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Under the influence of Kripke's acute analysis, there has been a growing trend of modern essentialism, or in other words, the assertion that there are 'essential' descriptors (rigid designators) that 'stick' with the thing being described in all possible worlds. Most influentially Kripke identified that any set of descriptions could not be definite in the way Russell imagined, since it was possible that a given X with descriptions Y and Z could have been existent in another world where Y and Z were not applicable to X.

Russell's descriptivist theory of names still holds a large degree of influence in analytical philosophy however. It is assumed especially in the way philosophers talk about existence. Existence is typically understood to be a general concept property which is instantiated in existent objects. This seems to largely hold only if we grant that existence cannot be attributed to singular things, which in turn typically only holds because singular things are held to be a collection of descriptions. If one were to rid of the last, grounding belief one would find new gates opened for conversation about what the nature of existence is.

In any case, it seems clear that Kripke's criticism has very serious and far-reaching consequences. As such, it is important to understand the responses that have been given to such criticism. What is the current debate being had about Russell's theory vs. Kripke's?

  • Can you give a reference tying non-existence of particulars to descriptivism? Frege-Russell were on board with Kant's "existence is not a property", and Meinongian theories where it is, are designed to quantify over non-existent entities, not to deny existence to particulars. Their proponents like Parsons are in fact sympathetic to Kripke, but both descriptivism and Kripke-Putnam are perfectly compatible with existence of particulars, they only disagree on how speakers pick out referents of names. Frankly, I can't think of anyone who advocated the non-existence, certainly not Russell. – Conifold Apr 14 '16 at 17:50
  • Sure. I can think of Carnap as a quick example (Carnap 1959, p. 74). Carnap denies existence can be said of the self because it would be attributing existence of a particular thing. And it seems odd that one shouldn't see the consequences and conclusions drawn about existence from the descriptivist theory, since such conclusions are prevalent in Frege and Russell themselves (although I do take the point that they are separate issues). I only contended that certain philosophers have not separated Frege's contribution in clarity of predication from his existential quantifier. – Ovid Apr 17 '16 at 15:48
  • From Almog's Naming without Necessity:"The reader of the Frege-Russell correspondence can appreciate how outraged Frege was to learn that Mont Blanc itself ("with all its snowfields") was part of the proposition expressed by "Mont Blanc is more than 4000 meters high". But Russell did not flinch. He stood by his view that Mont Blanc itself ("despite all its snowfields", as he nonchalantly put it to Frege) is a constituent of this "objective proposition"". I'd have to check Carnap, but it seems that Frege and Russell only disagree on how Mont Blanc enters propositions, not on its existence. – Conifold Apr 17 '16 at 21:10
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The main criticism is that were need descriptions to "know" what we're talking about, in particular in what Kripke called baptism. The first time we encounter an exemplar of a natural kind (say, a tiger) it is not enough to say that tigerhood is the kind of this exemplar, whatever it is, because the tiger might belong to several kinds depending on what we're interested about. The tiger is an exemplar of a mammal, of an organism, and so on. This is known as the "qua problem". There are also cases where a name does not refer to what it was intended to refer to when it was introduced. For example, Madagascar was initially the name of an African coast, not the island were know about today. Another problem concerns some terms, like Jade, that do not refer to any natural kind (because there are varieties with completely different chemical structures) yet are still in use today. The same goes for the way fishermen classify fishes: it doesn't have to map precisely the phylogeny, buy the clarification serves practical purposes. Nowadays philosophers typically hold mixed theories between descriptivism and direct reference.

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