Giorgio LandoCorresponding author

Tractarian Ontology: Mereology or Set Theory?

12/2 - Fall 2007, pages 247-266
Date of online publication: 15 November 2007
Date of publication: 01 November 2007


I analyze the relations of constituency or “being in” that connect different ontological items in Wittgenstein's Tractatus Logico-Philosophicus. A state of affairs is constituted by atoms, atoms are in a state of affairs. Atoms are also in an atomic fact. Moreover, the world is the totality of facts, thus it is in some sense made of facts. Many other kinds of Tractarian notions—such as molecular facts, logical space, reality—seem to be involved in constituency relations. How should these relations be conceived? And how is it possible to formalize them in a convincing way? I draw a comparison between two ways of conceiving and formalizing these relations: through sets and through mereological sums. The comparison shows that the conceptual machinery of set theory is apter to conceive and formalize Tractarian constituency notions than the mereological one.


Cite this article

Lando, Giorgio. “Tractarian Ontology: Mereology or Set Theory?” Forum Philosophicum 12, no. 2 (2007): 247–66. doi:10.35765/forphil.2007.1202.19.


Chisholm, Roderick M. Person and Object: a Metaphysical Study. London: Allen & Unwin, 1976.

Frascolla, Pasquale. Wittgenstein's Philosophy of Mathematics. London: Routledge, 1994.

Frascolla, Pasquale. Understanding Wittgenstein's Tractatus. London: Routledge, 2007.

Frege, Gottlob, Allan Janik, and Christian Paul Berger. “Briefe an Ludwig Wittgenstein aus den Jahren 1914–1920.” Grazer Philosophische Studien 33 (1989): 5–33. doi:10.5840/gps198933/3430.

Frege, Gottlob, and Richard Schmitt. “Frege’s Letters to Wittgenstein about the Tractatus.” The Bertrand Russell Society Quarterly 120 (2003): 11–30.

Gale, Richard. “Could Logical Space Be Empty?” Acta Philosophica Fennica 28 (1976): 85–104.

Glock, Hans-Johann. A Wittgenstein Dictionary. Oxford: Blackwell, 1996.

Russell, Bertrand. The Principles of Mathematics. Cambridge: Cambridge University Press, 1903.

Simons, Peter. “Tractatus Mereologico-Philosophicus? A Brentanian Look at Wittgenstein, and a Moral.” Grazer Philosophische Studien 28 (1986): 165–186. doi:10.5840/gps1986288.

Wittgenstein, Ludwig. Notebooks: 1914–1916. Edited by Gertrude Elizabeth Margaret Anscombe and Georg Henrik von Wright. Translated by Gertrude Elizabeth Margaret Anscombe. Oxford: Blackwell, 1961.

Wittgenstein, Ludwig. “Review of Peter Coffey, the Science of Logic.” The Cambridge Review. A Journal of University Life and Thought 34 (1913): 351.

Wittgenstein, Ludwig. Tractatus Logico-Philosophicus. Edited by C. K. Ogden. London: Routledge and Kegan Paul, 1922.

Wittgenstein, Ludwig. Tractatus Logico-Philosophicus. Translated by D. Pears and B. F. McGuinness, London: Routledge and Kegan Paul, 1961.