Edward Feser's Blog, page 57
March 4, 2018
It’s the latest open thread

Previous open threads linked to here, if memory lane is your thing.
Published on March 04, 2018 10:17
March 1, 2018
Hart on Five Proofs

Edward Feser has a definite gift for making fairly abstruse philosophical material accessible to readers from outside the academic world, without compromising the rigor of the arguments or omitting challenging details… Perhaps the best example of this gift in action hitherto was his 2006 volume Philosophy of Mind: A Beginner’s Guide (at least, speaking for myself, I have both recommended it to general readers and used it with undergraduates, in either case with very happy results). But this present volume is no less substantial an achievement…It is also a virtue on Feser’s part that the only God he cares to argue foris the God of “classical theism.” He does not waste any attention on debates (of the kind all too depressingly common in Anglophone philosophy of religion) over the possible reality of a single “supreme being” who exists alongside other, lesser beings, on the same ontological plane (so to speak), and set off from them only by virtue of his “maximal greatness,” or some other property that makes him far larger and far older than all other things. Feser clearly grasps that, even if one could prove that such a being exists, this would bring us no nearer to an understanding of the true source of all reality (which for monotheists, presumably, is what the word “God” ideally refers to), but would merely provide us with one more entity whose existence must be accounted for…
The third argument Feser calls the “Augustinian” proof; it proceeds from the reality of universals, propositions, abstract truths, logical possibilities, and so forth, to that reality in which all these things must necessarily subsist: which (so the argument at last concludes) must be the divine intellect… Feser manages to bring out the logical force of this approach better than most of its other expositors…
In sum, Feser’s is an admirable achievement, and this book can be recommended for the classroom quite vigorously – but also, happily, not onlyfor the classroom. It accomplishes much in a fairly compact space, and does so with exemplary clarity. In fact, it is among the best such volumes currently available in English.
End quote. I thank Prof. Hart for his very kind words. Hart also raises a couple of minor but useful criticisms, which I may address in a future post. As they say, read the whole thing.
Published on March 01, 2018 16:00
February 28, 2018
The Oxford Handbook of Freedom

Published on February 28, 2018 18:18
February 24, 2018
Carrier on Five Proofs

End quote. If, after fewer than two or three readings, you have the remotest idea what the hell Carrier is going on about here, you are a sharper man than I am. Certainly it has nothing at all to do with the Aristotelian proof. Yet Carrier goes on for paragraph after paragraph of this gobbledygook.
As near as I can tell after reading and rereading those mind-numbingly obscure passages, what Carrier is criticizing is an argument that tries to show that God is the cause of the universe arising from nothing. And as near as I can tell, his objection is something to the effect that if we think carefully about what a “nothing-state” would be, we will see that that theistic conclusion isn’t warranted. Other scenarios, such as a multiverse scenario, are no less likely or even more likely. Of course, this has, again, absolutely nothing whatsoever to do with what the Aristotelian proof actually says, and so Carrier’s objection would be completely irrelevant even if it were at all clear what that objection is. Carrier’s readers will learn as much about what my Aristotelian argument actually says as they would if they’d read an automotive repair manual instead. Only that would have been more lucid and interesting reading.
Here, Carrier seems to be making a mistake common to so many pop atheist writers and amateur philosophers, viz. attacking some argument he thinks he knows something about and feels confident he can refute, instead of what his opponent actually said. In this case, he appears fixated on the idea that causal arguments for God are essentially attempts to answer the question “Why is there something rather than nothing?” and that they all assume that there could at least in principle have been nothing. As anyone knows who has actually read my book (as opposed to reading weird things into my book), that is nowhere close to how any of my arguments proceed. In fact, I explicitly say in the book (at p. 155) that that is a bad way to frame the issue and that in my view there could not in principle have been nothing.
