Ockham's Razor

[Leif Roar]

That's not the argument from ignorance - that is the default position of reason! If you can't prove it true, then it is, by default, false. Yes. This is called "reason."

This is, however, not how the scientific method works. There you postulate theories and attempt to falsify them through experiment. You don't try to prove your theory - you try to disprove it. Until a theory is disproven, you consider it to be potentially true - you don't consider it false until it's proven.

 

[Upchurch]

Occam's razor example

 

[Pyrian]

But that's a far cry from your claim that we cannot use Occam's Razor to exclude the existance of an infinite number of non-essential, non-dectable entities.

I did not make that claim (in fact I made the opposite claim) - I made the claim that such a use of Ockham's Razor does not constitute proof.

If Ockham's Razor constitutes proof than at any moment you can say it proves your current understanding of the universe and therefore any and all subsequent contrary evidence could safely be ignored. THAT is what your position means.

You show no evidence of having comprehended my position at all.

 

[RichardR]

That's not the argument from ignorance - that is the default position of reason! If you can't prove it true, then it is, by default, false. Yes. This is called "reason."

You are just wrong here.

Argument From Ignorance IS:

"Arguments of this form assume that since something has not been proven false, it is therefore true. Conversely, such an argument may assume that since something has not been proven true, it is therefore false. (This is a special case of a false dilemma, since it assumes that all propositions must either be known to be true or known to be false.) As Davis writes, "Lack of proof is not proof."

You are confusing "assuming something is false" with "proving something false".

In case you missed it, there are an infinite - wait let me make that clearer - INFINITE number of propositions that cannot be proved false. You reject virtually all of them without hesitation. By what principal do you do this? Occam's Razor.

Without the Razor, you would be compelled to put invisible intangible elves on the same status as O.J. Simpson's guilt. Do you do this? Do you even think it would be desirable to do this?

Agreed. But you reject the others for the time being for reasons of parsimony, NOT because they have been proven wrong. Because they haven't been proven wrong.

 

[csense]

So by what principle do you rule out...the undetectable elf? .

You would rule out the undetectable elf from your own theory, using of course, Occam's Razor.
You can not however, rule out the undetectable elf from an alternate theory that is not proposed by you, especially if the theory is The Undetectable Elf Theory.
An observer of both though my choose to invoke the law of parsimony to satisfy their own judgement until such a time that one of the theories start predicting, in which case, everything changes.


Does that help?

 

[LW]

That's not the argument from ignorance - that is the default position of reason! If you can't prove it true, then it is, by default, false. Yes. This is called "reason."

My posting yesterday on this thread was quite concise since I had to hurry to a bus (which I still promptly missed as my workstation's clock is four minutes late).

But anyway, if you take that approach and apply it consistently, you'll end up really quickly in rather absurd conclusions.

For example, I can't prove that I slept last night. Using your reasoning, this means that I wasn't sleeping last night. However, I can't prove that I was awake, either. So, I wasn't awake. Now, if I wasn't sleeping and wasn't awake, what state was I in?

For a more formal example, consider the case where we have the set S = { a, b, c, } of propositional atoms and the set C = { a, a or b, not b or not c, not c } of four clauses. In classical logic, there are two basic approaches to examine the clauses and truth values of the atoms:

(1) we can examine the models of C; or
(2) we can examine the set of logical consequences of C.

As for the first case, C has two models (a truth assigment over atoms of S is a model of C it it makes all clauses in it true):

M_1 = { a, b, not c }
M_2 = { a, not b, not c }

As you see, a and c have the same truth values in both models, but the truth value of b doesn't affect the truth value of C.

If we take your approach that "if something can't be proven true it is false", then we have to reject M_1, since we can't prove that b is true. However, there is absolutely no reason to say that M_1 is not a model. After all, it satisfies all four clauses.

The set of logical consequences of C is the set of atoms that are true in all models of C. As C is satisfiable, this is simply the intersection of M_1 and M_2:

Concl(C) = { a, not c }

Again, you note that b is missing from the set. If your argument was true, then there should be "not b" in Concl(C).

The two above cases correspond to "brave" and "cautious" reasoning. An atom is possibly true ("brave") if it is true in at least one model, and it is necessarily true ("cautious") if it true in all of them.

But in a way you are correct since human reasoning is usually not classical. If somebody tells me that Tweety is a bird, then my default position is that Tweety can fly, even though I can't justify that using classical logic. However, if someone then tells me that Tweety is actually a penguin, my beliefs change into the direction that barring same extraordinary conditions Tweety can't fly. [But of course we all know that the SuperPenguin can fly without any troubles.]

There are a number of different non-monotonic semantics for logical sentences that are closer to the way how humans think (the most well-known example being probably Reiter's Default Logic). They are often much more convenient to use than classical logic in the knowledge representation sense as the existence of default values removes most of the burden of problem modeling from the shoulders of the modeler.

 

[jan]

Try applying Occam's Razor to this problem:

Start with a circle. The circle is in one piece, and remains in one piece when you put one dot anywhere on the circumference.

Now put a second dot anywhere on the circumference and connect the two dots with a straight line. You have divided the circle into two pieces. (The two pieces need not be equal in area.)

[abridged...]

