Topology Fact tweeted today:
‘It’s not so easy to free oneself from the idea that coordinates must have an immediate metrical meaning.’ — Albert Einstein
In searching for that quote I found:
The simple fact is that in general relativity, coordinates are essentially arbitrary systems of markers chosen to distinguish one even from another. This gives us great freedom in how we define coordinates…. The relationship between the coordinate differences separating events and the corresponding intervals of time or distance that would be measured by a specified observer must be worked out using the metric of the spacetime. (Relativity, Gravitation and Cosmology by Robert J. A. Lambourne, page 155)
Let’s re-write the first sentence by Lambourne to read:
The simple fact is that in semantics, terms are essentially arbitrary systems of markers chosen to distinguish one semantic even from another.
Just to make clear that sets of terms have no external metric of semantic distance or closeness that separate them.
And re-write the second sentence to read:
The relationship between the term separating semantics and the corresponding semantic intervals would be measured by a specified observer.
I have omitted some words and added others to emphasize that “semantic intervals” have no metric other than as assigned and observed by some specified observer.
True, the original quote goes on to say: “…using the metric of the spacetime.” But spacetime has a generally accepted metric that has proven itself both accurate and useful since the early 20th century. So far as I know, despite contentions to the contrary, there is no similar metric for semantics.
In particular there is no general semantic metric that obtains across all observers.
Something to bear in mind when semantic distances are being calculated with great “precision” between terms. Most pocket calculators can be fairly precise. But being precise isn’t the same thing as being correct.