Linked bibliography for the SEP article "Finitism in Geometry" by Jean Paul Van Bendegem

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If everything goes well, this page should display the bibliography of the aforementioned article as it appears in the Stanford Encyclopedia of Philosophy, but with links added to PhilPapers records and Google Scholar for your convenience. Some bibliographies are not going to be represented correctly or fully up to date. In general, bibliographies of recent works are going to be much better linked than bibliographies of primary literature and older works. Entries with PhilPapers records have links on their titles. A green link indicates that the item is available online at least partially.

This experiment has been authorized by the editors of the Stanford Encyclopedia of Philosophy. The original article and bibliography can be found here.

  • Ahmavaara, Yrjo, 1965a, “The Structure of Space and the Formalism of Relativistic Quantum Field Theory I.”, Journal of Mathematical Physics, 6(1): 87–93. (Scholar)
  • –––, 1965b, “The Structure of Space and the Formalism of Relativistic Quantum Field Theory II.”, Journal of Mathematical Physics, 6(2): 220–227. (Scholar)
  • Aiello, M., I. Pratt-Hartmann & J. van Benthem (eds.), 2007, Handbook of Spatial Logics, New York: Springer. (Scholar)
  • Andréka, H., J.X Madarász, I. Németi, & G. Seékely, 2008, “Axiomatizing Relativistic Dynamics Without Conservation Postulates”, Studia Logica, 89(2): 163–186. (Scholar)
  • Ax, J., 1978, “The elementary foundations of spacetime”, Foundations of Physics, 8: 507–546. (Scholar)
  • Bastin, T. & C.W. Kilmister, 1995, Combinatorial Physics, Singapore: World Scientific. (Scholar)
  • Benda, T., 2008, “A formal construction of the spacetime manifold”, Journal of Philosophical Logic, 37(5): 441–478.
  • Biser, E., 1941, “Discrete Real Space”, Journal of Philosophy, 38(Summer): 518–524 (Scholar)
  • Borwein, J. & K. Devlin, 2009, The Computer as Crucible. An Introduction to Experimental Mathematics, Wellesley: A K Peters. (Scholar)
  • Bridges, D. & F. Richman, 1987, Varieties of Constructive Mathematics, Cambridge: Cambridge University Press (LMS Lecture Notes Series 97). (Scholar)
  • Buot, F.A., 1989, “Discrete Phase-Space Model for Quantum Mechanics”, in M. Kafatos (ed.), Bell”s Theorem, Quantum Theory and Conceptions of the Universe, Dordrecht: Kluwer, pp. 159–162. (Scholar)
  • Chou S.C., X.S. Gao, & J.Z. Zhang, 1994, Machine Proofs in Geometry, Singapore: World Scientific. (Scholar)
  • Coish, H.R., 1959, “Elementary particles in a finite world geometry”, Physical Review, 114: 383–388. (Scholar)
  • Crouse, D. & J. Skufca, 2019, “Relativistic Time Dilation and Length Contraction in Discrete Space-Time using a Modified Distance Formula”, Logique et Analyse, 62(246): 177–223. (Scholar)
  • Dadić, I. & K. Pisk, 1979, “Dynamics of Discrete-Space Structure”, International Journal of Theoretical Physics, 18(5): 345–358. (Scholar)
  • Danielsson, N., 2002, Axiomatic Discrete Geometry, London: Imperial College. (Thesis submitted for MSc Degree in Advanced Computing). (Scholar)
  • Feyerabend, P., 1961, “Comments on Grünbaum’s ‘Law and Convention in Physical Theory’”, in H. Feigl & G. Maxwell (eds.), Current Issues in the Philosophy of Science, New York: Holt, Rinehart and Winston, pp. 155–161. (Scholar)
  • Finkelstein, D., 1969, “Space-time code”, Physical Review, 184: 1261–1279. (Scholar)
  • Finkelstein, D. & Rodriguez, E., 1986, “Quantum time-space and gravity”, in R. Penrose & C.J. Isham (eds.), Quantum Concepts in Space and Time, Oxford: Oxford University Press, pp. 247–254. (Scholar)
  • Forrest, P., 1995, “Is Space-Time Discrete or Continuous?—An Empirical Question”, Synthese, 103: 327–354. (Scholar)
  • Franklin, J., 2017, “Discrete and Continuous: A Fundamental Dichotomy in Mathematics”. Journal of Humanistic Mathematics, 7(2): 355–378. (Scholar)
  • Fritz, T., 2013, “Velocity polytopes of periodic graphs and a no-go theorem for digital physics”, Discrete Mathematics 313: 1289–1301. (Scholar)
  • Hagar, A., 2014, Discrete or Continuous? The Quest for Fundamental Length in Modern Physics, Cambridge: Cambridge University Press. (Scholar)
  • Hahn, H., 1980 [1934], “Does the infinite exist?”, in B. Mcguinness (ed.), Hans Hahn: Empiricism, Logic, and Mathematics, Dordrecht: Reidel, pp. 103–131 (originally published in 1934). (Scholar)
  • Hjelmslev, J.T., 1923, Die Natürliche Geometrie, Hamburg: Gremmer & Kröger (facsimile edition: hardpress.net, 2008). (Scholar)
  • Huggett, N. & C. Wuthrich, 2013a, “Emergent spacetime and empirical (in)coherence”, Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 44(3): 276–285. (Scholar)
