Certain words in natural language are more amenable to logical formalization. The conjunction "and" or weak conditional "unless" are easily applied to break statements into their constituent atomic parts.

Other parts of language are less clear. For instance, it's hard to say what the logical status of the adjective "rambunctious" is. It clearly has internal, logical limits to its application. (a "rambunctious apple" is logically incoherent), but what those limits are may be subsceptible to too many vague edge cases to be assessed or applied the same way in which logical connectives are (a "rambunctious house").

Claim P

I feel it may be possible to treat adpositions in a more formal manner, however. Although their internal limits of logical applicability may be more context-dependent than other connectives, or quantifiers, or modal operators, they don't necessarily suffer the same vagueness in applicability that adjectives or other parts of speech seem to.

Can anyone knock down this claim P and disabuse me of this idea? Or, alternatively, point me in the direction of any assessments or formalizations that have been done specifically with regards to classifying adpositional connectives?

I'm not after the formal linguistic treatment of adpositions and their use. I'm interested instead in qualifying the logical relationships these connectives exemplify, when they're extended to use in expressing concepts. For instance, that a member is "in" a set expresses a logical negation of "out" of that set (or vice-versa).

  • There is mereology which models the whole and part relationship; I'm not sure that this counts as a preposition - more a relation; perhaps the question could be inverted to ask are there languages which display a part whole preposition - though of course this isn't what you're after. – Mozibur Ullah May 10 '15 at 6:56
  • 1
    Temporal preposition (before,after,during...) can be analyzed using temporal logic (plato.stanford.edu/entries/logic-temporal/#4 ). Locative prepositions have been analyzed in formal semantics, using for example vectors: "behind the house" denotes the set of vectors that originate from the house and point behind it, now "tree is behind the house" is true when the vector from the house to the tree is in this set, this kind of formal semantics validates many intuitive patterns of reasoning (see phil.uu.nl/~yoad/papers/ZwartsWinterVectors.pdf, I haven't read it) – Johannes May 11 '15 at 0:10
  • As @Mozibur-Ullah mentioned there's mereology [plato.stanford.edu/entries/mereology/]. Not quite what you're looking for but it's a start. Long answer short is that I believe there hasn't been a philosophical formalisation of the topic. There have been linguistic investigations. Prepositions are actually one sort of adposition. Also, linguistics considers adpositions to belong to the function words, as opposed to the lexical words. – igravious May 19 '16 at 19:08
  • @igravious thank you! The wiki page on adpositional phrases made it clear I need to clarify this. – Ryder May 19 '16 at 20:14

You can look at the whole of topology as an investigation of the class of related propositions like 'within', 'in' and 'on'. The notion of open and closed sets captures the distinction between within and on, and together we get in.

Notions of continuity, compactness, etc. elaborate intuitions about what happens to boundaries and interiors when they are looked at in different ways.

Likewise, lattice theory captures 'over' and 'under', etc.

So I would consider this support for your Claim. But I would point out that if one large subtopic in mathematics, captures just three prepositions, and one of the most overloaded classes of notational conveniences captures just one other pair, this approach may be unproductively complicated to pursue.

  • Thanks for that. I suspected there would be a more robust program for the more clearly spatially-relevant prepositions- but I do think it ought to be possible to capture their internal logic in that they're constrained by the specific context in which they're used. For instance, a boundary condition of "x is in y" makes less sense if x is a concept and y is a region of space time; whereas x as an event is validly in y or not. I'm not convinced other prepositons "from", "of", "to" or "at" can't be similarly evaluated, if the relevant contexts can be similarly defined. – Ryder May 9 '15 at 21:54
  • I was assuming you would already need some general grammar and semantics approach before you got to the actual logic. That is what we have linguistics (or its little brother computer science) for. Knowing what kind of thing a preposition can attach to, and in general what a well-formed formula is, is a generative-transformation grammar question or a categorical semantics one. So that is linguistics or computation-theory and not really logic, in my book. – user9166 May 10 '15 at 0:41
  • Knowing "what sort of thing" an adjective can attach to faces this problem, but the reason I'm going after prepositions is because they face no such constraint. Prepositions attach or point or relate, actively, one or more variable items, whether they be concepts, processes, objects, regions, loci, or periods. The only constraint seems to be that items which "two-place" prepositions act upon are within the same domain. This isn't isn't to say there isn't any intrusion into linguistics, or CS. If all this could be explicated in terms of sets and existing logic I'd be quite happy. – Ryder May 10 '15 at 8:48
  • I think you are looking at prepositions too much in isolation. Yes, over can address a hill or a reaction or a person or a cause... But 'go over', 'get over', 'call over', 'cry over'... are only using the same word as part of different separable-prefix verbs with largely unrelated meanings. – user9166 May 10 '15 at 13:39
  • That is not philosophy, to my mind, but philology -- in this case how Latin and German notions of prefix lie nearer to opposite ends of a spectrum of what reference is, and we inherit both. – user9166 May 10 '15 at 13:46

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