Deeper, more profound answers require one to appeal to Linguistics. So I Googled "semantics of english prepositions" which revealed many references such as the following:
Applying Cognitive Linguistics to Learning the Semantics of
An Experimental Investigation by Andrea Tyler, Charles Mueller, Vu Ho.
At 26 pages, it is too long to reproduce here, but the following quote from p 2 of 26 (Introduction) should already convince you of and to evidence its helpfulness.
Language teachers and researchers have long recognized that the acquisition
of prepositions poses major challenges for second language learners (e.g., Celce-
Murcia and Larsen-Freeman, 1999). One reason for this is that the semantics of
prepositions are notoriously difficult to characterize. For instance, on first inspection,
the distinction between prepositions such as
is quite unclear. On one
hand, the sentence:
The picture is over the mantle, is a near paraphrase of:
The picture is
above the mantle.
On the other hand, the sentence:
Mary hung her jacket over the back
of the chair
is interpreted as meaning something quite different than:
Mary hung her
jacket above the back of the chair.
Additionally, prepositions tend to develop a complex
set of extended meanings, for instance,
has developed at least 16 meanings,
many of which do not appear to be systematically related. Although linguists have
long been aware that prepositions develop complex polysemy networks, the meaning
networks surrounding spatial markers (and the systematic processes of meaning
extension from which they result) have only become the foci of linguistic inquiry
in the last 20 years. Even the best descriptive grammars and dictionaries present
the multiple meanings of spatial language as largely arbitrary. Traditional accounts
have represented the semantics of English prepositions as arbitrary (Bloomfield, 1933;
Frank, 1972; Chomsky, 1995). Consequently, pedagogical treatments have often
suggested memorization as the best strategy. Studies show that accurate use of spatial
language is one of the last elements learned and many highly proficient L2 speakers
never attain native speaker-like use (e.g.,
Lam, 2009). Indeed, Lam found that L2
Spanish learners made virtually no gains in their mastery of the prepositions
over the course of four years of college Spanish.
Cognitive Linguistics (CL) offers an alternative perspective, suggesting that
the many distinct meanings associated with a particular preposition are related in systematic, principled ways (e.g., Brugman, 1988; Dewell, 1994; Dirven, 1993; Lakoff,
1987; Linder, 1982; Hawkins, 1988; Herskovits, 1986, 1988; Tyler and Evans, 2001a,
2003; Vandeloise, 1991, 1994)
Ensure to consult and try the many References on pp 22-26, which includes (on page 25) the following which I plan to read myself:
Tyler, A. & Evans, V. 2003. The Semantics of English Prepositions: Spatial Scenes,
Embodied Meaning and Cognition.
Cambridge: Cambridge University Press.