Edward Feser's Blog, page 31

Voila! An open thread! (Updated)

UPDATE 4/20: Lately the comments sections have been filling up quickly.  Some readers seem unaware that after the count reaches 200 comments, you have to click the "Load more..." prompt that appears in small print at the bottom of the combox in order to view newer comments.  That's part of Blogger's algorithm and out of my control, sorry.  So, if you're worried that your comment is not showing up, never fear.  It's there, but you have to click the prompt to see it.
How does an annoying off-topic comment suitable only for deletion get transformed into a stimulating on-topic conversation starter?  Through the magic of the open thread post.  Whatever is on your mind, from The Prestige to Under Siege, from the Ponzo illusion to jazz-rock fusion, from Paul Bernays to Ricky Gervais, post away and stand back in wonder as your comment not only doesn’t disappear, but may even get a response!

Though probably not from me (too busy, sorry) and definitely not if you’re a troll.  On that latter, perennial topic: Our latest pest is some weirdo who keeps posting odd comments under different names, carrying on conversations with himself while pretending it is other commenters who are guilty of this childish behavior.  As always, please ignore such people.  And as always, please resist any urge to respond to gratuitous abuse or other obnoxiousness in a way that is likely to spiral into an endless and unedifying exchange of insults.  As time and attention permits, I will delete this garbage.  Please remember that you are a guest here.  Act accordingly.

Also, too many people keep posting anonymously, making exchanges confusing.  If you don’t want to post under your own name or through a Google account, fine, but at least choose some one consistent pseudonym to post under so that people don’t have to keep trying to figure out which anonymous commenter said what. 

For anyone who is interested, earlier open threads are archived here.

Voila! An open thread!

How does an annoying off-topic comment suitable only for deletion get transformed into a stimulating on-topic conversation starter?  Through the magic of the open thread post.  Whatever is on your mind, from The Prestige to Under Siege, from the Ponzo illusion to jazz-rock fusion, from Paul Bernays to Ricky Gervais, post away and stand back in wonder as your comment not only doesn’t disappear, but may even get a response!

Though probably not from me (too busy, sorry) and definitely not if you’re a troll.  On that latter, perennial topic: Our latest pest is some weirdo who keeps posting odd comments under different names, carrying on conversations with himself while pretending it is other commenters who are guilty of this childish behavior.  As always, please ignore such people.  And as always, please resist any urge to respond to gratuitous abuse or other obnoxiousness in a way that is likely to spiral into an endless and unedifying exchange of insults.  As time and attention permits, I will delete this garbage.  Please remember that you are a guest here.  Act accordingly.

Also, too many people keep posting anonymously, making exchanges confusing.  If you don’t want to post under your own name or through a Google account, fine, but at least choose some one consistent pseudonym to post under so that people don’t have to keep trying to figure out which anonymous commenter said what. 

For anyone who is interested, earlier open threads are archived here.

Aquinas and the problem of evil

My article “The Thomistic Dissolution of the Logical Problem of Evil” has just been published in the journal Religions , and is available online.  (Follow the links to opt for either the HTML format or PDF.)  It is a contribution to a special issue devoted to responses to James Sterba’s recent book Is a Good God Logically Possible?  

What is mathematics about?

I commend to you James Franklin’s latest article “Mathematics as a Science of Non‑abstract Reality: Aristotelian Realist Philosophies of Mathematics.”  It’s a helpful brief survey of different ways that an Aristotelian alternative to Platonist and nominalist approaches to mathematics might be developed.  (Franklin explores these issues in greater depth in his book An Aristotelian Realist Philosophy of Mathematics .) 

Franklin approaches the dispute between these three views, and between alternative ways of spelling out the Aristotelian view, by way of the question: What is mathematics about?  The Platonist says that it is about a realm of abstract objects distinct from both the world of concrete material things and the human mind.  The nominalist says that it is not really about anything, since mathematical entities are in no way real.  The Aristotelian approach rejects nominalism and agrees with Platonism that mathematical entities are real.  But it disagrees with the Platonist about the location of these entities.  They are, for the Aristotelian, properties of concrete particular things themselves, rather than denizens of a Platonic “third realm.”

But exactly what sort of properties of concrete particular things?  Franklin suggests that different views which can plausibly all be characterized as broadly “Aristotelian” have proposed different properties as the ones mathematics is paradigmatically concerned about.  Some say that mathematics is fundamentally about the study of quantity; some say it is fundamentally about relations; some say it is about structure; and some say it is about patterns. 

Franklin discusses all of these possibilities and notes that, arguably, the study of relations and the study of structure more or less amount to the same thing.  The difference would be that the former starts with the elements of a structure and then works up to an account of how the relations between them give rise to a larger whole, whereas the latter starts with the whole and then works down to the relations between the elements.  The study of pattern might also be seen as the study of certain kinds of relations or certain kinds of structure.  So, these approaches to understanding what mathematics is about might, in Franklin’s view, plausibly be unified.  They can, in particular, be accommodated to the view that mathematics is about the study of the structural features of concrete reality.

What cannot be so easily assimilated to this approach, in Franklin’s view, is quantity.  For certain quantitative phenomena, though they have structural features, are not entirely reducible to structure.  (He gives size as an example.)  Hence Franklin thinks that there currently exists no entirely unified Aristotelian approach to the question of what mathematics is about.  We have to say that it is the science of quantity and structure (as he does in the subtitle to his book).

Varieties of realism

Franklin also has something to say about the main objections to Aristotelian philosophy of mathematics.  Now, in order to understand these objections and his responses to them, as well as the Aristotelian approach itself, it seems to me useful to compare the dispute in philosophy of mathematics to the more general dispute between parallel views about the problem of universals.  Recall that nominalism holds that universals like triangularity, humanness, etc. are mere fictions, whereas realism holds that they are real, something the human mind discovers rather than invents.  But there are several alternative ways of spelling out realism.

Platonic realism holds that universals are not only real, but exist in a “third realm” over and above both the world of concrete material things and any mind.  Aristotelian realism holds that universals are real, but denies that there is any such third realm.  Rather, it takes triangularity, humanness, etc. to exist only either in particular individual triangles, human beings, etc., or in minds which entertain these universals in abstraction from the particular individuals.

A third view, sometimes called Scholastic realism, can be interpreted as a kind of middle ground position between Platonic and Aristotelian realism.  Like Aristotelian realism, it denies that there is any “third realm” distinct from both the material world and all minds.  But like Platonic realism, it holds that universals are to be located first and foremost somewhere distinct from both the material world and finite minds – namely, in the infinitemind of God, where they function as the archetypes according to which God creates the world of concrete things.

You could think of Scholastic realism as “Aristotelianizing” Plato by bringing the realm of the Forms into a mind, namely the divine mind, thereby eliminating the third realm.  Or you could think of it as “Platonizing” Aristotle by making the divine mind function in something like the way the realm of the Forms does in Platonism.  Because it rejects the third realm and adheres to the Aristotelian twofold divide between the material world and minds, I tend to think of Scholastic realism as essentially a variation on Aristotelian realism.  But it is a dramatic enough modification that it is useful to have the separate label for it.

Now, applying these distinctions to the philosophy of mathematics, the mathematical Platonism Franklin is talking about obviously corresponds to Platonic realism about universals, and the mathematical nominalism he is talking about obviously corresponds to nominalism about universals. 

The Aristotelian philosophies of mathematics he describes correspond, naturally, to Aristotelian realism about universals.  But Aristotelian realism about universals, as I’ve said, takes universals to exist in two ways, even though it rules out the third realm of the Platonist.  They exist in concrete particulars themselves, but also in the intellects that abstract them from the particulars.  And it is the latter fact that opens the door to developing Aristotelian realism in a Scholastic realist direction.  The divine mind, qua mind, is technically not a Platonic thirdrealm, and thus stays within the letter of Aristotelian realism.  But it nevertheless functions much like Plato’s third realm does.  In particular, it gives the Scholastic realist a way of dealing with phenomena that Aristotelian realism has a problem with, such as uninstantiated universals. 

For example, consider extinct animals like velociraptors.  After they died out, the universal velociraptorwas no longer instantiated, and before human beings discovered its remains, no human mind entertained that universal.  So, during the long interval between extinction and discovery, the universal could be found neither in the world of concrete material things nor in human minds.  But what was true about the essence and properties of velociraptors did not change during that time.  What could have grounded that fact?  The Scholastic realist would answer that the universal still existed in the divine intellect.  (For exposition and defense of Scholastic realism, see chapter 3 of Five Proofs of the Existence of God.)

If you are a realist about mathematics, then, but reject Plato’s “third realm,” then there are two other realms where you might try to locate mathematical entities: in the world of concrete material objects, or in minds (including, in principle, the divine mind).  What, in Five Proofs, I label the Augustinian proof for God’s existence emphasizes the latter realm, and Scholastic realism is in that tradition.  Franklin instead emphasizes the former realm.  Naturally, one can also take mathematical entities to exist in both realms.  But one is likely to put greater emphasis on one rather than the other depending on which mathematical entities one takes to be most central to mathematics.

