Ockham's Razor

[Hegel]

Dictionary.com states that Ockham's Razor states that:
Entia non sunt multiplicanda praeter necessitatem.
Meaning Entities are not multiplied except when mecessary.

However I could not find any proof for this. If anyone could provide the philosophic proof, or a philosophic proof, I would be most grateful.

[T'ai Chi]

OR is only a rule of thumb.

If two theories, A (has m assumptions) and B (has n assumptions) both explain event E equally as well, then it OR is simply a rule of thumb to go with the theory A if m is smaller than n.

OR does not say that A is correct, etc., it just recognizes outside facts that A provides the same results as B, and has less assumptions than B, so therefore it is a good idea to stick with A instead of B.

[Hegel]

Originally posted by T'ai Chi
OR is only a rule of thumb.

If two theories, A (has m assumptions) and B (has n assumptions) both explain event E equally as well, then it OR is simply a rule of thumb to go with the theory A if m is smaller than n.

OR does not say that A is correct, etc., it just recognizes outside facts that A provides the same results as B, and has less assumptions than B, so therefore it is a good idea to stick with A instead of B.

However I have seen a lot of people use this in proofs. That is fine if there starting with this as an axiom, but then it is very easy to just state that their proof is worng, by saying this theory is wrong. For example, many people are trying to prove the non-existance of God using Ockham's Razor. This is a fairly big thing to prove, and one which I wouldn't accept with out some backing to the theory.

[toddjh]

It's a matter of how it's applied. A lot of people take Occam's Razor the way it's been popularized: "the simplest explanation is the best."

But that's not really the spirit of it. To me, the best example of how Occam's Razor should be applied is the concept of "theistic evolution." You have two competing theories:

1. Biological evolution occurs according to natural laws.

and

2. Biological evolution occurs according to natural laws, and God is orchestrating it all behind the scenes.

Occam's Razor applies because the second theory has an extra hypothesis that adds complexity without granting any new predictive power. There's no need to assume things that are completely irrelevant to the theory.

Jeremy

[Pyrian]

Hegel:
That is fine if there starting with this as an axiom, but then it is very easy to just state that their proof is worng, by saying this theory is wrong.Ockham's Razor should not be used in proofs. It's purpose is more in the formation of hypotheses. It's used to criticize hypotheses - typically hypotheses that add unnecessary complexity.Hegel:
For example, many people are trying to prove the non-existance of God using Ockham's Razor.It's worth noting that most of us jumped all over a similar attempt at disproving God in this very forum. Anyway, you have my permission to smack upside the head anyone claiming the Ockham's Razor proves anything.

Besides, disproving God effectively requires defining God first - once you do that step, it tends to be fairly straight forward, at which point anyone arguing simply switches their definition of God. This can be fun for a while - especially if I can push them into defining God in such a way that I can fit either myself or some basic law of physics into the definition - but inevitably gets boring or tangled up in the definitions of something like "all-loving," "omnipotent," or "omniscient." (I'm convinced that in their basic form all three of those are literally self-contradictory.)

[Lord Kenneth]

Here is a good example of Occam's Razor:

"Where does lightening come from?"

One could say Zeus does it, or it is caused by natural processes.

Well, massive evidence for the latter aside, we already know natural causes exist, so it is best to assume that rather than creating some unknown being as the cause.

Of course, if we were able to find this Zeus and find out how he creates thunder (that would be difficult!) that would be the most parsimonious explanation, because after that it would take more stretching to say that Zeus doesn't really do it (unless you had evidence of that).

[Dancing David]

The razor while useful is just a tool, not all tools work in all situations.

It gets to the notion of elegance, the simpler and more compact a theory the more elegant it is.

And there is the problem with defining simplicity.

A theist would say god does everything.
so this has been used to demonstarte idealism on this board recently by Franko. A god creating the illusion of the world is simpler to a theist than the actual world existing.

A materialist looks at it from the other side and says that the world exists as it is, a god is redundant.

A razor cuts both ways.

[Paul C. Anagnostopoulos]

Classic example: I'm discussing evolution and creationism with some folks. One of them is writing a book on "Christian Creationism." I very much doubt that every bit of Christian dogma is necessary to a theory of creationism. Why not a simpler form of creationism that makes minimum supernatural assumptions? (Well, because he's really writing a Christian apologetic.)

