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discuss their problems, and give mutual technical assistance in tracing
this first general semantic disturbance. Such meetings would stimulate enormously scientific productivity. In fact, without such a co-ordinating body, the present enormous technical developments in each branch of science preclude the revision of general principles, on which, in the last analysis, all other of our activities greatly depend. The first task then, is to find a co-ordinating principle, and present it to the scientific world.Psychiatry, and common experience, teach us, that in heavy cases of dementia praecox we find the most highly developed 'identification'. considerations suggest that
any identification, no matter how slight, represents a dementia praecox factor in our semantic reactions. The rest is only a question of degrees of this maladjustment. From this point of view, we will find dementia praecox factors even in mathematics. In physics, only since Einstein has this factor of un-sanity been eliminated, and this elimination has already produced an ever-growing crop of 'geniuses', which merely means, that some inhibitions of mis-evaluation have been eliminated from these younger men, and that they are humanly more 'normal' than the others.In mathematics, from a point of view, we must first of all
not identify different aspects of our mathematical behaviour, nor try to cover up these identifications of endless aspects by the one very old term 'mathematics'. This word, 'mathematics', in its accepted sense covers a non-existing fiction. What does exist, and the only thing we actually deal with, is human mathematical behaviour, human s.r, and the results of human mathematical behaviour and s.r. A treatise, say, on a new quantum mechanics, has no value to a monkey or a corpse, and only human mathematical behaviour and s.r, have any actual non-el existence, and is the only thing which actually matters. So we see that 'mathematics* covers a non-existent fiction if elementalistically separated from human mathematical behaviour and s.r. I use the term 'mathematics' in the non-el sense, and attempt to signalize some of the difficulties non-elementalism involves at this transitory stage.From a non-identity, structural,
non-el point of view, human mathematical behaviour must be treated uniquely as a physico-mathematical discipline, and postulational methods to be used exclusively as a most valuable checking method. To base mathematical behaviour and s.r on postulational methods exclusively, is to introduce dementia praecox factors into science, which only induces the spread of semantic maladjustment in life.Our main task in producing a
A revision of mathematical s.r, is in the elimination of identification from our s.r about 'infinity' and in the formulation of a definition of numbers in terms of relations. This would enable us to rebuild human mathematical s.r from a theory of numbers point of view, as a physico-mathematical discipline. The intrinsic, or internal theory of surfaces, and the tensor, or absolute calculus, are methodologically our most secure epistemological guides.I would suggest that mathematical and scientific readers who are interested in arevision should, at first, in their special fields, sketch in technical papers, |
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