Franklin points out that Aristotelian realists about mathematics tend to focus on physically realizable and perceivable mathematical properties like symmetry and ratio, whereas arguments for Platonic realism often focus instead on higher infinities, the perfection of geometrical idealizations, and the like.  This different focus is, I think, also reflected in the different ways that Aristotelian realism itself might be developed.  If your emphasis is on showing how mathematics can be accommodated to an Aristotelian epistemology, you’ll probably focus more on the sorts of mathematical properties Franklin does, and on finding ways to locate mathematical properties in general in concrete material reality.  If instead your emphasis is on showing how the strongest points in favor of Platonism (infinities, geometrical perfection, etc.) can be accommodated within a broadly Aristotelian metaphysics, you’re more likely to be willing to take Aristotelian realism in a Scholastic realist direction (unless you prefer to add a dash of instrumentalism to your realism – see below). 

Naturally, the former route is also a more promising one if, when doing philosophy of mathematics, you want to avoid having to appeal to inevitably controversial theological premises, defense of which would require getting into matters far removed from mathematics itself.  Scholastic realism is a more natural option to consider when you’re approaching mathematics from the point of view of debates in natural theology.  (Cf. my review in First Things of William Lane Craig’s book God Over All: Divine Aseity and the Challenge of Platonism.)

Objections to Aristotelianism

Franklin addresses three main objections to Aristotelian philosophy of mathematics.  The first is to hold that the Aristotelian approach is undermined by Frege’s famous critique in The Foundations of Arithmetic of John Stuart Mill’s empiricist account of arithmetic.  Now, in a post on Frege and Mill from some time back, I noted that while it is controversial whether Frege was fair to Mill himself, his criticisms were effective against the crude position often attributed to Mill.  Franklin points out that they are noteffective against a more sophisticatedposition than the one often attributed to Mill.

The second main objection to Aristotelianism is that higher infinities, and even huge finite numbers, are not plausibly instantiated in the physical world.  Here Franklin proposes two possible replies.  The first is to point out that this objection would prove too much insofar as it would, if effective, undermine natural science no less than an Aristotelian interpretation of mathematics.  For example, what Newtonian physics tells us about mass, distance, and force applies to values too large to be instantiated in the physical world, as well as to values that are instantiated.  Computational chemistry studies merely possible compounds.  And so on.  In other words, natural science studies uninstantiated universals.  If this is OK for science, why not for mathematics interpreted in an Aristotelian way?

The trouble with this response, though, as Franklin realizes, is that it just raises the question of exactly what the metaphysical status is of uninstantiated universals, whether those studied by mathematics or those studied by natural science.  Now, Franklin makes the perfectly reasonable point that an Aristotelian needn’t be a realist across the board.  One could take some mathematical entities to be real, but others to be merely useful fictions.  You have to go case by case.  But this is more plausible in some cases than in others, and Franklin allows that what he calls a “quasi-Platonist” account of some mathematical entities may be necessary.

Here, it seems to me, is a case where Aristotelian realism stands in need of development in a Scholastic realist direction.  The same can be said of the consideration raised by the third main objection to Aristotelianism considered by Franklin, which is that some mathematical entities (e.g. perfect circles and other geometrical entities) are idealizations that are never found perfectly realized in the physical world.  In response, Franklin points out that what applied mathematics strictly needs are only the approximations that are found in the physical world.  But this seems to me to miss the point.  For there are objective truths about the idealizations no less than there are about the approximations, and these cannot be grounded in what is actually there in the physical world.  As with infinities, Scholastic realism is able to deal with these in a way that an Aristotelian realism that avoids going in a theological direction is not.

Related reading:

Frege on what mathematics isn’t

The access problem for mathematical Platonism

Review of Craig’s God Over All: Divine Aseity and the Challenge of Platonism

Rucker’s Mindscape

David Foster Wallace on abstraction

Frege on objectivity

Frege on objectivity

It can be an interesting exercise every now and then to reread something that had a profound effect on you earlier in life.  In my case, Gottlob Frege’s grand 1918 essay “The Thought” is a piece that I find always repays renewed study.  I think I first read it almost 30 years ago, and it was one of several philosophical works on thought and language that began to break the hold on me of the metaphysical naturalism I had picked up as an undergraduate – though that was a slow process, taking a decade fully to unfold. 

At first blush, Frege’s subject matter – the nature of propositions, their truth values, and logic as the science concerned with the study of these – couldn’t be further removed from political philosophy.  But Frege was something of a Platonist, and as Plato knew well, metaphysics has political implications, not least when it is not directly concerned with politics at all.  For there can be no sound political order that does not recognize something non-political existing beyond it, by reference to which it can be judged. 

In “The Thought,” Frege reminds us that truth and the laws of logic are timeless and discovered rather than made – that, though they are grasped by time-bound human minds and conveyed through contingent human languages, they are independent of both.  Lacking an essential connection to any particular human mind, they constitute neutral territory on which all minds can meet.  The lesson is basic, but depressingly needed at a time when it seems there is almost nothing that is not becoming politicized, and where ideas are evaluated in terms of the motives, party affiliation, race, sex, or other irrelevant circumstances of the person presenting them, rather than by reference to disinterested criteria of truth and logical argumentation. 

Frege’s essay is very rich, and there are well-known secondary themes in it that I will pass over for present purposes, such as Frege’s anticipation of what is now called the “redundancy theory” of truth, and his treatment of indexical expressions.  What I want to focus on is the main theme, which is the objectivity of truth and logic.

Propositions

First let’s get clear on what Frege means by a “thought.”  He characterizes it as the “sense” of a sentence, and contemporary philosophers and logicians tend to prefer the word “proposition.”  To take some stock examples, consider the English sentence “Snow is white” and the German sentence “Schnee ist weiss.”  Being in different languages, they are different sentences, but they convey the very same proposition – namely the proposition that snow is white. 

A proposition is therefore not to be identified with a sentence or indeed with any other set of physical marks or sounds, linguistic or otherwise.  For not only can the same proposition be conveyed through different sentences, but it would remain either true or false even if there were no sentences to convey it through.   For example, the proposition that snow is white was true before English, German, or any other language existed, and it would remain true even if all languages went out of existence tomorrow.  Indeed, even if there were no material world at all, there would still be true propositions, such as the proposition that there is no material world.  Logical relationships between propositions would still hold as well.  For example, the proposition that all men are mortaland the proposition that Socrates is a man would entail the further proposition that Socrates is mortal whether or not Socrates, mortal things, or any other material thing existed.

Again, Frege refers to propositions as “thoughts.”  Consider the way that, if an English speaker uttered “Snow is white” and a German speaker uttered “Schnee ist weiss,” we might say that the two speakers had the same thought or were thinking the same thing.  What Frege is talking about, then, is not a thought in the sense of a particular psychological episode in the history of some individual mind – which is unique to the individual and thus cannot be shared by different minds – but rather the content that is grasped in the episode, which can be shared.  It is because of the psychological connotations of the word “thought” that many prefer the term “proposition,” and I’ll follow that usage here.

So, propositions, their truth values, and their logical interrelationships stand apart from human minds and language, and even apart from matter.  All the same, it is through the medium of language that we “grasp” them, as Frege puts it.  He writes: “The thought, in itself immaterial, clothes itself in the material garment of a sentence and thereby becomes comprehensible to us.  We say a sentence expresses a thought” (p. 292).  Because sentences function as the means by which propositions are grasped, and because we grasp them in particular psychological episodes that may have various contingent causes, people sometimes fall into the trap of supposing that truth, falsity, and logic are artifacts of human psychology or language.  Frege is keen to emphasize the fallaciousness of this inference.

Psychology and language

Psychology and logic are like apples and oranges.  When I reason from the propositions that all men are mortal and Socrates is a manto the conclusion that Socrates is mortal, there may be any number of psychological factors that bring about that episode of thinking.  Maybe someone put drugs in my coffee and that, for some reason, triggered the episode.  Maybe I have a deep-seated hatred of Socrates and secretly delight in the thought of his mortality.  Or maybe it has something to do with the way my psychology was molded by natural selection, or by capitalist economic institutions, or by the phallocentric heteronormative patriarchal hegemony, or whatever.  None of that is in any way relevant to whether the inference is a good one.   The conclusion does indeed follow logically from the premises, and that is that.  As Frege emphasizes, laws of psychology (if there are any) are one thing, and the laws of logic another.

Similarly, a sentence may have various connotations, and the uttering of it or entertaining of it in one’s mind may be associated with various moods, feelings, mental images, and so on.  None of that is at all relevant to the truth or falsity of the proposition expressed by the sentence, or to its logical relations to other propositions.

A written or spoken sentence is also a material entity, embodied in ink marks, sound waves, light patterns on a computer screen, or the like.  We can see and hear these.  But you cannot see, hear, or otherwise perceive the proposition expressed by the sentence, nor can you literally see or hear the truth or falsity of a proposition (even if you can see or hear things that lead you to judge it to be true or false) or the validity of an inference like the one about Socrates.  Truth, falsity, validity, consistency, and other logical properties and relationships are not material properties and relationships. 

