Descartes and substance

The paradigm of substance is the human self since we can verify its existence immediately. After Descartes, however, this self is understood as immaterial, thus making the material world insubstantial.* The material world became perfectly homogeneous since there was no longer any foundation in it by which things might differ.  All distinction was introduced into it from outside, and thus from immaterial substance. But the introduction of distinction into homogeneity gives us first of all numbers and shapes. Whammo – physics becomes math.

What can we say about this? It’s true that if we are the paradigm of substance that we have to decide whether we are more like or more dissimilar from the other things of sense. Is the self-reflection of human thought an insight into all natural things, or something that is better taken as dividing persons from nature?


*The Cartesian hypothesis of animals and plants as sort of machines is a logical extension of this, for they must perform complex operations without being substances.

All this is a different perspective on the modern critique of Scholastic occult ideas, the chief of which is substance. Substance, in the Cartesian view, seems to be a way of taking about what is unique to the immaterial, and therefore has no place in physics. Given human nature, we can expect the insubstantiality of nature to be accepted long after the theoretical basis of this (the immateriality of substance) is forgotten.

Two accounts of the material

In his Eschatology, Ratzinger several times quotes approvingly the claim that matter cannot be perfected. For Aristotle and the Greeks, the claim was not only wrong but confusingly wrong – how could anyone ever say something so obviously stupid? For them, things were material because they are ontological precursors to some other, more complete state. This meaning remains for us as well: call something building materials because we need to do something to make them complete; or course materials because they need to be worked over, written on, assimilated into consciousness, etc. Good grief, not only is material existence completable, completing it is the only reason you call it material. 

But the quotation makes perfect sense if matter is viewed not as an ontological precursor but as an eternal, foundational substance. There was a way in which things were material like this for the Greeks too – the heavenly bodies were eternal, fundamental substances that one could not make anything else out of, and so they could never be viewed as stuff that could be worked on to make some later, complete substance. One way to understand modern accounts of matter in ancient categories is to see all reality as being the fundamental particles, which were as eternal, substantial, and unchageable as the the heavenly bodies, while all other things (men, trees, and planets, etc) are no more substantial than the constellations, and for exactly the same reason.

This bivalence is implicit in the nature of matter itself. Matter remains through change and so is both the precursor to some later state and a reality that underlies any of the entities that arise from it and so has a bona fide eternity and foundational character.

Why call something “material”?

For Aristotle, a cow was material because it was an ontological precursor to a baseball mitt, a pile of black dirt, an ingredient in the spaghetti, etc. For Descartes, it was material because it had dimensions, its weight, its age, or in general because it could have some status on a Cartesian coordinate system. For us,  cows are material because they are composed of fundamental particles, though all this means is that a cow is material if we consider it as nothing but a bunch of material things. The tautology probably indicates a lack of interest in, or lack of ability to address the question.

The direction of recognition

The major premise of the Fourth Way is the only one that raises hackles:

More and less get said about diverse things insofar as they approach something maximal.

Magis et minus dicuntur de diversis secundum quod appropinquant diversimode ad aliquid quod maxime est.

One argument for the premise comes from what we might call the direction of recognition. Take a series of things that are more or less perfect, like three triangles more or less perfectly drawn. You recognize a better and worse, but in what order? It seems evident that you take an ideal and measure the degree to which each falls away from it rather than taking a bad triangle (or, what’s much less likely, the perfectly awful triangle) and remove its badness from it. You can touch up a picture by taking away its imperfections, but all our argument requires is that such touch ups are attempts to approach an ideal, not attempts to gain distance from an anti-ideal. The reason is that ideals are definite in a way that allows for an approach whereas failures to instatiate something don’t form a definite point of reference that we could distance ourselves from. A sloppily drawn face, a straight line, the spelling of my middle name, and a perfectly drawn hand can all be failures at portraiture, but these don’t coalesce into some definite point of reference from which we could remove imperfections. Logically, any recognition of an ideal from its inferiors happens only after some recognition of the ideal itself.

Judging something from an ideal does not require that we have a perfectly clear view of it – in the actual progress of discovery we usually tinker around to see what works rather than executing a perfectly top-down instatiation of a perfectly grasped ideal. But this tinkering and discovery doesn’t change the logical priority of ideal instantiations.

