Variation and Predication
Matthew Segall and Timothy Jackson have recently been having an engaging series of back-and-forth posts on this website concerning an “ontogenetic” philosophy. To quote from Tim’s post “Excess and ontogenesis”:
The point of departure for this project is deceptively simple: we reorient our conception of “Nature” (physis) from one grounded upon invariant structures, to one in which variation is primary, and all stable structures must be derived from it via a constructive, ontogenetic, account. There are no timeless Ideas; every individuated “thing”, be it actual or virtual, must be conceived as the product of a constructive evolutionary process.
In his post “Philosophies of Ontogenesis”, Matt had this critique, however:
His “variation first” postulate is a powerful wake up call for the old metaphysical and modern scientific habit of treating invariant identity as primary and differentiation as derivative. But the rub is that even to say “variation first” is already to treat variation as invariant, as a principle that must hold, everywhere, in order to do the philosophical work you want it to do. There’s no escape from the variation-invariance polarity. We can try to enthrone difference and demote identity, but we end up reinstalling identity just by virtue of insisting difference has priority.
Matt and Tim’s exchange is in a way an echo of an earlier debate that was held between John Dewey and Alfred North Whitehead, as documented in Whitehead’s essay “Analysis of Meaning.” According to Whitehead, Dewey had argued that Whitehead needed “to decide between the ‘genetic-functional’ interpretation of first principles and the ‘mathematical-formal’ interpretation.” He, not surprisingly, refuses to choose between either: “The historic process of the world, which requires the genetic-functional interpretation, also requires for its understanding some insight into hose ultimate principles of existence which express the necessary connections within the flux.” He then, most importantly, makes this assertion:
the persistent presupposition of final principles cannot be neglected by any philosopher who counts himself as a “radical empiricist.” For example, to take John Dewey’s language in his paper which is spread before me, the compound word “genetic-functional” means an ultimate metaphysical principle from which there is no escape. I am here in complete agreement with Dewey.
That is, to say that all principles derive via a process of variation is itself to assume a first principle that is invariant, that is not itself derived via a process of variation.
Arguments such as this one force us to reason through higher-order predication, so that their implications are not always obvious. I feel compelled to unravel such argumentation—as best I can. Talk of variation in the sense I have in mind (e.g., variation in traits among organisms) brings us into the realm of second-order predication. We are saying of a property (or trait, characteristic, feature - I am aiming to have a very neutral and liberal sense of what a property is in this piece), that it is either exemplified by all individuals (i.e., is invariant) or that it is not exemplified by all individuals (i.e., it is variant).
We could then say that all properties are in this sense variant, i.e., that there are no properties that are exemplified by all individuals. Per the argument cited above, the rebuttal could then be that we have thereby identified a property (namely, the property of being variant) that is invariant! However, if our earlier invariance and variance are second-order predicates (a predicate of a predicate), this invariance would in turn be a third-order predicate (a predicate of a predicate of a predicate). The argument thus wouldn’t necessarily have to be a flat-out contradiction (depending, that is, on what kind of type theory or set theory you’re interpreting your predicates in terms of). Still, it would be a Pyrrhic victory for the “variation as primary” camp. It would amount to the assertion that: 1. variation is universally the case for our first-order predicates, but with the implication that, therefore, 2. at least one second-order predicate is invariant (namely, the predicate asserted of all first-order predicates in 1).
Tim has interesting rebuttals to this argument in his post, “Variation and the limits of determinacy (Part One).
Indeed, these counterarguments begin to unsettle the assumptions behind my analysis. I believe that the main point of Tim’s first counterargument is given in this passage:
The first, and perhaps most straightforward, reason that this does not hold is simply that variation itself does not, in my conception, hold equally everywhere. Ontologies are stratified, which is to say that they have “layers” (or strata) which may be extraordinarily invariant. The world is not an inchoate smear of variation, but highly structured. Invariance may well be relative, but certain things or patterns are exceptionally stable, sometimes lasting billions of years.
The reasoning here seems to be that if we restricted ourselves to a particular subset of our wider domain, we could indeed say that some properties invariantly hold among the individuals of that subset. Therefore, variance is not universal. I find this argument unconvincing largely because I think it only works by shifting the definitions of invariance and variance that the reader would have had in mind up to this point. Before, I had taken variance to mean something like: a property P is invariant when (and only when) for all individuals x in our domain, x is P. Here, however, we would need to introduce a new, more relative meaning of “invariant”: a property P is invariant relative to X (where X is a subset of our domain) when (and only when) all individuals in X are P. However, we could still simply introduce the set D as our full domain and draw the same inference as before regarding the statement that all properties are not invariant relative to D. Given that we are concerned with metaphysics here, and thus the utmost generality of things, this would be the only meaning of invariant we’re especially concerned with. Since all other meanings are to this extent different properties, they would not affect our argument.