So, again, human psychological states and processes and language are merely the vehicles through which propositions and their logical relationships are conveyed to us.  The latter cannot be reducedto the former.  The supposition that logical relationships are reducible to psychological ones is often called psychologism, and Frege’s essay is a classic attack on this error.

The three realms

Frege famously argues that these facts yield the result that there are really three kinds of reality:

1. The “outer world” of material objects

2. The “inner world” of sensations, mental images, feelings, wishes, inclinations, and other psychological states and entities

3. The “third realm” of thoughts or propositions

Realms 1 and 2 differ in four key ways.  First, material objects are public entities, equally accessible to all observers.  By contrast, psychological states and entities are private.  Anyone can see the tree outside your window, but no one but you can “see” the mental picture you might form of the tree outside your window.  Anyone can hear you stub your toe and the yelp you emit as a result, but no one but you can literally feel the pain in your toe.  And so on.

Second, psychological states and entities have no reality apart from consciousness, whereas material things would exist whether or not we are consciously aware of them.  Third, psychological states and entities therefore require an owner, a subject in whose stream of consciousness they are to be located.  Material things, by contrast, exist independently of such subjects.  Fourth and finally, each psychological state or entity has only a single owner, and cannot be shared with others.  For example, your feeling of pain may be similarto mine, but it is not literally the samefeeling. 

Now, the entities of realm 3 are in some respects like and other respects unlike the entities of realms 1 and 2.  Like the psychological entities of realm 2, propositions cannot be objects of perceptual experience.  You cannot literally see the proposition that snow is white any more than you can see another person’s mental images or feelings.  But like the material objects of realm 1, propositions are nevertheless equally accessible to everyone, are independent of consciousness, and have no single owner but are the common possessions of all.

To appeal to the traditional Scholastic distinction between the mind’s faculties, we can note that the objects of realm 1 are known through the senses, those of realm 2 are known through the imagination, and those of realm 3 are known through the intellect.

Needless to say, Frege’s talk of a “third realm” is reminiscent of Platonism, and he is typically regarded as a kind of Platonist.  However, to accept the basic point he is making in the essay – the irreducibility of the entities of realm 3 to those of realms 1 and 2 – does not require that one endorse Platonicrealism, specifically.  One could instead develop the idea along either Aristotelian realist or Scholastic realist lines.  (See chapter 3 of Five Proofs of the Existence of God for discussion of these alternatives.)

As Frege notes, if, as psychologism claims, realm 3 were reducible to realm 2, there could in principle be no communication or disagreement between people.  Suppose, to take an example from Frege, that a sentence expressing the Pythagorean Theorem conveyed nothing more than a psychological state or entity rather than a proposition.  Then what Iwas referring to when I uttered this sentence (namely, some private denizen of my subjective stream of consciousness) would be completely different from what you were referring to when you uttered it (namely, some different private denizen of your own, different subjective stream of consciousness).  We would not be talking about the same thing when we used the sentence.  Hence one of us could not really teach the Pythagorean Theorem to the other, we could not really disagree about whether the other had properly understood it, and so on.  Indeed, the supposition that we even genuinely understood each other would be an error, because there would be no common meaning we were both grasping.

Frege does not develop the point much further, but as other philosophers have argued, psychologism and other forms of relativism are ultimately simply impossible to formulate in a coherent way.  They cannot possibly be correct.  Indeed, the very attempt to formulate them presupposes their falsity.  When you say, for example, that there are no true propositions independent of this or that particular human mind or collection of human minds, that claim is put forward as if it were itself true independently of the mind of the speaker and of anyone else’s mind.  When you say that what we take to be true, and the laws of logic, reflect nothing more than the way that natural selection, economic or cultural forces, or the like contingently molded the human mind, you appeal to claims (about how natural selection and the relevant economic and cultural forces work) that are put forward as if they were true before human minds ever came on the scene.  In defending such claims, you appeal to standards of logical argumentation as if they had an objective status that made them normative for all listeners, including those you are trying to persuade to endorse psychologism.  And so on.  (See chapter 3 of Five Proofs for further discussion.)

Practical and political implications

Frege says nothing about any practical or political implications his abstract metaphysical reflections might have.  But there are such implications, and profound ones. 

Politics is always to some extent given to ad hominemdiscourse, sentimentality, tribalism, and the like.  But in recent years these tendencies seem to have spiraled out of control.  Social media encourage kneejerk responses, groupthink, and relentless sarcasm and manufactured outrage in place of rational engagement.  Traditional news outlets have largely abandoned the aim and even the pretense of being objective.  Ideologies which rationalize the demonization of vast numbers of one’s fellow citizens and the peremptory dismissal of their views and concerns without argument now dominate mainstream politics.

Frege’s analysis reminds us of how literally illogical all of this is.  Consider how typical it is today to evaluate claims and arguments in terms of how “offensive” they are to this or that group, or in terms of their association with some purportedly disreputable person or political persuasion.  None of that matters in the least to whether a claim is true or false or an argument for it is cogent.  A claim can be true and an argument a good one even if they are offensive, and a claim can be false and an argument bad even if they are pleasant.  A disreputable person or party can put forward a true claim or a good argument, and an admirable person or party can put forward a false claim or bad argument. 

In short, the truth and falsity of a proposition and the strength or weakness of an argument are entirely independent of the character and motivations of the people who present them and the feelings and concerns of those to whom they are presented.  Deep down everyone knows this and is even happy to acknowledge it when doing so costs him nothing.  But we can be extremely reluctant to do so when it might entail admitting that a political opponent has a point, that one’s own side is not as virtuous and well-informed as one likes to suppose, or that one’s tender sentiments are irrational and ought to be ignored rather than coddled.  All the same, doing one’s best to acquire the habit of such objectivity is absolutely essential to being civilized and grown-up. 

Or consider the imbecilic notion of “cultural appropriation.”  As Frege reminds us, truth and logic float free of contingent human languages, and they float free of every other aspect of human culture as well.  The denizens of the “third realm” are not anyone’s private property but rather the common possession of all rational beings.  Naturally, there are moral reasons why a person might reasonably claim proprietary rights over some particular way of expressing an idea, as in a copyrighted book or movie.  But ideas themselves are not the sorts of things it makes sense to regard as the property of any individual or group.  Jewish, Christian, and Islamic thinkers of the Middle Ages who borrowed freely from the ancient Greek philosophers and from each other were not “stealing.”  Rather, they were simply accessing the same ocean of truth that belongs to all of us equally, and in doing so increasing our understanding of it.

Most dangerous of all, however, is the “hermeneutics of suspicion” that evaluates ideas and arguments in terms of some hidden sinister group interest they are alleged to serve.  This is analogous to the psychologism attacked by Frege, but writ large.  For Marxism, the hidden interest in question is always that of some dominant economic class.  For Nazism, it is that of some race or ethnicity that purportedly threatens the health and safety of one’s own Volk.  For Foucauldian postmodernism, it is that of some ever elusive but omnipotent and omnipresent “power” that frustrates the indulgence of desire.  And for Critical Race Theory and other brands of “wokeness” – which are essentially a synthesis of Marxian class analysis, Nazi racialism, and Foucauldian liberation from sexual and other social norms – it is “whiteness,” “colonialism,” “patriarchy,” “heteronormativity,” and other fantasized devil figures.  Objectivity itself is dismissed by this insane worldview as a mere tool by means of which these bogeymen maintain their “oppression.”  For the hermeneutics of suspicion, power alone, and not rational persuasion, is what matters.

The Marxists and the Nazis showed us where that mentality leads.   We can be saved from a similar disaster only if enough of us have the clarity of mind and courage to refuse to concede a single inch to those who refuse to acknowledge and abide by standards of truth and logic that transcend all individuals, all races, all cultures, all class and political interests.

Notoriously, Frege himself privately held repellent anti-Semitic and anti-Catholic attitudes.  That does not entail that he too ought to be “cancelled,” but, on the contrary, merely reinforces the lesson we ought to learn from him – that the value of a thinker’s philosophical ideas bears no essential connection to the defects of his personal character. 

Related posts:

Frege on what mathematics isn’t

Popper’s World 3

The absolute truth about relativism

Rucker’s Mindscape

Think, McFly, think!

Aristotle and Frege on thought

Tennant on Aquinas’s Second Way

Every now and then I point out examples of professional academic philosophers badly misinterpreting some traditional argument for God’s existence, or mind-body dualism, or a natural law conclusion in ethics, or some other idea that is out of step with the naturalistic zeitgeist.  This is, I think, a useful exercise, because it shows how the conventional wisdom on these matters does not rest on actual knowledge or understanding of the ideas criticized.  It is instead held in place by errors and unexamined prejudices that mainstream academics who do not specialize in these matters tend to repeat back to one another and pass on to each new generation of graduate students, who then enter the profession and also repeat them back to each other and to their own students.  This has, over time, created a general assumption that “everyone knows” that the arguments are no good and not worth investigating further, even though a little effort would show that what “everyone knows” is demonstrably false.

