In very general terms, prepositions express different kinds of relations between entities. Consider, for example, a common preposition like on, as in the following example:
(1) The books on the table are cheaper.
Here the preposition serves to relate two entities, a number of books and a table. The relation encoded by the preposition is a spatial one; one entity is located on the top surface of the other. It is easy to come up with other similar examples, where this concrete, spatial relation is encoded by on. A great many abstract uses of prepositions, may, in fact, be traced back to a concrete, spatial relation. Consider the following examples, where the prepositions are all used to encode temporal relations which can be derived from spatial ones):
(2) at 11 o'clock
(Time conceived of as a point; the concrete spatial meaning is found in: at his desk, at the bus stop, etc.)
(3) in the morning
(Time conceived of as an area; the concrete spatial meaning is found in: in the garden, in Japan, etc.)
(4) on Friday
(Time conceived of as a surface; the concrete spatial meaning is found in: on the table, on his head)
Other types of extensions of spatial meaning occur in the following examples:
(5) under the leadership of the professor
(Hierarchical position conceived of as vertical position)
(6) in love
(Emotion conceived of as a container. Note also the phrase fall out of love, with the same metaphorical construal.)
(7) through many different sources
(Instrument/Source conceived of as the traversal of three-dimensional space; the concrete spatial meaning is found in: through the tunnel)
Even though the use/meaning of prepositions can often be explained, it is much more difficult to predict what preposition is used in a given sense. Thus, the fact that we say on the pavement, rather than *in the pavement, whereas both in the street and on the street are possible (with some dialectal variation) cannot be predicted just based on our conception of spatial relations.
Similarly, the fact that in the margin refers to a concrete position on (!) a page, whereas on the margin refers to a metaphorical position in society has no straightforward logical explanation, and certainly cannot be predicted by general rule.
More on why it is difficult to say what prepositions mean (click to expand/contract)
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A Swedish perspective: On the use of prepositions (click to expand/contract)
Prepositions act as heads of prepositional phrases. They typically occur together with noun phrases, which function as complements of the preposition. Thus, the examples above can all be analysed using the following grid:
Noun phrases are by far the most common form of prepositional complement in English. However, prepositional complements may also take other forms.
Form of the complement
writing children's books
why I wrote this book
behind his desk
(a prepositional phrase)
(an adverb phrase)
It should be noted that neither that-clauses nor declarative to-infinitival clauses can function as complements of prepositions in English. Thus the following two examples are ungrammatical:
(1) *You can rely on (that) Mary will not miss the meeting.
(2) *We talked about to go to the Zoo.