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Jan 10 2008

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.

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