In high school, if not sooner, one learns theorems established more than two millenia ago by Euclid and Archimedes. I am thinking of the theorems expressed today by the equations
𝐶 = 2π𝑟,
𝐴 = π𝑟²
for the circumference and area of a circle whose radius is 𝑟, and
𝐴 = 4π𝑟²,
𝑉 = (4/3)π𝑟³
for the surface area and volume of a sphere whose radius is 𝑟. Continue reading
The miracles recounted in the Gospels are not violations of the laws of nature, because the Evangelists had no conception of those laws in the first place. So I argued in a post of June, 2022. Having encountered resistance to the argument, I return to it now.
One person did swim in the Bosphorus
here at Kireçburnu on New Year’s Day, 2024
There is a lot about R. G. Collingwood on this blog. Apparently that is why I had the opportunity to write the text below. Something close to it was included in Turkish last year with the Turkish translation of R. G. Collingwood’s Religion and Philosophy.
Din ve Felsefe was published in September, 2022, by Akademim (apparently “My Academy”), and what I wrote for it was a takdim (“an introducing”) or sunuş (“presentation,” from sunmak “to present”). In writing this, I made use of my own annotated version of Collingwood’s book (here as a pdf file, 475 pages, size B6, dated February 2025).
I have already quoted some of the takdim in the post called “‘It Was Good’.” This is based on how God checks his own work, according to the first creation myth in Genesis. The present post is occasioned by a checking of my own work. That work was in the post called “Antitheses,” which I have been reading again because
The “Antitheses” post could use work or even a replacement. When I wrote it, I thought all of its ideas were illuminated by the Antitheses in the Sermon on the Mount; however, this may have been more of a hunch than a conclusion.
I quoted a dictionary definition of antithesis as “an opposition or contrast of [two] ideas.” I would suggest further that those two ideas do not really oppose or contrast with one another, so much as they complement one another. By itself, “An eye for an eye” is ambiguous: is it a warning against too little punishment, or too much? Too much, if we read the injunction, “Resist not evil,” as a refinement of the meaning of the earlier rule.
I agree with Collingwood’s argument, sketched below, that when properly understood, punishment and forgiveness amount to the same thing. This would seem to be a possible interpretation of the teaching of Jesus Christ. There may be other interpretations as well. In any case, Collingwood observes,
The most perfect punishments involve no “incidental” pains at all. The condemnation is expressed simply and quietly in words, and goes straight home.
I can remember being punished in this way by my elders. However, in a conversation last year, when I suggested the possibility of merely verbal punishment, somebody who actually had a daughter was incredulous. Perhaps he would have told me there were alternatives to both of the options that Collingwood mentions:
if we are punishing a child, the tongue is a much more efficient weapon than the stick.
Nonetheless, Collingwood makes an even more extreme suggestion:
It is possible to punish without the word of rebuke; to punish by saying nothing at all, or by an act of kindness. Here again, we cannot refuse the name of punishment because no “physical suffering” is inflicted. The expression of moral feelings, or the attitude of the good will to the bad, may take any form which the wrongdoer can understand.
Collingwood is only working out the Proverb,
If thine enemy be hungry, give him bread to eat; and if he be thirsty, give him water to drink:
For thou shalt heap coals of fire upon his head, and the Lord shall reward thee.
Jesus put it more abstractly:
Love your enemies, bless them that curse you, do good to them that hate you.
Before passing to the actual takdim for Din ve Felsefe, let me note the possibility of broadening the scope of “Antitheses” to include single words that are antitheses in themselves.
see especially “Automatia,” on the Goddess of Chance, and the examples gathered for consideration with Iliad Book VIII, where the gates of heaven open automatically.
I noticed this in reading Iliad Book XVIII, because that is where Hephaestus forges Achilles’s new armor.
I think Raymond Smullyan alludes to the antithesis of the automatic in the dialogue called “Is God a Taoist?” The character called God is speaking here:
Often one uses the statement “I am determined to do this” synonymously with “I have chosen to do this.” This very psychological identification should reveal that determinism and choice are much closer than they might appear.
