Occams Razor

The philosopher WilliamOfOccam (1280?-1347?) is said to have said, "Entia non sunt multiplicanda praeter necessitatem" ("Entities should not be multiplied more than necessary").

"Of two competing theories or explanations, all other things being equal, the simpler one is to be preferred." (http://www.wikipedia.org/wiki/Occam%27s_Razor)

Or, to avoid multiplying unnecessary entities, I would say, "The simplest explanation is probably the right explanation." DoTheSimplestThingThatCouldPossiblyWork is old hat.... (-:

: Only in the saying, not in the doing! ;-> -- rj

-- BillTrost

: "The simplest explanation is probably the right explanation." has nothing to do with OccamsRazor. While a technical "try the simpler solution first" makes sense because you quickly see when something doesn't work and will try the next solution. Non-technical usage of "simple must be true" e. g. in terms of prejudices, ideologies, scapegoats and bogeymans are desastrous, because it's hard to prove them wrong. Occam was about philosophy, not technology, so it seems just plain false to interpret him that way. -- HelmutLeitner

Every time I see this phrase, I keep wondering why the term Occam's Laser hasn't been coined. Or what it would mean.

Do not multiply wavelengths more than necessary? ;)

Entia non sunt multiplicanda praeter necessitatem seems not to be from WilliamOfOccam. According to [1], he did write Quando propositio verificatur pro rebus, si duae res sufficiunt ad eius veritatem, superfluum est ponere tertiam ("When a proposition comes out true for things, if two things suffice for its truth, it is superfluous to assume a third") and Pluralitas non est ponenda sine necessitate ("Plurality should not be assumed without necessity").

[1] http://www.uni-karlsruhe.de/~ed01/Hyle/Hyle3/hoffman.htm

I don't think he was expressing a PrincipleOfParsimony for choosing between two competing theories, though. I think he was more interested in keeping a given theory from getting overly complicated.

Whoa - these sound like one and the same to me. If you have a theory that works with three entities, and you find it works with one less, then the third is superfluous, right? I think I see what you're getting at, though - if you have a theory with axioms {X,Y,Z} and another with {A,B} the theory with three axioms does not necessarily win over the one with two; one of them will probably be wrong for a specific reason. But what if there is absolutely no obvious reason why one theory should be better? Say, no one axiom is particularly controversial or 'heavy', and the axioms fit together perfectly in either theory? It is my opinion (but YMMV) that OccamsRazor should also be interpreted as 'all other things being equal, you should favor the sparsest theory'. -- LaurentBossavit

: It is, in practice, interpreted like that; mine is a quixotic fight to distinguish two different principles. -- tk

Moreover, I wouldn't say, "The simplest explanation is probably the right explanation," is a good paraphrase, or even obviously true in itself. The PrincipleOfParsimony doesn't seem to me to deal with the question of what is true, but of what is useful. I'd put it as, "Simplify your explanation." -- TomKreitzberg

"The simplest explanation is probably the right explanation" is now a theorem in information theory. google "proof of occam's razor"

But also see <http://econpapers.hhs.se/paper/wopsafiwp/93-10-065.htm>.

Yeah, but useful and true are deeply related. In 'real' science, all theories are incomplete; science is a process where you progress from theory to theory, each step resulting in a theory that is "more true", but requiring at each step a theory which is both somewhat true, and already useful. (Compare to XP, which says that software systems must always be useful, but will become better designed all the time.) The simplest explanation is the most useful, but it is the one that you are most likely to be able to either prove true, or easily disprove (that is, test). That's Popper's falsifiability criterion. -- LaurentBossavit

: I'm not inclined to agree that the useful and the true are deeply related, but then I write simulations for a living. -- tk
: According to Popper a theory can never prove "true". It may (or may not) work to predict the behaviour of a system. So a theory may easily prove "false" in a certain situation and thus be falsified, but even many successful predictions can't make sure that the theory couldn't fail in a different situation. (IIRC and if we talk about the same KarlPopper) -- HelmutLeitner

You are, of course, quite right. I should have said "prove locally true" or some such. BTW, note that "prove" is a cognate to "probe" - it has this entirely accurate connotation that you can never definitely assert the truth of a theory, but need to continuously probe it for weak areas - experiments that disprove it. Anyway, my point was that the simplest theories are the ones that lend themselves most readily to useful probing. -- LaurentBossavit

Superb, Laurent! With your permission, I'd like to make an entry on SoftwareEtymology for the verb 'to prove', with the above in some form or another. (I love learning that the "old timers" knew more than we give them credit for.) -- WaldenMathews, anyone care to guess my age? ;-) 36? nope (^), anyone else? 41?

