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An Introduction To Non-aristotelian Systems And General Semantics.

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ON ORDER
173
trcmely complex psycho-logical s.r of the organism-as-a-whole. In most cases, these attitudes determine not only the character of our work, but also other reactions which make up our individual and social life. Historically, the mathematicians have a steady record of achievement, and 'philosophers' (excluding epistemologists) one of uselessness or failure. Has this record something to do with the extensional and intensional attitudes ? In fact, it has. It is easy to show that the extensional attitude is the only one which is in accordance with the survival order and nervous structure, and that the intensional attitude is the reversal of the natural order, and, therefore, must involve non-survival or pathological s.r.
One of the simplest ways of approaching the problems of 'extension' and 'intension' is perhaps to point its connection with definitions. A collection may be defined, so we are told, by enumeration of its members, as, for instance, when we say that the collection contains Smith, Brown, Jones,. Or we may define our collection by giving a defining 'property'. We are told that the first type of definitions which enumerates individual members is to be called a definition by extension, the second, which gives a defining 'property', is to be called a definition by intension.
We can easily see that a 'definition by extension' uniquely characterizes the collection, Smith1 Browni, Jonesi,. Any other collection, Smith2, Brown2, Jones2., would obviously be different from the first one, since the individuals differ. If we 'define' our collection by intension; that is, by ascribing some characteristic to each of the individuals, for instance, that they have no tails, many collections of individuals without tails might be selected. Since these collections would be composed of entirely different individuals, they would be entirely different, yet by 'intension', or defining characteristic, they all would be supposed to be one collection.
Similar contrast exists between relations in extension, and relations in intension. These relations have been defined more or less as follows: 'Intensional relations are relations of "concepts"; extensional relations are relations of denoted facts'. Or, 'relations of intension are those which are ascertainable a priori; a relation of extension is discoverable only by inspection of the existent'. Or, 'intension covers the relations which hold for all the possible individuals, while extension holds only for the existent'. 'A relation of intension is one which is only discoverable by logical analysis; a relation of extension is one which is only discoverable by the enumeration of particulars', .*
All that has just been said are perhaps standard definitions; but, for my purpose, they are profoundly unsatisfactory. Because we have