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Description of a Notation for the Logic of Relatives

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From the introductory to "Logic of Relatives."Relative terms usually receive some slight treatment in works upon logic, but the only considerable investigation into the formal laws which govern them is contained in a valuable paper by Mr. De Morgan in the tenth volume of the Cambridge Philosophical Transactions. He there uses a convenient algebraic notation, which is formed by adding to the well-known spicul?/i> of that writer the signs used in the following examples. X .. LY signifies that X is some one of the objects of thought which stand to Y in the relation L, or is one of the L's of Y. X . LMY signifies that X is not an L of an M of Y. X .. (L,M)Y signifies that X is either an L or an M of Y. LM' an L of every M. L M an L of none but M's. L[-1]Y something to which Y is L. l (small L) non-L. This system still leaves something to be desired. Moreover, Boole's logical algebra has such singular beauty, so far as it goes, that it is interesting to inquire whether it cannot be extended over the whole realm of formal logic, instead of being restricted to that simplest and least useful part of the subject, the logic of absolute terms, which, when he wrote, was the only formal logic known. The object of this paper is to show that an affirmative answer can be given to this question. I think there can be no doubt that a calculus, or art of drawing inferences, based upon the notation I am to describe, would be perfectly possible and even practically useful in some difficult cases, and particularly in the investigation of logic. I regret that I am not in a situation to be able to perform this labor, but the account here given of the notation itself will afford the ground of a judgment concerning its probable utility....

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