Category Archives: Hitchens

Pertaining to Christopher Hitchens

Logic of Elliptic Curves

January 6, 2019 – 8:49 pm

In my 1997 doctoral dissertation, the main idea came as I was lying in bed one Sunday morning. Continue reading →

By David Pierce | Also posted in Aristotle, Mathematics | Tagged , , , , | Comments (1)

On Gödel’s Incompleteness Theorem

December 15, 2018 – 8:43 am

This is an appreciation of Gödel’s Incompleteness Theorem of 1931. I am provoked by a depreciation of the theorem.

I shall review the mathematics of the theorem, first in outline, later in more detail. The mathematics is difficult. I have trouble reproducing it at will and even just confirming what I have already written about it below (for I am adding these words a year after the original publication of this essay).

The difficulty of Gödel’s mathematics is part of the point of this essay. A person who thinks Gödel’s Theorem is unsurprising is probably a person who does not understand it.

In the “Gödel for Dummies” version of the Theorem, there are mathematical sentences that are both true and unprovable. This requires two points of clarification.

Continue reading →

By David Pierce | Also posted in Archimedes, Categorical Thinking, Descartes, Euclid, Mathematics, Philosophy, Science | Tagged , , , , , , , , , , , , , , , , , , , , , | Comments (10)

NL XXVII: Force in Politics

September 1, 2018 – 7:09 am

Index to this series

Executive summary (added September 12, 2018): When persons cannot rule themselves, they are ruled by force, as a duty, by other persons, for the benefit and pleasure of all. Force includes fraud and deceit; but their use must be limited, if those persons who are being ruled by force now will one day join the ruling class themselves. If a liberal and a conservative party take up respectively the ideals of democracy and aristocracy discussed in the last chapter, the parties must understand that each needs the other, in order to engage in the dialectic that aims for the best society. If somebody thinks the two parties waste energy, either in pretending to be in opposition to one another, or in actually being opposed, then that person is effectively wishing for tyranny.

In my last post on the New Leviathan (which was my first for this year), I said Collingwood would discuss the British parliament in Chapter XXVII. That chapter is now my subject.

The ruling class must incorporate new members from time to time, whether anybody thinks about it or not (27. 75). Anybody who does think about it may take up one of two goals (27. 77).

27. 79. To hasten the percolation of liberty throughout every part of the body politic was the avowed aim of the Liberal party; to retard it was the avowed aim of the Conservative party.

27. 8. The relation between them was consciously dialectical. They were not fundamentally in disagreement. Both held it as an axiom that the process of percolation must go on. Both held that given certain circumstances, which might very well change from time to time, there was an optimum rate for it, discoverable within a reasonable margin of error by experiment.

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By David Pierce | Also posted in Collingwood, History, New Leviathan, Philosophy, Philosophy of History | Tagged , , , , , , , , , | Comments (9)

NL XXI: Society as Joint Will

September 9, 2017 – 5:50 am

Index to this series

Executive summary (added September 10, 2018):

1.
I cannot say “I will” without recognizing the possibility of joining with others to say “we will.”
2.
A social consciousness consists of (1) a precise idea of one’s place in a society and (2) a vague sense of the society as a whole. The latter sense may be incorrect, having been foolishly accepted on the word of an authority.
3.
Properly understood, ruling, of itself and perhaps of a non-social community, may be all that a society does. It is the responsibility of the members alone.
4.
To form a society means (1) to form social relations and (2) to do this for some purpose. To focus on (1) yields the idea of a universal society—which cannot actually exist, despite foolish hopes for the League of Nations.
5.
The universal society cannot exist, because we produce a society by transforming an earlier community, and some trace of this must remain.
6.
Members of a society are equal, (1) in having the freedom to join and (2) in just being members. A society may create an inequality, as by delegating authority. There may be natural inequalities, not produced by the society itself; society may compensate for them, turn them into assets, or even depend on them, as in the case of initiative.
7.
Rule by force (in a non-social community) may be by rewards and punishments, that is, objects of desire and fear. These may be promised or threatened fraudulently. One who grows too accustomed to exerting force may lose freedom of will.
8.
Societies institute criminal law to mitigate members’ losses of freedom of will.
9.
Societies can be temporary or permanent.

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By David Pierce | Also posted in Collingwood, New Leviathan, Philosophy, Plato | Tagged , , , , , , , , , , , | Comments (7)

The Private, Unskilled One

May 19, 2017 – 5:55 am

I went into Istanbul’s Pandora Bookshop a month ago, looking for an English translation of War and Peace, since the Garnett translation I had read at college was falling apart. I was told the Oxford World’s Classics edition (with the Maude translation) was coming the next week, and it did come.

Elif Batuman, The Idiot, in Nesin Matematik Köyü, Kayser Dağı Mevkii, Şirince, Selçuk, İzmir, Turkey, 2017.05.18

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By David Pierce | Also posted in Categorical Thinking, Education, Harper’s, Maugham, Nesin Mathematics Village, Thoreau | Tagged , , , , , , | Comments (0)

Narnia

June 22, 2016 – 3:51 pm

The following notes about C. S. Lewis, The Chronicles of Narnia, are from four emails that I wrote in the fall of 2015. The emails rebut various objections to the Narnia books. I have put my emails here, because I noticed that a friend on Facebook was wondering whether her daughter was ready to read the Chronicles, or perhaps to be read to from them. I do not wish to write much on Facebook, for reasons detailed elsewhere in this blog; so I asked interested persons to read me here.

Side of boxed set of The Chronicles of Narnia from 1970s

I started reading the Chronicles in the summer before fourth grade. They had been on a list of suggested reading supplied by my school. I do not believe I was corrupted by those books, or by any other books; but anybody may read below for signs to the contrary! Continue reading →

By David Pierce | Also posted in Education, Facebook, Philosophy, Thoreau | Tagged , , , , , , , | Comments (2)