Comparing Mill And Russell's Descriptual Theory Of Names

Russell’s main point is that the logical form of any given referent in turn refers only to it’s definite description, and not to it’s “ordinary proper name”. If we were to write out the semantic and logical form of the definite description of Helvellyn, we would get:
[1] “The mountain in the Eastern Fells of the Lake District is 3,117′ high” and [2] ∃x(Lx ^ ∀y (Ly → x = y) ^ Ex) (Irvine, 2015) respectively, where in our predicate logic proposition [2], L refers to the property of being a mountain in the Eastern Fells of the Lake District and E refers to the property of being 3,117′ high. Effectively, this logical form states that there is one thing x, which satisfies the properties of being L and E. However crucially this definite description

One issue which he outlines is that of the “rigid designator”, which refers to a semantic expression which refers to the same referent in all possible worlds. Kripke argues that ordinary definite descriptions, regardless of how complex, always leave room for small changes in potential worlds, whereas the ordinary proper names are in fact rigid designators (Kripke, 1980: 70). Perhaps even with the widely accepted definite description, in a possible world a similar mountain to Helvellyn could exist in the Lakes with a second Tarn. This hypothetical mountain would satisfy the ordinary definite description for what we call Helvellyn, and yet we wouldn’t want to call this new mountain “Helvellyn” because it is notably different. Thus, under Russell’s descriptivism, Kripke arrives at an ad absurdism, in which we could be calling potentially very different items, places, and people the same thing only because they fit one another’s definite

A keen mountaineer may know enough about Helvellyn to identify it’s unique location and thus give it a definite description specific to it, however a layman may only be able to describe Helvellyn as “a famous mountain in the Lakes”. Should the layman as a consequence be able to call all famous mountains in the Lakes “Helvellyn”? However it doesn’t seem the case that even this layman would make the mistake of using the name “Helvellyn” to describe Blencathra. The alternative might be to say that the layman has no referent associated with the name, however clearly they do have some meaning associated with the name. Perhaps they might be able to recognise the mountain from photos, or know that it has cultural significance. In this case, we are identifying meaning that a potential person could get out of an ordinary proper name, without the accompanying definite description, which seems to go entirely against Russell and Frege’s accounts of