In philosophy, specifically in the area of metaphysics, counterpart theory is an alternative to standard (Kripkean) possible-worlds semantics for interpreting quantified modal logic.
Counterpart theory still presupposes possible worlds, but differs in certain important respects from the Kripkean view.
The form of the theory most commonly cited was developed by David Lewis, first in a paper and later in his book On the Plurality of Worlds.
Counterpart theory (hereafter "CT"), as formulated by Lewis, requires that individuals exist in only one world.
The counterpart theoretic formalization of modal discourse also departs from the standard formulation by eschewing use of modality operators (Necessarily, Possibly) in favor of quantifiers that range over worlds and 'counterparts' of individuals in those worlds.
An opposing view is that any object in time is made up of temporal parts or is perduring.
The C-relation is also known as genidentity (Carnap 1967), I-relation (Lewis 1983), and the unity relation (Perry 1975).
An important part of the way Lewis’s worlds deliver possibilities is the use of the parthood relation.
This is the view that a possible world is a concrete, maximal connected spatio-temporal region.
Still, we say true things like: It is possible that Hubert Humphrey won the 1968 US presidential election.
Some philosophers, such as Peter van Inwagen (1985), see no problem with identity within a world .
The problem is with an object’s accidental intrinsic properties, such as shape and weight, which supervene on its parts.
Ordinary properties, if one accepts the existence of universals, can be exemplified by more than one object at a time.
Sometimes, especially in the theory of relativity as it is expressed by Minkowski, the path traced by an object through spacetime.
The truth condition of this sentence is that "there exists some person stage x prior to the time of utterance, such that x is a boy, and x bears the temporal counterpart relation to Ted."
The traditional view, since Kant, has been that statements or propositions that are necessarily true are a priori.
But in the end of the sixties Saul Kripke and Ruth Barcan Marcus offered proof for the necessary truth of identity statements.
(Essentialism, the necessity of identity, and rigid designators form an important troika of mutual interdependence.)
According to David Lewis, claims about an object's essential properties can be true or false depending on context (in Chapter 4.5 in 1986 he calls against constancy, because an absolute conception of essences is constant over the logical space of possibilities).
Counterpart theory, qua-identity, and individual concepts can offer solutions to this problem.
That context can then be described using CT. Sider makes the point that David Lewis feels he was forced to defend CT, due to modal realism.
The theory is handy if we don't think it is possible for Socrates to be identical with a piece of bread or a stone.
Basically, individual concepts deliver semantic objects or abstract functions instead of real concrete entities as in CT. Kripke accepts the necessity of identity but agrees with the feeling that it still seems that it is possible that Phospherus (the Morning Star) is not identical to Hespherus (the Evening Star).
Therefore, CT forms an important part of our theory about the knowledge of modal intuitions.
Because a counterpart is never identical to something in another possible world Kripke raised the following objection against CT: One way to spell out the meaning of Kripke's claim is by the following imaginary dialogue: (Based on Sider MS) CT is inadequate if it can't translate all modal sentences or intuitions.