In response to the argument I actually gave for the existence of a purely actual actualizer (what Aristotle calls the Unmoved Mover), Carrier has absolutely nothing to say. He is very slightly better when responding to the arguments I gave for ascribing the divine attributes to the purely actual actualizer. But only insofar as this time he responds, at least initially, to something I really did write. Discussing my argument for attributing omniscience to the purely actual actualizer, Carrier begins:
[In] Feser’s formalization of this argument… Premise 41… [says] “the forms or patterns manifest in all the things [the substrate] causes… can exist either in the concrete way in which they exist in individual particular things, or in the abstract way in which they exist in the thoughts of an intellect.” This is a false dichotomy, otherwise known as a bifurcation fallacy. It’s simply not true that those are the only two options.
End quote. “Substrate” is Carrier’s word for the purely actual actualizer and not a good one, but let that pass. The main problem with this is that I would be guilty of a false dichotomy here only if I did not consider, and give arguments to rule out, alternatives to the two I refer to in premise 41. But of course, I do consider and give arguments to rule out alternatives to those two. (Carrier is here quoting from a summary of the argument, and ignoring what I say earlier and later in the book.) For example, I explicitly note at p. 209, in the context of discussing omniscience in greater detail, that a third alternative would be the Platonic view that forms exist in a third realm distinct from either concrete particular things or intellects. This is after I spend much of chapter 3 arguing against this third, Platonic alternative.
Furthermore, Carrier distorts what I say here because he collapses two steps of the argument he’s quoting from (steps 40 and 41) into one, without telling the reader that that is what he is doing. The argument up to step 40 establishes that the forms or patterns in question exist in the purely actual actualizer. Since the purely actual actualizer is not an abstract entity, that already rules out a third alternative such as the Platonic realm. Hence the thesis in step 41 is not the leap in logic that Carrier represents it as being.
Carrier, in any case, at this point unfortunately once again lapses back into vigorously attacking an argument that exists only in his imagination. For some reason, he seems to think I am adopting something like Plato’s view. (“Aristotle took Plato to task for the mistake Feser is making,” he writes. No, I don’t know what the hell he’s talking about either.) As if responding to something I had actually said, he writes: “It’s thus self-contradictory of Feser to insist that potential things must be ‘actualized’ somewhere,” and continues in this vein at obscure and tedious length. Since I never said anything of the kind, and once again can barely make heads or tails of Carrier’s remarks other than to note that they bear no relation to any argument I actually gave, I will skip these further irrelevancies and move on to what seems to be Carrier’s main objection.
Carrier proposes that instead of the purely actual actualizer, it is plausibly just space-time that is the ultimate reality. He thinks it could even be said to have the key divine attributes. He doesn’t endorse this position himself, but thinks that it no less plausibly follows from my premises than my own conclusion does.
One problem with this is that, contrary to what Carrier supposes, this would not be consistent with atheism, but would amount to a kind of pantheism. The main problem, though, is that space-time simply could not be the ultimate reality, for reasons that should be obvious to anyone who has read my book. Space-time, for all Carrier has shown, is contingent. Accordingly, its essence is distinct from its existence, it is by itself merely potential unless actualized, and thus it requires a cause distinct from it. Since it is extended, it is also in the relevant sense material (contrary to what Carrier asserts) and is composite rather than simple (contrary to what Carrier asserts). Of course, Carrier would reject these claims and the philosophical arguments I deploy in order to defend them, but the point is that he gives absolutely no non-question-begging reason to reject them.
There are plenty of other foolish remarks. For example, Carrier claims that the Aristotelian notions I deploy are “obsolete” and accuses me of “ignoring the sciences.” But he never tells us exactly whythe notions in question are obsolete or exactly what is the relevant scientific evidence that I ignore. And in fact, at pp. 43-60 I explicitly address the various scientific objections (from Newton, from quantum mechanics, from relativity, etc.) that might be raised against the Aristotelian proof and I explicitly address the charge that the argument presupposes obsolete Aristotelian scientific ideas and show that it has no force. Carrier says nothing in response to these points.
Carrier repeatedly asserts that my arguments must be non-starters because they are metaphysical rather than scientific. But of course, throughout the book I defend the claim that science is not the only rational form of inquiry. For example, at pp. 273-285 I explicitly argue against the scientism that Carrier simply takes for granted. He has nothing to say in response to those arguments either.
