Me:

If I tell someone to shoot to the goalpost and back, he may either sprint to the goalpost and return, or take a gun and shoot the goalpost and report back to me. But he will not try to fly to the moon because that's how he interpreted my statement. This points at the fact that there is a certain semantic ambiguity to words, however, they are also confined to a certain distance. How can one quantitatively measure such a semantic distance? And if semantic distance is not the right word for this because some other word exists, what is it?

ChatGPT said:

You're touching on an interesting area of semantics and pragmatics! The concept you're describing relates to semantic ambiguity and the range of meanings a phrase can have depending on context.

To quantitatively measure this "semantic distance," researchers often use techniques from computational linguistics, such as:

Word Embeddings: Models like Word2Vec or GloVe convert words into vectors in a high-dimensional space. The distance between these vectors can represent the semantic similarity or difference.

Contextual Embeddings: More advanced models, like BERT, take context into account, allowing for more nuanced interpretations of phrases based on their usage in sentences.

Semantic Similarity Metrics: Cosine similarity or Euclidean distance can be used on these vector representations to quantify how closely related different phrases or words are.

As for terminology, "semantic ambiguity" refers to situations where a phrase has multiple interpretations. You might also consider "semantic range" or "polysemy" when discussing the breadth of meanings a word or phrase can have in different contexts. The term "pragmatics" refers to how context influences meaning, which could also be relevant in understanding how instructions like "shoot to the goalpost and back" can lead to different interpretations.

So, while "semantic distance" captures the idea, exploring it through models and metrics related to semantic similarity and context would provide a clearer quantitative framework!

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