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jobermark: "there are definitely different kinds of definitions" -- That's certainly addressing the final point of my OP: +1. "1. As compressive notation: [...] the product of force and distance, just so we can refer to it efficiently." -- That's pretty much my perspective. However: in "sufficiently complicated contexts" there may be several overtly/formally distinct "definientia" which turn out (with effort by "practitioners") to be equivalent; thus correctly all being compressed/denoted as the same "definiendum term".
– user12262
Commented Dec 15, 2014 at 19:18
jobermark: "defining a new species of bird, [...] I can look at my clade diagram and see where the overlaps with other species are ruled out. But all of that on the chart is data" -- It's evaluated observational data: measured "trait" values. Which requires some undelying, stable, applicable definition for "how to". "So anything you say about all definitions must apply to all of them, or you need to go scold the entire field of [...]" -- As I tried to say in the OP: foremost I'd scold Wikipedia; aiming to improve it.
– user12262
Commented Dec 15, 2014 at 19:19
Did you read "Logical positivists like to imagine that all definitions really take the first form, at root, in some indirect way, and that all of language goes back to symbolic logic. But they are wrong: their enterprise fell apart under the weight of formal proof and observational data long ago. Even to the degree mathematics can be reduced to symbolic logic, the axioms of set theory are not strictly unique and therefore purely logical." Don't scold Wikipedia, because it is right. You, on the other hand, are subscribing to a philosophy of definition that fails.
– user9166
Commented Dec 15, 2014 at 19:49
Since not all definition really takes the form of compressive notation, but it is instead part of a massive feedback loop, just like all interpretation, these two other forms of definition are real and distinct from that. When you make a definition, instead of just relying on the (unattainable) precision of language, you must prove it will obey substitution criteria to an acceptable degree. That proof can be formal or experimental.
– user9166
Commented Dec 15, 2014 at 19:54
Yes, all experimental evidence is partially circular, and incorporates prior evaluations, yet it is used as proof. And yes, there is an underlying definition of "species" that allows one to order the separate definition of each species. But those definitions are both held up by observation, not mere language conventions.
– user9166
Commented Dec 15, 2014 at 20:06

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