~~ Paul

[fhios]

Originally posted by Hegel
Dictionary.com states that Ockham's Razor states that:
Entia non sunt multiplicanda praeter necessitatem.
Meaning Entities are not multiplied except when mecessary.

However I could not find any proof for this. If anyone could provide the philosophic proof, or a philosophic proof, I would be most grateful.

I've read a collection of his writings (translated out of the original latin, of course), and while he never seems to have stated this idea in just so many words, he did apply it agressively to the medival (sp?) world of ideas.
Occam was attempting to prove that all things--dogs, trees and tables for instance--owe their existance to a decision on the part of God--are "radically contingent upon God," in the words of the books commentator. This idea was of course nessecary to prove God's supremacy over the world, but it also contradicted the Aristotlean idea of a world of essences extending themselves into the phyisical world and picking up specific qualities ("accidents" in the terminology of the time; our expression "an accident of birth" stems from this usage) and thus become the individual dogs, trees and tables in our own universe.
To refute the idea of a world of essences, he argued that the mind was easily able to generalize the ideas of dog, tree and table from its experiences with individual ones, and that the idea of a world of essences was, therefore, surplassage, an entity without logical necessity. That was his use of that law.
Did this help?

[Hegel]

That helped, but did he have any evidence for it, or was it just a postulate of his theory?

[toddjh]

Originally posted by Hegel
That helped, but did he have any evidence for it, or was it just a postulate of his theory?

I'm not sure what kind of "evidence" a statement like that needs. It's more of a truism, like the weak anthropic principle. It's pretty obvious (to the modern scientific mind) that you shouldn't assume anything that doesn't have any explanatory power.

Jeremy

[fhios]

Originally posted by Hegel
That helped, but did he have any evidence for it, or was it just a postulate of his theory?

It's for use in purely theoretical matters, ones in which no empirical evidence points to one conclusion being superior to another.

[RichardR]

Originally posted by Hegel
many people are trying to prove the non-existance of God using Ockham's Razor. This is a fairly big thing to prove, and one which I wouldn't accept with out some backing to the theory. You can't prove the non-existence of God using Occam's Razor. You can use Occam's Razor to determine that there is no need to posit the existence of God to explain anything. That's an important difference.

Occam's Razor says don't invent unnecessary entities to explain something that can already be explained using only entities that are known to exist. That is not because Occam's Razor proves the unnecessary entities don't exist. It is because the additional entities are unnecessary inventions. Which means that you are only invoking them because you happen to like the idea, or because they are necessary for some belief system. The problem is, if you ignore Occam's Razor and invent entities which are not supported by evidence, there are an infinite number of entities you can invoke to explain any phenomena. For example, if I drop my pen and it falls to the ground, I can say it is because there are invisible pieces of elastic pulling it down, or I can say there are invisible fairies in the room that are doing it. And that approach leads nowhere.

It is explained quite well here: (http://www.skepticreport.com/tools/occamsrazor.htm)

[csense]

Originally posted by RichardR
You can't prove the non-existence of God using Occam's Razor. You can use Occam's Razor to determine that there is no need to posit the existence of God to explain anything. That's an important difference.

Occam's Razor says don't invent unnecessary entities to explain something that can already be explained using only entities that are known to exist. That is not because Occam's Razor proves the unnecessary entities don't exist. It is because the additional entities are unnecessary inventions. Which means that you are only invoking them because you happen to like the idea, or because they are necessary for some belief system. The problem is, if you ignore Occam's Razor and invent entities which are not supported by evidence, there are an infinite number of entities you can invoke to explain any phenomena. For example, if I drop my pen and it falls to the ground, I can say it is because there are invisible pieces of elastic pulling it down, or I can say there are invisible fairies in the room that are doing it. And that approach leads nowhere.

It is explained quite well here: (http://www.skepticreport.com/tools/occamsrazor.htm)


I think you're putting a skeptics spin on the interpretation.

Occams Razor doesn't distinguish between physical and non physical entities, nor does it distinguish between what is right and what is wrong, or what is correct and what is incorrect.
It makes no such qualitative statements, which is part of the problem when interpreting this tool.

[Some Friggin Guy]

Anyway, you have my permission to smack upside the head anyone claiming the Ockham's Razor proves anything.

Wouldn't you be able to use Ockham's razor to prove that Ockham shaved at least once in his life?:)

Sorry, I'm tired and couldn't resist.