If this is right, then Descartes is vindicated in his claim that the infinite good is known before the finite, even if it is not the first thing distinctly known in the order of discovery; and Aristotle’s theory of abstraction is a way of fleshing out what something is whose existence is already known in another way.

Physics and formalism

You could tell the whole story of physics after Galileo and Descartes as one that took motion and extension as basic and simple. Until then, both were complex, whether they were divided into Aristotle’s active and passive sources or Plato’s idea that the sensible is an accident projected from a substance into an utterly featureless screen or receptacle.

Leaving aside the active and passive, motion and extension became indistinguishable from their mathematical abstraction. While the story is that this made all causality agent and material, it in fact redefined causality altogether so that precisely defined causes no longer had precisely defined effects, making physics purely formal. Physical processes just acted without needing anything to act in or act on.

Except not. Some subject of action has always proved indispensable. Newton could not understand the world of physical action except as set apart from a much truer, purely formal world of absolute space and time which is infinitely precise and exact, and in relation to which the actual world of physical events was less than formal; and we only cast this purely formal world out by two different systems that made the observer an integral part of the definition of the physical. On the Newtonian picture, physics required falling away from pure formalism since it could not be absolute; for us it falls away from it because some observer is required to concretize and individuate the formal elements of the system. And so physics has never succeeded in being purely formal, but has always demanded a duality of principles, one which is formal and another which individuates and is unintelligible of itself.


-We visualize time as a backdrop or context or container – things are said to occur in it. Newton draws out the logic of this idea with his absolute time, or the time in virtue of which any clock could be corrected. In the same way that we can line up a hundred sticks and see how much they deviate from absolute equality of length, we can line up any set of periodic events and see how they compare to absolute uniformity.

-But time is not a context but a sort of exhaust product of a form in matter. It’s not a single stream all bodies are drawing from, but diverse streams coming out of the bodies themselves which combine and interact in various ways. This is why time, like space, has only a relative value. Just as change in space has no value except relative to some other specified body serving to give location, change in space has no value except relative to some other specified body serving to give it uniform temporal parts.

-We can discover various constant rules for the combining of these exhaust streams, and in this sense there is a “universal time”. This does not make time a context.

-We want rules of combining a product or effect with other products. This explains how relativity both allows for time to be longer or shorter (when it combines) and yet stay exactly the same for the one producing it. Put Alexander’s whole world on a spaceship travelling away from the rest of the earth at light speed and then coming back. As far as he is concerned, he lives the same 33 years he ever lived, even if the moment he dies his world opens to show everyone left behind much older.

Atheism before evil

Paul Draper argues that given the distribution of pleasures and pains we observe in the world, the hypothesis of indifference is more likely than theism. The basic fact is our observation of evil, but mine makes me not puzzled not about Draper’s conclusion but about his claim to an initial observation of evil that is not of itself already for or against theism. That some evils are like this might be true, but they are not the only sorts of evil, and the relations between these different sorts are problematic to Draper’s overall argumentative structure.

For reasons that should be clear later I’m stuck using personal examples and so this post will be testimonial-like. That’s unlike most of what gets posted here, but it is what it is.

My wife has insited on natural childbirth for all of our five kids. The pain is prolonged and rips flesh and muscle apart. She has no evidence that anaesthesia causes harm to either mother or child, but she will not use it. After birth, when she’s being sewn up or probed by doctors, she’ll take all the drugs on offer because she sees – I think rightly – an ontological difference between a medical procedure and giving birth.  Medical procedures are responses to disease, corruption or physical defects, but birth is not. Everyone agrees if there is nothing wrong with me, then the doctor has nothing to fix, but my wife observes her situation and does a modus ponens while many others demand the drugs and so are logically commited to the modus tollens. But there isn’t an observation of labor pain that isn’t one of these or another. Either there is something wrong with you (which you should fix if you can) or there isn’t (and so there’s nothing to fix). Your observation of the pain is a result of a pre-existent belief (or absence of belief) about the meaningfulness of natural processes. The analogy from this to a critique of Draper’s argument is pretty clear, but I want to argue that further analogue from observation too.

