explain everything: Goddidit. :wink:

[Socratoad]

Oh yeah, that... :giggles: Nevermind, then. How about starting a thread in the Hole about your new project?

Thanks for your suggestion, however I gotta flesh it out, metaphorically of course. Plus I really am lacking the necessary confidence right now. I'm working on it though.

[wade-w]

Well, my understanding is that Ockham's Razor is a guiding principle, not a theorem that requires proof. This means that a counter-example or two is not necessarily fatal to the Razor.

Also, keep in mind that logic itself cannot be justified in a rigorous manner. You can't prove everything; trying to do so will inevitably lead to circularity. One fundamental concept that must be accepted without proof is that logic works.

For example, Ockham's Razor is a part of the reason I am an atheist. OTOH, I recognize that since the Razor is a guiding principle and not a theorem, I could be wrong; thus I am also an agnostic.

[Dragar]

Well, my understanding is that Ockham's Razor is a guiding principle, not a theorem that requires proof. This means that a counter-example or two is not necessarily fatal to the Razor.

I'm looking for some justification of this guiding principle, though.

Also, keep in mind that logic itself cannot be justified in a rigorous manner. You can't prove everything; trying to do so will inevitably lead to circularity. One fundamental concept that must be accepted without proof is that logic works.

I know. I'm hoping this isn't like logic.

[Clutch Munny]

This is a good place to get a brief but clear sense of the problem with regarding OR as a methodological principle. (http://www.galilean-library.org/int6.html)

[wade-w]

The person that designed that page should be shot. I found it very difficult to read the text because of the background.

But the point made about Ockham's Razor is a good one.

[justaman]

Hey dragar!

I think the problem you highlight is an unsolvable one because of the nature of subjective experience. It is logically impossible to prove a theory true, only ever prove it false. This statement holds true for logic also, yet we can't test that because we are subjective. We can't get outside of logic in order to test it, in other words.

So the reason to prefer theories over others is a greater number of successes. The more successes, the more confident we can feel we are correct. I would slightly modify your suggestion about the smallest number of assumptions and say it is the theory that gives the most detailed explanation with the greatest amount of success.

Saying 'God did it', contains only one assumption, for instance, yet it makes virtually no attempt to be more accurate about the specifics of reality. 'God did it' doesn't explain nuclear fission, for instance. All it really resolves is the question for why we exist (which is a nonsense question in the first place, for mine).

That's not to say that the minimum amount of assumptions isn't important, but I think this is relative to how detailed the theory's observations actually are.

[Dragar]

Hey man!

You may be right. I've been trying to squirrel my way out of this one, but it's almost as bad as Hume's problem of induction.

So the reason to prefer theories over others is a greater number of successes. The more successes, the more confident we can feel we are correct. I would slightly modify your suggestion about the smallest number of assumptions and say it is the theory that gives the most detailed explanation with the greatest amount of success.

I'm only interested really in telling apart theories that make the same predictions, and explain the same number and type of observations.

Compare atheism with deistic theism (a God that doesn't interfere, ever - he's wandered off and got bored, or whatever). Both of us are at the least agnostic to this position. Both explanations are practically identical. They make the same predictions. It's impossible to tell from observation which one is correct.

Which one do we favour?

Hmm.

Thinking about it, we might be able to answer that using Burden of Proof. Can we relate that to this?

Saying 'God did it', contains only one assumption, for instance, yet it makes virtually no attempt to be more accurate about the specifics of reality. 'God did it' doesn't explain nuclear fission, for instance.

But in the same way, does General Relativity really explain gravity? Sure, we can say that gravity is produced by curvature of spacetime. But in the same way that saying 'God did it' just pushes the question further back, doesn't this explanation do the same? Why does mass distort spacetime? Nobody knows...

[Dragar]

Clutch Munny, thank you for the link. It's proving interesting reading. :)

[Clutch Munny]

It was pointed out to me that the author of that linked site has a more extensive discussion here (http://www.galilean-library.org/academy/viewtopic.php?t=39) .

It's an admirable summary of the main issues. Definitely worth a careful look-and-thinkitover.

[Hugo Holbling]

Well, no one has shot me yet. Our site is still under a design overhaul, as explained here (http://www.galilean-library.org/academy/viewtopic.php?t=57). While i'm still alive, i'll mention that an easier-on-the-eye version of the essay kindly recommended by Clutch is here (http://www.galilean-library.org/blog/2004/12/ockhams-razor.html).

If anyone is interested to know, the Copernican system was not simpler than the Aristotelian/Ptolemaic and employed a similar number of epicycles (i explained at the second link why "counting" is a bad way to determine simplicity). For information, the astronomical devices are covered here (http://www.galilean-library.org/galileo1.html#systems) (where there is no background to necessitate homicide).

[Dragar]

Hugo, thank you for those links. I'm rapidly drawing the conclusion that the statements made by our noble thinkers I quoted way at the top may in fact not be the best guidelines to follow...

[Socratoad]

Post deleted because I have just been informed that the information I supplied has become inoperative/obsolete/ no longer applicable.

I apologize for any inconvenience my previous entry may have caused

Regards, Toad

[Hugo Holbling]

Don't be so hasty, Dragar. Einstein carefully qualified his position, William of Ockham probably didn't say what your quote attributes to him at all (as i mentioned in the essay) and Newton was unable to follow his own advice in the Principia. If you contact me next week i could give you some references to look at for some more details. For now, what is the form of the challenge you've received?

[livius drusus]

Hugo, thank you for those links. I'm rapidly drawing the conclusion that the statements made by our noble thinkers I quoted way at the top may in fact not be the best guidelines to follow...

Or maybe even that science as a whole doesn't actually work in the way that such maxims seem to imply. It's way more interesting that that. :)

[Dragar]

Don't be so hasty, Dragar. Einstein carefully qualified his position, William of Ockham probably didn't say what your quote attributes to him at all (as i mentioned in the essay) and Newton was unable to follow his own advice in the Principia. If you contact me next week i could give you some references to look at for some more details. For now, what is the form of the challenge you've received?

Oh, it wasn't any more than 'parsimony is a poor guide for evaluating theories'. I tried to justify it, realised I couldn't think of a way to do so, and started this thread.

I should probably clarify where I'm coming from: I'm an undergraduate, studying theoretical physics. The vast amount of our time is spent studying...well, physics, and the underlying mathematics of the subject. There's little time left to address the methodology of science, and when it is mentioned it is only in passing. Considering I'm studying theoretical physics, I can see how this will ultimately result in some serious problems in my future work unless I can start putting together some semblance of a method for evaluating theories.

Regarding the quotations - I did not mean to say that the methods of those individuals was at fault. But that those quotations were not terribly illustrative of the correct methods, irrespective of whether they adhered by them or not.