I was reading Porter's What's is Meaning and ran into this beautiful paragraph which captures many properties of semantics that deal with the problem I ran into in the past.
A language is an infinite collection of phrases, sentences and discourses. This can be easily seen from the fact that any sentence can be made longer by combining it with another sentence - in fact, it is possbile to do this in very many different ways. (...)
Since humans are finite creatures, one of the main tasks of linguistic theory is to understand how their minds can give rise to the inifinity of language. This is one of the main reasons for the linguistic industry known as syntax (the field which studies how words are combined into phrases and sentences), but the infinity of language is equally an issue for semantics. Each of those infinite number of pieces of language has meaning, and the theory of semantics must somehow be able to link each one to the right meaning.
Apart from the issue of infinity, semanticists (like other linguists) also have to consider the fact that language is creative. We are constantly hearing new phrases and sentences, ones we've never heard before, and yet we somehow manage to figure out what they mean. (...)
I first ran into this problem here, which I described as "boiling frogs".
Semanticists seek to bring the infinity and creativity of language within the capacity of human minds by appealing to the principle of compositionality. In its simplest form, the principle says that the meaning of a piece of language is based solely on the meanings of its (linguistically relevant) parts, and the way they are put together.
I first ran into this observation here, which I described as "layering".
With the principle of compositionality, the infinity and creativity of language are comprehensible, since it means that we only have to know a finite number of basic things (the meanings of the smallest pieces of language and the methods of combining them), and this gives us enough knowledge to associate the right meaning with every bigger piece of language.
I first ran into the same insight here, which I described as "marginal costs".
I clearly empathize with "compositionality" coming from a compilers / programming languages background: programs are equally "infinite" in what they do and are expressed within a handful of syntactical and semantic constructs.
More to come, but I'm getting increasingly excited to learn that (maybe) linguistics and philosophy is the scientific area that is investigating the problems I ran into in the past.
It is such a relief to find somewhere you feel you "belong".