Occam's Razor: Valid tool of reason or evil mind control plot?

Great Debates
1

I was surprised to discover that there appears to be some disagreement on the SDMB about the proper application of Occam’s razor.

http://boards.straightdope.com/sdmb/showthread.php? threadid=140209

Occam’s razor was originally formulated by William of Occam in the 14th Century. It is literally translated into English as “Plurality should not be posited without necessity.” Though Occam gets the credit, the basic concept was known to Aristotle.

http://www.wikipedia.org/wiki/Occam%27s_Razor

Occam’s razor is a key element in scientific reasoning. “When confronted with two theories, each of which explain the available data, choose the simplest.”

Libertarian and Senor Beef believe that this formulation of Occam’s razor is wrong.

Both of these statements seriously misunderstand the basis of scientific reasoning. In science, theories are never “True” with a capital T, they are always provisionally “true” in the sense that they are always subject to disproof by additional data. Occam’s razor says that, when you must choose between two theories, each of which explain the data equally well you must choose the simpler theory and assume it to be “true” until it is contradicted by additional data. This is a valuable tool in ordinary everyday reasoning as well as in formal scientific reasoning. For one thing, it is usually deadly to wildly speculative conspiracy theories.

By way of getting the discussion rolling, let me dissect one of Libertarian’s posts.

**
Perhaps. So what? This has nothing to do with the validity of this version of Occam’s razor as a tool for choosing between different theories. When I apply Occam’s razor, I must use all the available data I have. If get additional data whether from making a new observation myself, learning about observations someone else made or whatever, I must again apply Occam’s razor to choose a new theory if the new data disproves my old one.

**
Once again, perhaps not. So what? All this means is that this formulation of Occam’s razor may not always be easy to apply, not that it is invalid. In any case, the subset of cases where Occam’s razor is difficult to apply is swamped by the almost infinite number of cases where it so ridiculously easy to apply that you don’t even realize you are doing it. Which are you inclined to adopt as a working hypothesis, that the SDMB is a collection of like-minded individuals generously subsidized by the Chicago Reader or that it is a massive mind-control experiment run by space aliens and that every poster, apart from yourself, are part of the alien plot?

One other point.

**
Even assuming, for the purposes of argument, that this is correct, it is a distinction without a difference. When I am evaluating a set of data, I must adopt a theory to explain it. I can certainly conclude that the data is best explained by a theory that is already offered by someone else just as I can formulate my own theory. Either way, I am “forming” what I believe to be the best explanation of the data. To put it another way, Occam’s razor as a tool for formulating “correct” theories is logically indistinguishable from Occam’s razor as a tool for choosing “correct” theories.

2

I think Occam’s Razor is meant to be utilitarian and heuristic. I doubt that you could say it is “logically” indistinguishable but you could probably say it is “effectively” indistinguishable (if the theorist isn’t a complete idiot.) If you want to debate whether or not it is “effectively” indistinguishable then you need to better define your terms lest we debate semantics.

3

The point is not simplicity for simplicity’s sake. It’s: don’t invent more and stronger assumptions when you can get by with fewer and weaker ones. Don’t multiply explanatory entities unless it increases your explanatory power.
In some sense it’s a defense against ad hoc reasoning, which, if not for the remarkable number of additional assumptions, could explain just about anything as well as any “simpler” explanation.

4

Ever since I read Dan Simmons’ excellent thriller Darwin’s Blade, I’ve appreciated the corollary to Occam’s Razor he puts forth in it, which bears the same name as the novel:

’All other things being equal, the simplest solution is usually stupidity.'

Heh-heh. Not as scientific, but it certainly speaks to human nature. :slight_smile:

5

Truth Seeker wrote:

If Popper is credible, then nothing in science may be true in any sense, but only false.

Also, I would translate the Parsimony Principle differently from you. Although I’ve seen your version, I believe that this version is correct: “Entia non sunt multiplicanda praeter necessitatum”. Do not multiply entities beyond necessity.

Apos wrote:

I agree with that completely.

