Circularity in Semantics, the Fifth Problem of Compositionality.
In our previous discussion, we explored the
principle of compositionality in semantics and identified four major problems
it faces: the difference between sentence and speaker meaning, the challenge of
contextualized meaning, the knowledge problem (linguistic vs. world knowledge),
and individual differences in word meaning. However, there is a fifth and
perhaps most significant problem: the problem of circularity.
What Is the Problem of Circularity?
Let’s break it down with a simple example.
Take the word 'coffee.' Previously, we saw that people have different ideas
about what coffee is—hot, black, and bitter for some; creamy, cold, and sweet
for others. But let’s imagine, for the sake of argument, that everyone in the
world agrees on a single definition: 'Coffee is a hot drink from beans grown in
Colombia that is black in color and bitter in taste.'
Now, suppose we want to teach this definition to a robot. We program the robot
with this definition, but the robot then asks: What does 'hot' mean? What does
'drink' mean? What does 'from beans' mean? What does 'black' mean? What does
'Colombia' mean? What does 'bitter' mean? What does 'taste' mean?
To answer, we provide dictionary definitions for each of these words. But each
of those definitions uses more words, which themselves need to be defined. This
process never ends—we are stuck in a circular loop where every word is defined
by other words.
This is the problem of circularity: Defining words with other words leads to an
endless cycle of definitions, making it impossible to reach a final,
foundational meaning.
Is There a Solution? The Role of Meta-Language
How can we escape this cycle? One proposed
solution is to define words not with other words, but with something entirely
different—such as codes or numbers. For example, we could assign the word
'coffee' a unique code, and 'gold' another code. This way, each word has a
distinct, unambiguous meaning that doesn’t rely on further verbal definitions.
This approach introduces the concept of a meta-language:
- A meta-language is a system (like code, numbers, or algorithms) used to
describe or define another language.
- It is free from individual interpretation and variable meaning.
- It provides a foundation for meaning that doesn’t rely on the same language
it is trying to explain.
Recap: The Five Problems of Compositionality
To summarize, the principle of
compositionality was introduced to explain the productivity of language—how we
can create and understand an infinite number of sentences. However, it faces
five major problems:
1. Sentence meaning vs. speaker meaning
2. Contextualized meaning
3. The knowledge problem (linguistic vs. world knowledge)
4. Individual differences
5. Circularity (the endless loop of word definitions)
The solution to the problem of circularity is to use a meta-language, such as
codes or numbers, to define meanings in a way that avoids the pitfalls of
self-reference.
Conclusion
The principle of compositionality is a
powerful idea in semantics, but it is not without its challenges. Understanding
these problems—and the possible solutions—brings us closer to unraveling the
complexities of meaning in language.
Reference:
SEMANTICS-5: Principle of Compositionality + Why We Need a Metalanguage. (n.d.). [Video]. YouTube. https://www.youtube.com/watch?v=bZ2uXzGeJiU