Polytropy

This essay ends up considering arguments that natural science – especially mathematical physics – is based on absolute presup­positions whose mythological expression is found in Christianity – especially the doctrine of Incarnation.

I take note along the way of continuing censorship of Wikipedia by the Turkish state.

Where to start

I have said glibly in this blog, as in “Effectiveness,” that everybody can be a philosopher. However, if philosophy requires knowing and citing the works of a host of writers and academics called philosophers, then it is not for everybody or even myself.

A friend has given me a relevant book, Exact Thinking in Demented Times: The Vienna Circle and the Epic Quest for the Foundations of Science, by Karl Sigmund (New York: Basic Books, 2017). I have learned from Chapter 2:

In 1895, an otherwise unremarkable university adminis­tration took the bold step of appointing a physicist to a chair in philosophy. The university was in Vienna. The physicist’s name: Ernst Mach.

… Mach’s approach to physics was historical. On the other hand, he had little interest in the history of philosophy, in contrast to traditional philosophers. Modern times had arrived. It was best to start from scratch, building up from the basics.

That much is second-hand and imprecise, but it is what I have for now. I have known the wish to start from scratch, but it can be presumptuous and dangerous. One may want to avoid the trouble of coming to terms with what already exists. A famous historical philosopher proposed to start from scratch in creating an ideal society; but he is known for irony:

“Well, then,” said I, “do you admit that our notion of the state and its polity is not altogether a daydream, but that though it is difficult, it is in a way possible and in no other way than that described …?”

“In what way?” he said.

“All inhabitants above the age of ten,” I said, “they [the genuine philosophers] will send out into the fields (εἰς τοὺς ἀγρούς), and they will take over the children, remove them from the manners and habits of their parents, and bring them up in their own customs and laws which will be such as we have described …”

This is Socrates, talking with Glaucon in Book VII (Stephanus pages 540–1) of the Republic of Plato, in Shorey’s translation of 1930–35 in the Loeb series. To achieve the perfect society, we must get rid of persons who already have their own ideas. In Pol Pot’s Cambodia, city folks were sent out into the fields, to work like peasants or to die.

Five pages earlier in the Republic (at 535c), Socrates complains about the actual condition of philosophy:

“Our present mistake,” said I, “and the disesteem that has in consequence fallen upon philosophy are, as I said before, caused by the unfitness of her associates and wooers. They should not have been bastards but true scions.”

I am not in a position to judge the appointment of a physicist like Mach to a chair in philosophy; but I note a more recent appointment. A student from my undergraduate logic course in Ankara went on to study logic in graduate school, and there he had a teacher who had entered philosophy with a degree in mathematics. That teacher said,

By the time I finished my doctorate I knew two things. First, that philosophy was so much more fun than mathematics; secondly, that I would only ever be a mediocre mathematician. In my last year as a grad student I applied for a lot of university jobs … and got absolutely nowhere … a couple of jobs then came up at the very last moment … One was in the maths department of City University in London; the other was in the philosophy department of the University of St Andrews … Why St Andrews offered me the job, to this day I have no idea. What made it even more bizarre was that they wanted me to teach not logic, but the philosophy of science.

Thus Graham Priest, as interviewed in What Is It Like to Be a Philosopher.

Ontology

At the end of my 2013 post “Psychology,” I took issue with Graham Priest’s treatment, in a popular logic book, of Anselm’s so-called Ontological Proof of the existence of God.

For now, I shall just mention Collingwood’s remark in An Essay on Metaphysics (Oxford, 1940, p. 185):

What Christians mean when they say that God exists is a complicated question. It is not to be answered except after a somewhat painstaking study of Christian theological literature.

We read Anselm’s proof at St John’s College, but perhaps indeed I did not understand it. When we got to Descartes, I understood the Ontological Proof to be not that some deity exists, but that we cannot help but believe it. As Collingwood goes on to say of the argument,

What it proves is not that because our idea of God is an idea of id quo maius cogitari nequit therefore God exists, but that because our idea of God is an idea of id quo maius cogitari nequit we stand committed to belief in God’s existence.

Collingwood grants that to see this, one needs a “bent for metaphysics” – metaphysics as the historical science of absolute presup­positions, as discussed in the previous post. When I was young, I had no bent for history, but an antipathy.

