The Oxford philosopher JL Austin once observed in a lecture that in English a double negative implied a positive meaning, whereas no language had been found in which a double positive implied a negative meaning. Another philosopher who was in the audience that day made a very simple counterclaim just by saying "yeah, yeah".

Over time words and expressions change in sound, in spelling and in use, sometimes at a snail's pace and sometimes almost overnight – as contributors to the Guardian's letters page have recently reminded us with reference to "cool". A change in meaning may follow a comprehensible if always tortuous path (from the coarse cloth, or bure, on the tables of medieval clerks to the modern bureaucrat, for example), or it may switch at a stroke into its opposite. Rien, the French word for "nothing", for example, is derived from the Latin rem, which means "something" (in the accusative case). By what path can a word get from meaning "something" to meaning "nothing"? It's like asking how anything can be "hot" and "cool" at the same time. Obviously, they can be – especially if you don't even know whether the jazz throbbing through the speakers is hot, cool, or just loud.

In Chekhov's short story Agafya, two rather disreputable fellows offer a girl a glass of vodka. She replies with a colloquial expression – Выдумал! – that means something like "Where did you get the idea [that I drink vodka]?" or "What put that idea into your head?" or "Don't insult me!" A thoughtful professional American translator of Chekhov expresses the force of the girl's response by "Oh! Please!" To my British ear, however, "Oh! Please!" is not a negative but an extremely positive expression. I can hear the young woman clapping her hands and springing to her feet to say in a squeaky treble, ooopleeeez! But for my American colleague, "oh please" is pronounced with an intercalated aspirated schwa between the first two consonants – p-h-er-leez – and for her it is a put-down, a wrist-slap, a no-no. The English word "please" means "yes" – and it means "no".

It's not enough to say that's just a difference between British and American English. Speakers of British English know that "Oh please" if said with the extra half-syllable between the p and l is a negative expression, just as Americans know that "Oh please" said with a rising intonation is a positive. When written down, the words oh please mean anything you want them to mean in the imaginary linguistic context your mind supplies. Same in French, as a matter of fact: merci means "thank you" and it also means "no thank you", depending on how you say it, in what circumstances, and to whom.

Most philosophers do not like expressions that mean one thing and its opposite. Aristotle came up with the law of excluded middle to get rid of them: "For any proposition, either that proposition is true, or its negation is." Yet ordinary language users are addicted to using and inventing expressions that mean one thing or its opposite depending on who's listening. Taboo words are almost always capable of reversing their meaning – they can be used for purposes that are diametrically opposed. Shit! may express strong disapproval in many circumstances, but among the right crowd it may equally well be used by the same speaker to express delight and surprise.

"Cool" probably didn't come to mean stylish, swish, glamorous or desirable by the same kind of forking path that makes please and shit into bipolar expressions. As an antonym of "hot" it probably had the power to mean "not angry", "not hurried" and all sorts of more desirable attributes than those that are normally associated with heat. It may well be that the first "cool" was nonchaloir, an Old French expression meaning "non-heat" (from the obsolete verb chaloir, "to be hot"). Given the muddled history of words moving from French to English and back again, "cool" – as in a "cool customer", "as cool as a cucumber" – might have started out as a translation of nonchalant into the local lingo. As we British do admire restraint in outward behaviour, it's no surprise that a nonchalant gentilhomme – a real cool gent – was one to be imitated and admired, and that coolness became associated with stylish and fashionable things.

Of course this is all speculation, as are most forms of word history. But just as languages constantly change and switch things around, so too are they surprisingly conservative, and what often seems most modern and trendy turns out to be a reminiscence or a revival of some forgotten form in the language of yore. It's possible that the present vast spread of "cool" in our own language (and far beyond, not just back into French baba-cool, but into Chinese 酷 kù as well) wouldn't have arisen without cool jazz; but it's just as likely that had jazz never been invented the idea that there's something stylish about not being hot (bothered, angry, puce…) would have given "cool" many of the meanings it now has.

In Tallinn and Tartu, however, what's really kool is school. No wonder Estonians are so high up the league tables.