Here’s another example, from Neil Tennant’s book Introducing Philosophy: God, Mind, World, and Logic, which contains a very poor treatment of Aquinas’s Second Way.  I don’t mean to bash Tennant, whose book is otherwise very interesting and who is a prominent and serious philosopher.  He is in no way condescending toward Aquinas’s argument, but simply rehearsing stock objections that he honestly takes to be compelling.  But that’s precisely the point.  The fact that even a thinker of Tennant’s stature can make the sorts of mistakes he does reinforces the point that the confidence with which mainstream academics dismiss such arguments is massively out of proportion to their actual understanding of them.

Here’s how Tennant glosses the Second Way:

[Aquinas] thinks that at the point ‘in’ time ‘at which’ the physical universe came into being, there was an act of creation – an event – involving the Deity… From this alleged initial event – the ‘prime moving’ – flow all causal chains through subsequent time.  Take any of these causal chains.  According to Aquinas, if we follow it back through time, we shall (in an atemporal sense) eventually arrive at a terminus in the past: the act of creation itself.  For Aquinas, there can be no back-tracking infinitely far, without end, into the past, along a causal chain of events. (p. 227)

Readers of my book on Aquinas and longtime readers of this blog will be groaning already.  But let me explain what is wrong with this summary in the course of addressing the four objections Tennant raises against Aquinas – all of which rest on misunderstandings that are obvious to anyone familiar with Aquinas’s general metaphysical views. 

First objection

Tennant’s first objection is directed against these lines from the Second Way:

But the series of efficient causes cannot possibly go back to infinity.  In all such series of causes, a first thing causes one or more intermediaries, and the intermediaries cause the last thing; when a cause is taken out of this series, so is the effect.

Tennant’s response to this is to suggest that Aquinas fails to consider the possibility of “causal over-determination” (p. 227).  He gives the example of an outlaw shot with deadly accuracy by two bounty hunters at the same time.  Even if the first shot to reach him hadn’t occurred, the second shot would still have killed him.  Hence, Tennant concludes, Aquinas is mistaken to suppose that the removal of a cause entails that the effect will not occur.

The problem with this objection is that it overlooks Aquinas’s distinction between causal series ordered per se and causal series ordered per accidens(sometimes described by later writers as the distinction between hierarchical and linear series of causes), and wrongly assumes that it is the latter sort of series that Aquinas has in mind in the Second Way.  A linear or per accidens causal series characteristically extends over time and is made up of members each of which has independent or built-in causal power.  One of the examples Aquinas gives is that of a father who begets a son who in turn begets another (Summa Theologiae I.46.2).  If the first member dies, the series can still carry on, because the son retains power to beget a son of his own whether or not his own father is still in the picture. 

Indeed, in many per accidens or linear series of causes, it is not even necessary that some particular preceding cause have been the one that produced the later effect.  Aquinas gives, in the passage just cited, the example of “an artificer [who] acts by means of many hammers accidentally, because one after the other may be broken.  It is accidental, therefore, that one particular hammer acts after the action of another.”  That the artificer used some particular hammer to produce the effect is “accidental” or non-essential to the continuance of the series, because some other hammer could have done just as well.  In other words, Aquinas himself makes more or less the same point Tennant does: In causal series ordered per accidens, the same effect could arise via alternative causal pathways.

The reason this acknowledgement is not fatal to the Second Way is that that argument is not talking about causal series ordered per accidens in the first place, but rather about causal series ordered per se.  Now, in a per se or hierarchical series of causes, the members are typically acting simultaneously rather than over time, and that is because the members other than the first have only derivative or borrowed causal power rather than built-in causal power.  Aquinas’s example in the passage from the Summa just cited is that of a stone which is moved by a stick which is moved by a hand.  The causes and effects in this series are simultaneous.  The stone is being moved by the stick at the same moment that the stick is in turn moved by the hand.  More to the point, the stick moves the stone only insofar as it is itself being moved by the hand, for the stick has no independent or built-in causal power.  It has causal power only qua instrument of the hand.

Now, the difference between the “later” causes in a per se or hierarchical series and the “first” cause of the series has nothing essentially to do with order in time and nothing essentially to do with numerical order either.  Rather, it is the difference between that which has only derivative, borrowed, or secondary causal power and that which has intrinsic, built-in, or primary causal power.  It is the difference between an instrument and that which acts throughthe instrument.  When, in various places, Aquinas rules out an infinite regress of causes ordered per se or hierarchically, what he is talking about is the impossibility of there being a series of causes having merely instrumental or derivative causal power without there also being something with built-incausal power which acts through the instrumental causes.  For example, he writes:

That which moves as an instrumental cause cannot move unless there be a principal moving cause.  But, if we proceed to infinity among movers and things moved, all movers will be as instrumental causes, because they will be moved movers and there will be nothing as a principal mover.  Therefore, nothing will be moved.  (Summa Contra Gentiles I.13.15)

Similarly, elsewhere he says:

For everything that is moved by another is a sort of instrument of the first mover.  Therefore, if a first mover is lacking, all things that move will be instruments.  But if the series of movers and things moved is infinite, there can be no first mover.  In such a case, these infinitely many movers and things moved will all be instruments.  But even the unlearned perceive how ridiculous it is to suppose that instruments are moved, unless they are set in motion by some principal agent.  This would be like fancying that, when a chest or a bed is being built, the saw or the hatchet performs its functions without the carpenter. (Compendium Theologiae I.3)

Now, this is what Aquinas is talking about in the lines from the Second Way that Tennant is responding to.  When he says there that if you remove the first cause or the intermediaries, the effect will not follow, he is not denying that in a temporal regress of causes ordered per accidens, some other cause might have produced the same effect.  He isn’t even talking about that sort of series at all.  Rather, he is saying that in the kind of series where every member other than the first acts merely as an instrument, the effect will not follow if the first cause or intermediate instruments are removed.  For example, the stone won’t be moved by the stick if the hand isn’t using the stick to move it. 

(Of course, some other stick or some other person could have moved the stone, but that’s irrelevant to Aquinas’s point.  His point is that, whichever stick and whoever’s hand we’re talking about, when someone uses a stick to move a stone, the stick acts only instrumentallyrather than with built-in causal power.  Hence, if you remove anythingwhich might act through the stick in order to push the stone, the stick won’t push it.)

Second objection

Tennant next claims that “Aquinas’s central inference has the form: Every event has a (distinct) cause; therefore, Some event caused all (other) events” (p. 228).  He then objects that Aquinas is here guilty of a quantifier-switch fallacy.  (This is the sort of fallacy committed, for example, by someone who reasons that if every reader of this blog is reading it on a computer, it follows that there is some one computer they are all reading it on.)

Now, Tennant does not pretend to be quotingAquinas here – which, of course, he couldn’t be, since Aquinas never actually explicitly says what Tennant attributes to him.  But neither does Aquinas implicitlysay any such thing, and once again, Tennant is misled because he is evidently unfamiliar with Aquinas’s metaphysics of causality, which forms the crucial background context for the Five Ways.  For again, when Aquinas reasons to a first cause, what he is doing is pointing out that something can’t serve as an instrument unless there is some non-instrumental cause acting through it.  Fallacious quantifier-switch style reasoning has nothing at all to do with that.

Now, someone might claim that Aquinas must still be committing such a fallacy in supposing that there is only one such non-instrumental or primary cause operating through all the instrumental or secondary causes.  But to raise such an objection would show only that one hasn’t actually read Aquinas beyond the brief excerpt from the Summa that contains the Five Ways.  For that there is only one ultimate first cause is not something Aquinas is claiming in the first place to have established in the Second Way.  He addresses that question later, in Summa Theologiae I.11.3 (and says a lot about it elsewhere too). 

Third objection

Even more egregious is this remark from Tennant:

[Aquinas] dogmatically rules out the perfectly consistent and imaginable scenario of a class of events extending infinitely far back into the past, without there being any temporally ‘first’ point.  Each event could be caused by a strictly earlier event, while yet no event is initial within the temporal ordering. (pp. 228-9)

In his third objection, Tennant rejects the suggestion that Big Bang cosmology might repair this alleged oversight of Aquinas’s.

Now, what I said in response to Tennant’s first objection already indicates what is wrong with this one, but let’s make the point more explicit.  Tennant is assuming, as so many unwary readers do, that Aquinas is, in the Five Ways, trying to establish that the universe had a temporal beginning and that God was the cause of that beginning.  But nothing could be further from the truth.  For one thing, and to repeat, when Aquinas rules out an infinite regress of causes, he is not talking about temporal regresses, which would involve per accidens or linear causal series.  He is talking about per se or hierarchical causal series the members of which are all operating simultaneously, here and now.  He is saying that there must be a primary or non-instrumental cause operating here and now through the secondary or instrumental causes that are operating here and now.  Whatever one thinks of his position, the issue of whether the universe had a beginning is completely irrelevant to it.

For another thing, Aquinas explicitly rejects in several places any suggestion that it can be proved philosophically that the world had a beginning.  He thinks that that is something we can know only via special divine revelation rather than through natural reason, and thus he consistently avoids getting into the issue when he argues for God’s existence.  For again, to reason causally back to a temporal beginning would be to reason about causal series ordered per accidens or “accidentally,” and when arguing for the existence of God, Aquinas does not appeal to that sort of series.  Indeed, he agrees with Tennant that we can’t prove that such series have a beginning.  Instead, he appeals to per seor hierarchical causal series.