I now take issue with Priest’s treatment of reason in his response to the question, “How did your world view change in college?” This is in the interview quoted above from What Is It Like to Be a Philosopher. Like mine, the college that Priest attended was called St John’s; but this was part of Cambridge University, and there,

for one thing, I started to think very seriously about my religion. Nagging doubts turned into skepticism, and eventually I decided that there were no rational grounds for Christianity. I became an atheist, which I am to this day.

In Buddhism, there is no god. There is therefore no such thing as divine revelation. The only ground one has for accepting something is that it stands up to reason, all things considered. That strikes me as eminently sensible. People who don’t use their reason are regularly conned in life. Sadly, I don’t think I need to give examples.

I interject the recollection of a couplet by Robert Frost, “Precaution” from Ten Mills, which was detested by a friend of mine in eighth grade:

I never dared to be radical when young
For fear it would make me conservative when old.

Not having accepted Christianity when young, I did not have to reject it when older.

Rationality is good. However, there are things that we accept, not because they stand up to reason, but because we need to stand on them in order to reason. These are the absolute presup­positions mentioned above. The most fundamental of them may be Descartes’s Cogito, “I am thinking.”

Presupposition

Simon Blackburn writes sympathetically about Collingwood’s absolute presup­posions, but I don’t think he has really understood them. “Those are the presup­positions,” he says,

that lie so far underneath the edifices we build that we cannot dig down to them. They remain invisible, if only because they would be at work determining the shape our digging would take, or what we could notice as we conducted it. We can never step on our own shadow. The only power that can reveal these presup­positions is that of time: later generations will see them, but we cannot. Myself, I find nothing shocking or surprising in this claim. The hiddenness of a presup­position is like the peculiarity of a fashion, obvious to subsequent generations but necessarily invisible to those whose fashion it is.

This kind of skepticism is foreign to Collingwood’s thought. For one thing, Collingwood is quite clear that we can know our absolute presup­positions. This is from An Essay on Metaphysics:

metaphysical analysis, the discovery that certain presup­positions actually made are absolute presup­positions, is an integral part or an indispensable condition … of all scientific work … meta­physical analysis is not difficult when you know what you are trying to do.

Part of being an absolute presup­position is having no logical connection to other absolute presup­positions; thus, when meta­physical analysis is done,

the literary form of a treatise in which a meta­physician sets out to enumerate and discuss the absolute presup­positions of thought in his own time cannot be the form of a continuous argument, leading from point to point by way of quasi-mathematical demonstration, as in the Ethics of Spinoza. It must be in the form of a catalogue raisonné, as in the fourth book of Aristotle’s Metaphysics or in the Quaestiones of a medieval meta­physician.

By the “fourth book” of the Metaphysics, Collingwood must mean Book Δ, also numbered as Book V, since there are Books Α, α, Β, and Γ coming before. Book Δ is the “philosophical lexicon,” where Aristotle defines concepts like beginning, cause, element, and so forth. Collingwood’s own Essay ends with a sort of catalogue raisonné of three examples: God, Kant’s metaphysics, and causation.

The skepticism imputed by Blackburn might indeed be inferred from passages of An Essay on Metaphysics such as,

If people became aware that in certain contexts they were in the habit of treating this or that presup­position as an absolute one, they would be unable to go on doing it.

However, people do become aware of treating a presup­position as absolute. They may then cease to do so. The quotation is from Chapter VIII, called “What Anti-Metaphysics Is.” There are three kinds of anti-metaphysics: progressive, reactionary, and irrationalist.

Progression

Collingwood’s chief example of progressive anti-metaphysics is the General Scholium of the Mathematical Principles of Natural Philosophy of Isaac Newton. The relevant paragraph is worth quoting at length, though I bold the key passages; I use the translation (from Newton’s Latin) of I. Bernard Cohen and Anne Whitman, University of California Press, 1999:

