Tag Archives: logic

Boolean Arithmetic

Mathematics can be highly abstract, though remaining 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.

Continue reading

Hypomnesis

When is a help a hindrance? The Muses have provoked this question. They did this through their agents, the cicadas, who sang around the European Cultural Center of Delphi, during the 11th Panhellenic Logic Symposium, July 12–5, 2017.

     Cicada, European Cultural Center of Delphi, 2017.07.15     
Cicada, European Cultural Center of Delphi, 2017.07.15

Continue reading

NL VII: “Appetite”

Index to this series

How can we compare two states of mind? This is the question of Chapter VII of The New Leviathan. The answer is contained in the chapter’s title. “Appetite” is a name, both for the chapter and for the fundamental instance of comparing a here-and-now feeling with a “there-and-then” feeling. We compare these two feelings because we are unsatisfied with the former, but prefer the latter.

It would seem then that appetite is at the root of memory. Thus we are among the ideas of the opening verses of The Waste Land of T. S. Eliot, who attended Collingwood’s lectures on Aristotle’s De Anima at Oxford (and was just a year older):

Continue reading

NL V: “The Ambiguity of Feeling”

Index to this series

Feeling differs from thought. Thought is founded in feeling; thought is erected on feeling; thought needs feeling. Thought needs feelings that are strong enough to support it. But thought itself is not strong (or weak); it has (or can have) other properties, like precision and definiteness. Thought can be remembered and shared in a way that feeling cannot.

The New Leviathan is a work of thought. It might be said that a work of thought cannot properly explain feeling. Collingwood more or less says this in Chapter V, even in its very title: “The Ambiguity of Feeling.” Continue reading

NL II: “The Relation Between Body and Mind”

Index to this series

I continue making notes on The New Leviathan (1942) of R. G. Collingwood (1889–1943). Now my main concern is with the second chapter, “The Relation Between Body and Mind”; but again I shall range widely.

Preliminaries

Some writers begin with an outline, which they proceed to fill out with words. At least, they do this if they do what they are taught in school:

He showed how the aspect of Quality called unity, the hanging-togetherness of a story, could be improved with a technique called an outline. The authority of an argument could be jacked up with a technique called footnotes, which gives authoritative reference. Outlines and footnotes are standard things taught in all freshman composition classes, but now as devices for improving Quality they had a purpose.

Thus Robert Pirsig, Zen and the Art of Motorcycle Maintenance, ch. 17. Does anybody strictly follow the textbook method? Continue reading

NL I: “Body and Mind”

Index to this series

“Body and Mind” is the opening chapter of Collingwood’s New Leviathan (1942). The chapter is a fine work of rhetoric that could stand on its own, though it invites further reading. In these respects it resembles the first of the ten traditional books of Plato’s Republic, or even the first of the thirteen books of Euclid’s Elements. The analogy with Euclid becomes a bit tighter when we consider that each chapter of The New Leviathan is divided into short paragraphs, which are numbered sequentially for ease of reference.

Continue reading

The Tradition of Western Philosophy

Note added October 16, 2018: Here I compare two projects of re-examining the philosophical tradition of the title. The projects are those of

  • R. G. Collingwood in An Essay on Philosophical Method (Oxford, 1933);
  • Stringfellow Barr and Scott Buchanan at St John’s College in Annapolis, Maryland, beginning in 1937.

I review

  • how I ended up as a student at St John’s;
  • how Collingwood has been read (or not read) by myself and others, notably Simon Blackburn;
  • how Collingwood’s Essay is based on the hypothesis of the “overlap of classes.”

I say that Collingwood writes well. This is corroborated, in a sense, in the Introduction to the 2005 edition of the Essay by James Connelly and Giuseppina D’Oro. These editors say of Collingwood’s critics M. C. D’Arcy and C. J. Ducasse,

both agreed that Collingwood’s language was imprecise, sometimes vague, and insufficiently analytical. This criticism was later echoed by A. J. Ayer in his Philosophy in the Twentieth Century where he remarked that ‘An Essay on Philosophical Method is a contribution to belles-lettres rather than philosophy. The style is uniformly elegant, the matter mostly obscure.’

At the end I quote three elegant paragraphs from Collingwood, which begin:

Assumption for assumption, which are we to prefer? That in sixty generations of continuous thought philosophers have been exerting themselves wholly in vain, and have waited for the first word of good sense until we came on the scene? Or that this labour has been on the whole profitable, and its history the history of an effort neither contemptible nor unrewarded?

We prefer the second assumption; and in this we may seem to follow Daniel McCarthy in “Modernism & Conservatism” (The American Conservative, September 25, 2012), an essay recently promoted on Twitter (which is why I return now to this post). The freedom embraced by modernism may drive one to conservatism, as it did T. S. Eliot. McCarthy quotes Donald Livingston:

The true philosopher recognizes that philosophical reflection consistently purged of the authority of the pre-reflective leads to total skepticism. In this moment of despair, hubristic reason … becomes impotent and utterly silent. It is only then that the philosopher can recognize, for the first time, the authority of that radiant world of pre-reflective common life in which he has his being and which had always been a guide prior to the philosophic act.

McCarthy comments on this,

Once reason has disestablished everything, including its own authority, what remains? The ground beneath your feet, the social order of which you are a part—things predicated not on any theory but on their immediacy. This is the profound conservatism to be realized from modernism.

Perhaps one may find this conservatism in some students and faculty at St John’s College; it is not inevitable, and Collingwood hasn’t got it, for all his admiration for Eliot.


A recent theme of this blog has been juxtapositions, especially of paintings, as in the articles “Pairing of paintings” and “More pairings” (both from July, 2013).

In this article I juxtapose two texts, from the 1930s. Both of them decry current intellectual troubles. Both find a solution in a return to the intellectual tradition. Continue reading

Psychology

The original purpose of this article is to record a passage in The Idea of History of R.G. Collingwood (1889–1943). I bought and read this book in 2001. I was looking back at it recently, because I was reading Herodotus, and I wanted to see again what Collingwood had to say about him and other ancient historians.

The passage that I want to talk about reminded me of some psychological experiments whose conclusions can be overblown. Writing before those experiments, Collingwood shows that the similar conclusions can be drawn, in more useful form, without the pretence of a scientific experiment.

Continue reading

Learning mathematics

This is mostly reminiscences about high school. I also give some opinions about how mathematics ought to be learned. This article originally formed one piece with my last article, “Limits”.

I learned calculus, and the epsilon-delta definition of limit, in Washington D.C., in the last two years of high school, in a course taught by a peculiar fellow named Donald J. Brown. The first of these two years was officially called Precalculus Honors, but some time in that year, we started in on calculus proper. Continue reading

Logic (notes on the finger-wagging Cratylus)

The senior essay that I wrote at St John’s College was called something like ‘An account based in Aristotle of the Law of Contradiction’. I do not know now what the point was. I had read the Metaphysics in a preceptorial, so I decided to spend even more time with this book in writing my essay. I remember noting ultimately that humans could indeed be self-contradictory. Hector was an example. To Andromache he described two incompatible expectations: that their son would win renown, and that the boy would die as an infant when the Greeks took Troy. Continue reading