I will be writing this answer using 2010 conversational English with a Flesh-Kinkaid grade level no higher than 14. I will be using the definitions of pragmatics and context found in the corresponding Wikipedia article.
Check out this video by Guy Steele. It's exactly what you need to see!
Did I get your interest with that opening paragraph? Do you know what I'm about to say? Do you care that the answer is "there's a pragmatic context present in the communication between scientists?" Even if I didn't, I highly recommend reading the transcript of the video I just linked. It actually does what you describe, so it's pretty much an answer in speech form! I'll put the specifics in a spoiler tag, in case you want to watch it unfold instead.
Guy Steele does not use a multi-syllable word in this presentation unless he has defined it using only single-syllable words and words he has defined. He bootstraps enough to actually explain those rules part way through, and then goes on to explain what he thinks a language should be.
Call me crazy, but I get a grin on my face every time he gets to the point where he can explain himself. That little strange loop gives me such mirth!
A fundamental challenge is that there is not always a noun which satisfies your needs. While one person may be satisfied with knowing that an article is "Christian," another person may believe the header should have mentioned that it was an article from the "Baptist" perspective. Another may think it obligatory to mention that the opinions were based off of Ralph Abernathy Sr.
In science, one might think that this is easier, but there's many fine distinctions between similar theories. Which of them should be mentioned at the start of the article?
The solution is best defined in terms of pragmatics. One of the successful models therein is Jakobson's functions of language.
Your question shows interest in the referential function of language which operates on the context. This blurb of assumptions would frame the assumptions and meanings for the rest of the article. Instead, scientific papers typically assume a context based on the expected reader of the article. If you're reading about environmentalism, you certainly have a sense of what "global warming" is, even if you don't believe it is occurring.
These papers then rely on small cues to adjust the context. I would argue that these are found in the "code" associated with scientific literature. These metalingual rules capture things you say and do not say in a paper. If a writer believes you may not understand what they mean by some word, they will give you clues via this code that they are about to say things differently. One great example of this is "Conclusion." In the conclusion section, you will see authors say things that they would not say anywhere else in the paper because it is accepted that conclusions have a little bit more subjectivity than the data which goes into the conclusion.
Why do they do this? Because, for the intended purpose of scientific papers, this is the best balance that we have come up with. An astronomer does not worry all that much about the planet he calls Saturn being confused with the Saturn from the Electric Universe (which does all sorts of things an astronomer would not associate with planets). This is the realm of scientists, and they define the language.
And the context cannot be completely defined using rigorous axioms. You can do decently, but anyone talking about axoims of science is soon going to have to dig into the axioms of mathematics. Past mathematicians who dabbled into the axioms of mathematics (Godel, Whitehead, etc.) have found that its impossible to do so within the frameworks they considered worthwhile. It's really a best effort.
The interesting question is how one can adapt. In a discussion between a theoretical physicist and a Buddhist, one may need to use more precise words when describing the discoveries of science. In a science classroom, where scientific realism is the lingua franca, you can just say things like "all matter is made up of atoms" and not have to dive into the noodely little assumptions that went into that.
Practically speaking, no field holds themselves to that level of rigor, not even mathematics. (okay, sometimes mathematics. I keep getting brutally corrected when I talk about "set theory" and someone has to point out to me that there are many set theories, not just ZF(C). Usually this happens because I asked a question right at the heart of why set theory comes in so many flavors!) The Buddhists don't. Nor do the Christians, or the Asian scholars, or the Aboriginal teachers.
If I may close with an anecdote, I've been studying Chinese martial arts for several years now. They'll typically have meanings for the Chinese words they use, but they steadfastly refuse to define some words (Yin, Yang, Tao, Wuji being the four that I find most noticeable in this sense). They'll give examples, but no definitions. For many years this infuriated me, because my Western beliefs in math and science always came with clear crisp definitions if I wanted them. So what do I do? I start trying to use my Western words to define the Chinese ones.
So what happens? This forces me to dig deeper into the clear crisp definitions that I rely on. As I dug deeper, what I found was that the Western words I used depended on for their crispness were founded in other words which were much less crisp.
Which brings me back to Guy Steele. I'll spoil a bit of my spoiler -- his presentation starts by assuming the meaning of all monosylabic words is agreed upon. Words like "True" are monosylabic. And if you look into philosophy, you'll find just how much thought has gone into trying to pin down a meaning for "True." And it brings me to a quote I love from Stranger in a Strange Land, from the perspective of a Martian who was never raised in a human society:
Short human words were never like a short Martian word — such as "grok" which forever meant exactly the same thing. Short human words were like trying to lift water with a knife.
And [God] had been a very short word.