Could Occam's razor lead you to the wrong conclusion?

[Brad Reddekopp]

This topic was split off from this one: viewtopic.php?f=3&t=8758

I recall once discussing Occam's razor (with Franc, I think) and being challenged to present a situation in which Occam's razor would lead you to the wrong conclusion. I couldn't think of any. Let's see if anyone here can come up with such an example.

[Centurijohn]

I recall once discussing Occam's razor (with Franc, I think) and being challenged to present a situation in which Occam's razor would lead you to the wrong conclusion. I couldn't think of any. Let's see if anyone here can come up with such an example.

Would an example also qualify where Ockham's razor possibly leads to the wrong conclusion, and is in any case insufficient?

[Brad Reddekopp]

In this thread, I'm not interested in the question of sufficiency. I'm interested in examples in which the razor would be likely to lead one to the wrong conclusion.

[vertigo]

I recall once discussing Occam's razor (with Franc, I think) and being challenged to present a situation in which Occam's razor would lead you to the wrong conclusion. I couldn't think of any. Let's see if anyone here can come up with such an example.

The theory that human behaviour is explainable in terms of evolution of genes is not a particularly good theory because the world we live in is vastly different to the animal kingdom. Even before knowing whether human behaviour was reducible to genes, we should anticipate the possibility that it would be different. This is because other animals have genes and we have genes and we appear to be quite different to them, which suggests that something more than genes is the reason for this difference. Probably, something that distinguishes us from animals plays a part. Language is surely one of the most elementary differences between humans and animals so that would be the place to start, investigating the role of language.

The theory that language partly determines behaviour is better than a purely genetic explanation but I don't know that Occam's Razor sees it this way.

[Brad Reddekopp]

Can you be a little more precise about how Occam's razor wouldn't "see it that way"?

I'm sure you know it, vertigo, but for any here who might not, keep in mind that the razor isn't merely a search for the simplest explanation, although we often describe it that way for economy's sake.

The principle states that the explanation of any phenomenon should make as few assumptions as possible, eliminating those that make no difference in the observable predictions of the explanatory hypothesis or theory. The principle is often expressed in Latin as the lex parsimoniae ("law of parsimony", "law of economy", or "law of succinctness"): entia non sunt multiplicanda praeter necessitatem, roughly translated as "entities must not be multiplied beyond necessity." An alternative version Pluralitas non est ponenda sine necessitate translates "plurality should not be posited without necessity." [2]

When multiple competing hypotheses are equal in other respects, the principle recommends selecting the hypothesis that introduces the fewest assumptions and postulates the fewest entities. It is in this sense that Occam's razor is usually understood.

from http://en.wikipedia.org/wiki/Occam%27s_razor

[plan 9]

The wikipedia page mentions some cases where occams razor was used as an argument for rejecting theories that later turned out to be true.

However, on many occasions Occam's razor has stifled or delayed scientific progress.[17] For example, appeals to simplicity were used to deny the phenomena of meteorites, ball lightning, continental drift, and reverse transcriptase. It originally rejected DNA as the carrier of genetic information in favor of proteins, since proteins provided the simpler explanation.

[vertigo]

Can you be a little more precise about how Occam's razor wouldn't "see it that way"?

I'm sure you know it, vertigo, but for any here who might not, keep in mind that the razor isn't merely a search for the simplest explanation, although we often describe it that way for economy's sake.

The principle states that the explanation of any phenomenon should make as few assumptions as possible, eliminating those that make no difference in the observable predictions of the explanatory hypothesis or theory. The principle is often expressed in Latin as the lex parsimoniae ("law of parsimony", "law of economy", or "law of succinctness"): entia non sunt multiplicanda praeter necessitatem, roughly translated as "entities must not be multiplied beyond necessity." An alternative version Pluralitas non est ponenda sine necessitate translates "plurality should not be posited without necessity." [2]

When multiple competing hypotheses are equal in other respects, the principle recommends selecting the hypothesis that introduces the fewest assumptions and postulates the fewest entities. It is in this sense that Occam's razor is usually understood.

from http://en.wikipedia.org/wiki/Occam%27s_razor

Well I think of the two theories that only genes count and that language should be treated as a cause Occam's razor suggests that we should choose the theory that makes fewer assumptions if they both explain the evidence. And they do explain evidence. The first theory says that human genes are such as to make us behave differently to other animals, this difference can be reduced to the genes, so we are different because our genes are different. The second says that our genes give us habits or tendencies but these can change in the presence of language, and language being a capacity that other animals lack is responsible for our different behaviour, specifically our greater cooperation with each other. According to this theory, we cooperate more because of language. I think it is simpler to think that our genes, which explain other differences like why some of us are blonde, some are tall, some are dark-skinned, etc, should be able to explain other differences also, in particular our greater cooperation.