God has already said,
Don’t you see that the so-called “laws of nature” are nothing more than a description of how in fact you and other beings do act?
Compare C. S. Lewis, as quoted in “Sacrifice and Simulation”:
When you say that falling stones always obey the law of gravitation, is not this much the same as saying that the law only means “what stones always do”? You do not really think that when a stone is let go, it suddenly remembers that it is under orders to fall to the ground. You only mean that, in fact, it does fall.
Lewis’s point is that there is another kind of law. Perhaps “law” then is another one-word antithesis.
Published in 1916, during World War I, Religion and Philosophy is the first book of R. G. Collingwood (1889–1943), but contains some of his finest writing and most inspired vision.
The vision is of a unified world. For example, punishment and forgiveness are not two kinds of justice, but one. Justice brings about “the criminal’s … regeneration and recovery into the life of a good society” (III.ii.2.b, page 179). This recovery inevitably involves “the pain of self-condemnation or moral repentance” (III.ii.2.b, page 178). Thus the just response to a crime is both
A theological term for justice is atonement. In reviewing Collingwood’s book for the International Journal of Ethics (Jul., 1917, Vol. 27, No. 4, p. 543), T. S. Eliot wrote,
The philosophical interpretation of the Incarnation, of the Atonement and of Miracle, are extremely well handled.
Incarnation and Atonement are the same thing for Collingwood, namely,
that taking-up of humanity into God which is called the Incarnation or the Atonement, according as the emphasis is laid on God’s self-expression through humanity or man’s redemption through the spirit of God. (III.i, page 147)
Miracles cannot be distinguished from ordinary events. For example,
Every cure is equally a miracle, and every doctor (like every other active and creative mind) a miracle-worker, in the only sense which can reasonably be attached to the word. (III.iii.3.a, page 211)
When so many people delight in classifying themselves, as by nationality, religion, sexuality, or football team, it is salutary that Collingwood points out,
To the eye of perfect insight … everything is unique. For such a consciousness there are no classes, there are only individuals; not in chaos, for every individual is related to every other … The true relation between individuals is not the resemblance which connects members of a class, but the co-operation which unites parts of a whole. (III.iii.3.b.ii, pages 213–4)
Collingwood may carry the unifications too far. He says, “there is no distinction whatever between Theology and Religion, so far as the intellectual aspect of religion is concerned” (I.i.2, page 12). Likewise, “the true religion and the true philosophy must coincide,” because “religion and philosophy are views of the same thing—the ultimate nature of the universe” (I.i.3.b, page 18). Even philosophy (or religion) and science are in principle the same:
It is no doubt possible to forget the whole in laying stress on isolated parts, as it is possible to forget details in the general view of a whole. But each of these is a false abstraction; we cannot identify the former with science and the latter with religion or philosophy. The ideal, alike for philosophy and science, is to see the part in its place in the whole, and the whole perfectly exemplified in the part. (I.i.3.c, page 20)
If the reader objects to the identification of theology, religion, and philosophy, Collingwood himself will agree in his next book, Speculum Mentis, in a footnote on the first page of Chapter IV, called “Religion”:
I may perhaps be permitted here to refer to a book called Religion and Philosophy which I published in 1916, and in which I tried to give a general account of the nature of the religious consciousness, tested and illustrated by detailed analyses of the central doctrines of Christianity. With much of what that book contains I am still in agreement; but there are certain principles which I then overlooked or denied, in the light of which many of its faults can be corrected. The chief of these principles is the distinction between implicit and explicit. I contended throughout that religion, theology, and philosophy were identical, and this I should now not so much withdraw as qualify by pointing out that the ‘empirical’ (i.e. real but unexplained) difference between them is that theology makes explicit what in religion as such is always implicit, and so with philosophy and theology. This error led me into a too intellectualistic or abstract attitude towards religion, of which many critics rightly accused me …
Religion, theology, and philosophy together are an example of the key idea of Collingwood’s 1933 book, An Essay on Philosophical Method: the overlap of classes. In one of the examples in the Essay, while doing one’s duty may always bring about or increase happiness, the concepts of duty and the promotion of happiness are not identical, and to think otherwise is what Collingwood calls “the fallacy of identified coincidents.” Thus he himself has committed this fallacy in Religion and Philosophy, regarding the two concepts in the title.