Thus far I have explained the phenomena of the heavens and of our sea by the force of gravity, but I have not yet assigned a cause to gravity. Indeed, this force arises from some cause that penetrates as far as the centers of the sun and planets without any diminution of its power to act, and that acts not in proportion to the quantity of the surfaces of the particles on which it acts (as mechanical causes are wont to do) but in proportion to the quantity of solid matter, and whose action is extended everywhere to immense distances, always decreasing as the squares of the distances. Gravity toward the sun is compounded of the gravities toward the individual particles of the sun, and at increasing distances from the sun decreases exactly as the squares of the distances as far out as the orbit of Saturn, as is manifest from the fact that the aphelia of the planets are at rest, and even as far as the farthest aphelia of the comets, provided that those aphelia are at rest. I have not as yet been able to deduce from phenomena the reason for these properties of gravity, and I do not feign hypotheses (Hypotheses non fingo). For whatever is not deduced from the phenomena must be called a hypothesis; and hypotheses, whether meta­physical or physical, or based on occult qualities, or mechanical, have no place in experimental philosophy. In this experimental philosophy, propositions are deduced from the phenomena and are made general by induction. The impenetrability, mobility, and impetus of bodies, and the laws of motion and the law of gravity have been found by this method. And it is enough that gravity really exists and acts according to the laws that we have set forth and is sufficient to explain all the motions of the heavenly bodies and of our sea.

Newton writes literally against meta­physical hypotheses (or presup­positions); while he does so, he is making progress in understanding the world; thus, he is engaged in what Collingwood calls progressive anti-metaphysics. Newton is still doing metaphysics, though without realizing it. Collingwood remarks,

Newton did not mean to warn his readers against his own metaphysics. He meant to warn them against the metaphysics of professional meta­physicians, in order to forestall the criticisms such people were likely to bring against his own metaphysics, which was an integral part of his own physics.

Evidently Newton did not know he had a metaphysics. He took the positivist view that “propositions are deduced from the phenomena.” Nonetheless, they are not simply that. For Ptolemy, the planets travelled on circles, or rather epicycles – circles on circles; for Kepler, the planets travelled on ellipses. I think the difference arose not from Kepler’s having better data (though he may have had it). Kepler was ready to consider that not every fundamental motion had to be linear or circular:

Not every irregularity of movements comes from heaviness and lightness, the properties of the elements; but some comes from the change of the distance too, as is clear in the case of the lever and the balance; and this cause produces intensification and remission of movements, as has been explained so far. We must however remark that there is nevertheless some kinship between the principles of heaviness and lightness in the elements and the natural inertia of the planetary globe with respect to movement, but no irregularity of movement is explained by this kinship.

But as regards the figure of the movement, the argument concludes nothing more than we can grant, namely that the movement bends back into itself. And not only the circular but also the elliptical are of such a kind; and so the assumptions are not denied. For in truth bodies which revolve about their axes are moved only in order that by their everlasting motion they may obey some necessity of their own globe – some bodies indeed in order that they may carry the planets around themselves in everlasting circles.

(Source: Book IV of Kepler’s Epitome of Copernican Astronomy, page 932 of Ptolemy Copernicus Kepler, Volume 16 of Great Books of the Western World, Encyclopædia Britannica, 1952; 24th printing, 1982.)

Doing any kind of natural science requires at least the presup­position that there is a nature to be studied. As Collingwood points out later in the Essay (p. 215),

Aristotle thought, and he was not the only Greek philosopher to think it, that by merely using our senses we learn that a natural world exists. He did not realize that the use of our senses can never inform us that what we perceive by using them is a world of things that happen of themselves and are not subject to control by our own art or any one else’s … This meta­physical error was corrected by Christianity.

I shall return to the subject of Christianity later.

Reaction

The complement of the progressive anti-metaphysics that Newton engaged in is reactionary anti-metaphysics, which is opposed to presup­positions that are actually coming into use. I would suggest the following example:

that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness.

In the 1963 March on Washington (recalled in “Joan Baez in Istanbul”), Martin Luther King referred to Thomas Jefferson’s 1776 presup­position as a creed whose true meaning was yet to be lived out. The election of Donald Trump to the Presidency of the United States has brought out a reactionary anti-metaphysics, which insists that, in a position of power, the crudest white man is to be preferred to the most refined black man (such as Barack Obama). The Civil War then is a nineteenth-century instance of reactionary anti-metaphysics; I looked at it in “War and Talk,” which is an essay on causation, or a “foray into the mystery of how things happen,” inspired originally by a chapter in War and Peace.

I think Collingwood must be alluding to the American Revolution when he gives 1775 as the year when “the principle of nationality first asserted itself in the modern world as a dynamic political force.” Here Collingwood is quoting Arnold Toynbee in “A Turning Point in History,” Foreign Affairs, January 1939. (For my own convenience, I am keeping here a “personal edition” of the article, with my highlighting.) Meditating on the Munich Agreement and what should be done about it, Toynbee seems to approve of the Agreement, saying that

many of us who were acquainted with the nationality map of Czechoslovakia and with the political and economic situation in the German-inhabited districts of that state were feeling an acute moral discomfort at the notion of fighting for the balance of power in defiance of the principle of nationality.

