I am puzzled by this. I do not see whether transitivity is a linguistic concept or not. In math they say a relation 'R' is transitive when xRy and yRz imply xRz. But that is bit circular because the definition of "imply" papers over the same details one wants to understand. Giving a common name to different (seeming) details is not a substitute for understanding what, if anything, they have in common.
Some types of transitive relation:
- Containment
- Dependency
- Becoming
- Any kind of ordering
These are not just "manner of speaking" different. Do they share something? Is it linguistic?
It does not seem mathematically sound to pretend they are the same, without understanding why. Also one can see a possible fallacy, where an argument shifts from 'containment' to 'dependency' or 'transformation'; having proved something for one but not for the other.
Update: Maybe (1) is an example of (2).
Update: Suppose reaching y from x along a directed path defines xRy. A hypothesis is that 'R' is transitive iff all other paths from x to y are homotopic to this one.
Update: I did not say it clearly: 'imply' is a transitive relation, so using it to define transitive relation is circular.
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