solid figures, form the concrete data of geometry, are a fundamental sort of quasi-entity without which exact science would be impossible. A second class of conventional quasi-entity consists in visual representations, and ranges from geometrical drawings and diagrams, through artistic pictures of all kinds, to carvings and sculptures. Of course there are material entities employed in all these cases, but such entities are not the subjects of which we think when we consider any representation as such in relation to some actual or hypothetical thing represented. Visual symbols form a third class of quasi-entities; the most important being letters, as symbols of articulate sounds, combined into written words and sentences, as symbols of spoken language; the next most important being the figures and symbols of arithmetic and algebra; while there is another class employed in musical notation, and there are special symbols which have a more or less mystical significance in folk-lore and religion. Fourthly there are numbers and magnitudes considered as the universal object-matters of the ideas expressed in arithmetical and algebraical notation, though largely suppressed in the mechanics of calculation. (A somewhat parallel quasi-entity is a musical composition considered as the object-matter of the auditory ideas expressed in a musical score.)
Magnitudes are in one sense more abstract (i.e., more general) even than lines and areas, yet they are concrete in that each is a definite subject, having indefinitely numerous relations to other magnitudes. A fifth and supremely important class of quasi-entity consists in ideas, as understood in the present article; that is, as definitely coined for human intelligence by means of logical terms.
The foregoing five classes of conventional quasi-entities, together with what have been termed natural features, are none of them entities proper, and do not in any case possess the rich and unfathomed variety of properties pertaining to material things; yet it is proper to regard them as subjects rather than as predicates, since each forms a center or nucleus of qualities or relations, and is not in itself any quality or relation. For the same reason the ideas and names of these quasi-entities are concrete and not abstract.
