Is it orthographically ok to capitalize first letters of important phrases? [duplicate]

Question

Say I am writing an article on something like the Riemann integral or morphogenesis. I have two questions regarding capitalization.

1. Is it allowed to capitalize the first letter of a composite name of importance. E.g.

   "The importance of the Lebesgue Integral cannot be overstated."

I feel like the 'integral' is as much part of the name of the thing as the mathematician Lebesgue it was named after and I would like to emphasise that. And speaking of emphasis:

2. Can I capitalize the first letter of a word that is the primary subject of a paragraph? Like e.g.

   "..trans-membrane signaling during Morphogenesis.."

It might be because I am german and we capitalize the first letter of nouns in general but I feel like this makes the word more significant and makes the writing more understandable in this way. (Ah, we are talking primarily about morphogenesis and not primarily about membranes.)

Answer 1

What the question is driving at is that something that is ordinarily a common noun may be treated as a proper name (or a part of a proper name) within a particular context. When it is, it is capitalised under the general rule that proper names are capitalised.

In other words, there is no special rule of English language about capitalising important words, but there may be special conventions within particular fields about what terms are to be treated as proper names. Because they are conventions, they depend on general acceptance within the field, and an individual author is taking a risk in trying to change the convention or create a new convention of this sort. If everybody who writes about the Euler’s constant leaves c lowercase, it is unwise for a particular author to start capitalising it; but if the convention had been established to write it as Euler’s Constant, no rule of English language would have been violated.

Answer 2

Grammar

It is ‘grammatically OK’ because capitalization of words is not grammar.

This is clear from the Wikipedia entry for Grammar:

“In linguistics, the grammar of a natural language is its set of structural constraints on speakers‘ or writers’ composition of clauses, phrases, and words.”.

Grammar is, and was, a characteristic of the spoken language, irrespective of whether the speakers are, or were, able to write. It developed before literacy.

Spelling, punctuation and capitalization are important for transmitting what is said, but they are not part of the structure of the language and are not grammar (even in German).

Orthography

Now that the question has become one of orthography, then it seems either to become one of usage — how rare is such usage — or of how people will react if the poster diverges from accepted usage.

Answers to the former can be obtained by reading published articles in the scientific fields in question. As a biological scientist I would say that you are unlikely to encounter the second example. If I wished to distinguish signalling during morphogenesis from that during some other process I would italicize the word, and I from my experience that is accepted practice. Likewise, I would find it strange to see the word capitalized, and think that a sub-editor (they still exist in some journals — I was savaged by one recently) would remove it.

(But you have no way of knowing that I am right, because this part of my answer is completely subjective — something I normally avoid on SE. I only added it because the question was changed and I’d gone to the bother of answering the original.)