- Criticisms of Mill’s Theory
The Mill view can be questioned in a couple of ways, similar to the criticisms raised earlier in regards to Russell’s theory of descriptions. Firstly, how does Mill deal with identity, and secondly, how does Mill deal with non-existent objects?
In terms of identity, consider the famous example concerning the planet Venus, and the fact that the ancient Greeks called the morning star (Hesperus) and evening star (Phosphorus) two different names. Since Mill claims that proper names merely denote an object, he cannot distinguish between the following two sentences: (1) Hesperus is Hesperus, and (2) Hesperus is Phosphorus. Because all these names refer to the same object, the Millian view would claim that the sentences are logically identical. However, this is clearly not the case as (2) tells us something useful, whether (1) is merely trivial.
The second problem concerns names with no bearer (such as ‘Santa Claus’) or names where the bearer has a questionable identity (eg ‘Homer’). Mill’s theory has trouble dealing with this because the proper nouns in these cases do not denote any particular object, so does that make the sentence meaningless then? In other words, the proper noun has failed to do its usual job of denoting an object, so we are left with nothing at all. However, a sentence such as ‘Homer was the author of the Iliad’ appears to make sense, and would seem legitimate.
Both Frege and Russell attempted to resolve these problems. Frege noted that the two Venus sentences used earlier are in fact different, so we need to work out a mechanism to highlight the distinction. More generally, ‘identity’ is a more complex relationship than people often assume. The sentences ‘a = a’ and ‘a = b’ would be considered identical under Mill’s theory, but Frege does not believe this is correct. ‘a = a’ can be known a priori, whereas ‘a = b’ can only be known through experience, so you cannot say that the two sentences are identical.
Frege suggested that proper names actually have two properties: reference (Mill’s idea of denotation) and sense (which could be seen as Mill’s idea of connotation). The sense of the name refers to the context of the argument and how it is presented. For instance, there is a difference between making a proposition directly, and quoting the same proposition as it’s been said by another person. More generally, ideas and interpretations differ across people and context. Two people might see the exact same colour but perceive it differently. We can say that the ‘sense’ varies for each observation.
The use of ‘sense’ also helps to overcome some difficulties with classical logic. If we say that A and B is true, then we should be able to replace ‘A’ with another true statement, and the resulting expression is still true. However, the new proposition will have a different sense to the old proposition, resulting in an entirely new interpretation. For instance ‘Napoleon recognised the danger and ordered his troops to retreat’ is quite different from ‘Napoleon was 45 years old and ordered his troops to retreat’. The ‘B’ statement in this case (‘Napoleon ordered his troops to withdraw’) picks up its meaning from the ‘A’ statement, so the sense varies between the two. Classical logic is unable to make these kinds of distinctions.
Referring to the Venus example again, both sentences have the same reference (they refer to the same object), however the sense varies. Hesperus refers to Venus as it was understood as the morning star, whereas Phosphorus refers to Venus as the evening star. Therefore, the two statements supply different types of knowledge.
Frege also believed that his solution deals with the problem of non-existent subjects. If we say ‘Santa Claus is coming tomorrow’, we have a sentence that lacks a reference (because it refers to a non-existent person) however it still has a sense, so people understand what we are talking about. Frege used the following example himself: ‘the celestial body most distant from the Earth’. We can understand the sense of this expression even though we have no idea of what it actually refers to.
- Saul Kripke on Naming
The Frege / Russell view was later criticised by Saul Kripke. Essentially Kripke argued that Frege and Russell did not do enough to explain why proper names are different from descriptions. According to Kripke, proper names are ‘rigid designators’ in that they denote the same object in every possible world. So when we speak of Napoleon, we are referring to the actual Napoleon that existed in our world.
But this is not the case with definite descriptions, as those objects satisfying the description may vary across possible worlds. If we use ‘the first Emperor of the French’ we would think of Napoleon in our actual world. However, in closely related worlds, Napoleon might never have become a military leader of France, so somebody else would have been the first Emperor (or they may have been no Emperor at all). So definite descriptions have a different interpretation to proper names
One response to Kripke is that definite descriptions are rigid designators as well, and should always be restricted to the actual world. Possible worlds should not be considered. So the ‘first Emperor of France’ will always be Napoleon.
Another of Kripke’s objections to Frege and Russell concerns the situation where a definite description is commonly thought to refer to a single person, but the use of the description is incorrect. Kripke uses the following example: ‘the person who first proved the incompleteness of arithmetic’. The commonly held answer to this is ‘Godel’, however what if the real person was somebody unknown called ‘Schmidt’ who happened to have his theory stolen by Godel. In this case, which person is the definite description actually referring to?
Kripke also refers to a similar case where someone uses a definite descriptor correctly, but doesn’t have any knowledge of what the descriptor actually means. Kripke mentions somebody using the name ‘Feynman’ to identify a ‘famous physicist’. Although this person is correct, they may not be aware that the category ‘famous physicist’ is general, and could be used to describe a number of people. This shows that a name and a description are two different concepts. Someone can use the name correctly without using the description correctly. It is uncertain how a descriptive theorist would deal with this.
Another question for a descriptive theorist to consider – according to Kripke – is to decide which descriptions are associated with which names. This is not always so straightforward, as people may have different ideas about different people, especially for people who are still alive. A good current example is Donald Trump, where you would likely receive a wide range of descriptions. The descriptive theorist has no way of evaluating these descriptions and determining which are true, even they directly conflict with each other.