Toynbee regrets that, after the Armistice of November 1918,

in the ensuing peace settlement we applied the principle of nationality for the benefit of every nation in Central and Eastern Europe with the exception of the three ex-enemy nations: the Germans, the Magyars and the Bulgars.

The result is now “a dominant Nazi Germany … the positive retribution for our sins.” Although the League of Nations is at the point of death, its principles of nationality and peaceful change have been carried out:

This autumn, populations amounting in the aggregate to as much as the total population of Ireland or Switzerland, and to more than the total population of Denmark or Norway, have been transferred from Czechoslovakian sovereignty to German, Hungarian and Polish sovereignty without war. Though, of course, this has not been achieved without an extreme threat of war, it is nevertheless an unprecedented event; and it would be hard to say that it is not good. And yet the League seems to be dying of it. She is like a mother dying in childbirth because the birth is so long overdue.

When persons such as myself come to Turkey and are horrified to learn of the population exchange with Greece of 1923, we should understand that this was also a project of the League of Nations. Collingwood’s general remark is,

The things that were done in the nineteenth century in the name of nationality, the things that are still done to-day, at what expense in life and wealth I shall not try to estimate, are done for the sake of an eighteenth-century ‘meta­physical’ idea.

The idea comes from John Locke, whose model of a parliamentary constitution was found, in the eighteenth century (according to Collingwood), to hold nationality “as a ‘natural’ basis, an absolute presup­position, of all political activity whatsoever.”

Late in the nineteenth century, by Collingwood’s account,

There were in especial two new developments to be opposed. There was a new physics, very different from that of Newton, which together with a new ‘non-Euclidean’ geometry was to produce what we now know as the physics of relativity. There was a new history, cutting itself loose from the age-old method of scissors and paste, which was to revolutionize the accepted view of the human world (and therefore of the political world) at least as completely as the new physics was to revolutionize the accepted view of ‘nature’. The spirit of nineteenth-century thought … expressed itself in two war-cries, each for a time celebrated in Germany, the country of their birth: ‘Back to Kant’ and ‘No More Metaphysics’.

Now comes the paragraph from which I quoted earlier:

… The ‘science’ which was to be protected by this cry of ‘No More Metaphysics’ was being in effect described as a reactionary science, one which could only be imperilled by a critical inquiry into its foundations. Behind that cry there lay a feeling that the constellation of absolute presup­positions made by this reactionary science was exposed to strains which could only be ‘taken up’ by keeping them in darkness. If people became aware that in certain contexts they were in the habit of treating this or that presup­position as an absolute one, they would be unable to go on doing it.

Collingwood talks at length and with emotion of the suffering and death caused by steam engines: see the quotation in “NL I: ’Body and Mind.” He cites a technical source, The Marine Steam-Engine, by R. Sennett and H. J. Oran, page 21. Collingwood has the third edition, of 1898; the fourth edition, of 1899, available from the Internet Archive, is probably the same:

The resultant Efficiency of the marine steam-engine or the whole propelling apparatus is made up of the four efficiencies just stated, and is given by the product of the four factors representing respectively the efficiencies of the boiler, the steam, the mechanism, and the propeller. Any improvement in the efficiency of the marine steam-engine, and, consequently, in the economy of its performance, is therefore due to an increase in one or more of these elements, and we shall deal with these several points, and in each case describe the efforts that have been made to increase the efficiency.

The efficiency of the marine steam-engine will be seen to be very low. Taking the best case indicated by our figures, viz. that of an engine which has the maximum efficiency in each of the four com­ponents of the resultant efficiency, the efficiency would be: –

(7/10) × (1/5) × ((8½)/10) × (6/10) = 357/5000 = .071.

The highest efficiency now attainable is, therefore, a little over 7 per cent, with the marine steam-engine, and is generally less say nearer 5 or 6 per cent.

In the original, the fraction slashes are horizontal bars, and parentheses are neither needed nor used. Collingwood cited this, “the standard text-book of those days,” while writing on board the M. V. Alcinous, en route to the Dutch East Indies in late 1938.

Metaphysics is not mysticism, but an application of the dictum I quoted from Speculum Mentis (1924) in the previous post: “All thought exists for the sake of action.”

