The informativeness of ‘Hesperus=Phosphorus’, commonly referred to as the ‘identity problem’, is an issue for the referential approach to meaning, which both Gottlob Frege and Bertrand Russell subscribe to. This essay will outline what the identity problem is, and why it is a problem for the referential approach to meaning. Generally speaking, a theory of reference is a theory that pairs expressions with the contribution those expressions make to the determination of the truth values of sentences in which they occur and when language is used to refer to something in the world. This essay will then outline and critically compare the response of Frege to this problem, with that of Russell. This essay will proceed to argue that Russell’s response to the ‘identity problem’ is more convincing than that of Frege, on the primary grounds that his concept of self causes more problems for his response than it solves. It is worth noting that while Frege had an earlier response to the ‘identity problem’, this essay shall focus on his final response based on ‘sense’ for the purposes of brevity.
The ‘identity problem’ is as follows. Reference theorists do not believe that identity statements are self, however (as Hesperus=Phosphorus reveals) they can often be informative. Hesperus is the evening star, the brightest star seen in the evening sky and later discovered to be the planet venus. Phosphorus is the morning star, the brightest star seen in the morning sky, and also later discovered to be the planet venus. Thus the two are co-referring terms, holding the same meaning. This is important for an ‘identity statement’ to be true, both sides must co-refer. If meaning is indeed a reference, both sides of a true identity statement should have the same meaning. From this, it follows that, when using a referential approach to meaning, the statement Hesperus = Phosphorus should be as uninformative as Hesperus = Hesperus. Yet one can reasonably assume that the first statement can be informative, while the second wholly trivial. To summarise: replacing co-referring expressions can turn uninformative statements into informative statements, as seen in the Hesperus=Phosphorus example. Therefore: meaning must be more than reference, which spells an issue for reference theorists such as Frege and Russell.
Frege concedes the issues posed by the ‘identity problem’, he opts to alter his account of meaning, attempting to accommodate the issue, rather than bite the bullet or argue against the problem. His solution is to introduce greater criteria to his definition of meaning, in order to sidestep the issues posed by the ‘identity problem’. He argues that “a difference can arise only if the difference between the signs provided corresponds to a difference in the mode of presentation of that which is designated”. This ‘mode of presentation’ Frege discusses, is sense. “The regular connection between a sign, its sense, and its referent is of such a kind that to the sign there corresponds a definite sense and to that in turn a definite referent, while to a given referent (an object) there does not belong only a single sense”.
Here Frege posits that while each ‘sign’ has a referent, the connection between the two is its sense. It is important to understand that Frege’s ‘sense’ is different from the use of the word sense in a traditional manner. Frege’s ‘sense’ refers to something objective unlike ideas, which he argues are liable to become oversaturated with feeling thus losing their aspect of objectivity which is crucial for Frege’s definition. To avoid the ‘identity problem’ recurring, Frege stipulates that two expressions may only have a different sense if a rational agent who fully understands them could doubt that they co-refer. Applied to the example of Hesperus and Phosphorus, a rational agent who fully understands them would doubt that they co-refer, hence the two would have a different sense allowing for the identity statement Hesperus = Phosphorus to be informative.
Unlike Frege, Russell doesn't attempt to sidestep the issue, rather he challenges it head-on, offering a solution by means of logical analysis. Russell asks his audience to consider definite descriptions of the form ‘the so and so’ and argues that proper names are merely abbreviations for definite descriptions. For example, the expression ‘the Queen of is having lunch’ would be translated via Russell’s logical analysis to the form ‘there is at least one Queen of, there is at most one Queen of, Anyone who is the Queen of is having lunch’. Russell’s approach translates proper nouns into their longer definite description, which allows him to avoid the ‘identity problem’. Applying his logical analysis to the specific Hesperus=Phosphorus issue would look as follows: the brightest object in the evening sky = the brightest object in the morning sky. While a sentence of the form ‘the brightest object in the evening sky = the brightest object in the evening sky’ (Hesperus = Hesperus) would evidently be trivial and uninformative, one of the forms ‘the brightest object in the evening sky = the brightest object in the morning sky’ would be informative. Thus Russell argues that he has solved the issues with the reference theory of names in regards to the ‘identity problem’.
This essay argues for Russell’s response to the ‘identity problem’ being the more appropriate and ‘better’ due to its merit and the weaknesses of Frege’s response. Frege’s response, where he elects to sidestep the issue, specifically his notion of ‘sense’ moves him into the path of more issues than it solves. Frege appears to assume, or not properly justify, the property of objectivity he attributes to sense. Frege distinguishes between ideas and sense as different types of thought, labeling ideas as laden with emotion and thus subjective. From this, he appears to insinuate that it, therefore, follows that as sense is the other aspect of thought, it must be objective if its counterpart is subjective. This is a fallacy in Frege’s reasoning and an unconvincing argument for the objective nature of sense. Human experience would also indicate that ‘sense’ has subjective qualities to it. Frege categorizes sense as a ‘mode of presentation’, yet considers that if an individual stumbles across an apple for the first time, might the ‘mode of presentation’ he encounters within (setting, ripeness, and the like) affect his sense? Even if one were to refute this argument and accept Frege’s dubious logic by which he argues for the objectivity of sense, this essay argues there is another grave flaw with the application of his notion of sense to the ‘identity problem’.
Frege posits that two expressions may only have a different sense if a rational agent who fully understands them could doubt that they co-refer. However, Frege’s use of the term ‘understands’ seems to mischaracterize the nature of understanding with that of ‘complete knowledge’. For example a geologist or alchemist hundreds of years ago would have a full understanding of gold, as would a chemist in the modern day yet both parties would doubt the two references in the unlikely scenario of them meeting and discussing gold. Frege might retort that evidently one of the two parties does not have a ‘full understanding’ of gold. For people to have a full understanding of the manner Frege stipulates, would be nigh impossible. As science and collective knowledge progress with the march of time, new information is discovered about things in the world that would change our understanding as Frege conceives it. It would also be nigh impossible for humans to have a full understanding of more than a handful of things in the world, so strict and unreasonable is the criteria of Frege.
It is worth considering a major challenge to Russell’s theory, specifically regarding his un-abbreviation of proper names to definite descriptions, Kripke takes issue with this aspect. He argues that due to Russell’s understanding of the use of names, people will run into issues meaning different things by the names used. This essay accepts Kripke’s critique and acknowledges that it poses grave consequences for the logical solution to the ‘identity problem’. However if one utilizes what is referred to as ‘the cluster theory of descriptivism’ a theory argued for by Searle, the challenge Kripke poses to Russell may be resolved. If a proper name is attached to a definite description, the person or thing who satisfies most of these descriptions (akin to a grading system) is the authentic referent. This essay accepts that by using Searle’s cluster theory and applying it to that of Russell, the major challenge posed by Kripke may be avoided.
To conclude, the informativeness of ‘Hesperus = Phosphorus’ poses a serious challenge and problem for the referential theory of meaning. Russell responds to this challenge, by defending his initial position and arguing the issue can be resolved by means of logical analysis. While this opens him to further criticism from Kripke, this essay has shown that using Searle’s cluster theory even may be avoided. On the other hand, Frege, rather than confront the issue, uses his notion of ‘sense’ to avoid it altogether. However, his response to the ‘identity problem’ creates more issues than it solves for his referential approach to meaning. Hence, Frege cannot adequately solve the issues created by his response, while Russell can and does despite confronting the issue without deviating as much from the central tenets of the referential approach to meaning. This essay takes Russell’s response to the ‘identity problem’ to be the superior response of the two.