In metaphysics, extension is, roughly speaking, the property of "taking up space". René Descartes defines extension as the property of existing in more than one dimension. For Descartes, the primary characteristic of matter is extension, just as the primary characteristic of mind is consciousness. This can be contrasted with current conceptions in quantum physics, where the Planck length, an almost unimaginably tiny quantity, represents reaching that distance scale where, it has been theorized, all measurement seemingly breaks down to that which can be subsumed at this scale, as distance only, or extension.
John Locke, in An Essay Concerning Human Understanding, defined extension as "only the Space that lies between the Extremities of those solid coherent Parts" of a body. It is the space possessed by a body. Locke refers to the extension in conjunction with solidity and impenetrability, the other primary characteristics of matter.
Extension also plays an important part in the philosophy of Baruch Spinoza, who says that substance (that which has extension) can be limited only by substance of the same sort, i.e. matter cannot be limited by ideas and vice versa. From this principle, he determines that substance is infinite. This infinite substance is what Spinoza calls God, or better yet nature, and it possesses both unlimited extension and unlimited consciousness.
The property of extension has not played a significant role in philosophy roughly since the time of Immanuel Kant. Kant maintained a distinction between the mind and the body, differentiating space as the realm of the body and time the realm of the mind. He makes only cursory mention of "extension," however, and no philosophers have dealt extensively with the topic since Kant's writing.
Infinite divisibility refers to the idea that extension, or quantity, when divided and further divided infinitely, cannot reach the point of zero quantity. It can be divided into very small or negligible quantity but not zero or no quantity at all. Using a mathematical approach, specifically geometric models, Gottfried Leibniz and Descartes discussed the infinite divisibility of extension. Actual divisibility may be limited due to unavailability of cutting instruments, but its possibility of breaking into smaller pieces is infinite.
Compenetration refers to two or more extensions occupying the same space at the same time. This, according to scholastic philosophers, is impossible; according to this view, only spirits or spiritualized matter can occupy a place occupied already by an entity (matter or spirit).
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