My wife asks people for prayer intentions in the final weeks of pregnancy and has me read her one intention per contraction. Contractions are intense and painful, but the woman gets a break between most of them (my wife tells jokes between them, or talks to the doctor or the doula, etc.) As the contraction swells up she usually gets a few seconds to prepare, and she starts making the low, controlled working groans that she uses to breathe her way through the next 60-120 seconds. The intention clearly enters into her work and it is clear that the pain becomes a side-effect of a work she is achieving. The intensity of the pain is something anyone seeing her could rejoice in because they can be confident that the intention is being achieved – even if the petitioner didn’t know what they should have intended. That said, it’s not as if my wife is smiling through all this or takes the pain as nothing. She doesn’t think “this is all for the best, I’m one with God” she just thinks “this is hurty and I want it to stop”.  Labor doesn’t become some happy-clappy religious experience just because you choose to make an offering of it. But what becomes clear to anyne who experiences this with her while believing what she believes is that God is most of all present in the world in a consciousness that suffers. Suffering is an energy that one can either harness or allow to dissipate, even if the experience of suffering will be the same whether he does the one or the other.

My goal in babbling about all this is to problematize the idea that pain and suffering are things that God needs to fix. There is an important truth to this if we are considering the beginning or end of the whole human family, i.e. the creation of the first persons called to salvation or the final reward of human life in the eschaton, but the matter is more complex for human life in via. In the same way that our observations of labor pain arise from logically antecedent judgments about nature, our observations about suffering and pain in general are results of logically antecedent judgments about God. We don’t get to view pain or suffering from some non-committed, supposedly scientific or “objective” state.


-Tradition is the opposite of innovation, but both share the common genus of “things irrationally treated as universally good”.  Political groups praising tradition are trading in the same sort of sloganeering as tech firms praising innovation.

-Tradition! Innovation! A Revolution! …In shaving!

-The most remarkable tradition in Catholicism is just that it continued to recite it the creed. This seems banal, but it is not what one would have predicted from a continuance of Old Testament religion. There, observance of Passover disappears for years, the vowels of the tetragrammeton are forgotten (though this happened later), the book of the law is found in the wall and surprises and saddens everyone with what it says (2 Kings 22). Imagine if the Church forgot about the Incarnation for a few centuries before rediscovering it in the process of renovating a cathedral.

-Traditions often become intolerable before we find anything better to replace them with, and to lose them to inferior things is also intolerable.

-Is traditionalism misplaced ancestralism? Rationalized or enlightened ancestor veneration? There is at least one important difference: the ancestor is a definitive historical moment, even where we don’t know how far we are from it or where exactly in history to locate it while the tradition claims to fade back to time out of mind. The tradition arises organically and from many sources while the ancestor just is a single source.

-Most time is cyclical: it’s Friday again, January again, 1:00 again, afternoon again, winter again. We tend to assume that this is not a physical meaning of time, but that scientific time must be either non-existent or linear. Is this only because time is already weird enough without having to understand its circular/linear duality?

Summa version: Mediation III

If all reality is within my mind, then all reality is representative (intentional).

The intentional relates to something other than itself.

Therefore, though any particular intentional thing might relate to another intentional one, all of them cannot (one can’t have a whole made of all relations, whether they are arranged in a circle or go on forever).

So there is some reality outside my mind. Call this intrinsic as opposed to intentional reality.

Short version:

Whatever is in the mind is relative.

the relative depends for its existence on the non-relative.

Therefore, what is in the mind depends on something outside of it.

Let God be the one whose intrinsic reality is greater than mine.*

If God himself were not the cause of my idea of him, then a being with less intrinsic reality than God suffices to explain my idea of him.

But then an idea would have a relation to more than what sufficed to explain its existence,** which is impossible.

Therefore, God exists.


*If there is more than one such thing, the greatest of them.

**There is nothing wrong with an idea having more logical implications than what gave rise to it (like the equality of persons) but we’re not considering logical implications in this argument.





The infinite vs. the whole

So what’s the difference between the integers and the infinite integers? There is nothing in the second that is not in the first, so what in the world can “infinite” add?

When you speak of numerals as infinite you mean something like no point in the enumeration hits the last thing that can be enumerated. This assumes that “infinite” always begins with some part of the integers and denies something of it. If this is right, “infinite” is a judgment about a part or a way of considering something as never whole.


If infinite means “no part is the last one”, then infinite is a claim made about parts.

Though the infinite is never whole, that which is infinite can form a whole. This does not happen by adding something “on the end” or by filling out the rest of the process. There is no end to add things to, nor a “rest of the process” to go through. The whole of which “infinite integers” is a part is just “the integers”; the latter being a whole while the former is never is.

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