In Religion and Philosophy, Collingwood spends little time on the so-called Ontological Proof. Having delivered a series of lectures on the proof, starting in 1920, Collingwood will devote to it a chapter, called “Philosophy as Categorical Thinking,” of An Essay on Philosophical Method. As an example or application of the Proof, he will show how the philosophical sciences of logic and ethics are not simply descriptive (or empirical), and neither are they simply prescriptive (or normative). They concern not just what we do, in thought or act, but what we try to do, by our own standards. To me, as a logician, this makes perfect sense. I am not a judge who can send you to prison for making bad arguments. I ought to be able to help you make your arguments clearer, if that is something you want.
A science such as logic and ethics (also aesthetics and economics) gives an account—in Greek, a logos (λόγος)—of the criteria that we apply in judging our own efforts. In a word, such a science is criteriological. Collingwood will not actually use this word until The Principles of Art of 1938. He will explicate the concept of a criteriological science more fully in An Essay on Metaphysics of 1940. Meanwhile, in Religion and Philosophy, we can see the germ of the idea, with philosophy as the example:
And if theology is to be a merely empirical science, it has a corresponding right to make uncriticised assumptions. But the sting of the criticism lies in the fact that theology claims to be more than this. It presents itself as a philosophy, a view of the universe as a whole, the ultimate ground of reality; and philosophy can take nothing for granted … a philosopher has no right to construct the nature of morality out of his inner consciousness, and end in the pious hope that the reality may correspond with his “ideal construction.” His business as a philosopher is to discover what actually are the ideals which govern conduct, and not to speak until he has something to tell us about them. (II.i.1.a, pages 59–60)
In An Essay on Metaphysics, Collingwood will observe that, while a purely empirical science of human feeling is possible, and this is what psychology properly is, the same cannot exist for thought. As he will already have pointed out in The Principles of Art, thought differs from feeling by being “bipolar” in the sense that it can be done well or not. Both thought and feeling are in the scope of Collingwood’s work:
As a teacher, I am supposed to judge whether my students are thinking successfully. This is not like judging their health, with blood test or thermometer; for this kind of judging can be done without the subjects’ active participation. A brain scan might show whether students are thinking rather than sleeping; but it will not show whether they are thinking well. On the other hand, the students should be learning how to tell for themselves whether they are thinking well.
For his own understanding of the impossibility of an empirical science of thought, Collingwood, in An Autobiography of 1939, will credit the work that has gone into Religion and Philosophy. He says there, for example,
In conduct generally we have certain actions, individual or social, designed to attain the ends of morality, utility, or the like; psychology will study these actions without asking whether they are right or wrong, but taking them merely as things done. In general, the characteristic of psychology is the refusal to raise ultimate questions. And since that is so, it is plainly not in a position to offer answers to them. (I.iii.1.a, pages 40–1)
One of those ultimate questions is simply whether what we are doing is any good. Collingwood thought he had work to do that was worth doing. During World War II, when he knew he was dying, he managed to publish one last book, The New Leviathan: Man, Society, Civilization, and Barbarism (1942), an account of what he thought was worth defending against the Nazis. The teaching of Jesus of Nazareth that he seems to have taken most to heart is Matthew 5:48,
Be ye therefore perfect, even as your Father which is in heaven is perfect.
For Collingwood, in Religion and Philosophy (I.iii.5, page 53),
the historical life of Jesus is the guarantee that man can be perfect if he will.
Collingwood applies the idea of perfection throughout Religion and Philosophy:
“A philosophical problem cannot be insoluble, though it may be too hard for you or me to solve satisfactorily” (II.iv.1.a, pages 123–4).
“Pain seems to involve imperfection only in the sense in which any one who has a thing to do and has not yet done it is imperfect; and in that sense imperfection is only another name for activity and perfection for death” (II.iv.1.b.i, page 126).
