lxvi INTRODUCTION TO THE SECOND EDITION
reactions (see chapter XXI) of the ruling classes, resulting in their im-becilic and suicidal behaviour. The ruling classes welcomed in many ways the totalitarians as an eventual safe-guard of their personal selfish interests. The extensional results are that the dreaded 'communists' and 'bolshevists' have united with the totalitarians, and today, 1940, the 'communists' are as 'imperialistic' as any czar has ever been.
To give another example ofdefined terms, it may be helpful to cite a paradox formulated by the mathematician Frege in connection with linguistic difficulties underlying mathematical foundations.
In a village there was only one barber, who shaved only those who did not shave themselves. The question arises whether the barber shaves himself or not. If we say 'yes,' then he did not shave himself; if we say 'no,' then he shaved himself. In daily life we deal all the time with such paradoxes, which if not clarified result only in bewilderment.
The term 'barber' as a term, since it omits the living human being, is a label for a fiction, because there is no such thing as a 'barber' without a living human being. By extension the given specialist in shaving, Smithy is not so simple. He is peppered with complex chain-indexes and dates. Thus, Smithy may be by profession a barber, Smithy may be a father, Smithi8 may be a member of the village council, and anyway Smithln is a living person who has his own life and personality outside his profession, and ultimately he has to shave himself if he does not want a beard, verbalism or no verbalism. Obviously the term 'barber' is over-defined, over-limited, by intension, and is under-defined by extension.
One of my co-workers, commenting on this paradox, suggested that the barber may be a woman and have no beard; or, the barber may be a beardless hermaphrodite or eunuch; or, the barber may have a full beard. Thus, we have only traditionally assumed, in analyzing this old paradox, that the barber was a man with a beard which was somehow shaved.
The difficulties of thisdefined terms situation affect not only our daily lives, but science as well. For example, H20 is by intension or definition over-defined; by extension or in practice we do not deal with 'pure' H20, which is only a symbol on paper, because actually unavoidable impurities are always present.
Similarly let us consider 'blood transfusion'. In the beginning we used the term 'blood transfusion' as over-defined; by extension it turned out to be under-defined, because different bloods have different characteristics, and often blood of one type killed the patient who had blood of another type.
Here I will list a few of the many heavy terms we use in science and