Sunday, 13 December 2009

English and quantifiers

Take the pair of sentences:

(1) If a gentleman is in the room, Becky turns on her charm.
(2) If every gentleman is in the room, Becky turns on her charm.

Most English speakers would probably see enough clear water between these two sentences to consider them distinct. Most people would also agree that:

(3) If any gentleman is in the room, Becky turns on her charm.

is more like (1) than (2). But ‘any’ behaves rather differently if we take the following sentences:

(4) Becky will flirt with any gentleman who is worth five thousand pounds per year.
(5) Becky will flirt with every gentleman who is worth five thousand pounds per year.

Here, unmistakably, ‘any’ is more like ‘every’. The subtle differences between (4) and (5) may involve perhaps Becky flirting with one gentleman of such means at a time (4), as opposed to all of them at once (5), or as many of them as come within her grasp at any given time as opposed to, again, all who have that sort of income. Quantificationally, (4) and (5) are equivalent.

More interestingly, in:

(6) Becky will flirt with a gentleman who is worth five thousand pounds per year.

the article ‘a’ has the force of ‘every’ as well. Alternatively, we could say that ‘a’ is like ‘any’, but not the ‘any’ of (3) but the ‘any’ of (4). If, in (6), we were to capture the sense of ‘a’ in (1), we would have to say:

(7) There is a gentleman worth five thousand pounds per year with whom Becky will flirt.

The conclusion which follows from these observations is that quantification in English is only nominally assigned to certain words. Both ‘a’ and ‘any’ can mean ‘one’ and ‘many’ – a rhyme which should make it easy to remember. The quantification of ‘the’ can also shift between ‘one’ and ‘many’, as in:

(8) The tiger caught an antelope.
(9) The tiger is a fierce animal.

Compare the respective paraphrases:

(10) There is a tiger such that if any tiger is identical to it then it caught an antelope. (thus there is only one such tiger)
(11) Any tiger is fierce.

Trying to impose any order on quantifiers in English is like herding cats, or tigers. Logic has only two quantifiers: universal and existential, and all we are left with is trying to fit the material to the tools.

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