Universality

In that previous post, I quoted also Eugene Wigner on Schrödinger’s assessment of the discovery of certain regularities as miraculous. An example was Galileo’s discovery “that two rocks, dropped at the same time from the same height, reach the ground at the same time.” Wigner goes on to assert,

The first reason that it is surprising is that it is true not only in Pisa, and in Galileo’s time, it is true everywhere on the Earth, was always true, and will always be true.

I find this remark oddly restrained, because I have no doubt that Galileo’s discovery is true, not only everywhere on Earth, but everywhere in the universe. Our ability to send the probe New Horizons to Pluto and beyond might be taken as evidence of the assertion; but I am not aware that anybody thought the evidence was needed. It seems to me that the physics of today is founded on the absolute presup­position that there is nothing unusual about the Earth, but experiments done here would have the same results on any other planet, and they can even tell us what is going on inside the Sun and other stars, in this or any other galaxy.

As quoted above, Newton seems to understand this. Nonetheless, there can be no evidence for the presup­position. Thus I don’t think it can be said to “stand up to reason,” in Graham Priest’s words. It is a foundation for all of the reasoning that goes into mathematical physics.

Religion

I quoted Collingwood as saying that “Aristotle’s meta­physical error was corrected by Christianity.” It has been argued further that the development of modern physics is grounded on the Christian doctrine of Incarnation, which grants to our world the regularities formerly found only in an inaccessible heaven:

In fact, what is the Incarnation, if not the possibility that the eternal God can be really present in the temporal world where we ourselves live, without thereby losing any of His absolute perfection? But, if being present in the sensible world does not lessen the perfection, the reason is that the world itself is (or, has been or will be) perfect, at least in a certain measure (a measure, furthermore, that nothing prevents us from establishing with precision). If, as believing Christians affirm, a terrestrial (human) body can be “at the same time” the body of God and therefore a divine body and if, as the Greek savants thought, the divine (celestial) bodies accurately reflect eternal relations among mathematical entities, then nothing any longer stands in the way of searching for these relations in the world below just as much as in the Heavens. Now, it is precisely to such a search that more and more Christians, beginning in the sixteenth century, passionately devoted themselves, followed afterwards by some Jews, Moslems, and pagans.

This is from “The Christian Origin of Modern Science,” by Alexandre Kojève, translated (evidently from French) by David R. Lachterman, The St. John’s Review, Volume XXXV, Number 1 (Winter 1984), pages 22–6. I have kept my copy of this issue of the Review since picking it up as a freshman at St John’s College in Annapolis; in February of the present year (2018), I recommended (in a tweet) the issue’s article on the White Rose. I have also valued the issue’s article “What Good and What Harm Can Psychoanalysis Do?” by Wolfgang Lederer, discussed in “Nicole at the Golden Horn.”

In his own essay, Kojève goes on to observe that, by changing the center of the universe, Copernicus moved the Earth not out of, but into, a privileged position, allowing it to share the regularity previously assigned only to the heavens. However, Kojève’s translator warns us, “The reader might be aware of Kojève’s gift for the ‘canularesque,’ a ‘put-on,’ as we might call it.” The editors of the Review follow Kojève’s essay with “A Comment on Alexandre Kojève’s ‘The Christian Origin of Modern Science’ ”:

Is this piece intended as an amusing joke, or should we be profoundly edified? Even if it is less of a canularesque or ‘put-on’ than may seem the case, as Kojève invites us to suppose, how are we to satisfy ourselves that it is not appallingly irresponsible? … Let me confess at once that, when it comes to history, I am deeply suspicious of the sort of intellectual operation in which Kojève engages: proposing single ideas as the causes of complex, multi-faceted historical changes …

I confess that au fin du compte I do not understand Kojève’s intention in his piece on the Christian origin of modern science. I yield to a vague though deep suspicion when I say, Caveat lector!

That’s the beginning and end of the warning by Curtis Wilson, a tutor at St John’s whom I was somehow aware of, especially as having an interest in science and mathematics, though I never spoke with him. I confess to being more disturbed by Wilson’s worry than by Kojève’s argument. In saying this, I assume Kojève gives no ammunition to Christian nationalists. Everybody in the world is already Christian, insofar as they enjoy the benefits of modern mathematical physics. There is no further need to try to spread certain ritual practices and mythologies; there is only, perhaps, a need to understand the real meaning of those practices and mythologies that exist.

