David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Bulletin of Symbolic Logic 14 (4):481-540 (2008)
In this paper we give probably an exhaustive analysis of the geometry of solids which was sketched by Tarski in his short paper [20, 21]. We show that in order to prove theorems stated in [20, 21] one must enrich Tarski's theory with a new postulate asserting that the universe of discourse of the geometry of solids coincides with arbitrary mereological sums of balls, i.e., with solids. We show that once having adopted such a solution Tarski's Postulate 4 can be omitted, together with its versions 4' and 4". We also prove that the equivalence of postulates 4, 4' and 4" is not provable in any theory whose domain contains objects other than solids. Moreover, we show that the concentricity relation as defined by Tarski must be transitive in the largest class of structures satisfying Tarski's axioms. We build a model (in three-dimensional Euclidean space) of the theory of so called T*-structures and present the proof of the fact that this is the only (up to isomorphism) model of this theory. Moreover, we propose different categorical axiomatizations of the geometry of solids. In the final part of the paper we answer the question concerning the logical status (within the theory of T*-structures) of the definition of the concentricity relation given by Tarski
|Keywords||Geometry of solids pointless geometry mereology foundations of geometry|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
Arianna Betti & Iris Loeb (2012). On Tarski's Foundations of the Geometry of Solids. Bulletin of Symbolic Logic 18 (2):230-260.
Alfred Tarski & Steven Givant (1999). Tarski's System of Geometry. Bulletin of Symbolic Logic 5 (2):175-214.
Luis Fernández Moreno (2001). Tarskian Truth and the Correspondence Theory. Synthese 126 (1-2):123 - 147.
Timothy Bays (2001). On Tarski on Models. Journal of Symbolic Logic 66 (4):1701-1726.
Steven Givant & Hajnal Andreka (2002). Groups and Algebras of Binary Relations. Bulletin of Symbolic Logic 8 (1):38-64.
Ignacio Jané (2006). What is Tarski's Common Concept of Consequence? Bulletin of Symbolic Logic 12 (1):1-42.
Greg Frost-Arnold (2004). Was Tarski's Theory of Truth Motivated by Physicalism? History and Philosophy of Logic 25 (4):265-280.
Jared Bates (1999). Etchemendy, Tarski, and Logical Consequence. Southwest Philosophy Review 15 (1):47-54.
Richard Vesley (1999). Constructivity in Geometry. History and Philosophy of Logic 20 (3-4):291-294.
Richard L. Kirkham (1993). Tarski's Physicalism. Erkenntnis 38 (3):289-302.
Richard C. Jennings (1987). Tarski - a Dilemma. Inquiry 30 (1 & 2):155 – 172.
Panu Raatikainen (2003). More on Putnam and Tarski. Synthese 135 (1):37 - 47.
Peter Milne (1999). Tarski, Truth and Model Theory. Proceedings of the Aristotelian Society 99 (2):141–167.
Mario Gómez-Torrente (1998). On a Fallacy Attributed to Tarski. History and Philosophy of Logic 19 (4):227-234.
Peter Milne (1999). Tarski on Truth and its Definition. Proceedings of the Aristotelian Society 99:141-167.
Added to index2010-09-13
Total downloads10 ( #157,223 of 1,168,039 )
Recent downloads (6 months)1 ( #140,420 of 1,168,039 )
How can I increase my downloads?