Islamic philosophy
Place and space

The Arab polymath al-Hasan Ibn al-Haytham (Alhazen; died c. 1041) presented a thorough mathematical critique and refutation of Aristotle 's conception of place (topos) in his Risala/Qawl fi’l-makan (Treatise/Discourse on Place).

Aristotle's Physics (Book IV – Delta) stated that the place of something is the two-dimensional boundary of the containing body that is at rest and is in contact with what it contains. Ibn al-Haytham disagreed with this definition and demonstrated that place (al-makan) is the imagined (three-dimensional) void (al-khala' al-mutakhayyal) between the inner surfaces of the containing body. He showed that place was akin to space, foreshadowing Descartes 's notion of place as space qua Extensio or even Leibniz 's analysis situs. Ibn al-Haytham's mathematization of place rested on several geometric demonstrations, including his study on the sphere and other solids, which showed that the sphere (al-kura) is the largest in magnitude (volumetric) with respect to other geometric solids that have equal surface areas. For instance, a sphere that has an equal surface area to that of a cylinder, would be larger in (volumetric) magnitude than the cylinder; hence, the sphere occupies a larger place than that occupied by the cylinder; unlike what is entailed by Aristotle 's definition of place: that this sphere and that cylinder occupy places that are equal in magnitude. Ibn al-Haytham rejected Aristotle 's philosophical concept of place on mathematical grounds. Later, the philosopher 'Abd al-Latif al-Baghdadi (13th century) tried to defend the Aristotelian conception of place in a treatise titled: Fi al-Radd ‘ala Ibn al-Haytham fi al-makan (A refutation of Ibn al-Haytham's place), although his effort was admirable from a philosophical standpoint, it was unconvincing from the scientific and mathematical viewpoints.

Ibn al-Haytham also discussed space perception and its epistemological implications in his Book of Optics (1021). His experimental proof of the intromission model of vision led to changes in the way the visual perception of space was understood, contrary to the previous emission theory of vision supported by Euclid and Ptolemy. In "tying the visual perception of space to prior bodily experience, Alhacen unequivocally rejected theintuitiveness of spatial perception and, therefore, the autonomy of vision. Without tangible notions of distance and size forcorrelation, sight can tell us next to nothing about such things."
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