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.

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