One must be careful when looking at previous work which apparently discusses presuppositions of adpositions; this is because aside from their technical sense, presuppose and presupposition have everyday senses which are somewhat different,Footnote 2 and even linguists may sometimes use these words in the latter senses, or they may think that they are using these terms in the standard linguistic senses when they are not. Consider, for example, Feigenbaum’s (2002) paper on prepositions of French and Hebrew, in which these words occur several times, first in relation to the following examples (p. 171), which are given to illustrate the “deletive” meaning of French sans ‘without’:

une maison sans jardin

‘a house without a garden’

une maison avec un jardin

‘a house with a garden’

Feigenbaum (ibid.) says:

Deletion can be defined as the relationship between a positive and a negative referent, where the negative referent presupposes a contradictory relationship with its affirmative counterpart. Thus, statement (1a) presupposes that houses have gardens and can therefore be considered to be antonymic with (1b).

First of all (1a) is not a “statement”, as it is simply a noun phrase. Further, it is not the kind of noun phrase which is frequently mentioned in lists of presupposition triggers (e.g. Levinson 1983:181–184), as it is indefinite; compare the garden behind John’s house (as in The garden behind John’s house is/isn’t large), which presupposes the existence of the garden in question. I think that (1a) involves a conversational implicature rather than a presuppositionFootnote 3: if houses did not commonly have gardens, it would be unnecessarily prolix to speak of a house without a garden, as it would be to order a hamburger without celery, since hamburgers are not generally served with celery. (I myself when ordering hamburgers often ask for them to be served without catsup, which is a sensible thing to do, since, at least in some eating establishments, the default situation is for them to have catsup.)

Consider also the following passage from Svenonius (2007:76):

S-selection is semantic selection, and is usually understood to hold of all the arguments of a head, not just its complements …. In this context I am interested in the s-selection by P for its complement; s-selection frequently surfaces in the form of presuppositions. For example, in presupposes that its complement be a container, and is infelicitous when the complement is not container-like. Being a presupposition, the requirement is preserved under negation (#The cat sat in the mat is odd in the same way as #The cat didn’t sit in the mat). Similarly, among takes a complement which is complex, between takes a complement which consists of two parts, inside takes a complement which has ‘sides,’ and so on

The reference to “constancy under negation” (Levinson 1983:168) shows that Svenonius is using presuppose and presupposition in a technical sense,Footnote 4 or believes that he is, and, more specifically, in a semantic sense (as opposed to a pragmatic sense).Footnote 5

However, the “presuppositions” involved are rather different from the examples usually brought up in discussions of semantic presupposition, e.g. the “King of France” and “stopped smoking” types of examples. Could they, however, fit under a pragmatic view of presupposition, such as that expressed by Stalnaker (1973:447)?

A person’s presuppositions are the propositions whose truth he takes for granted, often unconsciously, in a conversation, an inquiry, or a deliberation. They are the background assumptions that may be used without being spoken - sometimes without being noticed

It seems that they could, but aside from being different from “conventional or semantic” (Beaver and Geurts 2014) presuppositions, they are also rather different from “conversational” (ibid.) presuppositions e.g. “the presupposition that the interlocutor speaks English” (ibid).Footnote 6 One could say that Svenonius’ putative presuppositions of in, etc. are metalinguistic presuppositions (or assumptions), at least as he expresses them, because they have to do with properties of linguistic items (namely what their complements can be),Footnote 7 though of course these properties are connected with properties of the real world. If our notion of presupposition covers these metalinguistic assumptions, then the door is open for various other phenomena to be seen as presuppositions, e.g. c-selection and conventional implicatures.

