Parmenides, Modal Metaphysician

The philosopher regarded by some as the first metaphysician and modal theoretician to reflect systematically on the nature of possibility, necessity, and impossibility is the Greek presocratic philosopher and founder of the “Eleatic” school of philosophy, Parmenides, born around 515 BC. His one surviving work, On Nature, is a fragmentary poem describing the poet’s mystical journey by chariot to the temple of an unnamed goddess who instructs him in the two ways in which human beings approach reality, the “Way of Truth” and the flawed “Way of Appearance” or mere “Opinion” (doxa). In her discourse on the Way of Truth, the goddess further distinguishes three ways in which reality may be thought about or conceived: “that it is and must be,” “that it is not and it cannot be,” and “that to be and not to be are the same yet not the same.”

What Parmenides meant by these three paths (along with much else in his opaque and oracular poem) has been the subject of much debate, but one interpretation relevant to the history of the possibles has seen his three-fold path as an early distinction between the three modal categories of necessity, impossibility, and possibility, respectively.[1] On this reading, Parmenides’s “what is and must be” refers to those things which are necessary, “what is not and cannot be” to those things that are deemed to be impossible, and the intermediate realm of “what both is and is not” is presumably his way of characterizing the merely possible.

[1] Merrill Ring relates Parmenides’s interest in modality to the likelihood of his mathematical training among the Pythagoreans:

If, as there is good evidence for, he did begin his intellectual career among the Pythagoreasn, he was there exposed to sophisticated mathematical thought. One clear and obvious feature of mathematical discussion is frequent use of the various modal notions. For instance, an early mathematical discovery was that the result of multiplying any integer by 2 has to be an even number. A more complicated realization was that it is impossible to construct a right triangle whose hypotenuse is shorter than iether of the other twos sides. Even possiblity is easily spotted in mathematicians’ talks: “Can (say) 2,372 be divided by 3 without remainder?”

Very probably, Parmenides’ interest in modal concepts arose from his exposure to the frequent use of those notions in the mathematical work of the Pythagoreans. (Ring 91).

The Parmenideanism of Possible Worlds

Alexander Pruss (“The Actual and the Possible,” The Blackwell Guide to Metaphysics) provides an explanation of how possible-world semantics (or what I will here shorthand as PWS) works, an explanation that is at once immensely helpful and yet which, to my admittedly limited understanding, opens up a potentially important line of critique. Pruss writes: “Once possible worlds are introduced, one can say a proposition is possible if it is true at some world, necessary if true at all worlds, and contingent if true at some but not all, so that modal operators can be replaced by quantifiers. It is possible that there is a unicorn if and only if there is a possible world at which there are unicorns.” PWS, in other words, translates claims of the possibility of things or states of affairs into claims about hypothetical, possible worlds. Whenever you make a statement about something being possible, you are implicitly making a statement about some possible world.

The line of critique I have in mind originates in a suspicion that there is something deeply Parmenidean involved in PWS. The pre-socratic philosopher Parmenides, to review, argued in effect that, because all change involved a change in being, and because there can only be a change in being when something is either going into or out of being, and because non-being is unthinkable, change itself is therefore unthinkable and must be held to be impossible. It was Parmenides’s disciple Zeno who similarly formulated those famous paradoxes about the impossibility of motion (for an arrow to reach its target, it must first cross half the distance, but before it can do that, it must cross half of that distance, and so on, ad infinitum, making it impossible for the arrow to move at all).

Enter Aristotle, who using his famous act-potency distinction, sought to cut through the Parmenidean “Gordian knot” of change, arguing instead that change involves a relative and not an absolute form of non-being. Change is possible because a thing goes from having a given form or state in mere potentiality to then having that same form or state in actuality. So Parmenides was right that change from absolute being into absolute not-being, or absolute not-being into absolute being, was impossible (the Christian doctrine of creation ex nihilo, incidentally, is not a form of change, since literally nothing is being changed by the act of creation). Parmenides was wrong, however, in thinking that actual being was the only kind of being that there was.

On to my suspicion, which is that PWS commits a related (if not ultimately the same) error to that of Parmenides, in that it overlooks the respect in which possibility, which is to say potentiality, is a form of being within things, things that actually do exist. Possibility, after all, is a kind of being, a way of being, in which real things actually are. PWS, however, seems to implicitly deny that possibility is in things by interpreting all modal statements as statements about some world other than this one. PWS is Parmenidean because it evacuates this world of possibility in the same way that Parmenides failed to recognize potentiality for change as a real feature of this world. The possible worlds of PWS, accordingly, are each their own little Parmenidean monads, and which collectively comprise one great Parmenidean monad. Possible worlds are Parmenidean worlds, worlds of static existence within which all real modal work is being continually outsourced to some other possible, Parmenidean world. PWS, accordingly, would seem to make true change within any given world technically impossible, and in much the same way Parmenides did, inasmuch as change by its very nature involves the realization of something that was, prior to the act of change, a mere possibility, and hence (according to PWS) something inhabiting a different (possible) world altogether. In other words, it’s not just unicorns, as unrealized possibilities, that must be banished to an alternative, possible world, but any and all currently unrealized possibilities, including whatever currently unrealized possibility I will be doing five minutes from now. To get to that possible, future world, I will have to leave behind this currently present and actual but soon to be past and then only possible world. Change in this present world is therefore quite impossible, as Parmenides long ago explained. If I want a change of scene, I will have to travel to some other currently and, relative to me, only possible world (but then is the transition from our current, actual world to some possible world not itself an act of change?). For Aristotle, by contrast, possibility, or potentiality, is not a possibility or potentiality of worlds, but of things. Things change because things have possibilities besides or in addition to (or precisely on account of) their present actualities, their present mode, that is, of actual existence. In antiquity, moreover, it was this “common sense” approach to the world of Aristotle that won the day, in which case the possible-world semantics of much contemporary analytic philosophy begins to look something like Parmenides’s revenge.