Carrier alleges that the last chapter of my book, wherein I respond to the standard general objections to the project of natural theology, “only ‘succeeds’ by omitting everything that actually undermines his conclusions.” But not only does he give no actual examples of objections I ignore that undermine my conclusions, he explicitly declines to respond to anything I say in that chapter, claiming that “it won’t serve any function” to do so. (Evidently, responding to what an author actually wrote is not in Carrier’s view a “function” of a book review.)
Carrier characterizes the purely actual actualizer as “self-actualizing” and says that the intelligence I attribute to the purely actual actualizer is an “organized complexity.” This is cringe-makingly incompetent, for of course, no Aristotelian or Thomist would ever say such things. The divine intellect, being absolutely simple, is the opposite of complex, and God’s being purely actual entails that he is not actualized at all, let alone “self-”actualized. Such basic errors would by themselves suffice to show that Carrier simply doesn’t know what he is talking about, if that weren’t blindingly obvious already.
My favorite piece of Carrier incompetence is this:
Though there is a lot there of interest if you want to explore Feser’s theology – including a really bizarre, sexist argument for God being a man (around pages 246-57).
End quote. First of all, the argument he’s referring to is actually at pp. 246-48. Second, of course I do not argue that God is a “man.” In fact I explicitly say at pp. 246-7 that “since [God] is not a human being, he is not literally either a man or a woman. He is sexless” (emphasis added). Rather, I argue for the appropriateness of using masculine languagein a non-univocal way when speaking of God. Third, I do give actual arguments, which Carrier simply ignores. Fourth, of course Carrier couldn’t care less about all that, but is just interested in throwing out some red meat to the SJW crowd.
The rest is trash talk (“He’s done. Cooked,” “100% bullshit,” etc.), central casting New Atheist straw men (“Giant Ghost hypothesis”), and relentless and relentlessly question-begging dime-store scientism. Nothing intellectually serious.
It is hard to believe that Carrier actually read Five Proofs through, but I certainly did not bother to read the rest of his critique, judging that if what he has to say about the Aristotelian proof is this awful, it would be a waste of time and energy to proceed any further. If any reader has bothered to read it and found some gold among the dross, feel free to call our attention to it in the combox below.
Published on February 24, 2018 10:52
February 19, 2018
Drunk stoned perverted dead

There is also nothing necessarily perverse about using some thing other than one’s own natural faculties in a way that is contrary to its end (e.g. using a toothbrush to clean the sink rather than one’s teeth, or using a plant or animal for food). Moral reasoning is about what I, the moral agent, ought to do. It is because certain acts would actively frustrate my own natural ends, which are constitutive of what is good for me, that they constitute a perverse exercise of practical reason. Doing what frustrates some other thing does not per se frustrate my own natural ends, and thus is not intrinsically perverse in the relevant sense. (It may or may not be wrong for some other reason, but that’s a different question.) As I have suggested elsewhere, perverting a faculty is in this way comparable in its irrationality to a performative self-contradiction.
I have spelled out the nature of perverted faculty reasoning in detail in my article “In Defense of the Perverted Faculty Argument,” from my anthology Neo-Scholastic Essays . I respond there to all the standard objections, most of which are based on misunderstandings. The uninitiated reader who objects to the perverted faculty reasoning that follows is urged to read that essay before commenting, because odds are I’ve already answered your objection there. For example, please don’t waste your time or mine by raising tired purported counterexamples like the use of ear plugs, a sterile married couple having sex, etc. I’ve already explained in the article why these do not count as perversions of a faculty.
On to our subject, then: The standard natural law position is that the use of alcohol or drugs is always and intrinsically immoral when (a) it subverts reason, and (b) it does so for the sake of an end which is not itself prescribed by reason. If conditions (a) and (b) are not both met, then the use of alcohol or drugs is not always and intrinsically wrong (even if certain circumstances might make it wrong). Let’s elaborate on these two conditions.