The way I see it, there are two sides to science, the data and the theory. When we choose a theory, it directs how we should proceed to gather data. Choosing the simpler theory focuses attention on those general ideas that we think extend very far and we then seek to find the limit to which they extend. This holistic approach results in many things being explained in the same terms, and this allows them to relate to each other. But it can also limit exposure to alternate ideas that may turn out to have more merit. If our simple theory is that medicine is generally more effective at treating disease than natural supplements, that directs research towards finding the limits to which we can apply medicine. And if we follow that direction, the research evidence will be biased in favour of medical treatments. It simply doesn't allow research into alternatives because that would go against the base theory that medicine is more effective.

So we assume that medicine is more effective and proceed to use research to, in effect, make it more effective. And then we come to conclude that we were correct, medicine is indeed more effective. But this is self-fulfilling.

Now if we choose the simpler theory that genes can explain human behaviour, that would direct research into finding correlation between genes and human behaviour. And doing such research would tend to show that actually, genes are quite well correlated with behaviour. But actually, language will likely prove to be more better correlated with behaviour and that can only be discovered by doing that research. Otherwise, we might discover that blacks tend to be poorer and so consider that black genes are predisposed to poverty, perhaps because they are less industrious by nature, more savage, with genes closer to other animals than us whites. We might consider this a confirmation of our gene theory, that poverty is well correlated with genes given the racial make-up of society.

But as I said, language will tend to be better correlated. Poverty and certain language traits are far better correlated than poverty and black skin. Following this research direction it will be found that actually, educated people speak differently and blacks have generally had limited access to education. Their language bias correlates with their poverty, but this incorporates the notion that with education, these phenomena can be reversed. It suggests that experiment is warranted to refute the simpler gene theory, specifically the idea that education can change the situation. But this was not got from the gene theory, it came from the language theory.

So basically my point is, research should not be limited to falsifying the status quo theory because it can become self-fulfilling. Other theories should be considered simultaneously so that there are alternatives to compete with the status quo.

[vertigo]

Sorry, this last post of mine was rather preachy. People will interpret things in the way most favourable to them and however they do that will seem to be quite convincing. The way I explained it above, both those theories probably sounded quite convincing. As I see it, dogmatism is the problem because it is always possible to make a convincing argument by ignoring evidence against.

The whole debate about whether Occam's razor decides truth or utility is not particularly important, I don't think. Who cares, just use it judiciously. It can help to point out that actually a simpler theory is available, one that should be looked at, but it probably shouldn't rule out alternative theories. That would be a dogmatic application which I think would be wrong. But if I was pressed to give an answer, I'd say that the most useful theory that explains the phenomena is surely the best one to use.

[Vichy]

Ockham's Razor can lead one to an erroneous conclusion, but it would still be required for the conclusion to be (doxastically) justified. And we don't have any alternative to knowledge except doxastic consistency. That I know of.

[plan 9]

Do you mean by doxastic consistency that internal coherence of beliefs is the most important principle of justification and simpler theories are more likely to be consistent or do not add or change established beliefs that much.

[Vichy]

Do you mean by doxastic consistency that internal coherence of beliefs is the most important principle of justification and simpler theories are more likely to be consistent or do not add or change established beliefs that much.

The theory that requires more assumptions or more radical interpretations of information than are justified by given data and theory positively departs from doxastic consitency - we are 'inventing' premises. Of course, there is nothing to say that we should never give or consider such views - they may prove out to be correct. But they must be demonstrated, through some sort of syllogistic ratiocination or by introducing new information. Of course, what both of these mean is that to be accepted they must be found to conform with - doxastic consistency.
Jaako Hintikka is a good read on doxastic logic, and his Analysis of Aristotle is interesting.

Arguments in favor of doxastic consistency and utility-of-information more generally, strike me as at least considerable. Richard Joyce, in the Myth of Morality, discusses William James

William James is frequently interpreted as equating truth with utility, but
often his position sounds like the less ambitious and more plausible view
that truth is useful: “The possession of truth, so far from being here an
end in itself, is only a preliminary means towards other vital satisfactions.”
James starts with an obvious example of how on a particular occasion a true
belief is instrumentally superior to a false one: I am lost in the woods and
seek a house; I come across a cow-path, form the belief that the cow-path
will lead to a house, and act on the belief. If the belief is true I am saved;
if not, my life may be lost. Now suppose that on a different occasion I am
in the woods, but this time not lost and starving. Again I see a cow-path
and form the belief that it leads to a house, but this time I have no interest
in seeking a house, and therefore do not act on the belief. One may think
that in the second case it makes no difference whether my belief is true
or false. Perhaps I even have a whim to think myself miles from human
habitation, in which case I would slightly prefer that I be mistaken. James
disagrees.We never know whether and in what way a belief may be called
upon to serve action, and, given this, it is better that it be true than false –
“since almost any object may some day become temporarily important,
the advantage of having a general stock of extra truths, of truths that shall
be true of merely possible situations, is obvious.” In the vast majority of
cases having a true belief to act upon is more likely to bring satisfaction
of desire than having a false belief on the matter, and given that we don’t
know in advance how and when we are going to employ a particular
belief, the safest bet is to have the true one over the false one. This is not
to say, of course, that the true one is always available and accessible, but
when it is, we do well to have it.

