I’m going to shift modes for this post. Instead of reading a book or an article and then reflecting on it, I’m going to lay down my thoughts on a concept before digging in to any philosophical literature. In my inquiry into determinism and my thinking about free will, I continually encountered the concept of possibility. I never thought too deeply about it until recently. It seems simple enough, but my sense is that it plays a role in some of the ongoing disagreements in the free will debate. I know in the philosophical literature, possibility is dealt with in modal logic and modality in general, but I’m going to avoid that area for now. I’ll outline my views, then try to place them in the already existing philosophical landscape.
            First, I’ll use the notion of possible worlds. This is itself an already established philosophical concept that is not without controversy. But here I’ll just invoke the naïve version. A possible world is just another way you could imagine the world being. For example, there’s a possible world in which everything is exactly the same as it is now, except my book is on the floor instead of the table. There’s a possible world in which everything is basically as it is now, except there are no anteaters. There’s a possible world in which the Cold War turned hot. There’s a possible world in which Jupiter doesn’t exist. There’s a possible… you get the idea. An important note: here the word “world” actually refers to the entire universe, not just Earth.
            In building my ideas around possible worlds, I am already invoking one sense of possibility – logical or conceptual. A possible world must be conceivable by us, without logical contradictions. Is there a possible world where everything is as it is now, but 2 + 2 = 5? I don’t think so. In fact, I’m not sure what that even means. Is there a possible world where there is a barber who only gives haircuts to people who don’t cut their own hair, and yet who also gets haircuts somehow? Again, I don’t think so. There might be some philosophically interesting work to do in this area (knowing philosophers, I’m sure there is), but for now I’ll naively assume that we can agree, for any given case, whether a possible world is in fact possible in this way.
            Possible worlds are useful because, I believe, one way to make sense of a claim involving the concept of possibility is to translate it into the language of possible worlds. In order to outline how such a translation might be accomplished, I envision a kind of taxonomy of possibility involving nested sets of possible worlds. Associated with each set is a particular kind of physical variable whose value floats, is being changed, or is up for discussion. Bigger sets contain within them smaller sets. As we zoom in to smaller sets of possible worlds, we get closer, in some sense, to the actual world.
            In the largest set of possible worlds, the laws of physics are up for grabs. This set of possible worlds is itself broken down into three sets, each one containing the next. In the broadest set, we consider varying the type of entity that is used to describe how events unfold. By this I mean – do events occur according to mathematical laws? Do they occur at the whim of some all-pervasive agency? Do they just occur randomly or haphazardly? The evidence we have points to the first possibility. Within this subset of possible worlds, we vary the type or form of the mathematical laws describing the universe’s time evolution. Conceivably they could take any form, but in the actual world they take the particular forms they do (as of now, quantum mechanics, the standard model, and general relativity). In the final subset of possible worlds, we accept the mathematical formulation of the extant laws, but consider varying the empirical constants within the laws (e.g. the proton/electron mass ratio). If you’re familiar with arguments about the fine-tuning of the universe, they tend to play out within this set of possible worlds.
            The next set of possible worlds accepts the laws of physics we actually have (including empirical constants) and considers different outcomes to any inherently random events. These events could include the “initial conditions” of the Big Bang (if that’s a meaningful concept – perhaps it isn’t), spontaneous symmetry breaking, or the random outcomes of quantum measurements (under certain interpretations of QM). This set is where most talk of “possible” and “possibility” occurs.
            Now for the translation. I think it’s useful (though the nature of this utility is still unclear to me) to translate a statement about possibility into the language, and taxonomy, of possible worlds. Let’s explore this using the 10 modal statements from the SEP article on varieties of modality:
  1. No one can be both a bachelor and married. (‘Bachelor’ means ‘unmarried man’.)
  2. You could not have been born of different parents. (Someone born of different parents wouldn’t be you.)
  3. Nothing can travel faster than light. (It’s a law of nature.)
  4. One cannot get from London to New York in less than one hour. (Planes that fast haven’t been developed yet.)
  5. You cannot leave the palace. (The doors are locked.)
  6. You cannot promise to come and then stay at home. (It’s just wrong.)
  7. You cannot start a job application cover letter with “hey guys”. (It’s just not done.)
  8. You cannot castle if your king is in check. (It’s against the rules.)
  9. You cannot deduct your holidays from your taxes. (It’s against the law.)
  10. Fred cannot be the killer. (The evidence shows that he’s innocent.)
            Statement 1 involves logical possibility, so its translation is something like “there are no possible worlds in which married bachelors exist”. Likewise for statement 2 – there are no possible worlds in which you were born of different parents. Statement 3 assumes the laws of nature as they currently are, so it is equivalent to “there is no faster-than-light travel in any of the possible worlds with the extant laws of nature.” Statements 4 and 5 also assume the actual laws of nature, but they also assume more. In statement 4, we consider all the possible worlds in which human technological development played out more or less as it actually did. In none of these worlds does anyone go from London to New York in under an hour. In state 5, we consider possible worlds where humans evolved to possess a certain maximum physical strength and only locks of minimum strength exist. In all such worlds, people don’t leave palaces with locked doors. Statements 6 – 9 have inextricable normative components, so I won’t treat them here.
            Statement 10 involves a type of possibility I haven’t dealt with yet, epistemic possibility. Epistemic possibility can be expressed as an inability to precisely locate our actual world among all the sets of possible worlds. In translating statements 1-5 above, we considered a set of possible worlds defined by some implicit assumptions in each statement. For example, “nothing can travel faster than light” clearly assumes that the actual laws of nature pertain, so we consider only those possible worlds with the laws of nature as we know them. In none of these worlds does faster than light travel occur. But an unspoken part of the translation is the claim that the actual world belongs to that set of possible worlds. Epistemic possibility is uncertainty in this type of claim. An example – “there could have been 60,000 people at the stadium last night”. Translation – because we can’t precisely locate our world in the landscape of possible worlds, there is a set of possible worlds as of last night that all lead to today’s world. Among these possible worlds is at least one in which there were in fact 60,000 people at the stadium last night.
            That’s it for now. More on possibility next time.