First, what counts as subverting reason? Merely altering one’s mood is not problematic. As the Thomistic natural law theorist John C. Ford notes in his book Man Takes a Drink: Facts and Principles about Alcohol, the natural law position regards the use of alcohol as legitimate when it merely leads to “a mild lift, or a comfortable sense of relaxation – a mild euphoria” (p. 52), or “mild relaxation, or mild exhilaration, or cheerfulness” (p. 56). One’s reason can still be perfectly in charge of one’s behavior in this case. (Thus does Proverbs 31:6-7 say: “Give strong drink to one who is perishing, and wine to those in bitter distress; let them drink and forget their poverty, and remember their misery no more.”)
The trouble comes when reason is either no longer in charge or its control is impaired. This would be true, for example, of someone who has drunk so much that he cannot think or perceive clearly, or whose moral inhibitions have become relaxed, or whose other inhibitions are lowered to the point where he does things he would otherwise be too embarrassed to do, or whose motor skills have been impaired.
What about condition (b)? Doing something that one knows will suspend reason is not always and intrinsically wrong. For example, as Aquinas writes:
For it is not contrary to virtue, if the act of reason be sometimes interrupted for something that is done in accordance with reason, else it would be against virtue for a person to set himself to sleep. (Summa Theologiae II-II.153.2)
The kind of rational thing a human being is is a rational animal, and our animality requires us to sleep, which temporarily interrupts reason. This is not contrary to our nature, because the whole point of sleep is precisely to preserve the health of the whole rational animal. Similarly, when for the sake of surgery we take an anesthetic, we temporarily suspend reason but are not acting contrary to reason, precisely because our aim is to preserve the whole organism of which reason is a faculty. For the same reason, when alcohol or drugs are used for medical purposes even though it is foreseen that they will subvert reason, such use is not necessarily wrong. The situation is analogous to the amputation of a diseased body part for the sake of preserving the whole body. Reason temporarily suspends itself precisely for the sake of preserving itself.
What is wrong is when reason is subverted for the sake of something inferior toreason, as when someone deliberately drinks to the point of suspending reason merely for the sake of the more intense sensory pleasure this would bring. Reason subverting itself for the sake of something inferior to reason is perverse, in the “perverted faculty argument” sense of the word. It is reason acting directly contrary to (rather than merely other than) its own natural end. It essentially involves a rational animal deliberately trying to make of himself, if only partially and temporarily, a non-rational animal.
Naturally, there are also other considerations that make intoxication morally problematic, such as the risks to health and safety it can pose. But it is the perversion of the rational faculty that makes it always and intrinsically wrong to use alcohol or drugs to the point of subverting reason for the sake of mere sensory pleasure. It is a kind of self-mutilation of rationality, the highest and distinctive human faculty. Ford writes:
It is interesting to note that some theologians treat of drunkenness, especially habitual drunkenness, under the commandment “Thou shalt not kill.” The Fifth Commandment, besides forbidding murder and self-destruction, is taken to forbid self-mutilation and to command a reasonable care of one’s own life and health. There is also a psychological appropriateness in considering drunkenness a kind of suicide. Especially for the alcoholic, each cup has a little death in it, a little of that oblivion which he seeks, consciously or unconsciously. (p. 74)
Ford’s thesis that the drunkard or stoner seeks a kind of temporary suicide of his rationality is lent support by the way descriptions like wasted, smashed, bombed, hammered, stoned, dead drunk, etc. are used approvingly.
A common libertarian rhetorical trick is to speak as if there is hypocrisy or inconsistency in approving of alcohol while disapproving of other intoxicating substances. This is quite silly and overlooks an obvious distinction. It is easy for most people to use alcohol in the moderate way that results merely in the “mild exhilaration” or “cheerfulness” that does not subvert reason, and a great many people do in fact habitually use it in precisely this way. By contrast, many other drugs are used precisely for the sake of attaining a high that subverts reason. If someone approves of recreational alcohol use only insofar as it does not subvert rationality, and disapproves of the recreational use of other drugs only insofar as they do subvert rationality, then there is no hypocrisy or inconsistency at all.
