Thus \(D f, x)\) says the intension \(f\) designates the object \(x\).
In other words, it must be possible to designate the object of the belief via the expression understood as identical to itself in its material signification and without reformulation.
Kaplan analyzes the semantic rules governing the demonstrative 'that' in a similar way: relative to any possible context of use ⟨w, a, t⟩, an utterance of 'that' rigidly designates the object (if any) that is made salient by a's pointing gesture in that context [see the entry on indexicals for a more detailed discussion].
A rigid designator designates the same object in all possible worlds in which that object exists and never designates anything else.
First, a rigid designator designates the same object in all possible worlds as it is used in the actual world, not as it is used in other possible worlds in which the object gets picked out: for although we identify objects in other worlds by our own names, natives of some of these worlds use other names (Kripke 1980, p. 77).
Kripke (1980) famously argues that because a rigid designator designates the same object in all possible worlds, an identity statement in which the identity sign is flanked by two rigid designators must be necessarily true if it is true at all, even if the statement is not a priori.
Participants were presented with photos of two common objects on each trial; one object was designated the context and the other object was designed the target.
In the setup described, \(f\) and \(g\) do designate the same object, and identity of objects carries over across states.
Like other names, Kripke maintains, they are rigid: each designates just the object it actually designates in all possible worlds in which that object exists, and it designates nothing else in any possible world.
Since 1994, the Johannisthal/Adlershof area has been designated as the object of one of seven urban development programmes in Berlin by Berlin's Senate Department for Urban Development and the Environment (see Figure 3).
Both "Venus" and "the morning star" designate the same object.
