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Informativeness of ‘Hesperus = Phosphorus’ as a Problem for the Referential Approach to Meaning

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Explain why the informativeness of ‘Hesperus = Phosphorus’ is a problem for the referential approach to meaning. Critically compare Frege’s response to this problem with Russell’s.

The referential approach to meaning is the idea that the meaning of every expression is its referent. A referent is an object referred to by the utterance of a word. For example, “the capital of England” refers to London. There are a number of issues one can highlight with this approach, and due to the limitations that Frege’s response entails, Russell’s solution should be more accepted on the basis that it is more logically sound. The question of how we understand meaning from pro-nouns and adjectives also demonstrates that it’s impossible to draw upon meaning from reference alone.

The ‘Hesperus=Phosphorus’ problem is a challenge for the referential approach because it illustrates that when it comes to identity statements, there can be two seemingly separate things that have the same referent. The planet Venus appears in the evening sky in the western hemisphere, and in the morning in the East. The Greeks recognized the planet as ‘Hesperus’ (evening star), and ‘Phosphorus’ (morning star). If meaning is determined by referent, then ‘Hesperus=Phosphorus’ would imply that both terms have the exact same meaning. This is because the principle of compositionality states that the meaning of a sentence is the sum of the meaning of its parts, making the sentences “the evening star is a planet” and “the morning star is a planet” the exact same beliefs, despite us knowing that there is some difference in cognitive value. We can know that ‘x=x’ a priori, but further information is needed to know that ‘x=y’. If it were the case that the meaning of a word is its referent alone, then any identity statement would not be able to tell us anything new. Most people would agree that identity statements are in fact informative, which is why the issue challenges the referential approach to meaning.

The principle of identity substitution means that in an identity statement, it would follow that both terms (x=y) are identical and can co-refer. The principle only works in some contexts, but not in others. It is valid to say that the morning star is a planet and that the morning star is the evening star, to conclude that the evening star is a planet. However, one can also form identity substitutions to arrive at a conclusion that does not carry the same meaning as the initial intention. If one were to claim they wanted to be Batman for example, and given that Batman is actually Bruce Wayne, the conclusion according to identity substitution is that they want to be Bruce Wayne. This clearly does not have the same cognitive meaning as what that person initially meant when they said that they wanted to be Batman.

Frege's response was the proposal that two things can have the same referent, but the difference in meaning is provided by the sense of a word. The sense is provided by a common understanding between everyone who is “sufficiently familiar with the language” (Frege,1892). It follows, therefore, that the informative status of an expression depends on the sense of the words used. Different expressions can only have differing senses only if a rational being that fully understands them could doubt that they fully refer. ‘Hesperus=Phosphurus’ is therefore informative if Hesperus and Phosphorus have different senses, despite having the same referent. The sense of an expression is not an idea according to Frege, but rather the mode of presentation, which is a way of thinking about the object, and a condition for determining to mean. This means that pairs of co-referring terms such as Hesperus and Phosphorus may differ in sense. Therefore, the phrases “the morning star is a planet” and “the evening star is a planet” don’t have to express the same thought, even if the morning star is the evening star. Additionally, ‘the morning star is equal to the morning star’ and ‘the morning star is equal to the evening star’ do not express the same thought because propositions are the objects of propositional attitudes.

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Frege’s initial response to the problem of identity agreed that expressions in identity statements do co-refer. His principle of substitutivity for the problem in question would be as follows. Because Hesperus is a planet, and Venus is a planet, it follows that the statement ‘Venus is a planet’ has the same truth value as ‘Hesperus is a planet’. However, the issue of ‘Hesperus=Phosphorus’ still stands, as co-referring expressions do not have equal meanings. If a Greek understood ‘Hesperus to be visible’ when Hesperus is visible but does not know that Hesperus is visible whenever phosphorus is visible, then despite the sentences only differing by replacing co-referring expressions, they do not mean the same thing. Frege’s understanding of ‘thought’ is also something that differs from a modern understanding of the cognitive process, this is because it portrays an obscure picture of thoughts as not being mental objects, contrary to the scientific understanding of cognition.

