lxiv INTRODUCTION TO THE SECOND EDITION
ence are hopelessly antiquated, useless, confusing, and so eventually harmful. Their attitude even today is that all those problems were settled and disposed of by different monks in the Middle Ages. Modern researches reveal that nothing of the sort was settled or disposed of, and that a new, up-to-date revision is necessary to eliminate the false knowledge from which present day tragedies follow automatically. The reader is referred to the Encyclopaedia Britannica under such terms as 'nominalism', 'realism', and related terms.
As was explained before, for a revision of a system we must first get outside of the system. Only after producing a non-aristotelian exten-sional system can the aristotelian intensiqnal structure of our traditional system and language be properly evaluated.
Here we introduce a most important technical term which describes a fundamental characteristic of a correct attitude toward language; namely, that most terms aredefined'. They are over-defined (over-limited) by intension, or verbal definition, because of our belief in the definition; and are hopelessly under-defined by extension or facts, when generalizations become merely hypothetical. For instance, the euclidean parallels with their equal distance are over-defined by intension and under-defined by extension, as 'equal distance' is unnecessary and also is denied by facts. Similarly the newtonian equations are over-defined (over-limited) by intension, while under-defined by extension, which includes the necessary finite velocity of a signal (Lorentz-Einstein).
From these two examples alone we may see how heavy the problem is, as the discovery of a new important factor makes it obvious that most generalizations must bedefined, depending upon whether our attitude is intensional or extensional. Unfortunately only those who have studied psychiatry and/or general semantics can fully comprehend the difficulties involved. Different maladjusted, neurotics, psychotics, etc., orient themselves by intension most of the time. This means they evaluate by over-definition, just because they believe in their limited verbal-
* The terra 'over-defined class' was introduced to the best of my knowledge by Dr. A. S. Householder. This term is inadequate for our purpose, as it disregards the problems of intension and extension, which represent different types of evaluation. Besides, the term 'class' is very ambiguous. In science and life we deal mostly withdefined terms, as will be explained.