UBC Theses and Dissertations
Grammar and logic Fielding, David Anthony
The structure of our world is given in the grammar of our native tongue. If so people whose native tongue has quite a different grammar must be living in a quite different world. A logic such as Aristotle's may seem universal to the speakers of Greek, in fact it may seem universal to speakers of any Indo-European tongue, but the logic will hold good only for the 'universe' of the language or language-family in question. This implies a relationship between logic and grammar rather like the one Russell and Whitehead -claimed for mathematics and logic. Their Principia Mathematica tried to show that the mathematical notion of number rests on, or arises out of, the logical notion of class, that is, we come to understand what a number is through our grasp of what a class is. This thesis is a kind of Principia Logica: it suggests that the whole framework of common sense logic rests on, or arises out of, the grammatical structure of the language the logic was conceived in or took shape in terms of. And if so logical criteria come into being and take shape inside a language or language-family, and are dependent for their validity and even for their meaning on the structure of the language in question. To test, or to try to test, a mode of thought or an argument form against a logical system would be to put the cart before the horse: the logic only makes sense because the form of argument or mode of thought was there already. If so philosophers and logicians ought to think of the words 'world', 'universe' and 'universal' with tongue in cheek. In so far as a judgment seems to us universally true it is unlikely to hold good for the world of an alien language family. If our world is not the only world anybody writing logic or philosophy down ought to make it clear whose world he has in mind - and to do this it may be enough to make sure it is addressed to somebody in particular. Western philosophers seem to have addressed themselves to the whole world, or to mankind, or God. This thesis shows, if nothing else, how hard it can be to address even one other human being. To sum up with another analogy; it seems to me, as a single man, that the difference between one and two is greater than the difference between any other two numbers. There may be a world of difference between zero and one, but between one and two there's all the difference in the world - and that's the difference that matters. Perhaps the only way 1,000 differs from 1,001, as Frege puts it, is in the expression on its face.
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