Is there a philosophical reason to postulate the existence of entities without parts? It seems like everything in our experience is complex and has various pieces and parts or can be reduced to a more fundamental entity given scientific exploration; what reason is there for thinking that there is something that is non-reducible?

Here's an argument that the early modern philosophy Gottfried Wilhelm Leibniz gives for postulating the existence of an entity without parts, versions of which he gave from the 'middle' of his philosophical career--roughly, from about the time that he wrote the "Discourse on Metaphysics"--until the end, which, for present purposes, we can take to be the Monadology.

Leibniz starts from the fact that material things can all be subdivided--he actually says that material things not only can be divided, but that they are actually infinitely divided. Since a material thing such as a table can be, as it were, decomposed into infinite material parts, Leibniz argues--in a line of reasoning that is especially emphasized in his correspondence with the philosopher Antoine Arnauld based on issues in the "Discourse on Metaphysics," but elsewhere in his writings as well--that a material thing like a table is no more metaphysically real than a heap of stones, a flock of sheep, or a rainbow: the basis for this claim is Leibniz's view no TRUE ENTITY can be divisible. Consequently, Leibniz argues, if there are true entities, then they must be simple, immaterial things, that is, something like the monads, which have no parts and which, in Leibniz's ultimate formulation of his metaphysics in the Monadology ground the existence of all other things, and which, Leibniz concludes, not only exist, but are the only really existing things. (I leave aside the wrinkle that Leibniz also claims that material things are merely 'well-founded phenomena' phenomenally based, as it were, on the monads, not even things at all, a point closely related to his view that the only true entities are simple substances, but not directly following from it.)

Now, to be sure, Leibniz's position turns on his view that a true entity must be indivisible. Leibniz worries this point a great deal--for a masterful account of the ways in which he worries this point, I cannot recommend too highly R. C. Sleigh, Jr., Leibniz and Arnauld: A Commentary on Their Correspondence, which focuses on the correspondence, and Donald Rutherford, Leibniz and the Rational Order of Nature, which examines the topic more broadly across Leibniz's philosophical career.

The general issue about the relation between material parts and things is treated by numerous other early modern philosophers: Tom Holden undertakes a wonderful, searching examination of this topic in The Architecture of Matter: Galileo to Kant.

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