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.
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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.
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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.
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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.
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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.)
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Copernicus’ ideas gain support from a few astronomers

As astronomical observations became more comprehensive, and as sea-faring became more widespread, the need for better star-charts in order to have more accurate time-keeping and navigation became imperative. In order to meet this demand for increased accuracy, the method of epicycles outlined by Ptolemy became more and more complicated, and was extended in different ways by different mathematical astronomers until it became hard to say what the Ptolemaic system was. Instead there were a whole set of different calculations all based on the Ptolemaic system, all getting increasingly complicated. And none of them quite agreed with the full range of good naked-eye observations. (p. 139. 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…]

Copernicus and the laws of physics

In a previous post, we saw that the popular notion that the Copernican model of the universe was opposed because it implied a demotion for human beings is not supported by close examination of the views of the people actually living in those times. It is, instead, a revisionist version of events that gained ascendancy around 1700 or so.

In today’s post we will examine the myth that the immediate opposition to Copernicus was raised by religious people. The fact that the Copernican model was not perceived contemporaneously as a demotion already weakens the case for that story but there’s more.
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Was the Copernican model a demotion for human beings?

In this post, we will look at one particular myth surrounding the Copernican story, the one that says that Copernican ideas were opposed because they implied a demotion for human beings.

Nicolaus Copernicus (1473-1543) published De Revolutionibus Orbium Caelestium, his epic work describing a heliocentric system, in 1543 the year of his death. Until then, Ptolemy’s geocentric model described in his Almagest had been the one used for studying planetary motions. In this model, the Earth was at the center of the universe and every celestial body orbited about the center. The Almagest was the “first systematic mathematical treatise to give a complete, detailed, and quantitative account of all the celestial motions.” (Thomas Kuhn, The Copernican Revolution, p. 72) This work was so good and its methods so powerful, that it provided the framework for astronomical calculations for nearly 1500 years. It was the framework that guided Copernicus’ own work.
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Looking closely at scientific history

Since I started looking more closely into the history of science, there are two things that I have learned that I have recast into principles.

The first is that the more closely we examine important historical events in science, the less resemblance they bear to the popular condensed capsule versions that are learned in school or college or portrayed in the popular media. The earlier posting about Columbus and the flat Earth is a case in point.

The second principle is that while science textbooks are usually good for teaching the current principles of science, they tend to be bad for teaching anything about the history of science or the nature of science. In those cases, what they usually describe is better described as folklore rather than history.

Take for example one of the most famous of all scientific revolutions, the one associated with Copernicus. The popular version of this story goes as follows:

The ancient Greeks, while pretty good at mapping the stars and motion of planets, tended to create models of the universe that were strongly influenced by religious, philosophical, and aesthetic considerations, rather than on observation and experiment. Hence they came up with the idea that the Earth was the stationary center of the universe (which pleased those religious people who wanted to give pride of place to the home of God’s greatest creation – human beings) and that the stars and planets were embedded on the surface of a sphere that rotated around the Earth in circles, which pleased those philosophers with highly refined sensibilities who felt that since the circle and sphere were the most perfect geometric shapes, they had to play a central role in the cosmos.
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