Magidor (2013:141) has the same general idea as Svenonius;Footnote 8 in order to explain “category mistakes” such as that in (2):

Jill ducked under the theory of relativity. (ibid.:140)

she says, “the infelicity of all these category mistakes can be explained as instance of presupposition failure”; the presupposition in this example is triggered by under. Later (p. 145) she states:

the infelicity of [(2)] can be explained by assuming that ‘x φ-ed under y’ triggers (roughly) the presupposition that y is located in space (or, assuming prepositions are generally of type , the lexical entry for ‘under’ would be ); Since in standard contexts speakers take it for granted that … [the] theory of relativity has no spatial location … and [(2)] suffer[s] from presupposition failure and [is] thus infelicitous.,t>,t>,>

More generally, “Atomic category mistakes are accounted for by the claim that a wide range of expressions (including most verbs, adjectives, adverbs, and prepositions) are presupposition triggers” (ibid.) (Note that she does not refer to Svenonius in this book, indicating that she was unaware that he had put forth a similar idea.) However, Magidor says (p. 1) that “The king of the United States is drinking water” is a different kind of error than the category errors that she cites there (e.g.”John is drinking the theory of relativity”), and this seems odd, because according to her, both involve presupposition failure—are there then different kinds of presupposition or different kinds of presupposition failure? It would appear so, as she says (p. 146), “Having argued that category mistakes are infelicitous because they suffer from presupposition failure, a natural question one might raise at this point is what separates category mistakes from other instances of presupposition failure?” If one really believed that category errors were presupposition failures, the answer to this question would be “nothing”; one would not posit any significant differences between e.g. presuppositions triggered by a definite description and those triggered by a factive verb (other than obvious superficial differences).

However, in Magidor’s favor is the fact that the “presuppositions” which she mentions seem to pass the projection tests (pp. 134–138). The first projection test is simply the constancy under negation test, but, in my view, constancy under negation is not a sufficient test for presupposition.Footnote 9 For one thing, c-selection and conventional implicatures survive negation, e.g. in both Mary is poor but honest and It is not true that Mary is poor but honest the presence of but leads one to conclude that the speaker thinks that there is a contrast between being poor and being honest. Similar remarks apply to conditionals. Her supposed presuppositions also pass the projection tests involving conjunctions and questions, but once again, so will various other types of things, such as conventional implicatures.

Even if Magidor is correct, the presuppositions of adpositions which she posits are not of a type particular to this word class, and so are not of particular interest if we are focussing on presuppositions of adpositions.Footnote 10

On the other hand, Tyler and Evans (2003) bring up supposed presuppositions which may be restricted to adpositions and perhaps words of other classes with meanings similar to those of adpositions. In their paper on the polysemy of over, they state (p. 49), “a preposition presupposes a TR and LM, which are typically supplied linguistically, e.g. The picture [TR] is over the mantel [LM]”. Trajector (TR) and landmark (LM) name concepts of Cognitive Linguistics, the framework which Tyler and Evans are using; they (p. 110) describe these concepts as follows:

We call this abstracted mental representation of the primary sense [of a locative preposition] the protoscene. It consists of a schematic trajector (TR), which is the locand (the element located, and in focus), and it is typically smaller and movable; a schematic landmark (LM), which is the locator (the element with respect to which the TR is located, and in background), and is typically larger and immovable, and a conceptual configurational-functional relation which mediates the TR and the LM.

Although the “presupposing” which Tyler and Evans speak of does pass the negation test (The picture is not over the mantel also leads one to think that there is a picture and a mantel (or, more generally, that there is a “locand” and a “locator”)), they do not seem to be using presuppose in the technical sense.Footnote 11 Andrea Tyler (p.c.) has verified this.Footnote 12

However, their sentence does bring up a pitfall one might encounter when looking for presuppositions of adpositions: The picture is over the mantel certainly does presuppose the existence of a picture and a mantel, but this is because of the definite NPs The picture and the mantel, definite NPs being among the most familiar presupposition triggers, and not because of the preposition over. Given that most adpositional objects are NPs, and that even some indefinite NPs have been argued to be presupposition triggers (e.g. by von Fintel 1998), athough not specifically those in the complement position of PPs, a large proportion of sentences containing adpositions will have presuppositions about the existence of entities or objects named by their objects, but these presuppositions will not be of interest to us as they are not triggered by the adpositions themselves. Most probably, we will have to disregard many or all existential presuppositions in such contexts (though adpositions may be triggers of other types of presupposition); adpositions do not seem to be able to trigger existential presuppositions, which should not be a surprise—some verbs can trigger presuppositions, but not those of the existential type.

