La flèche de Peirce

A BOOLIAN ALGEBRA WITH ONE CONSTANT

4.12. Every logical notation hitherto proposed has an unnecessary number of signs. It is by means of this excess that the calculus is rendered easy to use and that a symmetrical development of the subject is rendered possible ; at the same time, the number of primary formulæ is thus greatly multiplied, those signifying facts of logic being very few in comparison with those which merely define the notation. I have thought that it might be curious to see the notation in which the number of signs should be reduced to a minimum ; and with this view I have constructed the following. The apparatus of the Boolian calculus consists of the signs, =, > (not used by Boole, but necessary to express particular propositions) +, -, X, 1, 0. In place of these seven signs, I propose to use a single one.

13. I begin with the description of the notation for conditional or "secondary" propositions. The different letters signify propositions. Any one proposition written down by itself is considered to be asserted. Thus,

A

means that the proposition A is true. Two propositions written in a pair are considered to be both denied.

Thus,

AB

means that the propositions A and B are both false ; and

AA

means that A is false. We may have pairs of pairs of propositions and higher complications. In this case we shall make use of commas, semicolons, colons, periods, and parentheses, just as [in] chemical notation, to separate pairs which are themselves paired. These punctuation marks can no more count for distinct signs of algebra, than the parentheses of the ordinary notation.

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