6

Just FYI, Skeptical Inquirer (a magazine that takes things like the Razor, Sagan’s words about “extraordinary claims require extraordinary proof”, etc., and applies them to all situations) defined the Razor very simply. In the end, they simply concluded that it was a sound principle for forming theories because, in practice, it tends to accurately predict the theory that is more credible over time. The theories that violate the Razor, multiplying entities beyond necessity, have in our experience been falsified while the “simpler” theories have stood the test of time once developed. Dozens of spherical orbits in complex interaction with each other, a patchwork meant to compensate for the geocentric circular orbit theory’s flaws, gave way to Kepler and his elliptical orbits.

The success of the Razor leads to its being adopted as a sound principle of scientific inquiry. Pretty much the same thing Mill would have said about inductive logic.

7

Having recently plowed through Popper’s work, Lib, even that is not correct. The falsification of a theory is a theory of falsification and is, in fact, just as open to speculation as the original claim was. Though he notes this himself, he tries to sidestep this problem by relying on something he already discredited—that is, verification [of falsification]. As I recall.

Apos notes:

No small problem here because “simpler” is a rather vague term indeed.

Truth Seeker, you say,

Well, knowing your ability for debate (and also knowing your respect for what you call “science”) I am not sure if this is shorthanded speaking or a genuine mistake. Occam’s Razor is not valid in any sense that I have found, other than simply being a method to choose between to competing theories.

Don’t be led astray by the notion of “explaining data equally well”, either. Given any set of data an infinite number of curves can be drawn which will “explain” the data obtained, especially when we are looking for something like a maximum variance or SD. Which curve is correct? The problem here is that we may genuinely need a more complicated formula to “explain” the data, though the simpler one (in this case, the one with the lowest exponent or number of terms) would be chosen first. But at each succesive application of the method (each new data point gathered) we can generate a whole new family of curves to explain the data again.

Interesting that you consider the former to be simpler intuitively.

Ask Winston Smith from Orwell’s 1984 which was simpler: that the Thought Police monitored his activities twenty-four hours a day or that there were times and places where he was safe from inspection. Obviously the latter is “simpler” in the same way the Chicago Reader is benevolent is “simpler”. But the demonstration of the validity of a theory is wholly independent from choosing a working hypothesis. Something is not prima facie absurd just because it is complicated—this is the misapplication of Ockham’s Razor, IMO. It is easier to test simple theories. In fact, I might offer this as a resolution to the point I mentioned to Apos: simplicity of a theory is the practicality of its testing given current knowledge, tools, and other resources.

[As ever, I feel compelled to note to any lurking atheists that William himself was profoundly religious and did not feel this principle of parsimony in any way affected that judgment.]

Actually, I don’t think it is deadly to them at all; I think it is simply used (almost definitionally) to point them out. It surely proves nothing.

8

Eris

I’m not sure what you’re saying, or how it contradicts what I said. Could you elaborate, and perhaps provide that portion of Popper’s text?

9

eris is certainly correct, and I believe William of Occam knew this. To use Occam’s Razor simply to evaluate two completing hypotheses, to my mind, is a misapplication. Occam used this principle to justify, among other conclusions, that God’s existence cannot be deduced by reason alone. He used the Razor almost purely for ontology.

It was adapted later by scientists, especially Newton, who claimed:

Hence the razor (or the Parsimony Principle) is best for building models that involve prediction. If you begin with too many unnecessary foundations for a theory, the chances of arriving at a manageable model are small. The purpose of a model, of course, is to start small, and add increasing levels of sophistication and abstraction onto a firm foundation to maximize its predictive power and minimize the number of assumptions required.

The most current common claim:

is manifestly not Occam’s Razor. It worded much stronger than Occam intended. Occam’s Razor was used to develop theories, not to choose between two that predict different outcomes. It is very easy to point out how subjective simplicity us, and how our ideas of simplicity are often not shared by the universe. Thus this perverse application of the Razor should never be used to justify a conclusion.

Hence Truth Seeker’s:

is completely incorrect. Occam says that you choose the simplest theory to test first. The Razor should never be used as a tool to determine truth value.

An interesting article on this extremely common misunderstanding is The Myth of Occam’s Razor, by W.M. Thorburn.

Occam was, of course, a churchman. I do not believe that he intended his razor to be applied to metaphysics.