  • ––– (eds.), 2013b, “Special issue: The emergence of spacetime in quantum theories of gravity”, Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 44(3): 273–364. (Scholar)
  • Järnefelt, G., 1951, “Reflections on a Finite Approximation to Euclidean Geometry: Physical and Astronomical Prospects”, Annales Academiae Scientiarum Fennicae, Series A, I. Mathematica-Physica, 96: 1–43. (Scholar)
  • Kilmister, C.W., 1994, Eddington’s Search for a Fundamental Theory: A Key to the Universe, Cambridge: Cambridge University Press. (Scholar)
  • Kragh, H. & B. Carazza, 1994, “From Time Atoms to Space-Time Quantization: the Idea of Discrete Time, ca 1925–1936”, Studies in the History and the Philosophy of Science, 25(3): 437–462. (Scholar)
  • Kulpa, Z., 1979, “On the Properties of Discrete Circles, Rings, and Disks”, Computer Graphics and Image Processing, 10: 348–365. (Scholar)
  • Kustaanheimo, P., 1951, “A Note on a Finite Approximation of the Euclidean Plane Geometry”, Societas Scientiarum Fennica. Commentationes Physico-Mathematicae, 15/19: 1–11. (Scholar)
  • Lyons, B. C., 2017, “The Applicability of the Planck Length to Zeno, Kalam, and Creation Ex Nihilo”, Philosophia Christi, 19(1): 171–180. (Scholar)
  • McKinsey, J.C.C., A.C. Sugar, & P. Suppes, 1953, “Axiomatic Foundations of Classical Particle Mechanics”, Journal of Rational Mechanics and Analysis, 2(2): 253–272. (Scholar)
  • Meessen, A., 1989, “Is it logically possible to generalize physics through space-time quantization?” in P. Weingartner & G. Schurz (eds.), Philosophie der Naturwissenschaften. Akten des 13. Internationalen Wittgensteins Symposium, Vienna: Hölder-Pichler-Tempsky, pp. 19–47. (Scholar)
  • Meschini, D., M. Lehto, & J. Philonen, 2005, “Geometry, pregeometry, and beyond”, Studies in History and Philosophy of Modern Physics, 36(3) 435–464. (Scholar)
  • Misner, C.W., K.S. Thorne, & J.A. Wheeler, 1973, Gravitation, San Francisco: W.H. Freeman. (Scholar)
  • Moore, A.W., 1993, Infinity, Aldershot: Dartmouth. (Scholar)
  • Regge, T., 1961, “General relativity without coordinates”, Nuovo Cimento, 19: 558–571. (Scholar)
  • Reisenberger M.P., 1999, “On relativistic spin network vertices”, Journal of Mathematical Physics, 40(4): 2046–2054. (Scholar)
  • Reisler, D. L. & N. M. Smith, 1969, Geometry Over a Finite Field, Fort Belvoir, VA: Defense Technical Information Center. (Full text: https://apps.dtic.mil/dtic/tr/fulltext/u2/714115.pdf). (Scholar)
  • Rovelli, C., 2016, Reality is not What It Seems. The Journey to Quantum Gravity, New York: Penguin. (Translated by Simon Carnell and Erica Segre, original published in 2014). (Scholar)
  • Silberstein, L., 1936, Discrete Spacetime. A Course of Five Lectures delivered in the McLennan Laboratory, Toronto: University of Toronto Press. (Scholar)
  • Simpson, Stephen G. (ed.), 2005, Reverse Mathematics 2001: Lecture Notes in Logic 21, Association for Symbolic Logic. (Scholar)
  • Smolin, L., 2018, “What Are We Missing in Our Search for Quantum Gravity?”, in J. Kouneiher (ed.), Foundations of Mathematics and Physics One Century After Hilbert, New York: Springer, pp. 287–304. (Scholar)
  • Smyth, M.B. & J. Webster, 2007, “Discrete spatial models”, in Aiello, Pratt-Hartmann & van Benthem 2007: 713–798. (Scholar)
  • Sorabji, R., 1983, Time, Creation & the Continuum, London: Duckworth. (Scholar)
  • Stillwell, J., 2016, Elements of Mathematics. From Euclid to Gödel, Princeton: Princeton University Press. (Scholar)
  • Suppes, P., 2001, “Finitism in geometry”, Erkenntnis, 54: 133–144. (Scholar)
  • ’t Hooft, G., 2014, “Relating the Quantum Mechanics of Discrete Systems to Standard Canonical Quantum Mechanics”, Foundations of Physics, 44: 406–425. (Scholar)
  • Van Bendegem, J.P., 1987, “Zeno’s Paradoxes and the Weyl Tile Argument”, Philosophy of Science, 54(2): 295–302. (Scholar)
  • –––, 1997, “In defence of discrete space and time”, Logique et Analyse, 38(150–152): 127–150. (Scholar)
  • –––, 2000, “How to tell the continuous from the discrete”, in François Beets & Eric Gillet (eds.), Logique en Perspective. Mélanges offerts à Paul Gochet. Brussels: Ousia, pp. 501–511. (Scholar)
  • Welti, E., 1987, Die Philosophie des strikten Finitismus. Entwicklungstheoretische und mathematische Untersuchungen über Unendlichkeitsbegriffe in Ideengeschichte und heutiger Mathematik, Bern: Peter Lang. (Scholar)
  • Weyl, H., 1949, Philosophy of Mathematics and Natural Sciences, Princeton: Princeton University Press. (Scholar)
  • White, M.J., 1992, The Continuous and the Discrete. Ancient Physical Theories from a Contemporary Perspective, Oxford: Clarendon Press. (Scholar)

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