To be sure, it is true that sensibilities about what substances it is licit to use in moderation can be to some extent culturally relative and reflect mere prejudice. Ford gives an amusing example to illustrate the point:
It was only a few hundred years ago that the devout priests of a certain religious order in Europe protested bitterly against the introduction of coffee at breakfast. They maintained it was expensive, luxurious, imported and exotic, not in keeping with religious poverty, and not befitting men dedicated to God. They insisted on retaining their traditional breakfast beverage, which was beer. (p. 58)
All the same, not all misgivings about the use of a drug are based on mere cultural prejudice, and the imperative of avoiding the deliberate suspension of reason provides an objective and clear criterion by which to distinguish substances that can be used in moderation and those that should be avoided altogether.
As Plato warned in the Republic, egalitarian societies tend to be increasingly dominated by the pull of the lower appetites, and increasingly impatient with the counsel of reason. As with our society’s ever deepening immersion in sins of the flesh and the rise of the ridiculous “foodie phenomenon,” accelerating laxity with respect to drug use reflects this decadence, rather than more careful and consistent thinking about the subject. If you won’t listen to Plato, at least listen to Animal House.
Published on February 19, 2018 11:29
February 13, 2018
Time, space, and God

The problems with this, from a Thomist (and more generally, classical theist) perspective, should be obvious. Space is extended. God is not. Time entails change. God is changeless. And if space and time are divine attributes, then we have to take a pantheist or at least panentheist view of the natural world. For the most general features of nature would then be aspects of God.
William Lane Craig thinks this isn’t quite right. He writes:
Newton… declares explicitly that space is not in itself absolute and therefore not a substance. Rather it is an emanent – or emanative – effect of God. By this notion Newton meant to say that time and space were the immediate consequence of God's very being. God's infinite being has as its consequence infinite time and space, which represent the quantity of His duration and presence. Newton does not conceive of space or time as in any way attributes of God Himself, but rather, as he says, concomitant effects of God. (Time and Eternity, p. 46)
Putting aside questions of Newton exegesis, would this get Clarke and Newton out of the frying pan? Only by landing them in the fire. For if time and space are “concomitant effects” or “the immediate consequence” of “God's very being,” then their existence follows of necessity from his. And there are several problems with this thesis.
First, it would entail that the act of creation was not free (or at least that the creation of space and time was not free). For according to this thesis, God cannot not create time and space. But freedom is one of the divine attributes, knowable even by way of purely philosophical argumentation. (See e.g. Summa Theologiae I.19.10; Summa Contra Gentiles I.81, I.88 and II.23; Five Proofs of the Existence of God , pp. 224-228.)
Second, for God to create of necessity would detract from his perfection. As Aquinas argues in Summa Theologiae I.19.3:
God wills things apart from Himself in so far as they are ordered to His own goodness as their end. Now in willing an end we do not necessarily will things that conduce to it, unless they are such that the end cannot be attained without them; as, we will to take food to preserve life, or to take ship in order to cross the sea. But we do not necessarily will things without which the end is attainable, such as a horse for a journey which we can take on foot, for we can make the journey without one. The same applies to other means. Hence, since the goodness of God is perfect, and can exist without other things inasmuch as no perfection can accrue to Him from them, it follows that His willing things apart from Himself is not absolutely necessary.
End quote. So, if this is correct, then if God is perfect, his willing of things other than himself is not necessary. But then, if his willing of things other than himself (in particular, time and space) isnecessary, then by modus tollens he is not perfect.
Similarly, in Summa Contra Gentiles II.23.8, Aquinas argues that since “agents which act by will are obviously more perfect than those whose actions are determined by natural necessity,” God must be free.
A third problem is that if the existence of time and space follows necessarily from God’s existence, then not only did they have no beginning but they in principle could not have had a beginning. This would not conflict with classical theism per se, but it would conflict with any version of classical theism which incorporates biblical revelation.
Fourth, we have a conflict with Catholic orthodoxy. The First Vatican Council teaches:
If anyone says that finite things, both corporal and spiritual, or at any rate, spiritual, emanated from the divine substance… let him be anathema.
