The One and the Many

A set is a Many that allows itself to be thought of as a One.

— Georg Cantor

How to solve the ancient problem of the one and the many?

Is the one just one, and the many merely many? Or can the one contain the many, and the many reveal the one?

Many fourfolds have been shown here. Are they different aspects of  one, greater fourfold?

Or are they completely separate, incomparable and  incommensurate, except for their common cardinality?

http://plato.stanford.edu/entries/problem-of-many/

[*4.84]

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4 Responses to “The One and the Many”

  1. Fourfolds and Double Duals, Part 2 « Equivalent eXchange Says:

    […] In addition to the symbolic fourfold presented in the previous entry Fourfolds and Double Duals, which includes the alchemical symbols for the four elements, here is another generic representation. This fourfold reminds me of the fourfolds Bright-Light-Dim-Dark shown in the early entry with the Four Elements, as well as the newer fourfold of The One and the Many. […]

  2. Stances Towards Truth | Equivalent eXchange Says:

    […] post The One and the Many may be used to develop these stances […]

  3. Notions of Equivalence | Equivalent eXchange Says:

    […] one of my favorite fourfolds — Structure-Function — with help from the fourfold of The One and the Many, I have (naturally) come up with four notions: Identities, Isomorphisms, Confluences, and […]

  4. Distinctions with and without Differences | Equivalent eXchange Says:

    […] I present a schema that divides the continuum between one and many into four: Sameness, Similarity, Distinction, and Difference. A member of the “being” camp […]

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