Necessary and sufficient conditions

(I am taking a break from original posts due to the holidays and because of travel after that. Until I return, here are some old posts, updated and edited, for those who might have missed them the first time around. New posts should appear starting Monday, January 14, 2008.)

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.

From Scopes to Dover-21: The death of ‘creation science’

(For previous posts in this series, see here.)

In the previous post we saw how the goal of trying to get creationist ideas back into the science classroom took the form of the birth of ‘creation science’ and calling for it to be taught along with evolution. While ‘creation science’ had no explicitly religious language, it was clearly a Genesis-based, young Earth, Biblical creationism. The 1981 Arkansas law calling for the balanced treatment of creation science and evolution was promptly overturned in 1982 by a US District Court judge.

The Louisiana ‘balanced treatment’ act of 1981 was less restrictive than the Arkansas one, since its call for teaching creation science merely meant talking about the “scientific evidences for creation and inferences from those scientific evidences”. So while that gave its backers initial hopes that it would survive constitutional challenge, by now the historical record of religious-based efforts to undermine the teaching of evolution, starting with the Scopes trial, was too heavy a baggage for these efforts to overcome. It had become increasingly difficult to argue that the fight against the teaching of evolution was not religion-based, and this ended up dooming the Louisiana statute. The Louisiana Act, like its Arkansas counterpart, was overturned by a US District Court. The case was then appealed to a federal Appeals Court, where the District Court ruling was upheld by a narrow 8-7 margin.
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Charles Darwin in his own words

I have written a lot about the theory of evolution and in the process have quoted short excerpts from various authors, Charles Darwin included. (Please see here for previous posts in this series.)

But in going back and reading the first edition of On the Origin of Species (1859), I am struck by how prescient Darwin was in anticipating the objections that would be raised against his theory and why. He could well have been talking about the situation today, except that then the people who were skeptical and who he was trying to persuade were his scientific colleagues. Nowadays scientists are almost all converts to natural selection (as he predicted might happen) and it is religious lay people who make the same objections he addressed long ago.

To get the full flavor of Darwin’s thinking and his style of writing, here is a somewhat long passage from his conclusions, where he summarizes his case (p. 480-484). The sections in boldface are my own emphasis. (Darwin’s complete works are now available online.)

I have now recapitulated the chief facts and considerations which have thoroughly convinced me that species have changed, and are still slowly changing by the preservation and accumulation of successive slight favourable variations. Why, it may be asked, have all the most eminent living naturalists and geologists rejected this view of the mutability of species? It cannot be asserted that organic beings in a state of nature are subject to no variation; it cannot be proved that the amount of variation in the course of long ages is a limited quantity; no clear distinction has been, or can be, drawn between species and well-marked varieties. It cannot be maintained that species when intercrossed are invariably sterile, and varieties invariably fertile; or that sterility is a special endowment and sign of creation. The belief that species were immutable productions was almost unavoidable as long as the history of the world was thought to be of short duration; and now that we have acquired some idea of the lapse of time, we are too apt to assume, without proof, that the geological record is so perfect that it would have afforded us plain evidence of the mutation of species, if they had undergone mutation.

But the chief cause of our natural unwillingness to admit that one species has given birth to other and distinct species, is that we are always slow in admitting any great change of which we do not see the intermediate steps. The difficulty is the same as that felt by so many geologists, when Lyell first insisted that long lines of inland cliffs had been formed, and great valleys excavated, by the slow action of the coast-waves. The mind cannot possibly grasp the full meaning of the term of a hundred million years; it cannot add up and perceive the full effects of many slight variations, accumulated during an almost infinite number of generations.

Although I am fully convinced of the truth of the views given in this volume under the form of an abstract, I by no means expect to convince experienced naturalists whose minds are stocked with a multitude of facts all viewed, during a long course of years, from a point of view directly opposite to mine. It is so easy to hide our ignorance under such expressions as the “plan of creation,” “unity of design,” &c., and to think that we give an explanation when we only restate a fact. Any one whose disposition leads him to attach more weight to unexplained difficulties than to the explanation of a certain number of facts will certainly reject my theory. A few naturalists, endowed with much flexibility of mind, and who have already begun to doubt on the immutability of species, may be influenced by this volume; but I look with confidence to the future, to young and rising naturalists, who will be able to view both sides of the question with impartiality. Whoever is led to believe that species are mutable will do good service by conscientiously expressing his conviction; for only thus can the load of prejudice by which this subject is overwhelmed be removed.

Several eminent naturalists have of late published their belief that a multitude of reputed species in each genus are not real species; but that other species are real, that is, have been independently created. This seems to me a strange conclusion to arrive at. They admit that a multitude of forms, which till lately they themselves thought were special creations, and which are still thus looked at by the majority of naturalists, and which consequently have every external characteristic feature of true species,—they admit that these have been produced by variation, but they refuse to extend the same view to other and very slightly different forms. Nevertheless they do not pretend that they can define, or even conjecture, which are the created forms of life, and which are those produced by secondary laws. They admit variation as a vera causa in one case, they arbitrarily reject it in another, without assigning any distinction in the two cases. The day will come when this will be given as a curious illustration of the blindness of preconceived opinion. These authors seem no more startled at a miraculous act of creation than at an ordinary birth. But do they really believe that at innumerable periods in the earth’s history certain elemental atoms have been commanded suddenly to flash into living tissues? Do they believe that at each supposed act of creation one individual or many were produced? Were all the infinitely numerous kinds of animals and plants created as eggs or seed, or as full grown? and in the case of mammals, were they created bearing the false marks of nourishment from the mother’s womb? Although naturalists very properly demand a full explanation of every difficulty from those who believe in the mutability of species, on their own side they ignore the whole subject of the first appearance of species in what they consider reverent silence.

