On Senses and References

May 5, 2025 | 970 words | 5min read

Paper Title: On Senses and References
Link to Paper: https://en.wikipedia.org/wiki/Sense_and_reference
Date: 1892
Paper Type: Philosophy, Philosophy of language
Short Abstract:
It thematizes a problem in the philosophy of language, where it sometimes seems that we have two terms with different meanings, even though they refer to the same object.

If we consider the two statements \(a = a\) and \(a = b\), the former is a priori true by definition of identity and appears to provide no new information. In contrast, the latter seems to offer new, non-trivial information and is not a priori obvious.

However, if we assume that both statements are true, then by transitivity, \(a = b = a\), and they would ostensibly have the same meaning, that is ’true’. But this leads to a puzzling conclusion: it would suggest that the statement \(a = b\) simply means that the names ‘a’ and ‘b’ refer to the same object—implying no informational gain. This is counterintuitive, as the identity statement \(a = b\) often conveys genuine knowledge, unlike the tautological \(a = a\).

Frege distinguishes between sense (Sinn) and reference (Bedeutung) as two components that together contribute to the meaning of a word. The reference of a word is the actual object it refers to—for example, the word “apple” refers to the physical object, an apple.

The sense, on the other hand, is the mode of presentation of the object. For instance, “apple”, “Apfel”, and “Malus pumila” all refer to the same object (an apple), but they present that object in different ways: the first is the English term, the second the German, and the third the scientific name.

Importantly, sense is not a spatial or physical component. Take the example of Plato. The expressions “teacher of Aristotle”, “author of the Republic”, and “student of Socrates” all refer to the same individual (Plato), but they differ in sense—they present Plato in different ways. These differences are not spatial or physical.

Frege also emphasizes that sense is not merely a subjective mental idea. For him, the purpose of language is communication. If sense were purely subjective—i.e. just what each person associates with a word—then effective communication would be impossible. Language must therefore rely on shared senses, not private mental images.

“With sense we do not mean a private mental image (Vorstellung), because if that were the case, language would become subjective and incapable of supporting communication.”

In modern terms, Frege’s distinction is often explained using the concepts of intension and extension:

• The extension of a term is the set of all objects it applies to (its referents).
• The intension is the concept or criteria by which we determine what falls into that set.

For example, the phrases “creature with a heart” and “creature with a kidney” might refer to the same set of beings (same extension), but their intensions differ—they express different properties.

It’s also important to note that some expressions can have sense without reference. A classic example is “Odysseus”. Even if Odysseus never existed, the name still has a sense—it presents a certain conception or mode of presentation—but lacks a real-world referent. The opposite is not true: we cannot have reference without sense, since the sense is what connects a name or word to its referent.

You can think of sense as the bridge between a linguistic expression and the object it refers to. For instance, with the expression “morning star”, the sense is what links the word to the actual celestial object it designates (Venus). Without this mediating sense, we would be left wondering what actually connects words to the world.

The Principle of Compositionality

One of Frege’s key contributions is the Principle of Compositionality:

The meaning of a sentence is determined by the meanings of its parts and the way they are combined.

For example, to understand the sentence “Hans is German”, it is sufficient to know what “Hans” refers to and what “German” means.

Ordinary vs. Non-Ordinary Language Use

Frege distinguishes between:

• Ordinary language use, where words and sentences refer directly to objects in the world (reference).
• Non-ordinary (or indirect) language use, where we speak about the sense of expressions rather than their referents.

The Principle of Compositionality only applies to ordinary language use. In non-ordinary contexts, substituting terms with the same reference can change the meaning of a sentence.

Examples of Non-Ordinary Language:

• Modal contexts (e.g. necessity and possibility): We cannot always substitute a necessary object with a contingent one, even if they refer to the same thing.
• Indirect speech (e.g. “Hans said ‘Peter was ill’”): Here we refer to the content of a statement, not just its truth conditions.
• Metalinguistic talk (e.g. “The word ‘apple’ has five letters”): We are referring to the word itself, not its referent.

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