Grice and Geach on relative identity and surmen

Speranza

Consider the notorious case of "surmen" (Geach 1967).

A pair of men are the "same surman" if they have the same surname.

E.g.

Herbert Paul Grice and Herbert Grice, his father.

George Hender Geach and Peter Thomas Geach, his son.

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And a "surman" is a man who bears this relation to someone.

So now, it appears that that two different men can be the same surman, since two different men can have the same surname.

As Geach insists, "surmen" are DEFINED to be men, so they are not merely classes of men.

Hence we seem to have an instance of relative identity, and obviously any similarity relation (e.g., x and y have the same shape) will give rise to a similar case.

Yet such instances of RI are not very interesting. It is granted all around that when 'F'  is adjectival, different Gs may be the same F.

Different men may have the same surname, different objects, the same colour, etc.

Turning an adjectival similarity relation into a substantival one having the form of an identity statement yields an identity statement in name only.

Reference

Deutsch, H. "Relative identity", Stanford Encyclopedia of Philosophy.
Geach, P.T., 1967: "Identity," Review of Metaphysics, 21: 3-12. Reprinted in Geach 1972, pp. 238-247.
–––, 1972: Logic Matters. Oxford: Blackwell.
–––, 1973: "Ontological Relativity and Relative Identity." In Munitz, M. (ed), Logic and Ontology. New York: New York University Press.
–––, 1980: Reference and Generality (third edition). Ithaca: Cornell University Press.
Grice, H. P. The Grice Papers. Bancroft Library.
Myro, in PGRICE, ed. Grandy/Warner