Science, religion, and Ockham’s razor

A few days ago I was working in my backyard when I noticed that the outdoor thermometer that I had fixed to a fence had disappeared. The mountings were still there but had been pulled away slightly. I thought that maybe the wind had blown it off and so I looked at the ground underneath but the thermometer was not there. There is a bed of pachysandra nearby and I looked nearby in it but no luck. I was baffled.

I pondered the various options for explaining the missing thermometer. One was that the wind had been strong enough to rip the thermometer from its mounting and blow it farther away into the pachysandra. The other was that it had fallen to the ground below and had then been taken away by squirrels or the neighbor’s cat. The third was that neighborhood children had borrowed it without permission for some experiment. The fourth was that the International Outdoor Thermometer Cartel (IOTC) had raised the price of these thermometers to such a high value that organized crime gangs were stealing them and selling them on the black market. The fifth option was that aliens had taken it away as a souvenir of their clandestine visit to Earth.

Given these options, I decided that #1 was the most likely one and looked in the pachysandra over a larger area, and sure enough. I found it.

The reason for this anecdote is that it illustrates that I used something that we all use all the time (whether we are consciously aware of it or not), and that is Ockham’s razor to make choices among competing theories.

According to the Encyclopedia Brittanica, the principle behind Ockham’s razor (also called the law of economy or the law of parsimony) was stated by the scholastic William of Ockham (1285–1347/49), as “Plurality should not be posited without necessity.” The principle is also expressed as “Entities are not to be multiplied beyond necessity.” Ockham did not himself use the word ‘razor’, that was added to his name later by others.

The principle gives precedence to simplicity, but there are two ways it can be used. In the first case (which is more closely aligned with Ockham’s intent), it says that you should not postulate more elements for anything other than the minimum required. For example, in the case of my missing thermometer, if I postulated one theory that a cat had taken it and a competing theory was that a cat that had a striped tail and a scar on its forehead had taken it, then in the absence of any extra information, the former theory is to be preferred. The latter theory just adds elements that do not add any necessary information to the explanation. The application of this version of the principle is fairly straightforward. One seeks the smallest subset of elements of a theory that provides an adequate explanation of whatever you are trying to explain.

The more problematic (and common) use of Ockham’s razor is when you try and apply it to a situation where there are two competing theories that share no common elements or there exist at least some necessary elements of one theory that the other does not possess. We commonly interpret Ockham’s razor in those situations as requiring us to choose the simpler of the two theories. But simplicity may well lie in the eye of the beholder and it may not be easy to get agreement.

So, for example, in the case of the thermometer that was found some distance away from its mountings, the simpler explanation (for me at least) was that of the wind. If called upon, I could call upon Bernoulli’s Principle and the laws of motion to support my preference. That explanation is simple enough to satisfy me.

But this may not be true for someone else. For them, a theory that alien vandals landed in my garden, tore the thermometer from its moorings, threw it away in the pachysandra and left in their spaceship, might be the “simpler” explanation in the eyes of someone who is a believer in the existence UFOs and space aliens. After all, it does not involve the use of calculus.

That is exactly the problem in many of the science and religion discussions, and we will see that in the next posting.

POST SCRIPT

In a comment to a previous post, Amanda (a former student who graduated a few years ago and is now doing her PhD in astronomy) sent me a link to an excellent New Yorker article that goes straight to the core intelligent design argument, cutting through all the confusion that often surrounds such discussions. The article is well written and lays out the basic premises of ID as well as clears up some popular confusion about how evolution and natural selection work. I strongly recommend the article and gratefully thank Amanda for bringing it to my attention.

Why scientific theories are more than explanations

At its heart, ID advocates adopt as their main strategy that of finding phenomena that are not (at least in their eyes) satisfactorily explained by evolutionary theory and arguing that hence natural selection is a failed theory. They say that adding the postulate of an ‘intelligent designer’ (which is clearly a pseudonym for God) as the cause of these so-called unexplained phenomena means that they are no longer unexplained. This, they claim, makes ID the better ‘explanation.’ Some (perhaps for tactical reasons) do not go so far and instead say that it is at least a competing explanation and thus on a par with evolution.
[Read more…]

Why ID is not science

In the previous posting, I pointed out that if one looks back at the history of science, all the theories that are considered to be science are both (1) naturalistic and (2) predictive. Thus these two things constitute necessary conditions.

