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How does Frege attempt to solve the puzzles of reference

Updated on July 13, 2012

How does Frege propose to solve the puzzles of reference and how reliable is his theory?

Both Frege and Russell agree that it is the role of the speakers’ beliefs which determine the semantics of names. However, they do not agree on most other points. Each attempt to offer theories of semantics and references which do not fall into the problems encountered by the referential theory of meaning. Frege attempts this with the application of ‘sense’, a means through which people are able to understand sentences without knowing the referent. Russell though claims that sense is unnecessary, instead it should be that singular terms should be understood as merely definite descriptions which describe rather than offer a referent. Russell’s theory was an attempt to overcome the necessity of sense in Frege’s. Whether Russell manages to offer a theory which surpasses Frege’s is often questioned. However, both seem to improve upon the referential theory of meaning.

There are four puzzles of reference which illustrate the problems encountered by the referential theory of meaning which claims that the only thing names contribute to a sentences meaning is it’s referent. However, there are glaringly obvious flaws with this idea put forward via semantic puzzles. The first puzzle is that of the apparent reference to non-existents which challenges the claim that the meaning of a name is its referent. The puzzle questions how references to, and claims about, things which do not in fact have physical manifestation can still be objectively understood. Claims about Santa Clause for example; one can claim that Santa owns reindeer and the reference and statement can be understood, yet Santa does not exist so how can a non-existent thing own anything. The problems lie in the logical propositions which state:

‘K1 (1) is meaningful (significant, not meaningless).
K2 (1) is a subject-predicate sentence.
K3 A meaningful subject-predicate sentence is meaningful (only) in virtue of its picking out some individual thing and ascribing some property to that thing.
K4 (1)’s subject term fails to pick out or denote anything that exists.
K5 If (1) is meaningful only in virtue of picking out a thing and ascribing a property to that thing (K1, K2, K3), and if (1)’s subject term fails to pick out anything that exists (K4), then either (1) is not meaningful after all (contrary to K1) or (1) picks out a thing that does not exist. But:
K6 There is no such thing as a ‘non-existent thing’’ (Lycan 2000: 13-14)

Which would lead to the conclusion that logically these statements referring to non-existents cannot be true. However, if statements such as these are commonly understood to have meaning then it must be that names cannot merely make reference to existing objects, they must be able to refer to the fictional. Sets of beliefs and a conceptual understanding of Santa exist in peoples minds to the extent that people would argue some statements about Santa could be true or false e.g. 'Santa wears blue’ would be considered false by many while ‘Santa wears red’ would be considered a true statement about Santa. However, some claim that the sentence must be meaningless as it is unclear what the sentence refers to, despite it’s seeming meaningful

Similarly, the problem of negative existentials also encounters the issues raised when referencing non-existent things. Sentences which claim the present non-existence of things which presently do not exist seem obviously meaningful and true. For example, the statement ‘the present King of France does not exist’ seems to have meaning as people would understand the statement and would consider it to have truth value given that there is no King of France. The individual references of a King and of France can be understood separately but as a whole the statement apparently has no meaning. This is because the claim that meaning only exists given an existent referent opposes the common sense view of these type of statements. If true then these sentences would have no referent to make a claim about, even if the claim is the referents non-existence itself. Furthermore, for the sentence to be about the current example of such a thing the thing must not only have existed at some point, it must exist at the moment of the statement. Despite this these sentences are understood and do seem to have meaning and truth value in common sense understandings.

Frege’s puzzle about identity considers identity statements containing two singular terms which identify the same referent. These statements simply attempt to claim that one is identical to the other. This type of statement need not be as trivial as it seems, they can be informative. For example ‘Saul Hudson is Slash’ is a true example of this type of statement, yet not everybody would have been aware of this. Being capable of teaching something new to the reader would mean this type of statement is capable of contributing meaning beyond the single reference it makes.

