ellauri088.html on line 86: Gustav Fechner (1801-1887) argued for psychophysical parallelism, according to which the mental and physical worlds run parallel to each other but do not interact. Fechner developed the Weber-Fechner law, according to which the perceived intensity of a stimulus increases arithmetically as a constant multiple of the physical intensity of the stimulus or in other words, changes of physical intensity gallop along at a brisk pace while the corresponding changes of perceived intensity creep along. The Weber and the Weber-Fechner laws were the first laws to provide a mathematical statement of the relationship between the mind and the body. Another significant contribution when S. S. Stevens (1906-1973) demonstrated that psychological intensity grows as an exponential function of physical stimulus intensity, that is, equal stimulus ratios always produce equal sensory ratios although different ratios hold for different sensory modalities. (Siis mitä? Aritmeettisesti vai logaritmisesti?)
ellauri096.html on line 191: Yes, there are infinitely many. Kurt Gödel’s incompleteness theorem demonstrated that any system that is strong enough to express arithmetic is also strong enough to express a formal counterpart of the self-referential proposition in the surprise test example ‘This statement cannot be proved in this system’. If the system cannot prove its “Gödel sentence”, then this sentence is true. If the system can prove its Gödel sentence, the system is inconsistent. So either the system is incomplete or inconsistent. (See the entry on Kurt Gödel.)
ellauri096.html on line 193: Of course, this result concerns provability relative to a system. One system can prove another system’s Gödel sentence. Kurt Gödel (1983, 271) thought that proof was not needed for knowledge that arithmetic is consistent.
ellauri096.html on line 195: J. R. Lucas (1964) claims that this reveals human beings are not machines. A computer is a concrete instantiation of a formal system. Hence, its “knowledge” is restricted to what it can prove. By Gödel’s theorem, the computer will be either inconsistent or incomplete. However, a human being with a full command of arithmetic can be consistent (even if he is actually inconsistent due to inattention or wishful thinking).
ellauri236.html on line 198: There exists in America an enormous literature of more or less the same stamp as No Orchids. Quite apart from books, there is the huge array of ‘pulp magazines’, graded so as to cater for different kinds of fantasy, but nearly all having much the same mental atmosphere. A few of them go in for straight pornography, but the great majority are quite plainly aimed at sadists and masochists. Sold at threepence a copy under the title of Yank Mags(4), these things used to enjoy considerable popularity in England, but when the supply dried up owing to the war, no satisfactory substitute was forthcoming. English imitations of the ‘pulp magazine’ do now exist, but they are poor things compared with the original. English crook films, again, never approach the American crook film in brutality. And yet the career of Mr. Chase shows how deep the American influence has already gone. Not only is he himself living a continuous fantasy-life in the Chicago underworld, but he can count on hundreds of thousands of readers who know what is meant by a ‘clipshop’ or the ‘hotsquat’, do not have to do mental arithmetic when confronted by ‘fifty grand’, and understand at sight a sentence like ‘Johnny was a rummy and only two jumps ahead of the nut-factory’. Evidently there are great numbers of English people who are partly americanized in language and, one ought to add, in moral outlook. For there was no popular protest against No Orchids. In the end it was withdrawn, but only retrospectively, when a later work, Miss Callaghan Comes to Grief, brought Mr. Chase's books to the attention of the authorities. Judging by casual conversations at the time, ordinary readers got a mild thrill out of the obscenities of No Orchids, but saw nothing undesirable in the book as a whole. Many people, incidentally, were under the impression that it was an American book reissued in England.
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