The observation is not original with me, I'll hasten to add; I think I read it in StephenJayGould. -- LaurentBossavit

Whoa. The reference to StephenJayGould just made a bell go off in my head. Is it just me or does the above description of XP (Software systems must always be useful, but may change over time) fit well with his explanation of the evolution of complex biological structures like compound eyes and wings...

Steven Jay Gould was brilliant, but he and a whole set of evolutionary theorists had an agenda to: a) disprove the assertions of TeilhardDeChardin
because: b) as an extension, remove any chance of there being any design by intent in evolution.

That expresses itself by the insistence that evolution occurs only at the individual level and that there is no bias/trend towards complexity in evolution. The human race and co-evolution both seem to argue against that. Jacob Bronowski was very critical of the use of Occam's razor in science. The insistence of theorists that evolution occurs only at the individual level is a prime example. It simplifies everything even if the supporting evidence is selective and complex.

BTW, I am an atheist in the truest sense in that I have no belief and see no reason to have one and have no interest in disproving something for which I see no belief.

-- PaulCubbage

[Could you adjust the above for improved clarity and provide references?]

But evolution cannot occur at the individual level. It requires variation to act upon, so needs a group of individuals. No evolutionist would insist evolution occurs only at the individual level, though they may describe its effects as visible at an individual level. -- sb

[You probably meant 'selection', not 'evolution'.]

I thought that RichardDawkins' argument in TheSelfishGene was fairly widely accepted by now:

evolution occurs at the level of genes (or more fundamentally, any things that carry information, are self-replicating with variation, and exhibit varying rates of replication depending on their environment),
the effects of evolution visible at all higher levels, including individuals and groups, are epiphenomena.

-- DavidSarahHopwood

Aye. See OrganicSimplicity for an elaboration.

OccamsRazor:

OO translation: Do not multiply objects without reason
Science translation: Always choose the simplest explanation of a phenomenon
- (also see [http://www.weburbia.com/physics/occam.html])

 (From another guy: "Make everything as simple as possible, but not simpler." -Einstein
  [http://www.brainyquote.com/quotes/quotes/a/alberteins103652.html])

Birth control translation: Do not multiply unnecessarily ;-) (Think "OnansRazor.")
Or just: KeepItSimple
Wiki translation: ThreadModeConsideredHarmful
(Never say "Wiki Wiki", when "Wiki" does the job. -- FridemarPache :-)

More about Occam and this principle can be found at http://www.in-search-of.com/frames/events/occam's.shtml.

-- YonatSharon

My version has been "Do need introduce entities unnecessarily." -- BenTremblay

For fun: http://zebu.uoregon.edu/~js/glossary/occams_razor.html

"Entities should not be multiplied more than necessary" ... OccamsRazor applied to this would show an element of redundancy, in that the statement "Entities should not be multiplied" encapsulates the concept sufficiently - and is shorter. The phrase "more than necessary" may be said to be subjective and dependent on an unspecified external context to which human judgement must be applied. This context includes an act of abstract or material creation, and whatever we create must have some aesthetic or functional value, the pursuit of which defines the necessity. My trite contribution to hackneyed banality.

I find "less is more" to be more compact...

...and "golf" to be more compact still =0)

-- RichardHundt?

I had three classes today (in reverse order):

Philosophy of Mind
Artificial Intelligence I (classic theories of AI)
Organizational Behaviour (ala OrgPatterns but by actual business types)

Now, in all three I heard OccamsRazor used today. Speaking of multiplying unnecessarily... -- SunirShah

Wow ... redundant or not, that sounds like one cool course load! -- EricHerman

Wow!..... What a simple explanation all this is of such a simple concept.

