Monads & Material Systems

In Leibniz’s metaphysics, monads are simple, immaterial, indivisible qualitative multiplicities enfolded in spatial unities—centers of perception, appetite, and an inner dynamism. Each monad is a living mirror that reflects the entire universe from its own limited perspective. 1 Moreover, the highest monads, that is, spirits, reflect in an imperfect way, as Scripture attests, the attributes of God: intellect, power, will, and so forth. 2 All monads develop their inner states in coordination with God’s pre-established harmony. Because monads do not interact causally, material systems cannot be explained by physical influence among extended things. Instead, bodies arise in a relational way.

Leibniz insists that bodies are actual. They are not mere illusions or shadows of thought. When he calls them phenomena bene fundata—well-founded phenomena, 3 he means that their being is grounded in the reality of monads. A body is not an invention of the mind but a structure of relations among simple substances. Its actuality is genuine, though derivative. A body is a relation among monads, not a substance independent of them. The unity of a body lies in the coordination of the states of the monads that compose it. Since relations cannot exist without their relata, bodies cannot exist apart from the monads on which they depend. Matter is therefore not a primitive substance but a derivative unity arising from the ordered multiplicity of monads. Its reality is relational rather than self-subsistent.

To call a body an “appearance” might suggest that it exists only in the imagination. Leibniz avoids this. Bodies are well-founded phenomena: they truly exist in the world, grounded in the order of monads. What we call extension, motion, and interaction is the phenomenal side of their underlying relational structure.5

  1. Gottfried Wilhelm Leibniz, Monadology §56, in Robert Latta (trans.), The Monadology and Other Philosophical Writings (Oxford: Clarendon Press, 1898), p. 258. Public domain. ↩
  2. Leibniz, Monadology §82, in Latta, The Monadology and Other Philosophical Writings, p. 268. Public domain. ↩
  3. Leibniz, Monadology §60, in Latta, The Monadology and Other Philosophical Writings, p. 259. Public domain. ↩
  4. Leibniz, Monadology §§62–63, in Latta, The Monadology and Other Philosophical Writings, pp. 260–261. Public domain. ↩
  5. Leibniz, Monadology §67, in Latta, The Monadology and Other Philosophical Writings, p. 262. Public domain. ↩

About the Author

Andrew M. Cavallo is a guitarist, composer, and self-produced musician. His debut album, Christendom Reborn, can be found on his YouTube channel.

He is the author of Gödel’s God Theorem, which presents the Leibniz–Gödel System, i.e. four interlinking arguments for God's necessary and unique existence. Cavallo has also published peer-reviewed research, including On Mario Bunge’s Concept of System Boundary, which is indexed by Harvard in the Smithsonian/NASA Astrophysics Data System (ADS).

Andrew M. Cavallo is a math education consultant specializing in logic and proof for college success. Most high school curricula stop at geometry proofs, leaving students unprepared for the rigorous reasoning required in college mathematics, computer science, data science, and rapidly advancing fields such as artificial intelligence and machine learning. His Closing the STEM Gap: Proofs for College Readiness is a 12-week program that closes this gap.

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