Hence, later in the Summa itself, Aquinas insists that “by no demonstration can it be proved, that the world did not always exist,” because “it is not impossible to proceed to infinity ‘accidentally’ as regards efficient causes”; for example, “it is not impossible for a man to be generated by man to infinity” (Summa TheologiaeI.46.2).  He makes the same point in other places, and indeed devoted one of his shorter works to arguing againstthose who claimed that it could be proved philosophically that the world had a beginning.  In other words, Aquinas firmly, explicitly, and repeatedly acknowledges what Tennant accuses him of “dogmatically” denying!

Fourth objection

Tennant’s final objection is to suggest that Aquinas’s argument would fail even if he were to establish a first efficient cause.  For “why should that be taken, without further ado, to be God, or even simply to be God's doing?  Why shouldn't it simply have happened, in a Godless universe?” (p. 229).

The problem with this objection is that Tennant is simply mistaken in assuming that Aquinas draws this conclusion “without further ado.”  On the contrary, there is muchado about it, beginning precisely in the pages that immediately follow the presentation of the Five Ways in the Summa.  There Aquinas argues at length that a first cause would, on analysis, have to have the divine attributes of simplicity, goodness, perfection, infinity, omnipresence, immutability, eternity, unity, knowledge, power, will, love, and so on.  Indeed, he devotes what in a modern edition comes to about 250 pages of dense argumentation to the topic just in the Summa Theologiae, and he says even more in yet other works.  In short, Aquinas does not simply assume “without further ado” that a first cause would have the attributes definitive of God.  Quite the opposite.

Again, I don’t mean to be too hard on Tennant, specifically.  There is nothing unique about his objections.  On the contrary, variations on them are constantly raised against Aquinas by mainstream academic philosophers and by mainstream academics and intellectuals from other fields (not to mention countless amateurs).  And yet they are all demonstrably based on egregious errors and misunderstandings.  Which, while it tells you nothing about Aquinas, says much about what you should think of mainstream academic and intellectual opinion. 

Related posts:

Clarke on the stock caricature of First Cause arguments

The straw man that will not die

An exchange with Keith Parsons, Part III

This is philosophy?

Warburton on the First Cause argument

The less Rey knows, the less he knows it

Straw men and terracotta armies

So you think you understand the cosmological argument?

Meta-abstraction in the physical and social sciences

One of the themes of Aristotle’s Revenge is the centrality of mathematical abstraction to modern scientific method, and the ways that it both affords modern physics tremendous predictive power but also, if we are not careful, is prone to generate philosophical fallacies and metaphysical illusions.  This is especially so where we are dealing with abstractions from abstractions – meta-abstractions, if you will. 

In his recent book on the philosophy of time, Raymond Tallis notes how this has happened in modern thinking about the nature of space and time.  First, physical space has come to be conflated with geometry.  Whereas the notions of a point, a line, a plane and the like were originally merely simplifying abstractions from concrete physical reality, the modern tendency has been to treat them as if they were the constituents of concrete physical reality.  But then a second stage of abstraction occurs when geometrical concepts are in turn conflated with values in a coordinate system.  Points are defined in terms of numbers, relations between points in terms of numerical intervals, length, width and depth in terms of axes originated from a point, and so on.  Time gets folded into the system by representing it with a further axis.  Creative mathematical manipulations of this doubly abstract system of representation are then taken to reveal surprising truths about the nature of the concrete space and time we actually live in.

You don’t have to be an Aristotelian to see the fallaciousness of all this.  From Berkeley to Whitehead to Lee Smolin, a diverse group of thinkers has cautioned against blithely reading off metaphysical conclusions from abstract models.  The predictive and technological successes of the abstractions have facilitated the fallacy, but it remains a fallacy all the same.  That’s why there is a longstanding debate in philosophy of science between realist, instrumentalist, and (the middle ground) structural realist interpretations of scientific theories.  The abstractions and predictive successes by themselves don’t settle anything.  Metaphysically revisionist arguments that begin “Relativity theory works, therefore…” are a bit like concluding, from the fact that you have found a certain road and highway map of Pennsylvania to be useful, that Pennsylvania must therefore really literally be nothing more than a perfectly flat white surface covered with black and red lines. 

In his book The Reformation in Economics, economist Philip Pilkington laments the ways in which the tendency to confuse what I am calling meta-abstractions with the concrete reality they are abstracted from can also infect social science and the policy recommendations based upon it.  He begins with some important points about abstraction in general.  In what follows I’ll note and expand on some of these points.

The nature of abstraction

First, following Kant, Pilkington notes that the concepts we arrive at via abstraction can have a greater or lesser degree of “homogeneity” with less abstract concepts, and with the concrete realities that fall under the concepts.  For example, the concept PLATE (as in a dinner plate) is closely homogeneous with the concept CIRCLE, as is a particular plate.  But it is less closely homogeneous with a more abstract concept like GEOMETRICAL FIGURE.  When we form concepts by abstraction, we mentally strip away concrete features of things and focus our attention on general patterns.  The more abstract the concept is, then, the more numerous are the features we are stripping away – and thus, the less there is in the way of actual concrete reality that we are capturing.  Now, Pilkington notes, the way economists represent the economy mathematically is very abstract indeed, and thus not closely homogeneous with the actual concrete economic facts. 

A second general point he makes, this time citing Berkeley, is that abstraction requires language, and, more generally, symbols.  For concepts cannot strictly be imagined.  Anything you can imagine – that is, form a mental image of – is going to be concrete rather than abstract.  To appeal to one of my stock examples, if you imagine a triangle, you are always going to form an image of some particular triangle, such as a blue right triangle.  But the concept TRIANGLE is completely universal, applying to red and green triangles as well as blue ones, acute and obtuse triangles as well as right ones, and so on.  More abstract concepts (like GEOMETRICAL FIGURE) are even further removed from anything we can form an image of.  At the same time, the way the human mind operates, we need to form some kind of image even when we entertain the most abstract of concepts, and need some kind of external sign by which we may record our thoughts about them and call the attention of others to them.  Hence we use words and other symbols.  For example, we represent the number four with the word “four,” or via the Arabic numeral 4, or the Roman numeral IV, or in stroke notation as ||||, or in some other way.

(Side note: There is a potential chicken-egg problem here insofar as nothing really counts as language in the first place – or at least, as language that goes beyond the expressive and signaling functions of which non-human animals are capable – apart from concepts.  Clearly, then, concepts and language must come about together.  But how does that happen?  Good question for another time, though for one possible answer I commend to you John Haldane’s “Prime Thinker” argument.)

Now, words and symbols are typically parts of systemsof words or symbols – for example, languages, and the numeral systems just referred to – and such systems vary in their expressive power.  Pilkington cites the famous example of the advantages in mathematical reasoning that a numeral system containing 0 makes possible, compared to systems which lack any corresponding symbol.  As Berkeley writes in Alciphron, in a passage quoted by Pilkington:

But here lies the difference: the one, who understands the notation of numbers, by means thereof is able to express briefly and distinctly all the variety and degrees of number, and to perform with ease and despatch several arithmetical operations, by the help of general rules.  Of all which operations as the use in human life is very evident, so it is no less evident, that the performing them depends on the aptness of the notation… Hence the old notation by letters was more useful than words written at length: and the modern notation by figures, expressing the progression or analogy of the names by their simple places, is much preferable to that for ease and expedition, as the invention of algebraical symbols is to this, for extensive and general use.

End quote.  Now, here’s the thing.  The results we get when using a system of symbols to some extent reflect the system of symbols we’ve chosen, the things we’ve chosen to group together under a symbol, the rules that govern the system, and the ways we’ve manipulated the symbols according to those rules – rather than the objective reality being represented by the system. 

Here’s an analogy.  In a pen and ink line drawing, an artist can use thick lines to represent some contours, thin lines to represent others, a break in the line to suggest yet others, series of lines or cross-hatching to represent shadows, and so on.  Splotches of ink can also represent shadows, though they could be used instead to represent blood or holes or bumps or any number of other things.  The artist might also draw in an illustrative style or a cartoony style, do a tight rendering or a loose sketch, and so on.  Now, a skilled artist might produce a likeness of a person, object, or scene that is so close that we might find it useful for identifying the person or thing, predict how it will look from different angles, and so on.  All the same, some features of the drawing will reflect only the mode of representation rather than the thing represented, and we could be led into serious fallacies and errors if we failed to keep this in mind – for example, if we thought that the thing represented really had a black outline around it, or if we concluded that there must be some interesting relationship between shadows, blood, and holes in things, on the grounds that they all looked like black splotches in the drawing. 

Similarly, since even the most useful system of symbols will have features that reflect the natures of the symbols and the system of rules governing them rather than objective reality, we need to be careful lest we assume that there must in objective reality be something corresponding to a given element of the system.

