Once more: is there such a thing as metaphysical necessity?

Some philosophers distinguish among three classes of necessary (or, conversely, impossible) things: (i) physical necessities (and impossibilities), meaning things that are going to happen (or can never happen) because of the ways the laws of physics are; (ii) logical necessities (and impossibilities), that is things that are true (or impossible) because of the laws of logic; and (iii) metaphysical necessities (and impossibilities), meaning things that are the case (or can never be the case) because of…? Yeah, the latter is the problematic one. Nobody doubts the existence of the laws of physics (though some philosophers reject that kind of talk and prefer to think in terms of causal regularities). Some people think that logical necessity / impossibility is actually the result of human constructs, since one can adopt different kinds of logic, but this is controversial. And then there is a small number of philosophers, the metaphysicians (sometimes they call themselves metaphysicists) who insist on a separate existence of the third category. And this is very controversial.

I wrote about metaphysical necessity / impossibility back in 2014, and then again (on the specific issue of “grounding”) in 2015. In both cases, I was rather skeptical of distinguishing metaphysical anything from either the physical or the logical realm. The way I saw it was this: logical necessity / impossibility > physical necessity / impossibility > contingency. That is, if something is, say, logically impossible, it is a fortiori physically impossible, and it can’t happen no matter what the specific circumstances. However, if something is happening, then it must be both physically and logically possible. And so forth. My argument in the past is that whatever examples of alleged metaphysical necessity / impossibility one would come up with it would either turn out to belong to the physical class or to the logical one, with nothing either in between or, somehow, above logic.

(For the rest of this discussion I will bracket two obvious questions: (a) where do the laws of physics come from? And (b) if logic is a human construct, then in what sense can we talk about logical necessity / impossibility? The only hint that I will give here is that I think the laws of physics themselves are a human construct, but they reflect a fundamental structure of reality. Something similar may be going on with logic. So there…)

Recently, a friend of mine and former student at CUNY’s Graduate Center (she has just successfully defended her thesis!) Antonella Mallozzi, has put out a very conveniently and nicely put together diagram to explore (and defend, in her case) the idea of metaphysical necessity as distinct from both the physical and the logical varieties. With permission from Antonella, I reproduce the diagram below, as it will guide us through the rest of the discussion. (Antonella has also guest edited a special issue on this topic for the journal Synthese, entitled “New directions in the epistemology of modality.” You can see her leading article here. I hear that my colleague Graham Priest, one of the best logicians out there, is also skeptical of the notion of metaphysical necessity, but I have purposely not read his paper, currently in print, so to be able to develop my own ideas.)

So what I’d like to do now is to go through each of Antonella’s possibilities for metaphysical necessity, briefly look at the examples that she presents, and see what happens. We will start with the right-center portion of her large circle (labelled “general metaphysical necessities”) and proceed counter-clockwise, one category and set of examples at a time.

(I) Logical, mathematical, and geometrical necessity (middle right of the large circle). Her examples here include “necessarily, everything is self-identical,” and: “necessarily, two plus two equals four.” As she points out, some philosophers are skeptical that these are examples of necessity, or that these statements are true, pointing to the existence of non-classical logics, non-euclidean geometries, etc. But I’m going to accept these examples as valid given certain axioms (classical logic, euclidean geometry, and so forth). You may disagree, of course, but as I mentioned above, I’m going to bracket any further discussion of this particular issue. Even if we do accept the examples, however, they fall squarely into the logical end of my continuum above, they are not distinctly metaphysical.

(II) Conceptual necessity (upper right of the large circle). Antonella here distinguishes between things that are epistemically necessary, but not metaphysically so (the part of the small conceptual circle that lies outside the largest one), and things that are both epistemically and metaphysically necessary (the little bit of the small conceptual circle that lies inside the largest one). An example of alleged epistemic (but not metaphysical) necessity is the following: “Julius” designates the inventor of the zip. It then is a priori (epistemically) necessary that if anyone invented the zip, Julius did. This seems to me a very weak sense of epistemically necessary, since it simply states that given that X is true, you better take X to be true. I think the use of the word “a priori” is misleading here, as it is obviously a contingent fact that Julius, and not someone else, invented the zip. More importantly, because of the latter possibility, even Antonella agrees that this is a case of metaphysical contingency.