It may be asked how far I extend the doctrine of the modification of species. The question is difficult to answer, because the more distinct the forms are which we may consider, by so much the arguments fall away in force. But some arguments of the greatest weight extend very far. . . I believe that animals have descended from at most only four or five progenitors, and plants from an equal or lesser number.

Analogy would lead me one step further, namely, to the belief that all animals and plants have descended from some one prototype. But analogy may be a deceitful guide. Nevertheless all living things have much in common, in their chemical composition, their germinal vesicles, their cellular structure, and their laws of growth and reproduction. We see this even in so trifling a circumstance as that the same poison often similarly affects plants and animals; or that the poison secreted by the gall-fly produces monstrous growths on the wild rose or oak-tree. Therefore I should infer from analogy that probably all the organic beings which have ever lived on this earth have descended from some one primordial form, into which life was first breathed.

And then the very last, almost poetic, words in the book (p. 490):

There is grandeur in this view of life, with its several powers, having been originally breathed into a few forms or into one; and that, whilst this planet has gone cycling on according to the fixed law of gravity, from so simple a beginning endless forms most beautiful and most wonderful have been, and are being, evolved.

Darwin’s achievements are truly magnificent, putting him in the same class as Einstein and Newton, among the greatest scientists of all time.

POST SCRIPT: The Larry Craig incident

Senator Larry Craig (R-Idaho) has taken some strong “family values” and anti-gay stands in the past, despite long standing rumors that he himself was gay. The recent news report that he had pleaded guilty to “lewd” conduct in a public restroom has caused speculation that his career is now over.

It is despicable to harass gays with anti-gay rhetoric and legislation, becoming even worse if those doing so are secretly gay themselves. But Talking Points Memo expresses well my unease with what happened to Craig in the most recent episode. It is not clear from published reports that he did anything that really warranted his arrest and that he was, as Josh Marshall says, essentially caught in a Catch-22 caused by his own risky behavior.

Glenn Greenwald documents the brazen contradictions that right-wingers are indulging in the way they respond to the recent Craig revelation, the reports that surfaced back in 2006 that he was gay, and the recent case of Senator David Vitter (R-Louisiana), another “family values” champion who was found to be a customer of prostitutes.

Petitions and politics in science

In a recent discussion on a listserv for physics teachers, someone strongly recommended the book The Politically Incorrect Guide to Science by Tom Bethell, saying that it exposed how mainstream science was suppressing some ideas for non-science reasons, in particular how the great weaknesses of evolutionary theory were being hidden.

I had not read this book myself but these kinds of arguments are familiar to me and Bethell had written an article describing his own book. It struck me as extraordinarily shallow, rehashing arguments that have long been discredited, and invoking misleading (and old) chestnuts about evolution occurring only by chance, and missing transitional forms, etc. In fact, he seemed to have drawn his arguments against evolution from the playbook of the intelligent design creationists, in particular Jonathan Wells’ book Icons of Evolution.

He even made the argument that the only thing that has been seen is ‘microevolution’ (small changes within species) and not macroevolution (change from one species to another). But the distinction drawn between micro- and macroevolution is untenable, since it has long been realized that there is a large overlap between varieties within species and between species as a whole, making the drawing of such distinctions difficult. Darwin himself pointed this out in his On the Origin of Species (chapter II), where he emphasized how difficult it was for even experts to classify whether animals were varieties within a single species or different species.

It is amazing that in this day and age people like Bethell still bring up Haeckel’s embryos. Modern biologists don’t take Haeckel’s misleading sketches seriously anymore since his theory was discredited more than a hundred years ago and only intelligent design creationists (IDC) keep bringing it up repeatedly to argue that scientists falsify things in order to buttress the case for evolution. In the documentary A Flock of Dodos IDC advocate John Calvert talks about how biology textbooks use Haeckel’s figures to mislead children but when asked to show this, thumbs through some textbooks and cannot find any examples. He had simply accepted this folklore uncritically. What use Haeckel has now is purely pedagogical.

The Haeckel case is analogous to someone finding that the Bohr model of the atom is still being taught in middle school science textbooks, “discovering” that Bohr’s model violates Maxwell’s laws of electromagnetism, and thus concluding that quantum mechanics is wrong and that children are being misled into accepting it. Quantum mechanics has come a long way since the Bohr atom and does not depend on it, just like evolutionary biology and Haeckel’s embryos. To keep bringing it up is a sign of desperation

Bethell’s argument about the fact that no one has seen half-bats and that therefore step-by-step evolution could not have occurred, reminds me of those people who say that it is absurd that an electron can go through two slits or that twins age differently based on their speeds. After all, has anyone actually SEEN an electron go through two slits? Has anyone actually SEEN twins age differently? If we haven’t seen such things directly, they must not occur, right? I have described earlier how incomplete the fossil record is, because fossilization is extremely unlikely, and how arguments that depend on the existence of gaps in the fossil record can never be satisfied because new gaps can always be created.

