Tag Archives: Bertrand Russell

On Gödel’s Incompleteness Theorem

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

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

NL XXIX: External Politics

Index to this series

Executive summary (added September 13, 2018, edited July 19, 2019): Dealing with other bodies politic is the third stage of political life, after societies’

  • formation (as if by marriage),
  • dominion over non-social communities (as if by having children).

Having been used in the first two stages, dialectic can be used in the third. Being the eristic of external politics, war has no psychological cause. War is a state of mind, which does not think non-agreement can become agreement. Pacifism has this state of mind.


External politics are international relations. These represent the third of the “stages” in political life (29. 1), which we enumerate:

  1. The joining of wills into a society, which rules itself (29. 11).
  2. Such a society’s ruling over a non-social community in a body politic (29. 12).
  3. Dealing with other bodies politic (29. 13).

Continue reading

NL XIV: “Reason”

Index to this series

Summary added January 29, 2019, revised May 8, 2019. Practical reason is the support of one intention by another; theoretical, one proposition by another. Reasoning is thus always “motivated reasoning”: we engage in it to relieve the distress of uncertainty. Reason is primarily practical, only secondarily theoretical; and the reason for saying this is the persistence of anthropomorphism in theoretical reasoning: by the Law of Primitive Survivals in Chapter IX, we tend to think even of inanimate objects as forming intentions the way we do.

Reasons for adding this summary of Chapter XIV of Collingwood’s New Leviathan include

  • the tortuousness of the following post on the chapter,
  • the provocation of a Guardian column by Oliver Burkeman on motivated reasoning.

Says Burkeman, whose “problem” is apparently motivated reasoning itself,

One of the sneakier forms of the problem, highlighted in a recent essay by the American ethicist Jennifer Zamzow, is “solution aversion”: people judge the seriousness of a social problem, it’s been found, partly based on how appetising or displeasing they find the proposed solution. Obviously, that’s illogical …

On the contrary, how we reason cannot be “illogical,” any more than how we speak can be “ungrammatical.” Logic is an account, or an analysis, of how we do actually reason; grammar, of how we speak. Of course we may make errors, by our own standards.

Rogier van der Weyden (Netherlandish, 1399/1400-1464), Portrait of a Lady, c. 1460, oil on panel, Andrew W. Mellon Collection
Rogier van der Weyden (Netherlandish, 1399/1400–1464),
Portrait of a Lady, c. 1460, oil on panel
National Gallery of Art, Washington; Andrew W. Mellon Collection

Context

There was a rumor that Collingwood had become a communist. According to David Boucher, editor of the revised (1992) edition of The New Leviathan, the rumor was one of the “many reasons why [that book] failed to attract the acclaim which had been afforded Collingwood’s other major works.” Continue reading

NL I: “Body and Mind”

Index to this series

“Body and Mind” is the opening chapter of Collingwood’s New Leviathan. 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.

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