[RichardR]

Originally posted by csense
I think you're putting a skeptics spin on the interpretation.

Occams Razor doesn't distinguish between physical and non physical entities, nor does it distinguish between what is right and what is wrong, or what is correct and what is incorrect.
It makes no such qualitative statements, which is part of the problem when interpreting this tool. I never said it did any of those things.

:confused:

[Pyrian]

Some Friggin Guy:Anyway, you have my permission to smack upside the head anyone claiming the Ockham's Razor proves anything.
Wouldn't you be able to use Ockham's razor to prove that Ockham shaved at least once in his life?:)*smack* :cool:

[Yahzi]

Originally posted by Lord Kenneth
Here is a good example of Occam's Razor:

"Where does lightening come from?"

One could say Zeus does it, or it is caused by natural processes.

That's not a good example. Todd gave a better example. To convert your example into a good one:

"One could say that electrons flow from the ground to the air, or one could say that Zeus causes electrons to flow from the ground to the air."

Occam's Razor proves stuff just fine. It is, in fact, the only proof you have that Santa Claus does not exist. Since absolutely everyone here agress that Santa Claus does not exist (and also elves, pixies, leprechauns, unicorns, dragons, compassionite conservatives, etc.), we must conclude that the Razor is in fact compelling in every single instance it is used - except God.

As usual, God gets a special exemption. No one objects when the Razor is used to disprove any of the infinite imaginary creatures made up by delusional lunatics and poets: only when God is subject to the Razor do people suddenly decide that it is somehow inadequate.

This special exemption says a lot about the notion of God, but nothing at all about Occam's Razor.

[Yahzi]

Originally posted by Dancing David
The razor while useful is just a tool, not all tools work in all situations.
The Razor is a fundamental principle of reason, right up there with the three basic laws of logic and the assumption that the world is law-governed.

Everyone uses the Razor every single time they frame any argument. Everyone assumes its absolute power, utility, and correctness every time they offer any explanation of anything.

It is far more than just a tool, and it is applied in every single argument ever advanced.

If it were not, I could legitimately disprove every explanation by offering an alternate explanation that was exactly the same as the first one, but had an invisible, intangible elf. Unless you are prepared to treat every explanation offered, of every phenomona imaginable, equally with the invisible elf explanation, then you are endorsing the Razor. And if you are prepared to do so, you are far to insane to have any logical conversation with. Hence we see that the Razor applies to everything except insane people.

[csense]

Occam's Razor is not a principle, and it specifically is not a principle of contradiction. As previously stated, it's use is limited to matters theoretical.
It is used to refine a given theory, or theories which are more similar, than they are dissimilar, so If anything, one can say it concerns itself more with identity.

Simplicity, or (the law of) Parsimony demands certain assumptions be made for it to be of any value whatsoever, and these assumptions are quite subjective.

Either way, to say that either of these two prove anything, is poor reasoning.

[Pyrian]

It is, in fact, the only proof you have that Santa Claus does not exist.I can come up with any number of empirical proofs that Santa Clause does not exist based on the predictions of the theory of his existence (starting with reindeer can't fly).If it were not, I could legitimately disprove every explanation by offering an alternate explanation that was exactly the same as the first one, but had an invisible, intangible elf.That is a fairly accurate description of most theoretical particle physics at this stage, Yahzi - they may call the elf "super-strings" and apply various mathematics, but it's still basically an invisible elf which does stuff.Hence we see that the Razor applies to everything except insane people.No, no, it applies to insane people as well.

The reality is that it doesn't prove anything, Yahzi, and if it did then 150 years ago we'd've had PROOF that relativity was incorrect, since Newtonian physics did the job as far as we could tell at that point.

It is a tool for winnowing hypotheses - and a good one. But it does not offer proofs.

[RichardR]

Originally posted by Yahzi
Occam's Razor proves stuff just fine. It is, in fact, the only proof you have that Santa Claus does not exist. Funny. I always thought you couldn't prove a universal negative.

Originally posted by Yahzi
Since absolutely everyone here agress that Santa Claus does not exist (and also elves, pixies, leprechauns, unicorns, dragons, compassionite conservatives, etc.), we must conclude that the Razor is in fact compelling in every single instance it is used And that appeal to popularity was a logical fallacy.

Originally posted by Yahzi
As usual, God gets a special exemption. Not here he doesn't.