As I have said in this series on evolution, to really appreciate the theory one has to get beyond the simple minded rhetoric of the kind that Bethell indulges in and look at the underlying details and the mathematics. The question of whether evolution is a “fact” is a red herring. “Theory” and “fact” are fluid terms in science. What is true is that the fully developed theory of evolution, known as the neo-Darwinian synthesis, is the most productive and useful theory in biology today, and forms the basis of almost all research in that field.

People who dislike the theory of evolution often point to the petition that the Discovery Institute (DI), the main driver of Intelligent Design Creationism (IDC), put out signed by 700 people that says: “We are skeptical of claims for the ability of random mutation and natural selection to account for the complexity of life. Careful examination of the evidence for Darwinian theory should be encouraged.” Such people cite this as evidence that the theory is weak and then ask: “Why are so many scientists jumping off the evolution band wagon?”

But scientists are taught to be skeptical and to examine carefully the evidence for any theory. And if a theory (like evolution) challenges their religious beliefs, they are likely to be even more skeptical of it. That is a natural human tendency. It does not take any effort for a mathematician or physicist or philosopher to say she is skeptical of evolution, just as it does not cost any biologist anything to say that he is skeptical of the big-bang. After all, in each case, they are not personally working with that theory and are unlikely to know anything about it in any detail and thus can let other factors have a greater influence. As of the time when there were 400 people who had signed on, about 80% were not even biologists. (The story of one religious scientist who signed on to the Discovery Institute statement and only later realized what was going on can be read here.)

Another problem with the petition wording is that although Darwin proposed the mutation and natural selection mechanism, developments since then have added other mechanisms such as gene flow and genetic drift, so even a biologist who sees no problem with evolution would agree that mutation and natural selection alone are not sufficient.

I personally am skeptical of ANY theory in ANY field as being the last word (or the ‘truth’) on the subject because the history of science teaches us that scientific theories have always been provisional. So for me the DI statement itself is nothing more than a platitude. The fundamental issue is whether the biological community feels that evolution is in a crisis, and as far as I am aware, the biological science community does not think so and continues to use that theory as the foundation for their work. So these kinds of statements are just meaningless. When biologists start using alternative theories to generate predictions and start getting positive results, then we can take those other theories seriously.

It is important to realize that despite so many years of pushing intelligent design creationism, the people at the Discovery Institute have not been able to generate even one prediction, let alone do any experiments to investigate their theory. What they are doing is not science, it is lobbying and public relations.

Statements like the ones put out by the Discovery Institute on evolution are, however, useful as indicators of what people desire or yearn for.

For example, I am skeptical of the idea of dark matter as the explanation for the anomalous velocity distribution of stars on the arms of spiral galaxies. Why? Mostly for aesthetic reasons. It seems a bit contrived to me and the idea of huge amounts of matter surrounding us that we cannot detect reminds me uncomfortably of the arguments for the ether before Einstein’s theory showed that the ether was a redundant concept.

I am hoping that a nicer theory than dark matter comes along and I know I am not alone in feeling this way and that other card-carrying physicists share my view. So if someone handed me a petition saying that I was skeptical of the theory of dark matter and would like the evidence for it to be examined carefully, that statement’s content would not be objectionable to me. I would totally agree.

But I would not sign because it is pointless. I have not done any real work to support my misgivings. I have not developed an alternative theory, generated hypotheses, made predictions, or explained any existing data. Physicists who actually work on the spiral galaxy problem (even if they were completely outnumbered by the people who sign a petition dismissing dark matter theory) would be perfectly justified in ignoring me and any other physicists who sign such a petition in the absence of any substantive counter-theory.

What the DI petition on evolution tells us is that there are about 700 people who wish and hope that a theory more congenial to them than evolution comes along. That’s fair enough but hardly major news. They have every right to feel that way and to say so. But it is by no means a measure of the merits of the theory, however many people sign on to it, and it is dishonest of the Discovery Institute to make such a claim.

Bethell’s thesis that the scientific community is conspiring to suppress the truth about the weaknesses of evolution is silly. Given that the US has high levels of religiosity and public skepticism about evolution and widespread unease that evolution is undermining religious beliefs, any scientist who found good evidence for special creation would be deluged with funding from both government and private sources and receive high visibility and acclaim. Furthermore, such a discovery would open up vast new areas of research. In such a climate, why would any scientist not publish findings that provided evidence for special creation?

People like Bethell are trying to achieve by public relations what they cannot do using science. They are not the first to try to do this and will not be the last. But they will fail, just like their predecessors.

POST SCRIPT: The insanity of the employer-based health care system

This question posed at a Democratic presidential candidates forum illustrates perfectly why we need a single-payer, universal health care system.

Mano Singham

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