Failure of Substitutivity also relates to the function of a singular term to identify a particular thing. This would lead to the expectation that when two singular terms denote the same referent, that it would be possible to substitute for one another in any given sentence without changing the truth vale of that sentence. This though does encounter problems, consider ‘Lois Lane believes that Superman can fly’. This would, in the fictional comic, be a true statement. Substitute Superman for his alter-ego Clark Kent and you have ‘Lois Lane believes that Clark Kent can fly’. This, however, would be considered an obviously false statement by any avid comic book reader. It therefore seems that singular terms must have further semantic properties beyond that of having a reference. In order to solve these puzzles this further property must be found.

Frege attempts to offer a solution to the issue of singular terms denoting more than just a referent. Initially, Frege suggests predicates are concepts acting to place objects into their truth values. This lead to names and predicates both having semantic value enabling them to influence a sentences truth value. So the whole sentence would count towards truth value, rather than just singular terms. Frege also proposes that names have both a reference and a sense. This introduced the thesis ‘it is possible to know the sense of an expression without knowing the semantic value’ (Miller 1998: 28). Therefore, the sense is what the listener understands from an expression, whether they know the reference or not. The accounts for people being able to understand a sentence regardless of it’s truth value, or their knowledge of it’s truth value.

In the case of Frege’s puzzle, the problem lies in sentences containing co-referential’s seeming to offer information despite their having the same referent. Frege claims that, customarily, these would indeed be co-referential statements. However, in belief contexts they refer to their sense; to grasp the meaning of a sentence one must understand it’s constituents, so to know the sense of a sentences it is required to know the sense of its constituents. So, in the case of the sentence ‘Saul Hudson is Slash’ it is necessary to understand the senses of both ‘Saul Hudson’ and ‘Slash’. But under Frege’s idea of sense it is possible to understand the sense of each name without knowledge of the referent. Therefore, it is possible to understand the sense of ‘Saul Hudson is Slash’ without knowing it’s truth value. The idea of sense also offers an explanation as to how people can understand sentences without knowledge of it’s truth value, as one can grasp its sense and thus understanding the meaning without knowing whether it is factual or not. This also explains why these types of sentences can be informative as the two singular terms do not in fact contain only the same information or referent, each has it’s own sense which allows for peoples varying understandings of each.

Frege’s theory can also account for the failure of substitutivity, allowing for different names with the same referent to the different senses. The intention is to assert that names with the same referent such as ‘Clark Kent’ and ‘Superman’ can in fact fail to be co-referential in the context of peoples beliefs. This is despite them both usually, outside of beliefs, referring to the same individual. Thus, ‘Superman’ does not refer to the referent, but rather to the senses of the name; ‘in belief context a name refers to its customary sense…[termed] its indirect reference’ (Miller 1998: 32). The indirect reference of a name can therefore differ greatly from the referent, allowing for peoples varying beliefs regarding the same thing when referenced through different singular terms. Therefore, although substituting one name for another can alter the truth value, in cases where the sense is the same for each (as opposed to just the referent) the truth value will remain the same.