The example of economics

In economics, Pilkington points out, one starts with abstractions like INCOME, CONSUMPTION, INVESTMENT, GOVERNMENT EXPENDITURE, EXPORTS, IMPORTS, SAVINGS and TAXES.  These already tend to run together very different phenomena.  For example, Pilkington says, CONSUMPTION can cover things as diverse as “the purchase of this book… dishwashers, bananas, underpants, blueprints for perpetual motion machines from dubious internet websites and cat-food” (p. 99).  INCOME might include Medicare payments that don’t actually go to households but rather directly to healthcare providers.  And so on. 

These abstractions are then replaced with algebraic symbols, such as Y, C, I, G, X, M, Sand T, respectively, in the case of the examples cited.  These enter into formulae such as (to borrow Pilkington’s examples) the national income identity:

Y º C + I + G+ (X – M)

or a formula representing the relationship between income and savings and taxes:

Y º C + S + T

Such equations can then be substituted into one another, which, after cancelling, yields:

I + G + X º S + T + M

Now, Pilkington notes, we are at this point really manipulating abstractions from abstractions – what I have, again, called meta-abstractions – and thus are even farther from concrete economic reality than the abstract concepts we started out with are.  That need not be a bad thing, but one must constantly keep in mind the limits of what can be captured in such representations and the way that the results of our manipulation of formulae might reflect the method of representation rather than empirical reality.  Pilkington writes:

Such algebraic abstraction is extremely useful, but it can also be used to throw up dust and allow people to engage in sophistical nonsense.  An awful lot of microeconomics is precisely this: nice, neat, formal abstractions that have almost a zero-degree of homogeneity with the real world.  They are far, far from Kant and his circular plate.  Rather, they tend to be made-up stories with no real empirical content.  They are, in that sense, fantasy constructions. (p. 100)

Borrowing a point from fellow economist Tony Lawson, Pilkington also points out that the method of mathematical modelling is such that the model is made into a closed system, with the result that the reality modeled is represented in a deterministic way.  This may be appropriate in physics, Pilkington says, but not when representing human action.  To treat economic behavior as if it were deterministic, even just for purposes of the model, is a clear case of reading what is really just a feature of the abstract method of representation into the reality represented, rather than reading it out of that concrete reality.

(I would add, though, that even in physics we should regard such models as simplifying abstractions, for reasons of the sort raised by Nancy Cartwright.  Of course, these days people are, in light of quantum mechanics, happy to allow that nature does not operate in a strictly deterministic way.  But even in the old days, the contrary supposition was not really justified.  The determinism was read out of the mathematical models and intonature, not out of nature itself.  Again, see Aristotle’s Revenge for discussion of such issues.) 

The bias in science

Now, here is a deep irony.  Mathematics is, quite rightly, widely regarded as a paradigm of objective and disinterested knowledge.  And its heavy use in modern science is a major reason why science too has a reputation for objectivity and disinterestedness.  But there is a fallacy hidden in the implicit inference.  For the fact that a mathematical technique is of itself free of bias simply does not entail that its application to some aspect of concrete reality is also free of bias.  And indeed it is not free of it.  When we apply mathematical models to objective reality, we are always making the tendentious assumption that there is nothing more to reality than is captured by the model – or at least nothing more to it that is relevant to the purposes for which we are constructing the model.  Of course, that assumption might be defensible and correct; but then again, it might not be.  Either way, it is an assumption, and one that is extrinsic to science itself.  It is a philosophicalassumption about science, an assumption that reflects further philosophical assumptions about what nature is like and about what the best techniques are for studying it.  As E. A. Burtt noted in his classic book, the tendency of many modern scientists has been to make an entire metaphysics out of what is really just a method. 

Pilkington too complains that scientists tend to make philosophical assumptions about which they are “completely unreflective” (p. 114).  For example, they “have a tendency to fall back on a reactive materialism as their default worldview” but “the details are never worked out – and if we are to be honest, it more so resembles an ideology than a properly reasoned and considered worldview” (pp. 113-14).  He also notes that, even when making grand but undefended philosophical assumptions, “most scientists arguably do not truly understand the philosophical implications of what they their theories tell them because they are so illiterate in the language of philosophy” (p. 114). 

Pilkington observes that though what he calls “lower-level physics” such as “Newtonian mechanics, electromagnetism, thermodynamics, the basic precepts of relativity theory and so on” are relatively free of bias, “speculations about the origins or nature of the universe” are not free of it and often verge on “crossing the boundary into metaphysics” (p. 121).  The former areas of study have a degree of empirical testability that the latter do not, but because they are all lumped together as “physics,” the latter inherits from the former an unearned prestige.

Then, as Pilkington notes, there is the fact that a branch of science like “Newtonian physics is almost completely bereft of politicisation because, say, the theory of gravity really makes no difference to how we as human beings organise our lives and build our societies” (p. 117).  However, when scientific study does have dramatic political implications, the evidence is clear that it is often massively biased.  (Pilkington cites the work of Brian Martin, who took as a case studythe debate several decades ago over the effect of supersonic transport aircraft on the ozone layer, and showed how politicized the science on both sides had become.)

Now, consider these four sources of potential bias in science: an excessive confidence in abstract mathematical models; a tendency toward a crudely materialistic analysis; a fallacious attribution of the prestige enjoyed by the directly testable areas of science to the untestable and speculative areas; and a subject matter that has dramatic implications for how we organize our lives and societies.  Have we seen these come together in any recent controversies?   Hmm?

Well, of course we have.  All four have been on display in the defense of the COVID-19 lockdowns, which involved an overreliance on speculative and faulty mathematical models; a fixation on the mechanics of the transmission of the virus while ignoring the psychological damage, destruction of livelihoods, and ruin to education caused by lockdowns; the ridiculous smearing of all skeptics as “science deniers,” as if questioning the lockdown was on all fours with rejecting the Periodic Table of Elements; and considerable politicization, putting vulgar sloganeering in place of dispassionate scientific argumentation and favoring more relaxed measures for political allies such as left-wing protesters.

Of course, opponents of lockdowns can also be influenced by political biases, no less than proponents of lockdowns can be.  That is precisely why, a year ago and early in the pandemic, I was defending the proponents against those who too quickly dismissed the initial lockdown as an unjustifiable infringement on liberty.  However, in the nature of the case it has always been the defenders of lockdowns, and not the opponents, who have to meet the burden of proof.  And as I also argued a year ago, the longer the lockdowns went on, that burden would inevitably become heavierrather than lighter. 

Yet as time went on, lockdown defenders largely acted as if the opposite were the case.  Indeed, they largely conducted themselves disgracefully, exhibiting precisely the reverse of the caution and humility that the four sources of potential bias cited by Pilkington should have made them especially sensitive to.  And at this point it is clear that the most draconian measures were a mistake, inflicting massive harms with no net benefits that could not have been achieved through less extreme measures.  But “mistake” is really far too mild a term for the callous arrogance and manifestly fallacious reasoning of people who imposed on others enormous costs that they mostly avoided themselves.  The dogmatic scientism that motivated this disaster in policy provides an object lesson in how philosophical errors are by no means of mere academic interest, but can have dramatic and indeed catastrophic real-world effects.

Related posts:

Concretizing the abstract

David Foster Wallace on abstraction

Cundy on relativity and the A-theory of time

Color holds and quantum theory

The particle collection that fancied itself a physicist

Think, McFly, think!

Metaphysical taxidermy

Lacordaire on the existence of God

Preaching on theological topics is a tricky business.  The more substantive and rigorous a sermon, the greater the danger of its being inaccessible to the average listener.  But the more accessible it is, the greater the danger of its being woolly and banal.  (In our egalitarian and mawkish age, the latter vice is by far the more common one.  Indeed, I don’t think I’ve ever heard a sermon that exhibited the former vice.)   The 19th-century Dominican theologian Henri-Dominique Lacordaire was famously able to strike the right balance.  Like other writers of the period, he has a style that to the contemporary reader is bound to seem a bit purple and prolix.  But, I think, he stops short of excess even on that score – indeed, the tone is, if anything, refreshing.  Whereas rhetorical excess in contemporary preaching tends to pull our attention downward, to our own petty sentimentalities, Lacordaire’s flourishes raise it up to God.

Theism or pantheism

Let’s consider the first of a series of sermons on that topic he delivered at Notre Dame in Paris.  The theme is God’s existence, and Lacordaire’s takeoff point is the first article of the Creed: “I believe in God, the Father Almighty.”  Lacordaire proposes the striking thesis that the only alternative to this conviction is the contrary affirmation: “I believe in nature, the mother almighty.” 

Given that our age is prone both to naturalism and to feminism, one might well wonder whether there is some connection between them.  I think that there is, but that is a topic for another time.  For, notwithstanding his arresting formulation, that is not in fact Lacordaire’s own theme.  The accent in his use of the phrase “nature, the mother almighty” is on the word “almighty,” for what he has in mind is a pantheistic conception of nature.  And the upshot of his striking thesis is that some kind of pantheism is the only alternative to the theism affirmed in the first line of the Creed.

Contemporary readers will find that surprising.  Surely, it will be suggested, atheism is an obvious third alternative.  But I would suggest that to understand why Lacordaire says what he does, we need to keep in mind the way in which the great classical theist tradition conceives of the divine, and how it differs from the excessively anthropomorphic way of thinking about God that prevails in modern times (a tendency that Brian Davies has labelled “theistic personalism” and David Bentley Hart calls “monopolytheism”).

