INTRODUCTION TO THE SECOND EDITION xlv
3. INADEQUACY OF FORMS OF REPRESENTATION AND THEIR STRUCTURAL REVISION
It is not generally realized what serious difficulties an inadequate, unduly limited form of representation or theory brings about This is well known in science. Thus, for instance, the euclidean and newtonian systems cannot deal successfully with electricity and so it was imperative to produce non-euclidean and non-newtonian systems, which do apply to the sub-microscopic electrical levels and also to the macroscopic gross levels. Similarly in life, the two-valued aristotelian system could not deal adequately with the electro-colloidal sub-microscopic levels of the functioning of our nervous systems, on which sanity depends. Thus the formulation of the present infinite-valued non-aristotelian system became also an imperative necessity.
I must stress that as the older systems are only special limitations of the new more general 'non' systems (see p. 97), it would be incorrect to interpret a 'non' system as an 'anti' system.
Such a non-aristotelian system is long overdue. It was retarded because of persecution by the church and other influential bodies, the general belief that 'Aristotle said the last word', etc., and particularly because of the inherent difficulties of such a revision.
The problem of inadequacy in the forms of representation has handicapped science and life a great deal until relatively adequate systems were produced. In life the situation is much more aggravated, for if our orientations and evaluations are inadequate, our predictability is impaired, and we feel with the poet Housman, 'I, a stranger and afraid, in a world I never made'. If we have a more adequate or proper evaluation, we would have more correct predictability, etc., (see p. 58 ff. and p. 750 ff.). We would then feel, 'We are not strangers, and not afraid, in this human mess you and I have made'.
Another of the main difficulties is that a language or a system of a given structure can be somewhat altered from within, but cannot be revised structurally without going outside the former system. For in-Itance, all the attempts to revise the structure of the euclidean and newtonian systems from within were ineffective. Those who revised these lyitems structurally had to go outside the systems first, after which they were able to produce different, independent, new systems. Only then did tn effective evaluation of the former systems become possible.
Similarly the aristotelian, two-valued, intensional system can be reviled structurally and evaluated properly only by building independently ft non-aristotelian, infinite-valued, extensional system. This verifies the contention of Bertrand Russell made in 1922 that there is a 'possibility'