If anyone… holds that God did not create by his will free from all necessity, but as necessarily as he necessarily loves himself… let him be anathema.
Fifth, the position Craig attributes to Newton is not really a coherent one, at least not on a Thomistic metaphysical analysis. For the position in question essentially holds that time and space cannot not exist and yet are not divine attributes. But if they cannot not exist, then time and space must be purely actual and there must be in them no distinction between essence and existence. But in that case they are divine attributes, since only of God can these things be said. On the other hand, if they are not divine attributes, then they must not be purely actual and there must be in them a distinction between essence and existence. In that case, though, it is false to say that they cannot not exist, since anything that is less than pure actuality, and anything in which there is a distinction between essence and existence, can in principle fail to exist.
So, there just is no sense to be made of the idea that there is something distinct from God that he cannot not create. If he cannot not create it then that is only because it cannot not exist, in which case it is purely actual and subsistent being itself and thus really identical with God. If it is really distinct from God, then it is not purely actual or subsistent being itself, and thus it can fail to exist and God can refrain from creating it. The supposed middle ground position between pantheism on the one hand, and affirming the contingency of time and space on the other, is an illusion.
Published on February 13, 2018 11:47
February 11, 2018
NOR on By Man Shall His Blood Be Shed

Catholics are so accustomed to hearing that opposition to capital punishment is pro-life that few may realize there are good reasons to support it. Those reasons are set forth in a systematic and convincing manner in By Man Shall His Blood Be Shed. Edward Feser and Joseph M. Bessette find the pendulum has swung too far in one direction in the capital-punishment debate (to the extent there is one today), and Catholics are confused when told that something their Church upholds, and has always upheld, is now considered immoral…Their approach is rigorously logical, philosophical, and biblical, and they defend capital punishment as an essential recourse for society to punish the worst criminals. Feser and Bessette never stray from Catholic teaching and tradition in their treatment of the subject…
In the tradition of Aquinas, the authors not only lay out a solid case for capital punishment but also address the various arguments against it – that it’s an affront to human dignity, that it doesn’t deter, that it forecloses the possibility of reform, and that the innocent might sometimes be executed. After careful examination, the authors find all such arguments wanting…
By Man Shall His Blood Be Shed asks much of the reader; its thorough and closely reasoned treatment of a complex subject allows no shortcuts. But those who persevere to the end are amply rewarded. Feser and Bessette accomplish what they set out to do: present a badly needed corrective to what recently has been a largely one-sided treatment of capital punishment. Catholics who are open to hearing the case for it – perhaps for the first time – will find this book indispensable.
Published on February 11, 2018 17:12
February 8, 2018
The latest on Five Proofs

At First Things, Dan Hitchens reflects on how the arguments of Five Proofs might be received in an age of short attention spans.
Jeff Mirus at Catholic Culture recommends Five Proofs.
At Catholic World Report, Christopher Morrissey kindly reviews Five Proofs. From the review:Whether all readers are convinced by Feser’s proofs or not, Feser’s lively approach in this book nonetheless demonstrates at least this much: despite all their bluster, natural theology’s funeral directors will inevitably be buried first. Feser takes a shovel to them.
End quote. Morrissey also offers some interesting critical reflections on the Augustinian proof (to which I may respond in a future post). As they say, read the whole thing. Some further comments from Morrissey at B.C. Catholic.
The blog Ontological Investigations is critically examining the book in a series of posts. Some of what is said is quite off-base (e.g. the false claim that I do not address the most serious critics). But overall this seems to be a serious attempt to grapple with the book’s arguments, and I may respond to some of it in a future post.