For classical theism – the tradition represented both by Neo-Platonic and Aristotelian philosophy and by the greatest minds of Christian, Jewish, and Islamic theology – the starting pointfor understanding what God is is to think of him as the ultimate reality, and the source of all other reality.  Most classical theists also regard God as personal insofar as he has intellect and will, but that has to do with the nature of God rather than with his existence.  Now, if you take this as your starting point in thinking about God, then the thesis that the ultimate reality is just nature itself is naturally going to smack, not of atheism, but rather of pantheism – of collapsing God down into the world, as it were. 

Now, for more anthropomorphic conceptions of God, the starting point for understanding what God is is instead to think of him as a person like us, only without our limitations.  He’s like Zeus or Odin, but without a body or the petty foibles and restrictions on his power that the gods of the pagan pantheons have.  At the same time, though, he is not conceived of in the terms by which classical theists have hammered out what being the ultimate reality entails – subsistent being itself, pure actuality, absolute simplicity, and the like.  Hence, for “theistic personalist” types, God ends up being more or less like a pagan deity after all, except for being unique, stronger, smarter, and better behaved.  Hence Hart’s apt label “monopolytheism.” 

Now, if your approach to conceptualizing God is of thatsort, then it is understandable why a view that denies the existence of any gods so conceived of would seem most fittingly labeled atheistic rather than pantheistic.  And the fact that most atheists today also conceive of God in theistic personalist rather than classical theist terms is one reason (I don’t say it is the only reason) why they tend to think of themselves as atheists rather than as pantheists.

(Long and bitter experience has taught me that at this point I need to reiterate that the dispute between classical theism and theistic personalism is not about whether God is personal or impersonal – even if some people seem hell-bent on perpetuating this misunderstanding.  Again, most classical theists, and certainly all Christian classical theists, affirm that God is personal.  They would not only acknowledge, but insist, that there is intellect and will in God, and that he is three divine Persons in one substance.  The dispute is instead about divine attributes such as simplicity, immutability, and eternity, and about whether God can be said to fall into any genus.)

It is worth adding that, though contemporary naturalists and atheists are certainly not the most reverent of personality types, even some of them are known to rhapsodize over the beauty of nature and the fundamental laws that govern it, in a way that really does not make much sense if you think of it all as just a big pile of particles differing only in size rather than significance from the little pile of dust and cobwebs that sits in the corner of your bedroom.  What this amounts to, I would argue, is an inchoate and distorted expression of our natural inclination to affirm the reality of and worship a divine first principle – a natural inclination which, due to original sin, gets manifested in all kinds of distorted ways not only in the history of religion, but also in the history of irreligion.  Naturally, the atheist will dismiss all this as a cognitive illusion generated by an overactive propensity to attribute agency to phenomena, blah blah blah.  The point, though, is that the inclination is there, however one wants to explain it.  And it lends further plausibility to Lacordaire’s thesis.

Four ways to God

Lacordaire does not, in his sermon, put forward rigorous proofs of God’s existence, as a Scholastic philosopher would in a metaphysical treatise.  The reason is precisely that he is giving a sermon rather than writing a metaphysical treatise.  But he does summarize what he takes to be four fundamental considerations that point to the truth of theism rather than the pantheism that he regards as its only realistic alternative.  They have to do with: nature, truth, conscience, and society.  Readers with a deep knowledge of the classical theist tradition will recognize in his remarks summaries of lines of argument that have indeed been developed more thoroughly and rigorously in that tradition.  Here are a summary of, and some comments on, these four considerations:

1. Nature: Lacordaire first emphasizes that when we consider the natural world, we find that it is limited and subject to physical law.  It therefore simply lacks the ultimacy that a first principle would have to have.  The world is of this nature rather than thatone; it is governed by these laws rather than those.  Why?  It could have been otherwise, yet it isn’t.  Hence it needs an explanation beyond itself, and therefore cannot itself be the ultimate reality.  Nature thus points beyond itself to a source that is infinite and subject to nothing outside itself.  It points away from pantheism to theism.

We can think of this as a generic formulation of the cosmological argument for God’s existence, which can be spelled out more rigorously and in detail in several different ways.  The versions I think the most powerful are what I have called the Aristotelian proof, the Neo-Platonic proof, the Thomistic proof, and the Rationalist proof, and I have expounded and defended them in Five Proofs of the Existence of God.  Lacordaire’s exposition is more loose and popular than any of those arguments, but there is nothing per sewrong with that given that he was, again, giving a sermon (any more than a popular exposition of any subject – whether quantum mechanics, restorative dentistry, or automotive repair – should be faulted on the grounds that it fails to satisfy the rigorous demands of the expert).

2. Truth: Lacordaire next discusses how the human intellect is able to arrive at knowledge of a body of truths that is infinite in contrast with the natural world’s finitude, and of which the natural world is but a shadow.  Anyone familiar with the classical and Scholastic traditions in philosophy will recognize that he is here alluding to the Platonic idea that in our knowledge of mathematics and of the essences of things, we are tapping into a realm of infinite, eternal, and necessary truths that outstrip both the material world and any finite mind or collection of finite minds.  And when Lacordaire goes on to argue that the reality of this realm in turn presupposes a divine mind, the knowledgeable reader will recognize in this a version of what I have called the Augustinian proof of God’s existence (and which I have also expounded and defended in Five Proofs). 

3. Conscience: The third consideration raised by Lacordaire has to do with the idea that our consciences take justice to be an objective feature of reality, and that we cannot ultimately make sense of this unless we recognize a divine lawgiver.  In other words, he is giving a version of the moral argument for God’s existence.

That is not an argument that I have myself defended or said much about.  That is not because I think it is wrong.  To be sure, and as I have often said, I think that at least the fundamental principles of natural law and their rationally binding force can be known just by studying human nature, albeit human nature as interpreted through an Aristotelian-Thomistic metaphysics.  You can do a great deal of ethics without having to bring theology into it, just as you can do chemistry and physiology without having to bring theology into it.  However, I would not deny that a completesystem of natural law requires appeal to natural theology, for reasons I discuss in the last section of chapter 5 of my book Aquinas.  And those reasons do indeed provide the basis for a version of the moral argument for God’s existence.

The reason I have nevertheless not talked much about that sort of argument myself is this.  In order to spell out such an argument, you need to defend the reality of teleologyas an intrinsic feature of the natural order, since that is absolutely crucial to making sense of natural law.  And in order to make sense of the notion of conformity to the divine will as the ultimate standard of the goodness of a human will, you need to spell out the sense in which the divine intellect is ultimately what orders things to their ends.  But by the time you’ve done all that, you’ve more or less spelled out the key ingredients of Aquinas’s Fifth Way of arguing for God’s existence – his version of a teleological argument.

Hence it has long seemed to me that the moral argument, rightly developed, is essentially a riff on or a corollary of the Fifth Way.  And in that case, one might as well just defend the Fifth Way itself (which I have done in several places, most thoroughly in my article “Between Aristotle and William Paley: Aquinas’s Fifth Way,” reprinted in my anthology Neo-Scholastic Essays).

I don’t mean to imply that the moral argument has no value.  On the contrary, there are no doubt contexts in which moral considerations are the appropriate ones to begin with in arguing for God’s existence.  But it seems to me that those would be contexts in which one’s audience is already prepared to acknowledge the objective reality of natural teleology and of moral goodness.  That was, needless to say, likelier in Lacordaire’s time than in ours, so that the moral argument seems to me less effective in current cultural circumstances, and in any event a less fundamental argument than the others I’ve mentioned. 

The astute reader may have noticed that Lacordaire’s first three approaches to establishing God’s existence roughly correspond to three of what Scholastic philosophers call the transcendentals – namely being, truth, and goodness.  In Scholastic thought, these are convertible, the same thing looked at from different points of view.  Hence, just as God is being itself, he is also truth itself and goodness itself.  And thus, just as we can arrive at knowledge of God through the first transcendental (by arguing from what merely participates in being to that which just is being itself, as in the different versions of the cosmological argument I referred to above), and through the second transcendental (by way of the Augustinian proof), so too, it stands to reason, should we be able to arrive at it through the third (e.g. by way of a moral argument). 

But that requires our having a sufficiently firm grasp of goodness as an objective feature of reality.  And though it deludes itself that it is especially morally enlightened, our age is in fact so extremely morally depraved and blind to natural goodness that the latter is no longer a very effective avenue by which to draw the mind upward to God.  (To revise Chrissie Hynde’s revision of Oscar Wilde, we are all of us in the gutter… and some of us seem quite happy to stay there.)

4. Society: Similarly more difficult to deploy today than in Lacordaire’s time is his fourth and final avenue of arriving at knowledge of God.  Lacordaire points out that skepticism about God’s existence and about the objectivity of truth and of justice have, historically, largely been confined to a small minority of society – namely the powerful and educated elite, who out of pride delude themselves into thinking that they have no need of such ideas, and are able to develop clever sophistries to rationalize their rejection of them.  The vast majority of society do not have the luxury of such delusions, and thus have been far less likely to fall into them.  The pain of ordinary life that has been the lot of most people historically has been such that they have had no desire to try to talk themselves out of what we are by nature inclined to believe – that there is a divine cause of the world, that truth is absolute rather than relative, and that there is an objective moral order to which we are answerable.

