Château Descartes

But if we are to select those dimensions which will be of the greatest assistance to our imagination, we should never attend to more than one or two of them as depicted in our imagination, even though we are well aware that there is an indefinite number involved in the problem at issue.  It is part of the method to distinguish as many dimensions as possible, so that, while attending to as few as possible at the same time, we nevertheless proceed to take in all of them one by one.  (Descartes, CSM, 63).

The final point we should bear in mind is that among the dimensions of a continuous magnitude none is more distinctly conceived than length and breadth, and if we are to compare two different things with each other, we should not attend at the same time to more than these two dimensions in any given figure.  For when we have more than two different things to compare, our method demands that we survey them one by one and concentrate on no more than two of them at once.  (Descartes, CSM, 65).


  • René Descartes, “Regulae ad Directionem Ingenii”, or “Rules for the Direction of the Mind”, pp. 9–78 in John Cottingham, Robert Stoothoff, and Dugald Murdoch (eds., trans., 1985), The Philosophical Writings of Descartes, Volume 1, Cambridge University Press, Cambridge, UK.
This entry was posted in Analytic Geometry, Cartesian Coordinate System, Cartesian Philosophy, Cartesian Product, Descartes, Dualism, Dyadicism, Inquiry, Logic, Mathematics, Philosophy, Reductionism, Relation Theory and tagged , , , , , , , , , , , , . Bookmark the permalink.

3 Responses to Château Descartes

  1. George Berger says:

    The foundational text for dyadic thought?  Nice if I am right

  2. Pingback: ⚠ It’s A Trap ⚠ | Inquiry Into Inquiry

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