## Leibniz's Logical Foundations of Physics

The main goal of my thesis is to reconstruct the formal philosophy of science of Gottfried Wilhelm Leibniz. I seek to bring together two disciplines – logic and physics (mechanics) – and show that they informed each other throughout the development of Leibniz’s thought.

The main hypotheses are (1) that Leibniz had developed an elaborate physical methodology based on his formal logical ideas; and (2) that his physical research has contributed to the development of his logical system. If (1) is established, then Leibniz’s scientific methodology could be seen as an early modern formal philosophy of science. It is known that Leibniz has developed a logical system equivalent to the 19^{th}-century algebras of logic.^{[1]}
Despite foreshadowing the latter by 160 years, he never published his findings and they went largely ignored.^{[2]}
As a result, his physical methodology which was built on logical foundations is underappreciated. Hypothesis (2) challenges a common view that the development of particular sciences in Leibniz was an outcome of more fundamental, metaphysical considerations.^{[3]}
I argue that the development was in fact parallel and the influence of ideas was reciprocal.^{[4]}

[1] It is demonstrated that Leibniz’s logical principles can produce a logical calculus equivalent to a Boolean semi-lattice. See Malink and Vasudevan (2015), Mugnai (2016). The claim has been proposed earlier, see Dürr (1930).

[2] Leibniz’s logical writings were rediscovered only through their publication in Couturat (Leibniz 1903) and, to a lesser extent, in Russell (1900). Couturat also produced an early study of the manuscripts in Couturat (1901).

[3] The dominating paradigm in the Leibnizian studies is that Leibniz’s physics was built on metaphysical foundations, see Hannequin (1906), Gueroult (1934), Garber (1985, 2004, 2009), Wilson (1989).

[4] This general intuition is expressed by Couturat: “[*characteristica universalis*] rests on the first principles of the sciences but does not presuppose their completion. On the contrary, it will be developed and perfected along with the sciences, whose instrument it will be” (1901: 64).

*References*

Couturat, Louis. *La logique de Leibniz*. Paris, 1901; reprinted Hildesheim: Olms, 1969.

Dürr, Karl. *Neue Beleuchtung einer Theorie von Leibniz. Grundzuege der Logikkalkuels*. Darmstadt: Reichl, 1930.

Hannequin, Arthur. “La philosophie de leibniz et les lois du mouvement.” *Revue De Métaphysique Et De Morale* 14/6 (1906): 775–95.

Garber, Daniel. “Leibniz and the Foundations of Physics: The Middle Years.” In *The Natural Philosophy of Leibniz*. Edited by Kathleen Okruhlik and James Robert Brown, 27–130. Dordrecht: Kluwer Academic Publishers, 1985.

Garber, Daniel. “Leibniz and Fardella: Body, Substance and Idealism.” In *Leibniz and His Correspondents*. Edited by Paul Lodge, 123-140. Cambridge: CUP, 2004.

Garber, Daniel. *Leibniz: Body, Substance, Monad*. Oxford: OUP, 2009.

Leibniz, Gottfried Wilhelm. *Opuscules et fragments inédits de Leibniz : Extraits des manuscrits de la Bibliothèque royale de Hanovre. *Edited by Louis Couturat. Paris, 1903; reprinted Hildesheim: G. Olms, 1961 and 1966.

Malink, Marko, Vasudevan, Anubav. “The Logic of Leibniz’s *Generales Inquisitiones de Analysi Notionum et Veritatum*.” *The Review of Symbolic Logic* 4 (2015): 1–66.

Mugnai, Massimo. “Leibniz e la logica.” *Matematica, Cultura e Società. Rivista dell’Unione Matematica Italiana*, 1/3 (2016): 241–257.

Russell, Bertrand. *A Critical Exposition of the Philosophy of Leibniz*. Cambridge: CUP, 1900; reprinted London: Routledge, 1996.

Wilson, Catherine. *Leibniz’s Metaphysics. A Historical and Comparative Study*. Princeton: Princeton University Press and Manchester: Manchester University Press, 1989.