Published on February 08, 2018 12:50
January 31, 2018
David Foster Wallace on abstraction

First they are given, say, five oranges. Something they can touch or hold. Are asked to count them. Then they are given a picture of five oranges. Then a picture that combines the five oranges with the numeral ‘5’ so they associate the two. Then a picture of just the numeral ‘5’ with the oranges removed. The children are then engaged in verbal exercises in which they start talking about the integer 5 per se, as an object in itself, apart from five oranges. In other words they are systematically fooled, or awakened, into treating numbers as things instead of as symbols for things. Then they can be taught arithmetic, which comprises elementary relations between numbers. (pp. 8-9)
This little narrative nicely illustrates the sense in which an Aristotelian would regard numbers as abstract objects. (To be sure, Wallace himself was not an Aristotelian, but it turns out that some of his examples and remarks are readily adaptable to Aristotelian purposes.) Numbers are objects in the sense that we can refer to them, attribute features to them, etc. They are abstractobjects in the sense that they exist only as abstracted out from concrete reality by the intellect. There can be five apples in mind-independent reality, or five dogs, or five donuts, but not five itself, considered as a kind of freestanding entity. The number five is not an “abstract object” in the Platonic sense of the term common in contemporary philosophy (viz. an object that exists in some third kind of way over and above intellects on the one hand and concrete particulars on the other), and could not be. For what is abstract is, for the Aristotelian, what results from abstraction, and abstraction is a mental activity of considering one aspect of a thing in isolation from other aspects.
The example also indicates, at least obliquely, both the power and the perils of abstraction. That mathematical reasoning is powerful goes without saying, and it would not be powerful if it didn’t get at something deep in the nature of objective reality. The intellect doesn’t make up mathematical truth out of whole cloth, but pulls it out from the concrete reality into which it is, as it were, mixed. The peril is that we can easily be “fooled” (as Wallace puts it) into treating mathematical objects as if they existed outside the mind in precisely the abstract way in which they exist within the mind.
Nor is it merely that abstract objects – numbers, geometrical figures, universals, etc. – do not exist in this third, Platonic way. Another peril is that we are tempted to take what are really just artifacts of the abstractive exercise to be features of mind-independent reality. Commenting on Zeno’s dichotomy paradox, Wallace writes:
[T]here’s obviously some semantic shiftiness going on here… [which] lies in the implied correspondence between an abstract mathematical entity – here an infinite geometric series – and actual physical space… [T]raversing an infinite number of dimensionless mathematical points is not obviously paradoxical in the way that traversing an infinite number of physical-space points is… [T]he translation of an essentially mathematical situation into natural language somehow lulls us into forgetting that regular words can have vastly different senses and referents. (p. 70)
As the example of Zeno shows, the tendency to confuse abstractions with concrete reality is the source of many metaphysical errors. To be sure, as Wallace immediately goes on to say of the specific muddle he calls our attention to:
Note… that this is exactly what the abstract symbolism and schemata of pure math are designed to avoid, and why technical math definitions are often so numbingly dense and complex. You want no room for ambiguity or equivocation. Mathematics… is an enterprise consecrated to the ideal of precision.
Which all sounds very nice, except it turns out that there is also immense ambiguity – formal, logical, metaphysical – in many of the basic terms and concepts of math itself. In fact the more fundamental the math concept, the more difficult it usually is to define. This is itself a characteristic of formal systems. Most of math’s definitions are built up out of other definitions; it’s the really root stuff that has to be defined from scratch. Hopefully… that scratch will have something to do with the world we all really live in. (pp. 70-1)
Wallace seems to think that the way people study math at more advanced levels tends to exacerbate the problem:
The trouble with college math classes– which classes consist almost entirely in the rhythmic ingestion and regurgitation of abstract information, and are paced in such a way as to maximize this reciprocal data-flow – is that their sheer surface-level difficulty can fool us into thinking we really know something when all we really ‘know’ is abstract formulas and rules for their deployment. Rarely do math classes ever tell us whether a certain formula is truly significant, or why, or where it came from, or what was at stake. There’s clearly a difference between being able to use a formula correctly and really knowing how to solve a problem, knowing why a problem is an actual mathematical problem and not just an exercise. (p. 52)
Now, this is an extremely important point, which applies well beyond mathematics itself. The sheer difficulty of reasoning about abstractions can lead us to overestimate the significance of the payoff, especially when the payoff is indeed significant in some respects. Nowhere is this truer than in modern physics. As Wallace writes:
The modern transition from geometric to algebraic reasoning was itself a symptom of a larger shift. By 1600, entities like zero, negative integers, and irrationals are used routinely. Now start adding in the subsequent decades’ introductions of complex numbers, Napierian logarithms, higher-degree polynomials and literal coefficients in algebra – plus of course eventually the 1st and 2nd derivative and the integral – and it’s clear that as of some pre-Enlightenment date math has gotten so remote from any sort of real-world observation that we and Saussure can say verily it is now, as a system of symbols, “independent of the objects designated,” i.e. that math is now concerned much more with the logical relations between abstract concepts than with any particular correspondence between those concepts and physical reality. The point: It's in the seventeenth century that math becomes primarily a system of abstractions from other abstractions instead of from the world.