But even if this is so, how, it might be asked, could it give us rational grounds for believing in these things?  Doesn’t it amount to a fallacious appeal to majority?  No, it does not.  What Lacordaire sketches out here seems to me best read as a version of what is sometimes called an “argument from desire” for God’s existence.  Such an argument first tries to establish that the inclination to believe in and desire God is built into our very nature.  The appeal to what most people have thought historically functions as evidence for this thesis.  The argument then appeals to the Aristotelian thesis that a natural inclination cannot be in vain – that is to say, that we cannot be directed by nature toward some end unless it is possible to achieve it.  The argument then concludes that given our natural desire for God together with this Aristotelian thesis, we can conclude that God really does exist.

Needless to say, such an argument would need a lot of spelling out in order to make it remotely plausible to most modern audiences.  Now, as I have said elsewhere, I think arguments of that sort can indeed be spelled out in a way that shows them to be plausible.  The trouble is that doing so requires so much in the way of defending various background metaphysical assumptions that by the time you are done with that, you will already have effectively laid the foundations for establishing God’s existence by some other and more direct argument (such as the arguments I defend in Five Proofs).  And in that case, the argument from desire will be otiose.  In short, Lacordaire’s fourth line of argument, like his third, is not wrong, but rather simply less effective as a way of drawing most contemporary readers’ minds up to God. 

But it isn’t just that intellectual error has made it harder for modern people to understand, much less see the force of, such arguments.  It is that the material prosperity that was once confined to a relatively small elite is now enjoyed by a vastly larger portion of society, which has the wherewithal to maintain itself in lifelong comfort, to distract itself with endless amusements, and thereby to deceive itself into thinking it has no need of God.  Christ famously said that it is easier for a camel to pass through the eye of a needle than for a rich man to enter the kingdom of God, and the reason has to do with the latter’s prideful sense of self-sufficiency, and the deadly vice of acedia that material prosperity tends to foster.  Hence the majority which, in Lacordaire’s day and in previous eras, hadn’t the luxury to entertain the sophistries he decries, is a much smaller majority today – and, in the contemporary West, perhaps not a majority at all.

Aquinas on video

Many readers will be familiar already with the Thomistic Institute’s outstanding Aquinas 101 series of videos, which provide brief introductions to a wide variety of topics from Aquinas’s thought.  The Institute has now announced a new video series, Aquinas 101: Science and Faith, which will explore topics such as evolution, neuroscience, miracles, quantum mechanics, psychology, scientific method, reductionism, and the like.  The series begins on March 16, and the videos will be released weekly.  And on March 10, the trailer for the series will premiere and the Institute will host a live Q & A.

The Thomistic Institute also makes available a wide variety of other excellent video materials.  And while we’re on the subject, I should also call attention to a similar but different project, the superb iAquinas series of videos, which are in English, French, and Spanish.  Hours and hours of worthwhile viewing!

Preventive war and quarantining the healthy

A “preventive war” is a war undertaken proactively against a merely potential enemy, who has neither initiated hostilities nor shown any sign of intending imminently to do so.  The Japanese attack on the United States at Pearl Harbor is a famous example.  This is not to be confused with a “preemptive war,” which involves a proactive attack on an enemy who has shown signs of intending to initiate hostilities.  The Arab-Israeli Six-Day War is a standard example. 

The Iraq war of 2003-2011 was sometimes characterized as a “preventive war,” though in my opinion that is, whatever else one thinks of that war, not an accurate characterization.  Rather, I think it fell under the category of “punitive war,” a war fought to punish an enemy nation for some offense (such as a violation of treaty obligations).   Whether it was justifiable under that description is not an issue I am addressing here.  What is relevant is that critics of the Iraq war who characterized it as a preventive war took it to be ipso facto unjust.  For while preemptivewar is generally thought to be justifiable, preventivewar is – rightly, in my view – widely thought not to be justifiable. 

The reason should be obvious.  Until a potential enemy has actually done something – such as actually attacking (which would justify a defensive war), or preparing to attack (which could justify a preemptive war), or in some other way actually committing a sufficiently grave offense (which might justify a punitive war) – said potential enemy is in all relevant respects innocent.  You cannot justifiably attack a nation merely for what it might do, any more than you can punish an individual for what he might do.

This is why we don’t arrest and punish gangsters even when we have good reason to suspect that they will at some point commit crimes, and don’t fine corporations even when we have good reason to suspect that they will at some point pollute.  You can justifiably inflict harm on people only for what they have in fact done, not for what you think they probably will do in the future, and certainly not for what they merely might do.

But don’t we rightly punish people for certain negligent acts, even when they don’t actually result in harm?  Yes, but that is because such punishments are relevantly analogous to preemptive war rather than to preventive war.  Suppose I use a flamethrower to clear away brush or scare off raccoons in my backyard.  Suppose I don’t actually end up igniting your yard or house.  I still have in fact put your property in imminent danger of harm, even if I had no hostile motive but was just being stupid.  And it is reasonable to forestall actions that are per se dangerous in this way by prohibiting them altogether, as well as by punishing them after they occur.

It would not be reasonable, though, to prohibit ownership of (say) chainsaws, merely because someone might be so stupid as to use them in a way that endangered others.  It is very difficult to use a flamethrower in your backyard in a way that does not pose an imminent grave risk to your neighbors.  But it is not difficult to use a chainsaw in a way that poses no serious risk to others.  Sure, I could do something really stupid with it – say, tying it to a rope, starting it up, and then swinging it around in a wide arc that crosses over your property line – but it is extremely unlikely that many if any chainsaw owners would do such a thing.  Flamethrower use in a neighborhood context is per sedangerous to others in a way that chainsaw use is not.

Now, this is the principle on which quarantining disease carriers is justifiable, at least when walking around with the disease is more like using a flamethrower than it is like using a chainsaw.  Hence, it is reasonable to quarantine people with bubonic plague.  But it would be unreasonable to quarantine people with the flu, even if occasionally there are people who die from the flu.  Quarantining someone with bubonic plague inflicts a harm on him – it takes away his freedom of movement and may thereby prevent him from making a living or going to school, cause emotional distress, and so on – but this is justifiable given that his walking about freely would impose a grave and immediate threat to others, just as using a flamethrower in your backyard would.  Quarantining such a person would be analogous to a preemptive war – the forestalling of a grave and imminent threat that the person actually does in factpose.

But it would not be reasonable to quarantine a person simply because he might get bubonic plague and pass it to others, or because he does in fact have an illness but one which merely might cause grave harm to another (such as the flu or a severe cold).  That would be analogous to a preventive war rather than a preemptive war, and illegitimate for the same reason.  You can justifiably quarantine Typhoid Mary.  But how can you justifiably quarantine Potentially Typhoid Mary, any more than you can justifiably attack a potentialenemy?  Or how could you justifiably quarantine Severe Cold Mary on the grounds that some people might in theory die if they catch her cold, any more than you could legitimately ban chainsaws on the grounds that someone somewhere might use a chainsaw foolishly? 

Now, COVID-19 is not remotely like bubonic plague, and while for some people it is certainly worse than the flu, for most people it is not.  And we know who is most vulnerable – the elderly and those with certain preexisting medical conditions.  So, how can it possibly be justifiable to quarantine those who do not have the virus, on the grounds that they mightget it, and then might go on to spread it to someone among the minority of people to whom it poses a grave danger?  Especially when there is an obvious far less draconian alternative, namely quarantining only those who do have the virus and those who are at special risk from it?  And especially when there is no proof that the more draconian measures are really necessary, and evidence that in fact they have no net benefit over less draconian policies? 

In short, how are lockdowns for vast populations of healthy people any more justifiable than “preventive war”?  How is the argument “If we don’t quarantine the healthy, grandma might die if they catch the virus and spread it to her” any better than the argument “If we don’t proactively attack country X, grandma might die if X attacks us”?  If those who start a “preventive war” are war criminals, what are those who have “locked down” the healthy and thereby destroyed livelihoods, inflicted severe mental distress, and set back the education of millions of children – and all for nothing, given the evidence that such policies have at the end of the day done little or no more good than less destructive ones have? 

Don’t answer: “But killing people in a war is worse than quarantining them!”  Of course it is, but that’s irrelevant.  Destroying the livelihoods, etc. of innocent people is not as bad as killing them, but it hardly follows that it isn’t extremely bad.  And since when is a government morally permitted to inflict whatever damage it sees fit on innocent citizens, as long as it stops short of killing them?

Related posts:

Lockdowns versus social justice

The rule of lawlessness

The experts have no one to blame but themselves

What “the science” is saying this week

The lockdown is no longer morally justifiable

The lockdown and appeals to authority

The burden of proof is on those who impose burdens

The lockdown’s loyal opposition

Some thoughts on the COVID-19 crisis