A seemingly useful false belief, moreover, will require all manner of
compensating false beliefs to make it fit with what else one knows. This is
what is so hopeless about Plato’s “medicine of deception”: for the citizens
of the republic sincerely to believe that their origin lay underground (to say
nothing of being partly made of metal), they would need to interpret large
amounts of the evidence of their senses in dramatically eccentric ways.
It is not merely that a stock of true beliefs is vastly more likely to be
helpful than a stock of false ones, but that the policy of aiming for the
truth, of having and trying to satisfy a general (de dicto) desire for the
truth – what we might simply call “critical inquiry” – is the best doxastic
policy around. Anything else, as Charles Peirce correctly insists, leads to
“a rapid deterioration of intellectual vigor.”

[vertigo]

On the subject of Occam's razor, it (Occam's razor) has the effect that scientific theories explain the currently observed evidence in a relatively contained manner. Such a theory is quite stable because within the relevant context what it predicts accords with the evidence, and outside of that context it makes relatively few predictions. For example, the big bang theory actually says very little. It explains the evidence that suggests the universe expanded from a primordial state, by saying that actually the universe did expand from a primordial state, but it says almost nothing else. Unless some of the experiments that produced the data that it explains were flawed, it is a very stable theory. For a theory to replace the big bang theory (for being invalid), it would need to explain more than the big bang theory explains. For instance, such a theory might explain the manner in which the universe expanded.

In the case of gravity, Newton's theory was replaced in a wider context than the evidence that supported it, and it could not be otherwise unless some of those base experiments were flawed. Within the relevant context, a theory that explains the evidence is very stable. Newton's theory of universal gravition did make predictions in a wider context, and only there could it be found to be less than accurate.

No new evidence can prove a theory wrong unless it makes untested predictions that may prove to be incorrect. A theory that does not make such predictions will be extremely stable but will have limited factual content. Although Occam's razor favors simpler explanations, we should not suppose that it means one should explain only the evidence; such a theory would in effect be a rephrasing of the evidence that it explains, a memory aid at best. But if a theory goes beyond the evidence that it serves to explain, it makes predictions and allows itself to be shown to be incorrect. Such a theory has a further purpose because it directs research.

So where there is something to be explained, theory can direct research into the phenomenon, and experimental data can show a theory to make correct predictions, but once we have the data, the theory becomes little more than a summary.

So let us consider theories to be of three types:

There are those theories that are fully motivated by evidence, they serve as a convenient description of the results. The philosophical question of whether some such theory is literally true is a separate matter. But the theory does serve to summarize the results.

There are those theories that have been tested in wider contexts and have been found to be false. Such a theory doesn't well summarize results and at best can be used as a convenient fiction that is true only sometimes.

And there are those theories that make untested predictions. They are useful to direct research but are tentative with respect to whether they may be thought of as literally true.

These three types of theories suggest the following. Any theory either summarizes only experimental results or makes predictions which are false or untested. Theories of the first, stable type can be thought of as literally true but have arguably no more factual content than the experimental results that they explain. And theories of the other types are false or potentially false, and unsuitable or potentially unsuitable as being thought of as literally true.

Surely no one should consider false theories to be literally true. Suppose that one should not consider potentially false theories to be literally true (yet). Should the remaining theories (of the first type) be considered literally true? Any two such theories could be different in character. Theories that are analogous to each other would be more believable. But this consideration goes against the idea that such theories should be considered to be literally true. At best, only qualified theories should be considered true, and this qualification might change. At best, these theories approximate the literal truth.

So as I see it, even theories like the big bang theory might come to be incomensurate with some other theory, such that another, less simple, theory is more suitable (more believable). To accept the big bang as fact is not to deny that it might be replaced with a system of theories that fit together better. Perhaps we might replace it with a theory whereby the universe appears to be expanding, but actually..., which is quite similar to how gravity appears to be a force in Einstein's theory. Strong statements like that evolution is a fact, not (just) a theory, ignore this point. Perhaps one day we'll consider evolution to be a figment of a more complex process, much like how protons and neutrons are now considered to be complexes of quarks.

I see the desire to decide what is literally true as being quite separate from using the experimental results. One doesn't need to know the literal truth about gravity to know that apples fall. One doesn't need to know what a proton actually is to build a nuclear power station. It is quite possible to disregard the question of what is literally true. In fact, I think it is advisable.

[Atheist Statist]

The answer is - yes.

[MustangGT]

The answer is - yes.

Care to support your assertion?

[Tmaq]

Occam's is only and always about efficiency, not truth. If there is evidence which distinguishes two theories, Occams' is irrelevant.

Given two different theories which make identical predictions about the same phenomenon, there's no reason to use the more complicated one. Occam says use the easier one. But using the harder one won't make your predictions wrong, it will only make them cost more.

What does Occam's say about Heisenberg's matrices vs Schroedinger's waves vs Diracs 'pilot wave'? "Use the one that makes the calculations easier" - and its not always clear which one does.

So to sum up; the answer is "'no" unless you mean the conclusion "efficiency = accuracy."

-Tom