Originally posted by Yahzi
No one objects when the Razor is used to disprove any of the infinite imaginary creatures made up by delusional lunatics and poets: only when God is subject to the Razor do people suddenly decide that it is somehow inadequate.

This special exemption says a lot about the notion of God, but nothing at all about Occam's Razor. But the Razor doesn't disprove anything.

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.

Originally posted by Yahzi
Everyone uses the Razor every single time they frame any argument. Everyone assumes its absolute power, utility, and correctness every time they offer any explanation of anything. I think the arguments put forward by believers on this forum demonstrate that not everyone uses the Razor every single time they frame any argument. :D

[RichardR]

csense:

Just to be clear here, do you think I was saying that the Razor could distinguish between physical and non physical entities, or distinguish between what is right and what is wrong, or what is correct and what is incorrect?

I would like to know what you think, because if that was the message I was putting over I need to re-write my message. Thanks.

[csense]

Originally posted by RichardR
csense:

Just to be clear here, do you think I was saying that the Razor could distinguish between physical and non physical entities, or distinguish between what is right and what is wrong, or what is correct and what is incorrect?



Well yes, it does seem like that is what you were inferring.

Here's what you said:


You can't prove the non-existence of God using Occam's Razor. You can use Occam's Razor to determine that there is no need to posit the existence of God to explain anything. That's an important difference.

Occam's Razor says don't invent unnecessary entities to explain something that can already be explained using only entities that are known to exist. That is not because Occam's Razor proves the unnecessary entities don't exist. It is because the additional entities are unnecessary inventions. Which means that you are only invoking them because you happen to like the idea, or because they are necessary for some belief system. The problem is, if you ignore Occam's Razor and invent entities which are not supported by evidence, there are an infinite number of entities you can invoke to explain any phenomena. For example, if I drop my pen and it falls to the ground, I can say it is because there are invisible pieces of elastic pulling it down, or I can say there are invisible fairies in the room that are doing it. And that approach leads nowhere.

There are three things that strike me here...one, I think the use of the term invent or invention is ambigious considering we are dealing with the theoretical, and it implies an assumption that those concepts which concern themselves with what we consider to be of a non physical nature, to be wrong, or at the very least to be a condradiction of logic and reason and therefore essentially useless.
Which brings me to my second point, that of necessity, which can be very subjective given that again we are dealing with the theoritcal, and whose supporting arguments, or evidence if you will, are grounded in pure reason.

My final observation is that there is a tendency to confuse observations or events that a theory is attempting to explain, and observations or events that a theory predicts.
[edited to add]
And even then, if true consequences are observed, it does not infer the truth of the theory since from the truth of the consequences, one may infer the truth of the ground, but only negatively. If one false consequence follows, then the ground must also be false, for if the ground were true, then the consequence must also be true since the consequence is determined by the ground. One can not infer conversely however since true consequences may be drawn from a false ground.

[Yahzi]

Originally posted by csense
Occam's Razor is not a principle, and it specifically is not a principle of contradiction. As previously stated, it's use is limited to matters theoretical.
This either means nothing or it is wrong.

If by limiting it to matters of theory, you simply mean it only applies to explanations, well of course. If you mean it only applies that boring old formal stuff that scientists do, then you are dead wrong.

It is not only a principle, it is a principle that you endorse and utilize every single day. It is the fundamental basis of reason. It is what distinguishes the true explanation from all the others.

Elsewhere I have discussed the 3 assumptions of science. 1) there is a universe that is knowable to approximation, 2) it is law governed, 3) we can tell the difference between approximations. Occam's Razor is effectively number 3: to refute it, or assert it does not apply, is to assert that our theorys of the universe are indistinguishable. This is a common new age position, and it is wrong.

The explanation that rain is caused by condensation is unquestionalbly superior to the explanation that rain is caused by condensation and an invisible intangible elf. Surely you agree. So by what principle do you rule out the explanation containing the useless, undetectable elf? Why, by the principle of Occam's Razor.

[Yahzi]

Originally posted by RichardR
Funny. I always thought you couldn't prove a universal negative.
All these arguments revolve around what "prove" means. If by proof you mean something so certain you'd unhesitatingly stake your life on it, then yes, we can prove things.

But if by proof you mean an impossible standard that cannot be met except for trivial cases of definition, well, then, no. Is that surprising? Is it meaningful?

