Tag Archives: Timothy Gowers

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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Logic of Elliptic Curves

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

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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

My question has two particular instances.

  1. At a mathematical conference, can theorems “speak for themselves,” or should their presenters be at pains to help the listener appreciate the results?

  2. When the conference is in Greece, even at one of the country’s greatest archeological sites, does this enhance the reading of ancient Greek texts, or is it only a distraction?

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