The issue with Frege’s principle of substitutivity is that co-referring terms can lead to different truth values as well as meanings. Consider a man called Joe, who believes Hesperus is a planet. He also believes that Venus is a planet. If he does not know that Venus is Hesperus, it means that one of his beliefs is false while the other is true (if he claims to see the planet), despite the two terms co-referring.

Frege’s response to this issue is that the truth value does not depend on what is referred to by a word. The expression is not about planets, as Joe could believe that Hesperus is a planet even if they don’t co-refer. The belief ‘that Hespserus is a planet’ is a thought that refers to the expression ‘Hesperus is a planet’. This makes the true value of the content irrelevant because we can still derive meaning from the contextual sense of the belief and its referent. Frege’s response to the argument against substitutivity is limited because it denies the importance of true value as a context to meaning.

Whilst Russel would agree with Frege that co-referring expressions do not need the same truth value, he rejects Frege’s distinction between sense and reference. In contrast to Frege’s understanding of sense being indicated by ‘modes of presentation’, Russel believes that one can talk about objects directly. His theory of definite descriptions is an alternative approach to the identity problem that illustrates replacing co-referring expressions can turn uninformative statements into informative ones. Replacing Hesperus with Phosphorus alters the truth value of the belief that ‘Hesperus is the morning star, and phosphorus is the evening star’. Names are usually descriptions according to Russel, and because we can determine truth-value via description, ‘Hesperus=Phosphorus’ can be informative because of the description of each name. The thought we associate with the phrase “Hesperus=Phosphorus” is “The star in the morning sky is the same star as the star in the evening sky”. The phrase ‘the x’ means that there is only one x, making it a definite description. Other predicates such as ‘an x’ or ‘some x’ are therefore indefinite.

To avoid the identity issue, Russel proposed that names are not referents, but rather just a thought of a definite description. This is what enables a statement to have meaning and truth value. The expression: “The Loch Ness Monster” can be treated as a singular term, and is a definite description. In contrast, Frege’s theory can establish meaning but fails to incorporate any truth value because the expression “Hesperus does not exist” would be neither true nor false. Because Russell’s descriptive approach allows for truth value, it is far more comprehensive than Frege’s view which implies that the mind uses a reference and sense for each word in the expression to gain meaning. As humans, we empirically know that this is not the thought process that allows us to understand the meaning of a name.

In all, whilst both Frege and Russell are both advocators for the referential theory of meaning, they differ in their approach towards the problem of identity that comes with the informative nature of “Hesperus=Phosphorus”. Whilst Russel’s argument maintains that referents are mediated by description, Frege noted that referents are determined by both context and modes of presentation, thus adding two levels of meaning. Frege’s added flexibility by these two levels of meaning is outweighed by the logical consistency of Russell’s argument that the co-referring names of ‘Hesperus’ and ‘Phosphorus’ are related to definite descriptions. Whilst this may be so, both approaches have the significant weakness that they impose a definition of meaning that cannot satisfy every issue given the relativistic nature of language. In light of this, it makes sense to advocate Wittgenstein’s view of ‘language games’, in that meaning is determined by an understanding of context, or use within its relative community.


  1. G. Frege: On Sense and Reference (1892); p37-46 found online at
  2. Kemp, Garry (2013) “What is this thing called Philosophy of Language” Ch 1,2,3.
  3. Schwarz, Wolfgang “Mind, Matter Language; Lectures 6, 7:Intensional Semantics; Russell on descriptions” (Sept-Oct 2019)
  4. P.F. Strawson: On Referring (1950). Mind 59 (235): 322-326
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Informativeness of ‘Hesperus = Phosphorus’ as a Problem for the Referential Approach to Meaning. (2023, April 21). Edubirdie. Retrieved March 3, 2024, from
“Informativeness of ‘Hesperus = Phosphorus’ as a Problem for the Referential Approach to Meaning.” Edubirdie, 21 Apr. 2023,
Informativeness of ‘Hesperus = Phosphorus’ as a Problem for the Referential Approach to Meaning. [online]. Available at: <> [Accessed 3 Mar. 2024].
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