Would someone like to refactor this page with one simple explanation!!! :-) -- Mike Thomas

"Plurality should not be assumed without necessity." What if this philosophy were hard-coded into our entities at birth? Can you imagine a society where we all implemented this into our daily lives? For instance, the other day I wanted to absorb some humanity, so I went to a cool little coffee house I knew of. A little, out of the way place, poorly located but with a devoted following. It had gone out of business and been replaced with some weird alternative office. So I went to one that's been in business at least 15 years. It was in one of the better, more popular locations, always a massive crowd, great place. It was replaced with a sports burger joint. These 2 places had pretty much only coffee in common. There was no plurality in the design or implementation of these places. They were each geared towards different crowds and supported different comfort levels. My question is, is Starbucks a necessity? Just because it's got throngs of caffeine addicts lined up at the doors every morning doesn't mean that they need that coffee. Starbucks provides a great work environment, a decent cup of coffee and a lot of convenience. But where's the love? Every single one has been stamped out like the others and the patrons have to be a Starbucks person to fit in. This is just one way I've noticed that unnecessary pluralization can be bad. It creates homogenization and sterilization of our society through consumerism and mass output of only sometimes necessary product. I think if it were incorporated into our lives we would place a higher value on quality over quantity, deep sustenance over instant gratification, but our lives would also probably be a lot more difficult and simplistic at the same time. -- LeeNathan

A thought occurs to me: Superficial appearances. For instance, two items may indeed appear to explain how something works. However, this does not mean that is how it ACTUALLY works (LOOK! AN OBJECTIVIST! RUN!). Later on, more is learned of things not at first dreamed of - and we discover that the two things did not REALLY explain how it worked, except in the context of a now discredited perception of how the universe was built. We thought we had a handle on physics with the 'ether theory' until we started looking at chaos and frequency dispersal of radiation of hot objects. The 'VIOLET CATASTROPHY' threw physics into a terrible state, as they realized their fundamental framework and basis for understanding was ALL WRONG. Einstein and others came along in the midst of this chaos, and an entire new understanding was knitted together.

But our new understanding is, of course, completely perfect, and devoid of any such error.

Of course. ;-)

-- KirkBailey

(See TheStructureOfScientificRevolutions.)

Science is not about being right, although it seems that way to most people, I would guess. When OccamsRazor is applied, it should be applied for the sole purpose of reducing complexity without losing the power of prediction. In fact that's what science is all about: A theory is 'true' to the extent that its predictions end up being true. Here's the mind-bender: All theories are wrong. Based on empirical evidence and OccamsRazor, the simplest theory about science is that all scientific theories are wrong and will be shown to be wrong in the near future. It's just beginning to sink in for me. It seems now that wrongness or rightness are totally unimportant. In the end, the only thing that is important is prediction.

Indeed - science and the scientific method in particular are about disproving things. Kelvin could use science could show that the Sun could not be made of coal, but it took a while to find out what it could be made of instead. You can only really prove something in physics if you know every single possible solution (and know that you know) so that when you have eliminated all but one you can be confident that the remaining solution/explanation is the correct one. Likewise, we believe today that we know that the Sun is powered by fusion and no one is seriously thinking that there are any problems with that explanation - but there might be. However, we can make calculations based on the theory and they are very much in accord with what we see and so we feel that there's not much chance of there being something wrong. It's when mathematics and observation no longer match that we know it's time to find a new theory.

And, ideally, as each theory eliminates more incorrect explanations the level of mismatch between the mathematics of the current theory and the observed reality decreases, allowing us to make more accurate predictions, faster computers, and better car tyres etc. because we can trust the engineering that is founded on the physics better - there are fewer surprises remaining to cause bridges to collapse or dams to burst. In that sense, we expect all scientific theories to be wrong in the sense that they are always being replaced by something which more closely approaches but never quite reaches a state where everything is accounted for.

Occam's Rant?

There are some Christians who call themselves pro-science, who do not believe in superstitious nonsense about seven-day-creation or floating spirits which whisper evil in men's minds, instead believing in the scientifically grounded concepts of "evolution" and "mental illness".

This attitude is, in fact, decidedly anti-scientific. It violates one of the deepest principles of science, that of Occam's Razor.

There are, one could argue, two reasons to believe in God as per the Bible. One is to reason by induction, by thinking that evidence in this universe actually points to the Bible. Theoretically, maybe, but anyone who can honestly follow the evidence and be lead to the Bible is so very bad at logical reasoning that I would rather not include them in this essay. Perhaps some other time.

The other way does not necessitate incompetence: simply declare that the existence of God, as per the Bible, is axiomatic. No way to disprove that; axioms literally must be true, because they define truth. And ultimately everyone has to take their axioms on faith, so you're really not in a different position to anyone else.