What about metaphysical conceptual necessities? Antonella gives two examples: “necessarily, anything colored is extensive,” and “necessarily, there is a valley in between two mountains.” She also adds, however, that some people think these are logical, not distinctly metaphysical necessities. The case seems particularly clear for the second example: once one defines mountains as things that have peaks and are surrounded by valleys, then it is obviously logically necessary that if there are two mountains next to each other they will be separated by a valley. As far as the color example is concerned, it sounds to me like a case of contingency due to biology: colors are not “out there,” but rather the result of the interaction between physico-chemical properties of materials and the specific physiological and perceptual apparatus of a given organism. Perhaps one could say that more obviously intrinsic physical properties necessitate extension (meaning, something more than a geometrical point), but now that begins to look like a physical necessity, and even that is doubtful, if one accepts certain radical views of what actually constitutes the physical world.

(III) Grounding and mereology (top of the large circle). Antonella’s examples are “necessarily [P&Q] is grounded in [P], [Q],” and “necessarily, everything is a part of itself.” I have expressed my skepticism about the concept of grounding in metaphysics elsewhere (it’s pretty vague and slippery, and doesn’t seem to add anything), but Antonella herself comments that some people would consider these examples of logical necessity, not a distinctive metaphysical class.

(IV) Ethical-deontological necessities (upper left of the large circle). “Necessarily, violence is wrong.” Well, no. My ethics is a naturalistic one, so I don’t think there is anything that is necessary in that realm, at all. Ethics is very clearly, to me, a human construction, constrained by our biology as social animals capable of language, which means it isn’t entirely arbitrary, but also that there is nothing necessary about it. I am, most definitely, not a deontologist.

The last two classes of metaphysical necessities proposed by Antonella are important, because they fall into the circle labelled “distinctively metaphysical” (or Kripkean, in honor of the highly influential philosopher Saul Kripke, currently at CUNY’s Graduate Center). That is, in her mind these are the ones that cannot be reduced in any way to logical or physical necessities, so let’s pay particular attention.

(V) Causally-nomic (lower left of the large circle). Even Antonella readily admits that it is controversial whether anything at all falls into this group! Her examples include the laws of physics and chemistry, but it is an open question to say the least why the fundamental laws of physics are the way they are (those of chemistry, presumably, can be reduced to physics). It may be that they could not possibly have been different, because of the way the causal world is structured; or perhaps they could have been different, and the ones we observe are that way because of contingency. The first scenario would seem to be a case of physical necessity, while in the second scenario the only constraints would be imposed by logical impossibility and necessity. Again, no distinctive metaphysical criterion appears to be required.

(VI) Finally, we get to the most promising class, that of “de re,” a posteriori things that have their source in the fundamental nature, or essence, of things (lower part of the large circle). The pertinent examples are classics of the metaphysical literature: “necessarily, water is H2O,” or “necessarily, I could not have had different parents then the ones I actually have.” I am, however, utterly unconvinced. Water is H2O either as a matter of physical necessity (if the laws of physics could not have been otherwise) or it is a contingent fact about our universe (if the laws of physics could have been different). As for my parents, that seems an entirely contingent fact of our biology. For instance, if humans were a clonal species that reproduced by budding, “I” could have had a lot of different specific parents and still be “me” (not to mention that this example depends on one’s conception of personal identity, a controversial issue in its own right).

I guess this third look at metaphysical necessity / impossibility, despite Antonella’s brave and very clever attempt, still leaves me unmoved. I keep thinking that the logic > physics > contingency conceptual scheme is sufficient to account for all examples that have been presented, and that metaphysics is an artificial category situated between logic and physics: each alleged example of metaphysical necessity turns out, upon closer inspection, to be either a case of logical necessity, or one of physical necessity. But I remain open to be convinced otherwise. Stay tuned for a fourth possible look at the issue, a few years down the road!