Abstract
In this paper we develop a reconstruction of the Tractatus ontology. The basic idea is that objects are unsaturated and that Sachlagen are like molecules. Bisimulation is used for the proper individuation of the Sachlagen. We show that the ordering of the Sachlagen is a complete distributive, lattice. It is atomistic, i.e., each Sachlage is the supremum of the Sachverhalte below it. We exhibit three normal forms for Sachlagen: the bisimulation collapse, the canonical unraveling and the canonical bisimulation collapse. The first of these forms is unique modulo isomorphism, the second and third are simply unique. The subset ordering on normal forms of the second and third kind reflects the ordering of the Sachlagen.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Aczel, P. (1988). Non-well-founded sets. CSLI lecture notes (Vol. 14). Stanford: CSLI.
Black, M. (1971). A companion to Wittgenstein’s Tractatus. Cambridge: Cambridge University Press.
D’Agostino, G., & Visser, A. (2002). Finality regained: A coalgebraic study of Scott-sets and multisets. Archive for Mathematical Logic, 41, 267–298.
Fine, K. (2000). Neutral relations. The Philosophical Review, 109, 1–33.
Leo, J. (2008). The identitity of argument-places. The Review of Symbolic Logic, 1(3), 335–354.
Leo, J. (2008). Modeling relations. Journal of Philosophical Logic, 37, 353–385.
Marion, M. (2004). Ludwig Wittgenstein, Introduction au “Tractatus logico-philosophicus”. Philosophies. Presses Universitaires de France, Paris.
Rieger, A. (2000). An argument for Finsler–Aczel set theory. Mind, 109(434), 241–253.
Wittgenstein, L. (1961). Tractatus logico-philosophicus. London: Routledge & Kegan Paul.
Author information
Authors and Affiliations
Corresponding author
Additional information
Dedicated to Roel de Vrijer on the occasion of his 60th birthday.
Rights and permissions
Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Visser, A. A Tractarian Universe. J Philos Logic 41, 519–545 (2012). https://doi.org/10.1007/s10992-011-9182-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10992-011-9182-6