Thought, classes, diagonal method

New Perspectives on Thought, p 337

It was only with the advent of computers that people actually tried to create "thinking" machines, and witnessed bizarre variations on the theme of thought. [...] As a result, we have acquired, in the last twenty years or so, a new kind of perspective on what thought is, and what it is not.

Classes and Instances, p 351

There is a general distinction concerning thinking: that between categories and individuals, or classes and instances. [...] It might seem at first sight that a given symbol would inherently be either a symbol for a class or a symbol for an instance --but that is an oversimplification. Actually most symbols may play either role, depending on the context of their activation.

What Does a Diagonal Argument Prove? p 423

Cantor's proof uses a diagonal in the literal sense of the word. Other "diagonal" proofs are based on a more general notion, which is abstracted from the geometric sense of the word. The essence of the diagonal method is the fact of using one integer in two different ways --or, one could say, using one integer on two different levels [...]

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Marc Girod
Last modified: Thu Mar 5 13:55:46 EET 1998