Category Archives: Collingwood

Concerning the philosopher R. G. Collingwood (1889–1943). Many if not most of my posts concern Collingwood somehow, so this category may not be of much use. See Articles on Collingwood for some articles by other persons

Abraham and Gideon

The general question of this post is how Pascal’s thinking in the Pensées relates to the thinking of himself and his contemporaries about the physical and mathematical worlds.

The specific question is why Pascal juxtaposes Abraham and Gideon in two fragments of the Pensées.

A possible answer to the specific question is that God demands sacrifices of both men.

Caravaggio, Sacrifice of Isaac, 1603, Uffizi

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Reason in Pascal

In some of the Pensées, Pascal contrasts reason with instinct, passions, folly, the senses, and imagination.

Here I investigate Pascal’s raison, after one session of an ongoing discussion of the Pensées that is being carried out on Zoom.

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Feminist Epistemology

I

By character count, the bulk of this post, in the third and final part, is my notes on

  1. Elizabeth Anderson, “Feminist Epistemology and Philosophy of Science,” Stanford Encyclopedia of Philosophy, February 13, 2020. 61 pages.

There are things I already thought, owing to philosophers such as Robin George Collingwood, Mary Midgley, and Robert Pirsig, if not Henry David Thoreau.

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Law and History

I learned about Peter Turchin recently through his profile in the Atlantic by Graeme Wood. I had learned about the Atlantic article from historians on Twitter such as James Ryan, who does “Turkish history and other stuff,” according to his own Twitter profile, and who tweeted in response to Wood’s article,

This is really interesting research, but, uh, it is only history in the way that a particle physicist does history.

In response to that, a thread began:

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Pacifism

Pacifism is properly pacificism, the making of peace: not a belief or an attitude, but a practice. Mathematics then is pacifist, because learning it means learning that you cannot fight your way to the truth. Might does not make right. If others are going to agree with you, they will have to do it freely. Moreover, you cannot rest until they do agree with you, if you’ve got a piece of mathematics that you think is right; for you could be wrong, if others don’t agree.

The book *Dorothy Healey Remembers,* with photo of subject

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Articles on Collingwood

This article gathers, and in some cases quotes and examines, popular articles about R. G. Collingwood (1889–1943).

  • By articles, I mean not blog posts like mine and others’, but essays by professionals in publications that have editors.

  • By popular, I mean written not for other professionals, but for the laity.

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Mathematics and Logic

Here is another in the recent spate of mathematics posts. I take up now, as I did in my last post, some material that I had originally drafted for the first post in this series.

Whenever it has been designated for its own post, material can grow, as has the material of this post in the drafting. Large parts of this post are taken up with

  1. the notion (due to Collingwood) of criteriological sciences, logic being one of them;

  2. Gödel’s logical theorems of completeness and incompleteness.

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More of What It Is

I say that mathematics is the deductive science; and yet there would seem to be mathematicians who disagree. I take up two cases here.

From Archimedes, De Planorum Aequilibriis,
in Heiberg’s edition (Leipzig: Teubner, 1881)

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What Mathematics Is

Mathematics “has no generally accepted definition,” according to Wikipedia today. Two references are given for the assertion. I suggest that what really has no generally accepted definition is the subject of mathematics: the object of study, what mathematics is about. Mathematics itself can be defined by its method. As Wikipedia currently says also,

it has become customary to view mathematical research as establishing truth by rigorous deduction from appropriately chosen axioms and definitions.

I would put it more simply. Mathematics is the science whose findings are proved by deduction.

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Map of Art

The bulk of this post is a summary of the chapter on art in Collingwood’s Speculum Mentis: or The Map of Knowledge (1924). The motto of the book is the first clause of I Corinthians 13:12:

Βλέπομεν γὰρ ἄρτι δι’ ἐσόπτρου ἐν αἰνίγματι

For now we see through a glass, darkly

The chapter “Art” has eight sections:

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