[Leif Roar]

Originally posted by Yahzi

All these arguments revolve around what "prove" means. If by proof you mean something so certain you'd unhesitatingly stake your life on it, then yes, we can prove things.

Of course, by that definition a lot of people find the bible to be "proof good enough." It's not really a good definition, as a) it doesn't separate between what's true and what's merely useful and b) people can be frightfully irrational about what they'll stake their lives on.

(Edited to fix a typo.)

[Pyrian]

Yahzi:
If by proof you mean something so certain you'd unhesitatingly stake your life on it, then yes, we can prove things.Would you unhesitatingly stake your life on the assertion that quarks are elemental? Would you have unhesitatingly staked your life on the assertion the electrons were elemental, back when there was no evidence to suggest they were made up of anything else? Would you have unhesitatingly staked your life on the assertion that matter was infinitely divisible, back before there was any evidence to the contrary?

Ockham's Razor is incredibly useful for ruling out the infinite number of other possibilities in the universe, but pretty much every time its been used its been eventually shown to be wrong. I'd hardly call that measuring up to the word "proof".

[Lord Kenneth]

Originally posted by Pyrian
Ockham's Razor is incredibly useful for ruling out the infinite number of other possibilities in the universe, but pretty much every time its been used its been eventually shown to be wrong. I'd hardly call that measuring up to the word "proof".

Occam's razor is applied with the given evidence, you know...

Ha, pretty much every time it's used it's been eventually shown to be wrong? Ridiculous. Tell me that next time I don't assume that it was aliens who took a bite out of my sandwich...

[Pyrian]

Lord Kenneth:
Occam's razor is applied with the given evidence, you know...Of course it is - that's my point. The given evidence is never complete. There are an infinite number of wrong answers, but there's usually a right answer you'd never think of which would be ruled out by Ockham's Razor - and justifiably at that.

Thus, it does not and cannot constitute proof.Lord Kenneth:
Ha, pretty much every time it's used it's been eventually shown to be wrong? Ridiculous. Tell me that next time I don't assume that it was aliens who took a bite out of my sandwich...The problem isn't with the aliens assumption, the problem is with declaring that all solutions other than the simplest are necessarily incorrect and proven incorrect by the razor.

[Lord Kenneth]

Originally posted by Pyrian
Of course it is - that's my point. The given evidence is never complete. There are an infinite number of wrong answers, but there's usually a right answer you'd never think of which would be ruled out by Ockham's Razor - and justifiably at that.

Thus, it does not and cannot constitute proof.The problem isn't with the aliens assumption, the problem is with declaring that all solutions other than the simplest are necessarily incorrect and proven incorrect by the razor.


I don't think anyone says it is proof.

It's simply the most likely solution given what we know.

[Pyrian]

Lord Kenneth:
I don't think anyone says it is proof.Yahzi:
Occam's Razor proves stuff just fine.

[RichardR]

csense:

Thanks for your reply. I believe Occam's Razor is one of the main aspects of critical thinking that the woo woos don't get, and consequently I have been trying to explain why we use it, so that it makes sense. (Incidentally, I believe the other main thing we need to teach woo woos is the meaning of argument from ignorance, but that's a subject for another thread.) I have been finding it hard to explain why we use it, because I realize I've been applying it (without realizing what it was called), it most of my life. It seems so obvious to me (and probably most skeptics), that I'm finding it hard to explain to someone who doesn't see things the way I do. So I appreciate the feedback.

However, I am confused over a few points, and I wonder if I have got something wrong or am just explaining myself poorly. In the interest if getting to the bottom of this:

Originally posted by csense
There are three things that strike me here...one, I think the use of the term invent or invention is ambigious considering we are dealing with the theoretical, and it implies an assumption that those concepts which concern themselves with what we consider to be of a non physical nature, to be wrong, or at the very least to be a condradiction of logic and reason and therefore essentially useless. I intended the word "invention" to apply to physical and non-physical things, so you confuse me a little here.

Perhaps "invention" is too loaded a word. I want to get over the idea that the additional assumptions are not backed by any evidence and therefore they must be fabricated, or made-up (invented). Perhaps I should say the additional assumption is "not backed by evidence that it exists, and therefore there is no reason to suppose it exists".

Less emotive – but does it get the message over?

