Do we need relative identity?
George Englebretsen · Notre Dame Journal of Formal Logic · 1982
In a recent paper in which they attempt to provide a logic for relative identity Routley and Griffin [4] distinguish between those theories which (like the early Wittgenstein's Tractatus 5.53-5.534)seek to eliminate identity statements from natural language altogether and those which preserve identity (absolute or relative) for natural language.Wittgenstein would formulate natural language in a notation that would permit no more than one singular term for each item in the domain.Nevertheless, his is not the only way to eliminate identities.There is another, older, way which simply denies a special syntax for natural language identities.The old way is syllogistic.Although Aristotle first built the syllogistic system, it was Leibniz who first envisaged the possibility of extending and strengthening syllogistic into a universal logic, a logic which takes all natural language sentences as syntactically categorical.Unfortunately, Leibniz enjoyed little success in his attempts to build such a logic.The general inaccessibility of his logical work until recently and the spectacular success of mathematical logic during the past hundred years have contrived to make the old Leibnizian program seem archaic and pointless.In a recent series of papers Sommers has succeeded in recalling, revitalizing, and, to a large extent, completing the program Leibniz had worked at for so long (see [5]-[ 13]).On Sommers' theory any assertoric sentence can be reparsed logically as a subject and a predicate.Every assertoric sentence is logically categorical.A subject is a quantified term and a predicate is a qualified term.Terms per se, unquantified and unqualified, are logically homogeneous, and may be negated or unnegated, and may be simple or complex.Most importantly, terms may be either singular or general.In other words, in the new syllogistic singular terms are logically on all fours with general terms.They are fit for the same logical roles usually reserved for general terms.This means that they can be quantified or qualified and so occur as either subject-terms or predicate-terms.