Cambridge Reading Group 22nd October 2013

As part of the semester one seminars for 2013-2014, the Cambridge Kant Reading Group read Daniel Warren’s ‘Kant and the Apriority of Space’.

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One Response to Cambridge Reading Group 22nd October 2013

  1. James Collin says:

    Here’s a thought. Kant took it to be necessary that space was 3-dimensional. Bracketing the possibility that space is transcendentally ideal for the moment—of course, you might think I’m bracketing the most interesting thing here—most people who are paid to think about these things now reject the necessary 3-dimensionality of space on the grounds that spaces with more dimensions are possible; and the standard argument for this is the following. A 3-dimensional space can be modelled as ℝ3 = ℝ X ℝ X ℝ with each n-tuple representing a point in 3-dimensional space. Methods of this sort allow for higher-dimensional spaces to be represented, since extending or generalising the model to represent higher-dimensional spaces is quite straightforward. 4 dimensional space is represented as ℝ4, 5-dimensional space as ℝ5, and so on.

    But why think a thing like this constitutes grounds for taking higher-dimensional spaces to be metaphysically possible? Why think that because a model of 3-dimensional space can be extended in this sort of way (and remain coherent), higher-dimensional spaces themselves are possible, or even coherent? Why think that because (i) there is a space which can be represented using ℝ3, and (ii) there is nothing in consistent about ℝ4, that (iii) there could be a space that is represented by ℝ4? Now, there may be other good reasons to think that (iii) is true, but the standard argument looks to be enthymematic at best.

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