The Latin, by the way, is Pluralitas non est ponenda sine neccesitate and Frustra fit per plura quod potest fieri per pauciora. The phrase that Libertarian quoted is not actually found in any of Occam’s works, but was written by a later scholar.

10

“I have a theory which predicts [such-and-such].” Experiment is performed, data is collected which contradicts this theory. We might then be inclined to say that this theory is falsified. But then, we may instead say, “I have a theory which predicts [the previous theory] is false.” See? We collect the same data in either case; and, each theory is just as open to falsification as the other.

I will look up the quote tonight. I fear I may have incorrectly said that he resorted to verificationism when he may not have, so I would like to withdraw that comment.

11

Maeglin posted this above:

Is the debate merely that this common conception is not Occam’s Razor and should not be called such, or that this idea is in fact incorrect and should not be used?

12

—No small problem here because “simpler” is a rather vague term indeed.—

Uh, I didn’t mention “simpler” there, and I’m not sure Occam did either.

Occam’s Razor reflects, in a way, the idea that knowledge should be built upwards, not downwards. We don’t start out knowing the right theories, or the right assumptions. We try to start from the assumptions that seem the weakest (i.e. don’t claim much, and can gain wide support and agreement), and see how far we can get. We build from what seems to hold.

Think of the pragmatism of this from just the perspective of what assumptions can gain wide support. If we can prove something with only the most basic assumptions about reality that almost everyone will concede, then we don’t need to try positing really complex and controversial ones to get to the same place.

Likewise, think of the pragmatism of fewer assumptions in terms of testing an idea: we know much better what the model is really relying on, and there are far fewer interactions to consider. That doesn’t make adding more and stronger assumptions BAD, it’s just that their cost in terms of potentially unbalancing a model should be balanced by their ability to actually explain more than you could before.

13

Lib, here is the relevant text. It is from section 22, “Falsifiability and Falsification”.

He then goes on (in footnotes) to discuss a problem of infinite regression, and each time he counters his own dialectic foil with the notion that though it is infinitely regressive in theory, we never use infinite regression. We needn’t even test the falsifying hypothesis once, we need only be able to test it. Of course, this only means we needn’t test any hypothesis at all, as the falsifying hypothesis is logically not different from a regular one; both predict a specific event, and both have basic statements (his term, and it is loaded) which will demonstrate their falsification.

As far as my comment about verificationism, it was false. I apologize.

Apos, “weak” is no less intuitive of a word than “simple”. Use what you like. Defining it as, “don’t claim much, and can gain wide support and agreement” is no better than saying the simplest one says the least and has little implication. Vagaries we should like to expunge, no?

14

quasi bump to let others no I actually posted something there…

15

**
eris, please, you’re weirding me out. Are you seriously asking why a theory involving a charitable act by a group of humans is intuitively simpler than a theory involving 1) space aliens, 2) a mind-control experiment, 3) directed at you personally and 4) a conspiracy involving everyone except you?

In reading the responses to this thread, there seems to be some confusion about “truth” as it relates to using Occam’s razor in scientific reasoning. Here’s a thread that might help bring the issue into focus.

Basis for the scientific method

There also seems to be some misunderstanding as to the point of using Occam’s razor as a reasoning tool.

**
This is correct, but misleading. If the theories predicts two different outcomes, then you need simply do an experiment to determine which outcome actually occurs. This outcome is new data which must now be explained. If the simpler theory can’t explain it, then it must be discarded. A theory should be as simple as possible, but no simpler.

**
This, however, is incorrect. In science, Occam’s razor defines “truth.” This has many different permutations. If two theories predict identical outcomes, the simplest theory is “true” for the purposes of science. It may be that gravity fairies precisely mimic the predictions of general relativity and that general relativity isn’t actually “true.” Since there is, however, no way to determine whether there really are gravity fairies, we discard this theory. Indeed, general relativity itself would have been discarded had it made predictions precisely identical to those of Newton.

Any time you can test theories by gathering data that will or will not agree with a particular theory, Occam’s razor is uneccessary. There is no theory to test “first.” If two theories are explaining the same data, you are testing both theories simultaneously when you test a hypothesis for which the theories predict different outcomes.

