Studies and Exercises in Formal Logic

Note 165 — Chapter V

Reading edition

Hamilton’s “geometric scheme,” which he himself describes as “easy, simple, compendious, all-sufficient, consistent, manifest, precise, complete” (Logic, II. p. 475), fails to satisfy this condition. He represents an affirmative copula by a horizontal tapering line (), the broad end of which is towards the subject. Negation is marked by a perpendicular line crossing the horizontal one (). A colon (:) placed at either end of the copula indicates that the corresponding term is distributed; a comma (,) that it is undistributed. Thus, for All S is P we have,—

horizontal tapering line

same with a bar

S : , P ;

horizontal line tapering to right

and similarly for the other propositions.

Dr Venn rightly observes that this scheme is purely symbolical, and does not deserve to rank as a diagrammatic scheme at all. There is clearly nothing in the two ends of a wedge to suggest subjects and predicates, or in a colon and comma to suggest distribution and non-distribution” (Symbolic Logic, p. 432). Hamilton’s scheme may certainly be rejected as valueless. The schemes of Euler and Lambert belong to an altogether different category.

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