So, to sum up:
one dot: one piece
two dots: two pieces
three dots: four pieces
four dots: eight pieces
five dots: sixteen pieces

What do you predict will be the number of pieces with six dots? What equation relates dots to pieces? Draw a circle yourself, put dots on it and connect the lines, then count the pieces to see whether you got the answer that you predicted.

What does this tell us about Occam's Razor (if anything)?

Try applying the syllogism to this problem:

A man has 3 apples. If throws one at a woowoo, how many does he have left?

If you fail to solve this problem using the syllogism, does that mean you can't prove anything with the syllogism?

If you can't change your car tire with a tuning fork, does that mean the tuning fork doesn't work?

Yahzi, I think you didn't get what Brown was trying to explain you. Brown was not trying to make the trivial point that one principle can't solve all problems. The problem here is: the shortest explanation of your observation is:

number of pieces = 2 ^ (number of dots -1)

Any other attempt to explain our observations would require more entities, that means, would be permitted by the Razor.

The punch line is of course that the relation stated above fails for larger numbers of dots.

Generally, science can be only an attempt to approximate the truth. We can't know if it ever tells us the truth. Ockham's Razor just tells us which theory we should prefer as being more likely to be true, to get rid of all those invisible elfs. But the invisible elf could be true, and further scientific progress may find a way to render the elf visible.

 

[Brown]

Brown was not trying to make the trivial point that one principle can't solve all problems. The problem here is: the shortest explanation of your observation is:

number of pieces = 2 ^ (number of dots -1)

Any other attempt to explain our observations would require more entities, that means, would be permitted by the Razor.

The punch line is of course that the relation stated above fails for larger numbers of dots.

Basically, that's right; and the relation doesn't hold for a smaller number of dots, either (zero dots: one piece). (By the way, the relation between dots and pieces is really a fourth-order equation.)

The point is that you have to be careful about the difference between making a hasty generalization and applying Occam's razor. If all you know is:
one dot: one piece
two dots: two pieces
three dots: four pieces
four dots: eight pieces
five dots: sixteen pieces
then use of the equation number of pieces = 2 ^ (number of dots -1) is just as good at describing the relationship as the fourth-order equation or any other equation... and it's simpler. But if you know how these numbers are generated (and I described that procedure in detail), then you have to be careful about reaching a hasty conclusion and saying that the conclusion is supported by Occam's razor.

As has been pointed out by many others, Occam's razor is not a hard and fast rule, but is useful for making a decision as to whether something makes sense. Another way to look at it is to say that whoever seeks to supplant a simpler solution with a more complicated one has the burden of proof... and sometimes that burden can be satisfied!

 

[Pyrian]

Brown:
Another way to look at it is to say that whoever seeks to supplant a simpler solution with a more complicated one has the burden of proof... and sometimes that burden can be satisfied!

I like that. I like that a lot...

 

[jan]

Sometimes it can be a non-trivial task to decide which one of two theories is more parsimony.

For example, is the assumption of an absolute space an unnecessary entity within Newton's mechanics? Mach adviced that it should be dropped, but it depends on how you state the problem.

If you state it as the trilemma

"absolute space or inertial reference frame or arbitrary reference frame"

then it seems quite obvious that you only need an inertial reference frame. But if you state it as the dilemma

"absolute space or arbitrary reference frame"

(an arbitrary reference frame could be, for example, the spinning reference frame in which the earth doesn't revolve) then you have good reasons to stick with the absolute space (otherwise, you would be left without explanation for the Coriolis Force).

Needless to say, as soon as you replace absolute space with ether, then the fact that light exists becomes strong evidence that absolute space exists. So it would have been a shame to throw out absolute space to satisfy Ockham and Mach just to be forced to reintroduce another kind of absolute space to be able to explain the existence of light.

 

[Walter Wayne]

The problem when applying the Razor is that few people understand the Razor or even know of its existence. I think skeptics instinctively apply it when examining woo woo claims, but believers do not. That's why I think it is important in promoting critical thinking, to explain why we use it. I think we need to explain the thought processes involved rather than go on about it as though it were some kind of skeptics' law.

I heartily agree with this statement. Almost any rule becomes simpler to apply across a range of situations once one understands the principles behind it. I think even many skeptics do not understand the reason behind the rule.

I believe there are two reasons behind applying Occham's Razor, one practical and one logical. The practical reason behind the Razor is to prevent the "infinity of entities", which would make the practice of science incredibly difficult. Many people have pointed this out on the thread.

But there is another very logical reason for the Razor. It prevents us from saying things we don't actually know. Given the examples we have seen above, let us suppose we have two theories on lighting. The first we will call hypothesis A and the second hypothesis Z. Hypothesis Z is in fact hypothesis A with the addition of Zeus. I set about to proove that Hypothesis Z, and I collect data and show that my evidence is entirely consistent with my Zeus hypothesis. However, if someone shows that hypothesis A and Hypothesis Z predict the exact same results, it becomes obvious that my experiment didn't "test" Zeus in any way. So by including Zeus I have in fact stated something I do not know. Occham's razor prevents from stating things we don't know.

A while back the Skeptical Inquirer had an article talking about three tools for skeptics. One of the lines that I liked from it was along the lines of we use Occhams razor not because the universe is simple, but because it is complicated (I don't have the exact quote here). I like the line because it clears up one misconception that we often see in popular references to the rule i.e that it assumes a simple universe.

Walt