“The world we see around us is not a stationary, already-existing, given totality, but a totality in the making: its unity consists only in the striving towards unity on the part of the minds which constitute it. This does not mean that its completion lies at some point in the future; it is a completion that never is and never will be attained for good and all, but one which is always being attained. The life of the world, like the life of a man, consists in perpetual activity” (II.iv.3.a, pages 140–1).
“God’s attitude towards the sins of men must be one which combines condemnation of the sinful will with love and hope for it; these two being combined not as externally connected and internally inconsistent elements of a state of mind, but as being the single necessary expression of his perfect nature towards natures less perfect, but regarded as capable of perfection” (III.ii.3, page 180).
One may raise here the same sort of question that Eliot did:
Mr. Collingwood attacks the problem of evil by conceiving of God “not as imposing his will on the world from without, but as himself sharing in all the experiences of other minds.” “God is the absolute good will.” Mr. Collingwood admits that the universe is a totality only in posse. One is tempted to ask whether the omnipotence and absolute good will of God are also in posse.
Read the book and see what you think!
Edited September 25, 2026, just to link to a more recent annotated version of Collingwood’s Religion and Philosophy
In the first creation myth in the first book of the Hebrew Bible, God is always looking back at what he has been doing, to see whether it is any good. It always is, but he cannot have known in advance that it was going to be, and this is why he has to check his work.
So it seems to me. In any case, when we create things, part of the job is checking our work.
The new Turkish translation of Collingwood’s Religion and Philosophy
with introduction by yours truly
Executive summary. An experiment has been performed to detect whether we are living in a simulation. The experiment is to tell Abraham to sacrifice his son. Whatever he does, he breaks a law. Thus there is more to the world than can be understood by natural science.
Altınova, Ayvalık, Balıkesir, Türkiye
Looking towards Lesbos, Greece
September 20, 2022
We reach now the Analogy of the Sun and the associated Divided Line.
The highest fronds take the setting sun in Altınova
September 27, 2021
This post is based on recent readings, often on or through Twitter, of the following writers.
Having originally posted this essay on January 9, 2021, I edited and augmented it, on January 19 and December 19 of that year. I return to it now, on June 22, 2023, having posted “On Dialectic,” two days ago; this one is another post that quotes lots of people, and I want to check how it reads. It reads fine, to me, although I did have to correct occurrences of “behavior” spelled as “behavor.” Moreover, although I had forgotten what was here, I recognized it instantly as I read; another reader would not experience this recognition.
What stands out most to me now is Christa Peterson’s suggestion,
A representation of our own gender … could … be a means of picking out people as who we are co-gendered with …
As the essay already suggests, if you replaced “gender” with “race,” then the resulting speculation could get you called a racist, and that is supposed to be something bad. However, if we replace “gender” with “sex,” we obtain a proposition that is fundamental to contemporary biology, as I understand it, because evolution is
I think this is why Nina Paley can say, in a blog post called “Why I Don’t Use ‘Preferred Pronouns’,” which I referred to also in “Imagination,”
Like most mammals, I can’t help but identify someone’s sex with +99% accuracy. (… Women, I think, are better at identifying sex than men, either due to instinct or conditioning for survival …)
We know that there are two sexes, and we know who is of which sex, the way we know that some foods are good to eat. However, Peterson seems to think of this knowledge a bit differently:
Trans people’s dignity and legitimacy does not depend on the success of any one attempt to conceptualize their experience. But the most common way, in terms of “gender identity,” is perfectly functional. The commitments of the popular notion are minimal: people have an internal sense of their own gender that can come apart from their knowledge of their assigned sex, and is generally fixed, and certainly not revisable in the way ordinary beliefs are.
What is the word “assigned” doing here? Does whether you are trans depend on whether somebody made a mistake when checking one of the boxes marked “male” and “female” at your birth?
A lot of old PSA’s about drugs are on YouTube and the Web Archive, and sometimes they are linked to by articles that ridicule them. There is one that I have not been able to find, perhaps from around 1970, in which parents confront their teenager with the drug paraphernalia that they have found in his room. The boy storms out of the house, saying, “You don’t understand!”
