Bibliography

The Branches of Geometry; Existential Graphs [R]

Abstraction names two wholly different operations. One of them consists in supposing some feature of the fact to be absent, or at least leaving it out of account. I call that prescissive abstraction. The other changes ‘This man is shy’ to ‘This man is affected with shyness’. [—] In non-prosaic language it changes a predicate into a subject (extending the term subject beyond the subject nominative to the subject accusative and subject dative, – in short, to what are called the direct and indirect objects of the verb). “The rose smells very sweetly” is by hypostatic abstraction converted into “The rose possesses a delightful perfume.” So “Cain killed Abel” is changed to “Cain caused the death of Abel.” Perfume and death are hypostatical abstractions. They denote entia rationis, whatever that may mean.

Necessity […] is that mode of being which is not subject to the principle of excluded middle, since it may neither be that A is necessarily B, nor that A is necessarily not B. [—] How can the principle of excluded middle fail to apply? By the function of determination being given over to the person addressed.

We certainly have the notion of objective possibility, whether there be such a thing or not. It may be defined as that mode of being which is not subject to the principle of contradiction since if it be merely possible that A is B, it is possible that A is not B. [—] How can the principle of contradiction fail to apply to anything? By something being held in reserve and not expressed.

Abstraction names two wholly different operations. One of them consists in supposing some feature of the fact to be absent, or at least leaving it out of account. I call that prescissive abstraction.