By Furui S., Sandhi M.M. (eds.)
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Extra info for Advances in Speech Signal Processing
But do they always agree? If a person drives his car over a stretch of straight road, he observes that the road is of the same width all along. He knows it to be so by comparison with the size of his car and by comparison of the size of his car with his own size; in other words, it is a tactile fact. Now, if he turns around and looks at the road just traversed, he sees 34 MATHEMATICS IN FUN AND IN EARNEST "with his own eyes" that the road is getting narrower as it extends back into the distance and seems to vanish into a point.
The concrete object realizes the logical object in the same way that the stretched string realizes the geometrical straight line. The idea of pure existence of the logical object is realized by a natural or concrete object in the same fashion and to the same degree as the ideal rectitude of a straight line is realized by the crude rectitude of the string. But no concrete object realizes the abstract object any more MATHEMATICS AND PHILOSOPHY 57 closely than it can realize the geometrical idea of a point.
If the liquid reaches above the middle line of the tube in one case, it will be just as much above that line in the other. " Does not that sound familiar? All this is good reasoning and conforms perfectly to the pattern we have been considering. But what made you think of turning the tube upside down? This is invention. It is an indispensable part of reasoning, but it is not reasoning, or at least it is a different aspect of reasoning. In the case considered another method, another invention could have served the purpose just as well.
Advances in Speech Signal Processing by Furui S., Sandhi M.M. (eds.)