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The Spatial Aspect

Briefly ...

We experience the spatial aspect directly and intuitively as here, there, between, around, inside and outside. Spatial properties include shape, position, size, angle, orientation, proximity, surrounding, overlap, and so on. Things that gain their meaning from the spatial aspect include particular shapes (triangle, line, spiral, etc.), angles, distances, holes, space, area, dimension and so on. Like quantitative functioning, spatial functioning feels to us like a static property. A wiggly line is spatial, but if we call it a 'path', then we are importing some kinematic meaning of 'going'. Dooyeweerd's discussion of the spatial aspect is, unfortunately, all over the place and interwoven with discussion of its relationship with other aspects [NC:II, 63-65,85-96,98-106].

The good possibility that the spatial aspect introduces into temporal reality, which have no meaning in the quantitative aspect, are simultaneity and continuity. A quantitative thing in temporal reality, such as a set, can never exhibit two different amounts (e.g. 6 and 7) simultaneously, but a spatial thing, such as a triangle, is both here and there simultaneously since it extends from here to there and over all in between. If it did not, the triangle would be incomplete. The extension from here to there is continuous, not in discrete steps.

It is this that makes so-called irrational number(nesse)s like the square-root of 2 meaningful: as amounts, they cannot be arrived at by application of quantitative laws. In this we see the quantitative aspect antecipating the spatial, in that some amounts cannot be discovered except by antecipating spatial meaningfulness (e.g. 'square'). An example of retrocipation from spatial to quantitative is length: a spatial property that also obeys quantitative laws.

Defining the Aspect x

Kernel x

rather than: Note: The kernel meaning of the spatial aspect needs to be as true for one-dimensional space as for two- and three-dimensional.

Some central themes x

Common Misconceptions x

The Aspect Itself

Non-Absoluteness x

Special Science x

Institutions x

Shalom x

Harm x

Contributions from the Field x

The Aspect Among Others

Law-dependencies x

Analogies x

Antinomies x

Notes x

Hartshorne's Discussion

In a classic volume, The Nature Of Geography, Hartshorne discusses at some length what is the kernel of Geography. Is it:

Rather, the kernel of Geography is:

(Now we have access to other planets, presumably their surfaces would also be included in that.) "Differentiation" is the kernel of the analytical aspect, from which the central activity of science or close study comes. So what is being studied is areas - which is, in two dimensions, what Dooyeweerd proposed as the kernel of his spatial aspect.

Spreading Out & 'Continuous Extension'

We call the kernel meaning 'spreading out'. But Dooyeweerd suggested the kernel was 'continuous extension'. We replace that with 'spreading out', because I have found that 'continuous extension' can be misleading, referring for example to how projects continuously extend their deadlines and costs!

The more important question, however, is why the kernel is either of these (continuous extension or spreading out) rather than, for instance, position, length, shape, etc.? A recent discussion I had with a mathematician about might throw some light on this - there is something fundamentally different about continuous numbers ('reals') and integers.

Comments Received x

This is part of The Dooyeweerd Pages, which explain, explore and discuss Dooyeweerd's interesting philosophy. Questions or comments would be welcome.

Copyright (c) 2004 Andrew Basden. But you may use this material subject to conditions.

Written on the Amiga with Protext.

Created: by 31 March 1998. Last modified: 30 August 1998 rearranged and tidied. 7 February 2001 copyright, email. 4 February 2002 spatial anticipation of the pistic in Tolkien's Galadriel. 21 January 2003 Spatial anticipating social in Alexander. 24 August 2005 brought up to date with .nav,.end, some rewriting of start. 30 January 2006 quotation from NC,I:31, rid counter. 27 February 2007 Curved and fuzzy shapes. 14 October 2008 simultaneity and 'true of 1D'. 17 July 2009 'spreading out'. 14 June 2010 line of sight. 22 September 2010 Dooyeweerd's and Basden's kernels. 21 September 2016 briefly.