Possibility and the possible have long been treated as the bastard third cousins of philosophy. This is true even though there are entire areas and sub-disciplines of formal logic that are nominally dedicated to studying those topics. The problem is that the approaches taken to the nature of the possible (and I will be using that term and “possibility” as more or less interchangeable cognates) as parasitic upon the ideas of “necessity.” In formal terms, possibility and necessity are supposed to stand on equal footing. But in approach and intention, that almost never occurs. This is discouraging, to say the least, since our sense, our feeling, of possibility is a very real aspect of our feeling of reality overall, whereas our only notions of necessity are the abstract, or even recondite, mathematical constructions we make of a thing we can have no experience of whatsoever.
Thus, necessity and possibility are traditionally represented with a box and a diamond, respectively. When attached to a sentence, schematically represented by “p” or “r”, then merely asserting “p” becomes the stronger claim of “necessarily p”, or “p is necessarily true,” represented by “□p.” Similarly then, “possibly r,” or “r is possibly true” is schematized as “◊r.” Either can then be treated as a shorthand form for the other using a variation of DeMorgan’s rules: “□p = ~◊~p”, and “◊r = ~□~r,” where “~◊~p” reads as “not-possibly not-p” and “~□~r” reads as “not-necessarily not-r.” This is all very handy for when you are doing formal logic, but a little thought might well lead one to doubt that any so mechanical and reductive formulation is capable of actually representing reality. Is necessity real at all? And even if it is, why would it be nothing more than a truth-functional inversion of possibility? Meanwhile, there is nothing mechanical about possibility itself, even as we mechanize – for purposes of convenience – what we end up saying about the possible. Right there is the rub: the reality and what we say about that reality are not the same at all. And while I cannot escape the use of words to do so, it is to the experience of the possible that I now wish to turn. Continue reading