"The first phrase is meant to designate rigidly a certain length in all possible worlds, which in the actual world happens to be the length of the stick S at t0. On the other hand 'the length of S at t0' does not designate anything rigidly. In some counterfactual situations the stick might have been longer and in some shorter" (Kripke, 55).
This quote helps demonstrate the reference of names, rather than defining of names, by providing a very visual example; the use of measurements. It showcases the potential differences between the characteristics normally defined of X as some attribute to it, and shows how these characteristics can change depending on other circumstances, in this case other worlds. It helps illuminate the differences between rigid designators and nonrigid designators as well as 'a priori' and 'necessary'.
I agree with the logic that names carry some designation and reference in and of themselves. Kripke's argument makes more intuitive sense to me as it is more circumstantial than Frege-Russell's strict definitions.
"Mathematics is the only case I really know of where they are given even within a possible world, to tell the truth. I don't know of such conditions for identity of material objects over time, or for people" (Kripke, 43).
Kripke does not believe that there are any concepts beyond mathematics which are capable of having inarguable or interpretative qualities. Aside from this exception, Kripke's argument asserts that definitions of Xs as a way of designation is a circumstantial method.
I wonder, based on scientific reduction, if physics are another example of this as they are grounded on mathematics. This seems like an obvious example to miss, so I am puzzled whether they have a different quality from mathematics making them interpretive or whether Kripke used mathematics as an umbrella for hard sciences.
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