Which makes the second big change seem paradoxical: math’s new hyperabstractness turns out to work incredibly well in real-world applications. In science, engineering, physics, etc. (pp. 106-7)
But this tremendous effectiveness can be misleading (and I should note that in what follows I go beyond anything Wallace himself says). Modern physics is very difficult indeed; unlike mathematics, it is concerned with the physical world; and the payoff in predictive and technological success is enormous. The temptation is strong to conclude that everything in the mathematical model of the world presented by physics corresponds to something in physical reality, and that there is nothing in physical reality that isn’t captured by the model presented by physics.
But it simply isn’t so, and the mathematical abstractness of physics is precisely what guarantees that it isn’t so. Abstraction by its very nature leaves out much that is in concrete reality, and the more abstract the model arrived at (as when, to use Wallace’s nice phrase, we are dealing with “a system of abstractions from other abstractions”), the more that is left out. Physics can no more tell you everything there is to know about the material world than learning how to count oranges can tell a child everything there is to know about oranges. As Bertrand Russell put it in a passage I’ve often quoted:
It is not always realised how exceedingly abstract is the information that theoretical physics has to give. It lays down certain fundamental equations which enable it to deal with the logical structure of events, while leaving it completely unknown what is the intrinsic character of the events that have the structure… All that physics gives us is certain equations giving abstract properties of their changes. But as to what it is that changes, and what it changes from and to – as to this, physics is silent. (My Philosophical Development, p. 13)
Or, as Russell put it more pithily and wittily elsewhere:
Ordinary language is totally unsuited for expressing what physics really asserts, since the words of everyday life are not sufficiently abstract. Only mathematics and mathematical logic can say as little as the physicist means to say. (The Scientific Outlook, p. 82)
Like Zeno, contemporary popularizers of science, and sometimes scientists themselves, confuse mathematical abstractions with concrete physical reality and draw absurd metaphysical conclusions. This is precisely what happens when it is claimed that relativity has shown that time and change are illusory, as Lee Smolin and Raymond Tallis have recently pointed out. Indeed, as Tallis emphasizes, the tendency in modern physics is to abstract from the notion of time whatever isn’t space-like, but also to abstract from the notion of space everything but pure quantity – and thus to treat time as an abstraction from an abstraction, in other words.
But again, now I’m going beyond Wallace, so I’ll stop. Much more on these subjects forthcoming in the philosophy of nature/science book I am currently working on.
Further reading:
Concretizing the abstract
Think, McFly, think!
Progressive dematerialization
Rucker’s Mindscape
Five Proofs of the Existence of God , Chapter 3
Published on January 31, 2018 17:43
January 30, 2018
Coming to a campus near you

On Saturday, March 17, I will be presenting a paper on the topic “Cooperation with Sins Against Prudence” at a conference on Cooperation with Evilat the Dominican House of Studies in Washington, D.C. The other conference speakers will be Steven Long, Msgr. Andrew McLean Cummings, Christopher Tollefsen, and Fr. Ezra Sullivan, OP.
On Thursday, April 12, I will be speaking at Baylor University on the topic of capital punishment and natural law. The event is sponsored by the Thomistic Institute, and more information will be forthcoming at the Institute’s website.
On Thursday, April 19, I will be speaking at Southern Evangelical Seminary on the topic of the nature of God. Details forthcoming.
More talks for this year to be announced. Stay tuned.
Published on January 30, 2018 10:43
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