ONT Re: Logic As Semiotic
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| When have then three different kinds of inference.
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| Deduction or inference 'à priori',
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| Induction or inference 'à particularis', and
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| Hypothesis or inference 'à posteriori'.
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| It is necessary now to examine this classification critically.
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| And first let me specify what I claim for my invention. I do not claim that it is
| a natural classification, in the sense of being right while all others are wrong.
| I do not know that such a thing as a natural classification is possible in the
| nature of the case. The science which most resembles logic is mathematics.
| Now among mathematical forms there does not seem to be any natural classification.
| It is true that in the solutions of quadratic equations, there are generally two
| solutions from the positive and negative values of the root with an impossible
| gulf between them. But this classing is owing to the forms being restricted
| by the conditions of the problem; and I believe that all natural classes arise
| from some problem -- something which was to be accomplished and which could be
| accomplished only in certain ways. Required to make a musical instrument;
| you must set either a plate or a string in vibration. Required to make
| an animal; it must be either a vertebrate, an articulate, a mollusk, or
| a radiate. However this may be, in Geometry we find ourselves free to make
| several different classifications of curves, either of which shall be equally
| good. In fact, in order to make any classification of them whatever we must
| introduce the purely arbitrary element of a system of coördinates or something
| of the kind which constitutes the point of view from which we regard the curves
| and which determines their classification completely. Now it may be said that
| one system of coördinates is more 'natural' than another; and it is obvious
| that the conditions of binocular vision limit us in our use of our eyes to
| the use of particular coördinates. But this fact that one such system
| is more natural to us has clearly nothing to do with pure mathematics
| but is merely introducing a problem; given two eyes, required to form
| geometrical judgements, how can we do it? In the same way, I conceive
| that the syllogism is nothing but the system of coördinates or method of
| analysis which we adopt in logic. There is no reason why arguments should
| not be analyzed just as correctly in some other way. It is a great mistake to
| suppose that arguments as they are thought are often syllogisms, but even if this
| were the case it would have no bearing upon pure logic as a formal science. It is
| the principal business of the logician to analyze arguments into their elements just
| as it is part of the business of the geometer to analyze curves; but the one is no
| more bound to follow the natural process of the intellect in his analysis, than the
| other is bound to follow the natural process of perception.
|
| CSP, CE 1, pages 267-268.
|
| Charles Sanders Peirce, "Harvard Lectures 'On the Logic of Science'", (1865),
|'Writings of Charles S. Peirce: A Chronological Edition, Volume 1, 1857-1866',
| Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.
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