This is an important fact to realize when so-called intelligent design (ID) advocates argue that theirs is a ‘scientific’ theory. If so, the first hurdle ID must surmount is that it meet both those necessary criteria, if it is to be even eligible to be considered to be science. It has to be emphasized that meeting those conditions is not sufficient, for something to be considered science, but the question of sufficiency does not even arise because ID does not meet either of the two necessary conditions.
[Read more…]

What is science?

Because of my interest in the history and philosophy of science I am sometimes called upon to answer the question “what is science?” Most people think that the answer should be fairly straightforward. This is because science is such an integral part of our lives that everyone feels that they intuitively know what it is and think that the problem of defining science is purely one of finding the right combination of words that captures their intuitive sense.

But as I said in my previous posting, strictly defining things means having demarcation criteria, which involves developing a set of necessary and sufficient conditions, and this is extremely hard to do even for seemingly simple things like (say) defining what a dog is. So I should not be surprising that it may be harder to do for an abstract idea like science.
[Read more…]

Necessary and sufficient conditions

The problem of finding definitions for things that clearly specify whether an object belongs in that category or not has long been recognized to be a knotty philosophical problem. Ideally what we would need for a good definition is to have both necessary and sufficient conditions, but it is not easy to do so.

A necessary condition is one that must be met if the object is to be considered even eligible for inclusion in the category. If an object meets this condition, then it is possible that it belongs in the category, but not certain. If it does not meet the condition, then we can definitely say that it does not belong. So necessary conditions for something can only classify objects into “maybe belongs” or “definitely does not belong.”

For example, let us try to define a dog. We might say that a necessary condition for some object to be considered as a possible dog is that it be a mammal. So if we know that something is a mammal, it might be a dog or it might be another kind of mammal, say a cat. But if something is not a mammal, then we know for sure it is not a dog.

A sufficient condition, on the other hand, acts differently. If an object meets the sufficient condition, then it definitely belongs. If it does not meet the sufficient condition, then it may or may not belong. So the sufficient condition can be used to classify things into “definitely belongs” or “maybe belongs.”

So for the dog case, if a dog has papers certified by the American Kennel Association, then we can definitely say it is a dog. But if something does not have such papers it may still be a dog (say a mixed breed) or it may not be a dog (it may be a table).

A satisfactory demarcation criterion would have both necessary and sufficient conditions because only then can we say of any given object that it either definitely belongs or it definitely does not belong. Usually these criteria take the form of a set of individually necessary conditions that, taken together, are sufficient. i.e., Each condition by itself is not sufficient but if all are met they become sufficient.

It is not easy to find such conditions, even for such a seemingly simple category as dogs, and that it the problem. So for the dog, we might try define it by saying that it is a mammal, with four legs, barks, etc. But people who are determined to challenge the criteria could find problems (What exactly defines a mammal? What is the difference between an arm and a leg? What constitutes a bark? Etc. We can end up in an infinite regression of definitions.)

This is why philosophers like to say that we make such identifications (“this is a dog, that is a cat”) based on an intuitive grasp of the idea of “similarity classes,” things that share similarities that may not be rigidly definable. So even a little child can arrive at a pretty good idea of what a dog is without formulating a strict definition, by encountering several dogs and being able to distinguish what separates dog-like qualities from non-dog like qualities. It is not completely fool proof. Once in a while we may come across a strange looking animal, some exotic breed that baffles us. But most times it is clear. We almost never mistake a cat for a dog, even though they share many characteristics, such as being small four-legged mammals with tails that are domestic pets.

Anyway, back to science, a satisfactory demarcation would require that we be able to find both necessary and sufficient criteria that can be used to define science, and use those conditions to separate ideas into science and non-science. Do such criteria exist? To answer that question we need to look at the history of science and see what are the common features that are shared by those bodies of knowledge we confidently call science.

This will be discussed in the next posting.

POST SCRIPT

I feel that the American media have not given nearly enough attention to the recently leaked secret and explosive “Downing Street memo” from the British secret service that reveals that Bush intended to invade Iraq all along and lied about it to the American people. Juan Cole says that the memo clearly reveals what has been long strongly suspected.

