Tag Archives: Isaac Newton

What It Takes

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.

The post falls into sections as follows.

  • Where to start. To the thesis that everybody can be a philosopher, an antithesis is that persons with the professional title of philosopher ought to know the history of their subject.

  • Ontology. Disdain for this history may lead to misunderstanding of Anselm’s supposed proof of the existence of God.

  • Presupposition. To prove anything, you need a pou sto, or what Collingwood calls an absolute presupposition.

  • Progression. Newton rejected antiquated presuppositions.

  • Reaction. Coal-burners and racists reject new presuppositions.

  • Universality. From the 47th chapter of the Tao Te Ching (in the translation of Gia-fu Feng and Jane English):

    Without going outside, you may know the whole world.
    Without looking through the window, you may see the ways of heaven.
    The farther you go, the less you know.
    Thus the wise know without traveling;
    See without looking;
    Work without doing.

  • Religion. To say that we can know the laws governing the entire universe is like saying a human can be God.

  • Censorship. Thus everybody who believes in mathematical physics is a Christian, if only in the way that, by the Sun Language Theory, everybody in the world already speaks Turkish.

  • Trinity. That the university has several departments, all studying the same world – this is supposed to correspond to the triune conception of divinity.

This post began as a parenthesis in another post, yet to be completed, about passion and reason. To anchor that post in an established text, I thought back to David Hume, according to whom,

Reason is, and ought only to be[,] the slave of the passions, and can never pretend to any other office than to serve and obey them.

David Hume, A Treatise of Human Nature

Continue reading

Effectiveness

Preface

First posted May 17, 2018, this essay concerns Eugene Wigner’s 1960 article “The Unreasonable Effectiveness of Mathematics in the Natural Sciences.” I wrote a lot, which I now propose to summarize by section. (The meditations also continue in the next article.)

  • Some things are miraculous. Among Wigner’s examples are

    • that mathematics is possible at all, and
    • that “regularities” in the physical world can be discovered, as by Galileo and Newton.

    For Wigner, we should be grateful for the undeserved gift of a mathematial formulation of the laws of physics. This makes no sense theologically – and here I agree with the character Larry Darrell in Somerset Maugham’s novel The Razor’s Edge. Wigner’s idea that our mathematical reasoning power has been brought to perfection makes no sense to me either.

  • Everything is miraculous. Here I agree with Collingwood in Religion and Philosophy. A miracle cannot be the breaking of a natural law, since such a thing cannot be broken. A great artist like Beethoven follows no rules in the first place, or makes them up as he goes along; and he is like God in this way.

  • Natural law. That it cannot be broken is part of the very concept of natural law. Quantum phenomena and the theory of relativity have not in fact been brought under a single law; for Wigner, it may not be possible.

  • Mystery. Not only can we not define miracles, but (as we should have observed in the first place) we cannot even say when they happen. If like Wigner we call something miraculous, this means it cleanses our own doors of perception, in the sense of William Blake.

  • Definitions. In his treatment of miracle in Religion and Philosophy, Collingwood shows the futility of trying to define a term when you are not sure how to use it. He makes this futility explicit in The Principles of Art. If we are going to think about the use of mathematics in natural science, this means we ought to be mathematician, natural scientist, and philosopher; and not just “natural scientist,” but physicist and biologist, since if mathematics is effective in physics, it would seem to be ineffective in biology.

  • Being a philosopher. We are all philosophers, in the sense that Maugham describes in the story “Appearance and Reality,” if only we think. All thought is for the sake of action. This does not mean that thought occurs separately from an action and is to be judged by the action. We may value “pure” thought, such as doing mathematics or making music or living the contemplative life of a monk. This however moves me to a give a thought to the disaster of contemporary politics.

  • Philosophizing about science. For present purposes, compart­ment­al­ization of knowledge is a problem. So is the dominance of analytic philosophy, for suggesting (as one cited person seems to think) that big problems can be broken into little ones and solved independently. In mathematics, students should learn their right to question somebody else’s solutions to problems. In philosophy, the problems themselves will be our own. Philosophy as such cannot decide what the problems of physics or biology are, though it may help to understand the “absolute presuppositions” that underlie the problems. Philosophers quâ metaphysicians cannot determine once for all what the general structure of the universe is. This does not mean they should do “experimental philosophy,” taking opinion polls about supposedly philosophical questions. What matters is not what people say, but what they mean and are trying to mean. As Collingwood observes, metaphysics is an historical science.

For more on the last points, see a more recent article, “Re-enactment.” (This Preface added June 3, 2018.)


I am writing from the Math Village, and here I happen to have read that Abraham Lincoln kept no known diary as such, but noted his thoughts on loose slips of paper. Admired because he “could simply sit down and write another of his eloquent public letters,”

Lincoln demurred. “I had it nearly all in there,” he said, pointing to an open desk drawer. “It was in disconnected thoughts, which I had jotted down from time to time on separate scraps of paper.” This was how he worked, the president explained. It was on such scraps of paper, accumulating over the years into a diaristic density, that Lincoln saved and assembled what he described to the visitor as his “best thoughts on the subject.”

Thus Ronald C. White, “Notes to Self,” Harper’s, February 2018. My own notes to self are normally in bound notebooks, and perhaps later in blog articles such as the present one, which is inspired by the 1960 article called “The Unreasonable Effectiveness of Mathematics in the Natural Sciences,” by Eugene Wigner.

