In the legal and logical maxim Contra principia negantem non est disputandum, what exactly does principia mean?
In English, the word principle means an abstract proposition, or something deep in the nature of things, which is the source of more-concrete or surface-level conclusions or consequences. For example, when parties agree in principle, they make an agreement that omits details expected to be worked out later; the principle of relativity in physics means that the reference point for a coordinate system shouldn't have any bearing on the substance of a physical law; judges in common law are said to extract a principle from a precedent case that implies a conclusion for the present case; etc.
I wonder, though, if the Latin principium in the maxim is broader, maybe even having the same meaning as the the English word premise, which carries no implication of abstractness. Another possibility is foundation, which is usually understood in this kind of context in English as referring to abstract principles but can also refer to concrete facts, as in “This accusation has no foundation in evidence.”
Here are two examples of usage where principium could be interpreted as designating a proposition by its role as starting point for reasoning, without implying that it must be abstract, though neither case is clear:
Schopenhauer invokes the maxim to summarize this: “In every disputation or argument on any subject we must agree about something; and by this, as a principle, we must be willing to judge the matter in question.”
Lenin criticizes Struve's invocation of the maxim as an attempt to treat the “principle” that private property drives economic progress as a raw historical fact. Lenin counters, “that depends on how these principia are formulated.” His point seems to be that Struve's “principle” can in fact be fruitfully disputed, by appeal to the common ground of genuinely concrete historical fact—another kind of principium.
The earliest invocation of the maxim that I'm aware of is by Duns Scotus, which I think is clearly limited to abstract principles:
Si autem hic discursus non sit convincens, multa principia revocantur in dubium, quæ supponitur a Philosophis; contra autem negantem principia communiter recepta, non est disputandum.
By the way, I got interested in this several years ago, before I started studying Latin seriously, when I worked a little on the Wikipedia page about this maxim. I wondered if in translating principia as principles, we might have been seduced by “false friends”. I discussed it with Wareh, the editor who did most of the work on the page, here and here. He persuaded me that principles seems to be the accepted translation. It’s not Wikipedia's place to provide an original translation if a standard one already exists. Here on StackExchange, of course, we can go a little further and even put two and two together if someone can find some relevant historical usage.
Wareh suggested, perhaps most wisely of all, that the meaning of principia in this context is vague, and that this has given the maxim vitality. If there is specific evidence for that, I'd be especially interested in hearing it.