There’s a lot that I don’t understand. I must not, since it seems childish, but is coming from adults. Some of these adults stormed the US Capitol the other day; others encourage them; still others are professors of philosophy.
“Human egg and sperm cells.”
Asimov’s New Guide to Science (1984), page 600
My subject is the Chronicles of Narnia of C. S. Lewis (1898–1963). I consider this heptad of books (published 1950–6) as constituting (1) literature (2) for children (3) that I continue to enjoy in my sixth decade, having started in my first.
By literature, I mean a work of art whose medium is prose. Prose may also be a work of craft, intended to fulfil some purpose. This purpose could be to serve a market for fantasy or children’s books. Art as such has no purpose that can be specified in advance.
Writing for children may take certain liberties that annoy adults.
As with any post in this blog, I write out of my own personal interest. As a child, I read other fantasies, such as those of Lloyd Alexander, John Christopher, Ursula LeGuin, and J.R.R. Tolkien. Only the works of C. S. Lewis have stayed with me. This essay may be considered as an exploration of why, or least an example of how.
To do injustice is worse than to suffer it. Socrates proves this to Polus and Callicles in the dialogue of Plato called the Gorgias.
I wish to review the proofs, because I think they are correct, and their result is worth knowing.
Or is the result already clear to everybody?
Whom would you rather be: a Muslim in India, under attack by a Hindu mob, or a member of that mob?
You would rather not be involved; but if you had to choose, which option would be less bad: to be driven to an insane murderous fury, or to be the object of that fury?
This essay was long when originally published; now, on November 30, 2019, I have made it longer, in an attempt to clarify some points.
The essay begins with two brief quotations, from Collingwood and Pirsig respectively, about what it takes to know people.
The Pirsig quote is from Lila, which is somewhat interesting as a novel, but naive about metaphysics; it might have benefited from an understanding of Collingwood’s Essay on Metaphysics.
A recent article by Ray Monk in Prospect seems to justify my interest in Collingwood; eventually I have a look at the article.
Ideas that come up along the way include the following.
For C. S. Lewis, the reality of moral truth shows there is something beyond the scope of natural science.
I say the same for mathematical truth.
Truths we learn as children are open to question. In their educational childhoods, mathematicians have often learned wrongly the techniques of induction and recursion.
The philosophical thesis of physicalism is of doubtful value.
Mathematicians and philosophers who ape them (as in a particular definition of physicalism) use “iff” needlessly.
A pair of mathematicians who use “iff” needlessly seem also to misunderstand induction and recursion.
Their work is nonetheless admirable, like the famous expression of universal equality by the slave-driving Thomas Jefferson.
Mathematical truth is discovered and confirmed by thought.
Truth is a product of every kind of science; it is not an object of natural science.
The distinction between thinking and feeling is a theme of Collingwood.
In particular, thought is self-critical: it judges whether itself is going well.
Students of mathematics must learn their right to judge what is correct, along with their responsibility to reach agreement with others about what is correct. I say this.
Students of English must learn not only to judge their own work, but even that they can judge it. Pirsig says this.
For Monk, Collingwood’s demise has meant Ryle’s rise: unfortunately so since, for one thing, Ryle has no interest in the past.
In a metaphor developed by Matthew Arnold, Collingwood and Pirsig are two of my touchstones.
Thoreau is another. He affects indifference to the past, but his real views are more subtle.
According to Monk, Collingwood could have been a professional violinist; Ryle had “no ear for tunes.”
For Collingwood, Victoria’s memorial to Albert was hideous; for Pirsig, Victorian America was the same.
Again according to Monk, some persons might mistake Collingwood for Wittgenstein.
My method of gathering together ideas, as outlined above, resembles Pirsig’s method, described in Lila, of collecting ideas on index cards.
Our problems are not vague, but precise.
When Donald Trump won the 2016 U.S. Presidential election, which opinion polls had said he would lose, I wrote a post here called “How To Learn about People.” I thought for example that just calling people up and asking whom they would vote for was not a great way to learn about them, even if all you wanted to know was whom they would vote for. Why should people tell you the truth?
