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Where in London the Central line (red) is distinct from the Piccadilly (dark blue), which is markedly different from the Hammersmith and City line (pink), New York's map has designated the same forest green to the 4, the 5 and the 6 lines.
Heckert and Lucas [11] designated the same type locality for the Jim Camp Wash Bed as for the Agate Bridge Bed and Rainbow Forest Bed, northwest of Rainbow Forest.
In contrast, our data revealed that among Swiss workers with a restricted standard of living (deprived), men and women reliably designated the same 2 items from the potential list of 10: the inability to save 100 Swiss Francs monthly, and to contribute to the 3rd pillar superannuation fund.
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A rigid designator designates the same object in all possible worlds in which that object exists and never designates anything else.
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.
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).
A two-dimensionalist adds that if both designators rigidly designate the same entity diagonally, then the statement is a priori, as 'Watery stuff = wet, drinkable … stuff' is, or as 'H2O = H2O' is.
Kripke would say that if both designators in an identity statement rigidly designate the same entity, then the statement is necessarily true, as 'Water = H2O' is.
A two-dimensionalist naturally understands this claim as one that concerns horizontal rigidity: for her, if both designators in an identity statement rigidly designate the same entity horizontally, then the statement is necessarily true, as 'Water = H2O' is.
The notion of a rigid designator comes from Kripke (1980), who (roughly speaking) defines a rigid designator to be an expression that designates the same thing with respect to all possible worlds.
So, 'Aristotle' designates the same man in these various counterfactual circumstances; it is a rigid designator.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com