Papers on a table with a view of trees and a distant hill between stone columns

Continue reading

Boolean Arithmetic

Mathematics can be highly abstract, even when it remains applicable to daily life. I want to show this with the mathematics behind logic puzzles, such as how to derive a conclusion using all of the following premisses:

  1. Babies are illogical.
  2. Nobody is despised who can manage a crocodile.
  3. Illogical persons are despised.

The example, from Terence Tao’s blog, is attributed to Lewis Carroll. By the first and third premisses, babies are despised; by the second premiss then, babies cannot manage crocodiles.

George Boole, The Laws of Thought (1854), Open Court, 1940

Continue reading

NL XXV: The Three Laws of Politics

Index to this series

Executive summary (added September 11, 2018): The the three laws of politics are that (1) within the body politic, there is a ruling class, which is a society proper; (2) the ruling class can take in members from the ruled class; (3) the ruled and ruling classes will resemble one another, so that e.g. rulers of slaves will become slavish themselves. I compare such laws with physical laws, as discussed by Einstein; but on this subject, a look ahead to Chapter XXXI, “Classical Physics and Classical Politics,” would be in order. Meanwhile, by the Second Law, the body politic, or its ruling class, can be a permanent society; Nazi claims about the youth or senility of different states are bogus. There are further gradations within the ruling and ruled classes, according to strength of will; a weak will can be strengthened by another person’s stronger will through induction.


A pervading theme of the New Leviathan is freedom of will. Whether we actually have it is only a pseudo-problem (13. 17). Some persons have been fooled into thinking it a problem, perhaps by the misleading myth that free will is a divine gift, like life itself, breathed into our nostrils when, in Genesis 2:7, God forms us of the dust of the ground. As Collingwood observes at the end of Chapter XXIII, “The Family As a Society,” we are born neither free nor in chains. We have to grow up. Growing up is becoming free.

The Book of Genesis Illustrated by Robert Crumb (New York: Norton, 2009)

Continue reading

Nature and Death

Thoughts on mortality and the evolution of the universe, occasioned by a funeral and by Collingwood’s Idea of Nature and Plato’s Phaedo

Cebeci, Ankara, 2016.05.17

When the husband of my second-grade teacher died, I wanted to pay my respects. My father took me to the funeral home, where I hid behind him as he greeted the family of the deceased. My teacher was not among them. When invited to view the body, I looked over and saw it, lying off to the side in an open casket. I had never seen the man when he was alive. I declined the opportunity to gaze at his lifeless form. Until I came to Turkey, this was my closest approach to the materiality of death—except for a visit to the medical school of the University of New Mexico in Albuquerque. There, as part of the laboratory program at St John’s College in Santa Fe, students viewed dissected human cadavers.

Continue reading

NL XVIII: Theoretical Reason

Index to this series

Reason is primarily practical: it explains why we do what we do. Secondarily, reason explains why others do what they do (18. 1): this makes reason theoretical, though not entirely so, since questions about others arise from, and are answered by, our relations with those others (18. 11). The experimental method involves such relations: we do something to the world, to see how it will respond (18. 12).

Continue reading

The Istanbul Seaside

The original purpose of this article was to display and explain two photographs by me: one of a seaside park, the other of an abandoned car. I do this, and I talk about the stresses and compensations of the big city. I continue with the theme of Freedom from an earlier article of that name.

It is now early December in Istanbul, 2014. We have hardly seen the sun for weeks. Some rain falls almost every day. One has to learn to go out when one can. Last Saturday was cloudy, but dry, so we walked down to the Tophane-i Amire—the “Cannon Foundry Imperial.” The name is romantic, because it dates from Ottoman times, and because, like Koh-i-Noor, it is in a Persian grammatical form that is obsolete in Turkish. Today’s name of the cannon foundry would be Amire Tophane.
Continue reading

NL VI: “Language,” again

Index to this series

This is about language: language the concept, and “Language,” the sixth chapter of Collingwood’s New Leviathan. We shall consider language in a very basic way, not as a means of communicating what we know, but as the way we come to know things in the first place.
Continue reading

NL III: “Body As Mind”

Index to this series

In Chapter I of The New Leviathan, we stipulated that natural science, the “science of body,” must be free to pursue its own aims. But we ourselves are doing science of mind, and:

1. 85. The sciences of mind, unless they preach error or confuse the issue by dishonest or involuntary obscurity, can tell us nothing but what each can verify for himself by reflecting on his own mind.

All of us can be scientists of mind, if only we are capable of reflection: Continue reading

Psychology

Preface (January 17–18, 2019). This essay is built around two extended quotations from Collingwood:

  1. From the posthumous Idea of History (1946) with the core idea, “people do not know what they are doing until they have done it.”
  2. From An Essay on Philosophical Method (1933), about how logic is neither a purely descriptive nor a purely normative science.

The quotations pertain to the title subject of psychology for the following reasons.

  1. Psychological experiments show that we may not know what we are doing until we have done it.
  2. Psychology is a descriptive science.

Psychological experiments can tell us about what we do, only when we presuppose the general applicability of their findings. This is true for any descriptive science. Philosophy demands more. A philosophical science like logic is categorical, in the sense of the second listed quotation, because it is what Collingwood will later call criteriological. I go on to discuss criteriological sciences as such in “A New Kind of Science,” but not here.

Continue reading