Originally posted by csense
Which brings me to my second point, that of necessity, which can be very subjective given that again we are dealing with the theoritcal, and whose supporting arguments, or evidence if you will, are grounded in pure reason. Occam's Razor says "…without necessity", so I think we need to keep it in some form. Perhaps "unless the hypothesis cannot be explained without" the additional assumption. It's less subjective but less punchy. Does it get the message over?

Originally posted by csense
My final observation is that there is a tendency to confuse observations or events that a theory is attempting to explain, and observations or events that a theory predicts. Sorry – I'm don't understand how my explanation was doing that.

[RichardR]

Originally posted by Yahzi
All these arguments revolve around what "prove" means. If by proof you mean something so certain you'd unhesitatingly stake your life on it, then yes, we can prove things.

But if by proof you mean an impossible standard that cannot be met except for trivial cases of definition, well, then, no. Is that surprising? Is it meaningful? This just sounds like argument from ignorance – your opponent can't prove it true so it is false. Now, I agree that when something tested again and again and always fails the test (eg homeopathy), then it is sensible to conclude unless any new evidence appears that the thing is false. But this is a special case where we draw a conclusion because of the weight of all the failed tests. Occam's Razor can be applied in the absence of any such data, and in that case Occam's Razor doesn't prove anything.

[Brown]

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.)

Put a third dot anywhere on the circumference and connect the dots with straight lines. You have divided the circle into four pieces.

Put a fourth dot anywhere on the circumference and connect the dots with straight lines. You have divided the circle into eight pieces.

Put a fifth dot anywhere on the circumference and connect the dots with straight lines. You have divided the circle into sixteen pieces.

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)?

[Yahzi]

Originally posted by Pyrian
Ockham's Razor is incredibly useful for ruling out the infinite number of other possibilities in the universe, but pretty much every time its been used its been eventually shown to be wrong. I'd hardly call that measuring up to the word "proof".
This is false. Once again, I ask you: how do you know that invisible intangible elves are not an integral part of the weather cycle? Ruling out the infinite possiblities is done so frequently, and properly so, that its accuracy rate must approach infinity. Your insane notion to the contrary is just, well, insane. The razor is not some dusty sawhorse that is trotted out once a decade or so. It is a principle you are using right this very instant. It is fundamental to the process of reason.

Your claim that it doesn't prove anything is tantamount to saying that reason and logic do not prove anything. Perhaps you are just trying to say that they are not "evidence," and given the wrong evidence will produce the wrong result. Agreed. 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.

[Yahzi]

Originally posted by RichardR
This just sounds like argument from ignorance – your opponent can't prove it true so it is false.
:eek:

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."

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?

As for applying things with insufficient data, well yes. This is the difference between a valid argument and a sound one. So what? The fact that you can use logic to reach false conclusions if you start from false or inadequate premises does not lead you to make statements like "you can't prove anything with logic."

[Yahzi]

Originally posted by Brown
Try applying Occam's Razor to this problem:

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]

Originally posted by Pyrian
Of course it is - that's my point. The given evidence is never complete. There are an infinite number of wrong answers, but there's usually a right answer you'd never think of which would be ruled out by Ockham's Razor - and justifiably at that.
This is so deeply confused.

On the one hand it seems to be a statement of nilhism - that nothing can actually be known, since the evidence can never be complete.

On the other hand it just seems like an incorrect application of the principle. Apparently rulling out any number of invisible intangible elves as possible explanations also rules out the right answer, which gives the impression that the right answer is some number of elves. After all, there are an infinite number elf theorys (1 elf, 2 elves, etc.) and only one non-elf theory, so by simple averaging we should assume that there are some number of elves involved, right?

Logic gives you the wrong answer if you apply it wrong, or start with the wrong premises. But you would hardly condemn or abandon logic for that reason, nor would you make the claim that "logic doesn't prove anything."

[LW]

Originally posted by Yahzi

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."

However, you should note that this principle doesn't hold in formal logic.

[Leif Roar]

Originally posted by Yahzi

:eek:

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 (http://flem.keenspace.com/d/19990509.html)

[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]

Originally posted by Yahzi

:eek:

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: (http://www.intrepidsoftware.com/fallacy/ig.php)

"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".

Originally posted by Yahzi
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]

Originally posted by Yahzi

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]

Originally posted by Yahzi

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]

Originally posted by Brown
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)?

Originally posted by Yahzi

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]

Originally posted by jan
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]

Originally posted by RichardR
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