By the way, since “truth” in science is provisional, it is perfectly acceptable to act as if two contradictory theories are “true,” at least until they can be tested. We do this all the time in ordinary life, especially when one theory, while unlikely to be true, would have very great consequences if it were true. The odds of contracting rabies from a dog bite are pretty remote. However, if you are bitten by an unknown dog, you’ll need to get a series of painful rabies shots.

**
Well, in a sense, it is. Remember, we are talking about choosing between theories that explain all the available data. People in this thread seem to be saying that the simplest theory may not turn out to be true. However, no one will know that until there is additional data.

To put it another way, on what basis would you choose a more complex theory rather than a simpler one? By definition, you cannot do so based the data – you haven’t any data that isn’t explained equally well by the simpler theory.

When you choose a complex theory when a simple one will do, you are doing exactly what William of Occam warned against. You are needlessly multiplying entities, whether physical laws, conspiracies or angels.

I do not claim that Occam’s razor is a guide to some sort of ultimate Platonic “truth.” However, it is a guide to scientific truth as well as everyday truth because it necessarily incorporates all the data you have at any given time. Needless complexity is just that – needless. Maybe you are being followed by a telepathic mime that everyone can see except you, but it’s more likely that people are laughing at you because of your new haircut.

Unfortunately, because of professional obligations, this will be my last post here for a number of weeks or, possibly, months. A pity, really, as I would have enjoyed continuing this discussion as well as others. Ave atque vale, SDMB!

16

Yes, an evil mind-control plot is plausible in that I can think of all sorts of motivations and reasons why someone would want to do such a thing (to study me, for instance). The act of charity has the nagging problem of explaining kindness when rational actors should be vying for control over each other.

Paging Mr Svinlesha…

You might check out the problem of incommensurability between competing theories. As far as critical experiments go, check out the Duhem-Quine thesis. I can ramble on about these, too, if you’d prefer. But seek and ye shall find.

17

Eris

Glad you bumped, because I missed your post. (I bet the hamsters skipped a beat.)

Yes, I’m familiar with that passage, and I often point out that, despite all its fanfare and celebration, falsifiability itself is not falsifiable.

18

No doubt, Lib. Indeed, back on topic here, Ockham’s Razor itself cannot be proposed as a theory of support for any methodological act of science. For if it is used to form or choose between theories, then we cannot look to the success of those theories as evidence of Ockham’s Razor (well, not without begging the question, anyway!). I would direct RexDart’s attention to this point.

Also, Truth Seeker:

But at each time you collect data, you are presented with an infinite amount of theories to choose from. This is what has lead people like Quine, Kuhn, Duhem, and many, many others to say that a scientific theory is underdetermined by the data that is gathered from it, for the data doesn’t make the theory; rather, the theory explains the data.

19

Ockham’s razor is a simple hieuristic algorithm that says all else being equal, choose the curve that has the fewest coefficients or can be most simply parametrized. There are two sorts of contention for application of the razor. 1) who determines when all else is equal? Some evidence may be more equal than others. 2) Who determines which parametrization is simplest or which polynomial has the fewest coefficients? This is especially true when we are dealing with scientific data which has uncertainties plodded along with it. The easiest mapping of a trend may be linear, but whether that’s the “correct” mapping is clearly debatable.

20

So, let me see if I am following this.

William of Occam says that when predicting the mechanism of an unknown process, or phenomenon, no element should be added to the prediction unless it is necessary to explain the process, and if such an element is added, the presence of the element is in and of itself reason to suspect the validity of the explanation. This is interpreted by some as a contention that in real world terms, simpler mechanisms are more probable than complex mechanisms.

It seems to me that Occam’s Razor has been used to imply that simplicity is a characteristic of truth, when simplicity in this case is offered as an element to explain a mechanism (truth itself). By that evaluation, simplicity is an element William would have rejected as needless multiplication of entities. It is not necessary to the phenomenon, and is therefore not a reasonable addition to an explanation of how to evaluate it.

So, there seems to me to be a very important, and powerful reason to reject the statement that simplicity, even relative to other options, is a characteristic which should be taken as indicative of truth. The premise fails on the basis of William’s own observations.

But then, I never have been all that good at this logic stuff.

Tris

“We better get back, cause it’ll be dark soon, and they mostly come at night, mostly.” ~ Newt, Aliens ~