The Bush administration, and some credulous or loyal members of the press, have long tried to blame U.S. intelligence services for exaggerating the Iraq threat and thus misleading the president into going to war. That position was always weak, and it is now revealed as laughable. President Bush was not misled by shoddy intelligence. Rather, he insisted on getting the intelligence that would support the war on which he had already decided.

Cole’s article, where he lays out the sequence of events, is a must read.

The comparison with Darwin and ID

I am a bit of a veteran of the battles that have been waged by so-called intelligent design (ID) advocates to challenge science in general and the theory of evolution in particular. Although not a biologist, I have always had an interest in both physics and the underlying philosophy of science. In the mid-to-late 1990’s I was in the process of writing my first book Quest for Truth: Scientific Progress and Religious Beliefs (which was published in 2000), and it was towards the end of that period that the ID advocates started getting more vocal, at least in Ohio. I was initially drawn to the discussion because of their claim that ID was a scientific theory, which naturally raises the question of what makes a theory, any theory, scientific. As this was a central topic of my book, I looked into ID ideas, although not in any great depth at that time.
[Read more…]

Catholic and Protestant reactions to Darwin’s ideas

When reading and writing about the Copernican revolution and the religious opposition to it (see here, here, here, here, here, and here for that story in sequence), what immediately struck me were the similarities that that episode in scientific history had to the more recent religious opposition to Darwin’s ideas.

Edward Larson in his book Summer for the Gods from which he has published an extended excerpt points out that (in America at least) there was little formal opposition to Darwin’s ideas from the time of publication of Origin of Species in 1859 until about 1920 or so. (Opposition in England started much earlier and I will explore that question in a later posting.)

So as in the case of Copernicus, there was no religious opposition to a seminal work of science until about sixty years after its publication, and the initial religious opposition once again came from the Protestant camp. Initially, the fundamentalist Protestant movement was focused only on fighting “modernism” in the form of the so-called “higher criticism” which consists of “the study of the sources and literary methods employed by the biblical authors.” Such critical methods are not favored by the religious fundamentalists, who see the Bible as divinely inspired and infallible and thereby beyond any criticism. It was only later that Darwinism came to be included under the modernism umbrella.
[Read more…]

The rise of Catholic objections to Copernican ideas

(For those following the Copernican postings in sequence, I made a mistake. Today’s posting should have appeared BEFORE the one that dealt with The role of Protestant opposition to Copernicus. Sorry about that!)

The last myth that I will address concerning the Copernican revolution is that it met immediate, widespread, and religious opposition from the Catholic Church. This took the form of releasing the full force of the Inquisition against his ideas, which resulted in Copernican Giordano Bruno being burned for advocating those ideas and Galileo being forced to recant his support for Copernicus’ sun-centered universe. This is the view, for example, expressed by Bertholt Brecht in his famous play Life of Galileo.
[Read more…]

The role of Protestant opposition to Copernicus

For many years after the publication of Copernicus’ book De Revolutionibus Orbium Caelestium in 1543, his ideas remained within the mathematical astronomy community. The more popular books on astronomy and cosmology either were unaware of his work or chose to ignore them. But there were a few non-astronomers such as poets who were aware of his work and they ridiculed it for advocating a moving Earth, not because of any ideas of heresy. It was though the poets and other popularizing writers of that time that Copernicus’ ideas became more widely known.
[Read more…]

The myth concerning circular orbits

In this posting we will examine the myth that the Copernican revolution was hampered by its insistence that the orbits be circles.

To understand the reasons behind this we need to look at the work of an influential, but often unrecognized, player in the Copernican revolution, the astronomer Tycho Brahe (1546-1601). He is considered the greatest naked-eye astronomer. He lived just before the invention of telescopes and the accuracy, scope, and reliability of his observations had enormous impact on the field.

It is interesting that Brahe, like most astronomers at that time, rejected Copernicus’ ideas of a moving Earth. He could not accept the arguments for the Earth’s motion, seeing that as creating more problems than solving them. In fact, he developed his own system (called the Tychonic system) that was mathematically equivalent to the Copernican system, but had the Earth as a stationary center. (p. 202. Most of the material in this post is from Thomas Kuhn’s book The Copernican Revolution and page numbers are from that book.)
[Read more…]