22

Fig 7 asserts that there are more than one man. Fig. 8 asserts that everything is identical with itself. Fig. 9 asserts that everything is identical with something and is other than something.

The system as thus far developed is called the Beta development, the Alpha development being the system without the lines of identity. A Gamma is required. For example, Fig. 8 does not express the principle of identity since it merely asserts, as a fact, that anything is identical with itself. The Beta development is limited to the expression of propositions de inesse.

In order to represent the reasoning of mathematics in all its fullness, two improvements must be made. In the first place the operation of hypostatic abstraction must be rendered practicable. This has been the object of jeers since Molière died in enacting the recipiendaire in the 8th Intermède of the