Censorship

Here I recall the Turkish language reform. Intended to free the language from supposedly foreign elements, the reform started changing Turkish beyond recognition. This was checked by Mustafa Kemal Atatürk’s Sun Language Theory, whereby there could be no foreign elements in Turkish, since source languages like Persian and Arabic were already Turkish. Geoffrey Lewis discusses all of this in The Turkish Language Reform: A Catastrophic Success (Oxford, 1999).

A relevant Wikipedia article cites only a later source, whose main subject is Hebrew. I might add to the article a citation of Lewis, but Turkey does not allow me direct access to Wikipedia, and the site itself does not allow editing through the roundabout means whereby I am able to read it. The organization Turkey Blocks monitors internet censorship in Turkey, and as founder Alp Toker points out to Paul Benjamin Osterlund in the latter’s article “Turkey marks one year without Wikipedia” (The Verge, April 30, 2018),

Essentially, Turkey has handed over editorial control of Wikipedia to its loudest critics and foreign interests abroad. Hence, the narrative about Turkey’s history, culture, and politics is today being written by outsiders who are even more critical than the country’s own citizens whose voices are now denied.

Trinity

I return to the article of Kojève and the criticism by Wilson, who finds no evidence that early modern scientists were consciously influenced by the doctrine of the Incarnation. He allows that the “Kojèvian” might say,

The founders of modern science failed to recognize the hidden factor that permitted them to do what they did. That was the dogma of the Incarnation, the sole doctrine that could overcome the double transcendence of God in paganism.

As Kojève has explained it, this double transcendence means the pagan cannot come face to face with God, even through death. Wilson says,

I am not an Hegelian in historical matters … I do not believe it is reasonable to see the almost endlessly complicated history of human thought and affairs as the realization of the Idea.

Here then we are back to assertions of what is reasonable. Wilson goes on to mention some of the complications alluded to: the Reformation; the discovery of the New World, and of the wisdom of ancient Greek texts; “the internal disintegration of scholastic thought through its own self-criticism”; imports from China of compass, gunpowder, and printing; the spread of printed books; the horse collar and triple crop rotation.

All of this recalls the rejection of Aristotle’s theory of final causes that was part of the development of modern science itself:

Typical of the whole movement is Bacon’s celebrated gibe to the effect that teleology, like a virgin consecrated to God, produces no offspring … He meant that when an Aristotelian scientist accounted for the production of a certain effect by a certain cause by saying that the cause had a natural tendency to produce that effect, he was really telling you nothing at all, and was only distracting your mind from the proper task of science, namely the discovery of the precise structure or nature of the cause in question.

This is Collingwood in The Idea of Nature (Oxford, 1945), a posthumous publication of lectures delivered originally in 1934 and 1937. It is practically meaningless to say that the Christian doctrine of the Incarnation caused the rise of modern science. To do modern science is to accept the Incarnation, at least in a form stripped of its mythology.

By Collingwood’s argument in An Essay on Metaphysics, the scientific study of nature is based on the absolute presup­positions that (1) there is a world of nature, (2) which is a world of events, and (3) this world is governed by one set of laws, although (4) “there are in this world many different realms,” governed by particular laws. Thus, it would seem, there are departments of physics, chemistry, biology, and so forth, within one university. Collingwood argues that the failure to recognize all four of these absolute presup­positions is what caused the fall of the Roman Empire; it wasn’t barbarian invasions. Apparently Toynbee argues the same thing in Volume IV of A Study of History – “published while this Essay was in the press,” Collingwood says in a note at the end of the chapter.

According to Collingwood, the Patristic writers understood why the Empire declined and what the remedy would be:

By believing in the Father they meant … absolutely presupposing that there is a world of nature which is always and indivisibly one world. By believing in the Son they meant absolutely presupposing that this one natural world is nevertheless a multiplicity of natural realms. By believing in the Holy Ghost they meant absolutely presupposing that the world of nature, throughout its entire fabric, is a world not merely of things but of events or movements.

These presup­positions must be made, they said, by any one who wished to be ‘saved’; saved, that is to say, from the moral and intellectual bankruptcy, the collapse of science and civilization, which was overtaking the ‘pagan’ world.

The title of the chapter is “Quicunque Vult,” meaning “Whoever wishes [to be saved]”; these are the first words of the Athanasian Creed.