On the other hand, I might be assuming incorrectly regarding just what kind of metaphysics we are concerned with here. Tim’s next point gets to the really essential core (and I’ve been holding off on getting to this in arguably a problematic way, teasing the reader through exercises that might be about to explode):
A more speculative reason why the ontogenetic stance’s postulate of primary variation functions differently from a standard invariant is that this is not a substantialist framework. Variation is not a “thing” that varies, it’s “just” variation. This is an operational metaphysics. I know this is a somewhat tricky concept, for which I apologise. I can’t explain it in full detail here because this article is going to be far too long as it is. I think that saying that “variation is just a new invariant” is implicitly substantialist because it avails itself of the logic of “recapture” in that there is implied to be some “thing” that is varying and which all the invariance is in some sense “internal” to (and dissolves back into).
He later continues in a similar vein:
The point is that there isn’t some fundamental or primordial “X that varies” – variation is more generic than any “X”. But it’s nothing like a traditional invariant, because it operates in a completely distinct manner, and thus the image of the world that arises from taking it as a primary principle is quite distinct. Variation is not a “system” that all invariance is “internal to”.
I would interpret the above to consist of two major denials. First, our claims are not grounded in or made true by anything like individuals exemplifying properties (and thus, on higher levels, properties exemplifying properties), or even individuals belonging to classes (or however else one wishes to model one’s semantics in terms of individuals relating to abstract objects). We are not able to draw ontological commitments in this way from our (largely linguistic) claims. This, in turn, leads to his denial of “substantialism”: the view that our ontology involves substances that have attributes, or things having properties, and we speak rightly when we can predicate the right properties of the right things. Thus, to assert that variation is primary is not really to commit ourselves to some “X that varies.” As he also put it in a comment to my recent post: “it is exceptionally difficult to avoid tacitly substantialising processes such that we may as well be speaking of objects-with-dynamics.”
Secondly, there is no domain of all of reality, or nature as a whole, such that we could make universally quantified statements over said reality. As Tim also puts it:
Nature – physis – is happening, yes. But I call the “Spinozist fallacy” (not that he necessarily got there first) that characteristic rationalist and substantialising move which projects the properties of loci onto a (fictitious) “whole”. Being “whole” or “complete” or having mereological relations are things that apply to systems, but all the systems don’t add up to One Big System or Substance, they are haloed and perforated by the “non-systemic”, the un-pre-canalised. Physis is apeiron. Non-unitary.
Thus, I was making an illicit (or at least, less than fruitful) move when I went from “a property P is invariant relative to X” to “a property P is invariant relative to D” where D supposedly encompasses all of reality. There is no such domain to range over—at least not in any effective thinking. We shouldn’t reason with a model of reality akin to a Boolean algebra, or the Boolean algebra without a zero one gets out of classical mereology: there is no greatest element or universal sum. We can only ever reason about parts of reality at any one time.
I am interested in these two denials (the denial of a “substantialist” grounding of our claims, and the denial of a “whole” our statements can universally quantify over), because in a sense the first is in direct opposition to the reading of Whitehead I recently offered, whereas the second gets at a point needing clarification in said reading of Whitehead. I read Whitehead as offering a factualist ontology, where our experiences are capable of grounding our claims (i.e., making propositions true) exactly by virtue of being factual, involving individuals exemplifying properties (and relations). My piece, thus, in a way consists of arguing for a “substantialist” reading of Whitehead (and judging by his comment, I think Tim agrees on that verdict). At the same time, Whitehead has a kind of radical perspectivism whereby facts do not all belong to one world. Rather, each occasion of experience is its own world, being its own unique perspective on a unique set of facts. Truths are relative to standpoints in the creative advance—that is, relative to the set of facts that an occasion of experience is confronting. This raises the interesting question: can we still have universally quantified statements that assert things, invariantly, about reality as a whole, past, present and future? In Whiteheadian terms, this is the question of if we can still have metaphysical propositions, and Whitehead’s answer is emphatically yes. That, however, is an issue I will have to expand on further later.
I may be off in my interpretation here; perhaps I too conveniently brought these views into a neat relationship with what I myself have been thinking about recently. Either way, it should be emphasized here that I am talking about two denials. Tim clearly has a positive position he’s also putting forward, but it’s one I’ll probably need to read up on more to better comprehend. The justifications for any philosophical position are going to be complex enough to never be easily presented or argued for, so one cannot judge too quickly. Still, I suspect a good deal of the justification I would want will involve explaining the relationship between our claims and the reality those claims are answerable to. By “claim” I do not thereby just mean a linguistic phenomenon – but perhaps more like the product of our inquiry so far as it is considered at all capable of success and answerable to correction and reasoning. If we want something that is more operational than substantial, I’d nevertheless wonder what our explanation of these operations is.