I read this from the perspective that if truthful testimony is the foundation of the legal system, then the definitions that are given are to help determine truthfulness of the testimony.
Truth is not absolute truth, it is the relative truth from the position of the observer. Hence space time is not relevant to testimony (it would be relevant to “objective” data such as where were the skid marks from the accident). I think “in front” of and “in back” of should be included as another dimension as it is relevant to perception (see things in front of you); bodily organization (support and structure in back vs execution in front); movement (generally forward) and position relative to others (you usually like both your friends and enemies in front of you).
I like the definition of dimensions as being organized as the consistent relationship between objects (causation). This is how fields of study should be organized, but I have never experienced anyone explain it that way in my education. Commensurable/incommensurable defines where a dimension begins and ends. This places limits on a person claiming expertise, as they have to explain what rules they are going by and what objects have relationships that are and are not explained by those rules.
My understanding is that intelligence is largely the ability to predict future events from exact sequences of past actions. This is the reason narrative is essential in legal procedures (and the reason narrative is so fragmented in deconstructionist productions. This also mirrors how humans construct reality.
The definitions are provocative and I can see how they might have profound implications in attempting to constructing a universal language for approaching a consensus on truth.
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