But if you were to declare God axiomatic, then the conclusions and deductions you would draw from this kind of an axiom is very different to what anyone starting with the rules of evidence and logic would deduce. If you're going to believe in God as Axiomatic, then Occam's Razor demands that you believe also in seven-day-creation. It says so in the Bible, so there's every possibility that it could be true, even if you think that the book of Genesis is a poetic parable. And it's a far less convoluted explanation than evolution. You cannot possibly believe in the convoluted and in some cases not wholly explicable theory of evolution if there's a simpler explanation. If you start with theories about a unique past, immutable physical laws and logic, then there is no simpler explanation, but if you start with a divine being who claims to have created all life (without necessarily being specific as to whether He did so directly or indirectly) then it is much simpler to assume that this Axiomatic being simply brought all life, and everything else besides, into existence in an act of divine will.

Or consider schitzophenia, a mental disorder characterized by sudden spells of intense paranoia. At least, that's what the godless false prophets of science would have you believe, but it's a very long chain of inferences. One would have to believe that the origin of decisions is in the brain, rather than the soul. And if that were true, then where is free will? It can't be dictated by chemical imbalances in a bodily organ. No, far simpler to believe that there is no schizophrenia, and in fact people diagnosed with it are simply choosing to be evil and rebel against God, spurred on by insidious invisible spirits sent by the Devil.

All this and more Occam's Razor demands that you must believe, if you believe in God. The fact is that Jack T Chick is the very model of perfect Christianity (or he would be, if only he could draw better). So why are there so many Christians who profess to be enlightened, to believe in evolution, and brain functions, and the preposterous idea that the stars are lightyears away when one can clearly see that they are painted onto the dome of the sky?

Could it be because they know, on some level, that their religion is all lies?

Could it be because they accept a rational explanation for the universe because it's useful, except insofar as it contradicts those things they wish to cling to most dearly, the illusions of free will and life after death?

Picking and choosing what is real and what is not is slightly more ... difficult ... than that, I'm afraid.

Interesting idea, but why does "The Bible is the Truth" follow from "There is a God"? It seems like the same leap from "Dave Barry and Kurt Vonnegut are a funny writers" to "Dave Barry wrote this somewhat funny chain email, and Kurt Vonnegut gave this funny speech at the 1997 MIT commencement.". Occam's Razor may support that jump, until you add any other evidence, at which point it demands you go with the simpler explanation "Sometimes people incorrectly attribute a bit of writing to give it more authority"

It follows because God, with a capital G, is the Abrahamic god from which Islam, Christianity, and Judaism derives, and thus, at the very least, the Old Testament is truly God's Word, and thus, simply must be taken as true, as per God itself. It took me several readings myself, and was about to write a rather lengthy retort, but I now recognize the subtlety of the author's words. Read it carefully, and you'll see it's actually a critique of the use of Occam's Razor -- that is, treating Occam's Razor as a function F(a,b), where a is a scientific explanation and b is a religious indoctrinated explanation, the result will depend on what you were brought up to believe. If you grew up in a scientifically inclined household, the result is 'a'; otherwise, 'b'.
[You (and, it seems, the author of Occam's Rant) forget that there are other filters in science than just OccamsRazor. OccamsRazor only selects from among a set of equally valid theories, choosing the one with the weakest assumptions (in particular, abductive assertions or axioms). Science filters religious theories using something else entirely: supporting evidence for the initial hypothesis (ShiftingTheBurdenOfProof is rejected) and falsifiability (ideally practical).]
You are entirely wrong about me. I'm a firm believer in the scientific method, and have no compassion for religious belief systems of any kind. Yet, I was born and raised to be a good little catholic. My response was to answer a question (see the very first bullet point) asked by another respondent. Be sure to read, and actually comprehend, the context of discussion before jumping to conclusions about the posters. You've demonstrated an intense ignorance over my position in the matter, and just made yourself look like an abject fool because of it.
[This isn't about position. It's about the logic. What you believe isn't as important on an intellectual forum as the reasoning you apply. OccamsRazor simply cannot filter between religious and scientific explanations... not unless you can measure them, by some means, to have 'equal validity'. If you're going to explain "it follows because" it is best if you don't start with a category error.]

{[(Oh my Axiomatic Being! I love that rant. Now I want to see some GeorgeCarlin!)]}

Incidentally Occam, were he alive today, would surely choose a 1-bladed razor, not these nonsensical 3 or more blade razors.

I was going to respond with a tirade to the text above, but upon re-reading it, I found a hidden double-meaning which actually proved my point beautifully and eloquently. Nicely done.

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