In their (2001) book on the Tungusic language Udihe, Nikolaeva and Tolskaya say the following when discussing postpositions of this language which mean ‘with’ in the comitative sense:

The postposition mule ‘with, as distinct from geje and zuŋe, presupposes a close “inalienable” association between two participants, which must constitute a “natural” pair: a husband and wife, a mother and son, cf.: ogbö eni mule ‘elk with female’. So (772a) below can only be understood as meaning that I climbed the tree with my own (and not somebody else’s) younger brother.

Their example (772a) is below:

Bi neŋu mule mo:-tigi tukti-e-mi

me younger.sibling with tree-lat Footnote 13 climb-past-1sg

‘I climbed the tree with my younger brother.’ (ibid.:413)

Once again the “presupposition” probably passes the negation test, i.e. I assume that the negative version of (3) also gives the impression that neŋu refers to the younger sibling of the speaker. However, also once again, I am dubious about whether this is presupposition in the relevant sense; if neŋu does not refer to the younger sibling of the speaker, (3) will be semantically ill-formed but not in the same way as “The present King of France is bald” is—I think that it would still have a truth value, unlike the King of France sentence (on a semantic rather than pragmatic treatment of presupposition). Irina Nikolaeva (p.c.) and Maria Tolskaya (p.c.) have confirmed that in this paper presupposes was not meant in a technical sense; the former author said, “It was meant in a general sense: “requires a close inalienable association”.Footnote 14

Kemmer and Bat-Zeev Shyldkrot (1996:366) discuss the difference between French toucher and toucher à, both meaning ‘to touch’, as in the following examples (ibid.):

Cet enfant touche à tout ce qu’il voit.

‘That child touches everything that he sees.’

Elle a touché le radiateur.

‘She touched the radiator.’

They say:

there is a subtle distinction in usage between these forms: a greater degree of intentionality is associated with toucher à, as in the case of [(4a)], in which the child is touching objects on purpose, presumably to explore them. Toucher without the preposition presupposes nothing about intentionality, and is the normal form to use in situations where the subject participant has accidently touched something.

If toucher alone does not have a presupposition “about intentionality”, we can infer from the above passage that toucher à, and specifically à in this context, does have such a presupposition. However, it is not clear to me that it is a presupposition, even though it seems to survive under negation: in one reading Cet enfant ne touche pas à tout ce qu’il voit the child touches some things, but not everything that he sees, and this touching was done intentionally. One might argue that this is not a presupposition, but rather it is an entailment. Consider an English sentence with the same meaning:

That child is intentionally touching everything that he sees.

This sentence of course gives the impression, and in fact entails, that the touching was intentional. If we negate it, forming That child is not intentionally touching everything that he sees, and if we put stress on everything, there is still the impression that the touching is intentional, but I would say that this is because the word intentionally entails (and in fact explicitly expresses) intentionality. This means that here, and more generally, as I have already remarked, constancy under negation may not always be a good test for presupposition.Footnote 15

We have seen that many uses of “presuppose(s)” and “presupposition(s)” in connection with adpositions do not seem to involve presupposition in the technical sense, and that some uses of these terms in a technical sense may not be correct or may involve “presuppositions” which seem rather different from presuppositions as they are generally conceived of. Further, some of the presuppositions which have been attributed to adpositions are not limited to adpositions (those involving s-selection), and thus are not of interest to a study specifically on adpositional presuppositions. We now turn to some adpositions which may trigger presuppositions.