Infinite Divisibility in Leibnizian Philosophy

A detailed Summary of Infinite Divisibility in Leibnizian Philosophy

Divisible Bodies and the Search for Substantial Unity

In his meditations, Des Cartes posits that extension is the essential property of substantive bodies. In analyzing of the malleable properties of wax, he claims, "I would not be making a correct judgment about the nature of wax unless I believed it being capable of being extended in many more different ways than I will ever encompass in my imagination, (21)." For Des Cartes, extending, (in size, quantity, length, width, depth, and in various "shapes, positions and local motions, (44)"), is as essential to the nature of bodies as thinking is to the nature of minds. He believes that since he cannot will or control his perception of substances, they must either exist as bodies unless God is deceiving him by giving him false perceptions, (55). However, since Des Cartes has proven that God exists and that he is perfect, he couldn't be a deceiver. Thus, Des Cartes concludes that in spite of his limited perception, the bodies must exist, and they must at least possess the prope!

Leibniz disagrees with Des Cartes, not about the distinctiveness of extension as a property that characterizes bodies, but more radically with Des Cartes' initial ass

"Since every mind is like a world apart, self-sufficient,...containing infinity, and expressing the universe, it is as durable, subsistent, and absolute as the universe of creatures itself. Thus we should judge that it must always behave in the way most proper to contribute to the perfection of the society of all minds...There is also a new proof for the existence of God in our system...For the perfect agreement of so many substances which have no communication among them can only come from the common source, (145)."

He claims that a monad, as a "principle of action" is intelligible "since in it there is something analogous to what there is in us, namely appetite and perception, (180)." His reasoning for this assertion is that "the nature of things is uniform, and our substance cannot differ altogether from the other simple substances of which the whole universe consists, (181)." Here he seems to be appealing some kind of natural order and coherence, (uniformity) in the universe to justify the earlier assertion that all mutations flow from primitive forces, (monads). But is this observation made of anything more than an appeal faith, (for which he criticizes Des Cartes)? Is his argument for the ultimate reality of monads simply a mathematical model to show God's presence in the orbiting of every electron and the division of each cell?

Leibniz would argue perhaps that this coherence is a proof for the existence of God, rather than suggesting that God proves the existence of coherent monads.

------------------------------------------------------------------------

umption that the extension of matter would be enough to account for real unified substance. In this essay, I will demonstrate how Leibniz, using the argument of infinite divisibility, denies that matter or bodily extension could be the essence of substance. Leibniz introduces this idea in his Primary Truths, where he makes the following claim:

Leibniz believes that there is an inherent unity in the composition of a watch, a human being, an army, and indeed in everything that we perceive, despite the fact that each of these things can be broken down into smaller parts. "In real things, namely in bodies, the parts are not indefinite, but are assigned in a certain way, in accordance with how nature has actually instituted divisions and subdivisions; and although these divisions might proceed to infinity, nonetheless, everything results from certain first constituents, that is, real unities, although infinite in number...." He believes that bodies are composed according to a natural

Some common words found in the essay are:
Primary Truths, Des Cartes, Des Cartes', des cartes, essence substance, Substantial Unity, leibniz believes, proof existence god, substance leibniz, argument infinite, real unities, leibniz argue, infinite divisibility, unity substance, molecules atoms,

Approximate Word count = 1739
Approximate Pages = 7 (250 words per page double spaced)

Category: History