THE DIAGRAMMATIC REPRESENTATION OF PROPOSITIONS.
125. The use of Diagrams in Logic.—In representing propositions by geometrical diagrams, our object is not that we may have a new set of symbols, but that the relation between the subject and predicate of a proposition may be exhibited by means of a sensible representation, the signification of which is clear at a glance. Hence the first requirement that ought to be satisfied by any diagrammatic scheme is that the interpretation of the diagrams should be intuitively obvious, as soon as the principle upon which they are based has been explained.[165]
[165] 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,—
S :
, P ;