Russell raises objections to Frege’s use of sense to solve these puzzles. In Russell’s opinion, the use of sense is unnecessary, an obsolete additional explanation. For Russell definite descriptions only describe, they don’t refer. Russell’s theory of definite descriptions focuses on the definition of ‘the’ in the context of definite descriptions. Frege held definite descriptions to be proper names as they hold objects as their semantic value. Thus, Frege’s theory defines the semantic value of a definite description as the object it stands for. The affect this has on the truth-value of a sentence is reliant on it’s standing for a certain object. In the case of the definite description ‘the King of France’, as this has no object in reality it must follow that it has no semantic value. This would lead to the idea that it cannot have make a contribution to the truth-value of the sentence, thus ‘the King of France’ has no truth-value, neither true nor false. Although the king of France does not exist in reality, it does have a conceptual existence as people can understand its meaning and grasp the concept even without a real life figure to place this idea upon. Russell however approaches the problem in an extremely different way; he claims that definite descriptions are not in fact proper names. In claiming this it would seem that, if not proper names, definite descriptions would not be given their semantic values by the objects they stand for, if there are any objects they stand for in reality. Russell’s criticism of Frege’s definition of definite descriptions argues that Frege does not give definite descriptions the correct form of semantic value. Definite descriptions being proper names in Frege’s view mean that their semantic values lie in objects. Russell though maintains that definite descriptions are in fact functional expressions which do not have objects as their semantic values. Russell therefore avoids the problem of apparent reference to non-existents by ‘treating ordinary names as disguised definite descriptions’ (Miller 1998: 62). For Russell the only genuine proper names can be ‘this’ and ‘that’ and only when they are not referring to physical objects. Proper names are only those which cannot succumb to the problem of apparent reference to non-existent. It therefore seems the only proper names are those which refer to sense-data when in the present situation. According to Russell, statements such as ‘the founder of Motown is 82 years old’ is in actuality a generalisation being equivalent to ‘There is at least and at most one thing that founded Motown, and he is 82 years old’. For apparent reference to non-existents this would mean statements such as ‘the present King of France is bald’ to be understood as ‘there is at least and at most one thing that presently kings France, and it is bald’. In the case of negative existential statements such as ‘the present King of France does not exist’, this can lead to the statement ‘There is at least and at most one thing that presently kings France, and it does not exist’. Further, this can be translated into ‘it is not the case that: there is at least and at most one thing that presently kings France’. So it seems that Russell too is able to deal with the problems associated with the puzzles.

However, Russell’s theory has problems put forward by Strawson. In Russell’s theory the sentence ‘the King of France is bald’ is false because the king in question does not exist. Strawson would argue that the speaker has produced an ‘ostensibly referring expression that has misfired: the speaker has simply failed to refer to anything’ (Lycan 2000: 22). In this argument, it is the sentence has simply failed in its attempt to make a complete statement; ‘the King of France is bald’ is not false in the way that ‘the Queen of England is bald’. Strawson claims that what can be true or false are ‘statements made when speakers succeed at saying something’ as not all meaningful sentences make statements. Strawson further criticises Russell’s theory by claiming that the statements ‘the King of France is bald’ asserts that there is ‘one and only one king of France’ (Lycan 2000: 23). However, although the speaker presupposes there being one king of France, it is not something that is being asserted by the statement. This criticism faces problems as Russell did not in fact make any claims regarding assertions. Strawson also highlights that descriptions are most often related to the context. In Russell’s theory the statement ‘the table is covered with books’ can be understood as ‘at least one thing is a table and at most one thing is a table and anything that is a table is covered with books’ which can entail that ‘there is at most one table, in the entire universe’ (Lycan 2000: 24). There are many options for Russell in overcoming this problem but either way the problem of how quantifiers get restricted when in context remains. This though is a problem which exists external to Russell’s theory so does not pose particular problems for him. Donnellan though simply claimed that, in some cases, definite descriptions are used merely as names, simply referring an individual. In these cases, Russell’s theory fails to explain what is being said.

In conclusion, Frege’s theory does manage to account for each of the four problems which were encountered by the referential theory of meaning. The theory of sense also manages to be easily translated into common sense and typical understanding of language. However, the introduction of sense does seem an unnecessary, conceptual idea for the seemingly simple idea of reference. Russell’s theory attempts to overcome the need for ‘sense’ and instead uses the idea that singular terms are definite descriptions. This theory again manages to overcome the four puzzles of reference. However, Russell’s theory also falls down to criticism. It thus seems that, though both theories are understandable and applicable in some senses, another theory of reference is perhaps what is needed to account for these problems in a simple and less criticised manner.


Lycan, W. 2000. Philosophy of Language: a contemporary introduction. London: Routledge.

Miller, A. 1998. Philosophy of Language. Montreal: McGill-Queen’s University Press.


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    • conradofontanilla profile image


      5 years ago from Philippines


      I enjoyed reading your piece. However, I wish you used a book of Russell as reference. In one of his books, I read that Russell said, assert existence on a definite description. Not on a name. Analysis of a name results in a contradiction.


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