Cogprints

On the Inherent Incompleteness of Scientific Theories

Mathen, Jolly (2004) On the Inherent Incompleteness of Scientific Theories. (Unpublished)

Warning

There is a more recent version of this eprint available. Click here to view it.

Full text available as:

[img]
Preview
PDF
183Kb

Abstract

We examine the question of whether scientific theories can ever be complete. For two closely related reasons, we will argue that they cannot. The first reason is the inability to determine what are “valid empirical observations”, a result that is based on a self-reference Gödel/Tarski-like proof. The second reason is the existence of “meta-empirical” evidence of the inherent incompleteness of observations. These reasons, along with theoretical incompleteness, are intimately connected to the notion of belief and to theses within the philosophy of science: the Quine-Duhem (and underdetermination) thesis and the observational/theoretical distinction failure. Some puzzling aspects of the philosophical theses will become clearer in light of these connections. Other results that follow are: no absolute measure of the informational content of empirical data, no absolute measure of the entropy of physical systems, and no complete computer simulation of the natural world are possible. The connections with the mathematical theorems of Gödel and Tarski reveal the existence of other connections between scientific and mathematical incompleteness: computational irreducibility, complexity, infinity, arbitrariness and self-reference. Finally, suggestions will be offered of where a more rigorous (or formal) “proof” of scientific incompleteness can be found.

Item Type:Other
Keywords:theory complete godel tarski self-reference incomplete belief Quine-Duhem underdetermination observational/theoretical distinction God entropy complexity infinity mathematical valid empirical meta-empirical breuer's theorem computational irreducibility TOE faith doubt
Subjects:Philosophy > Philosophy of Mind
Philosophy > Philosophy of Science
ID Code:3987
Deposited By: Mathen, Jolly
Deposited On:15 Dec 2004
Last Modified:11 Mar 2011 08:55

Available Versions of this Item

References in Article

Select the SEEK icon to attempt to find the referenced article. If it does not appear to be in cogprints you will be forwarded to the paracite service. Poorly formated references will probably not work.

Aczel, Peter (1988), Non-Well-Founded Sets. CSLI Lecture Notes 14, Center for the Study of Languages and Information, Stanford: Stanford University.

Adelberger, E. G., B.R. Heckel, and A.E. Nelson (2003), “Tests Of The Gravitational Inverse-Square Law”, Annual Review of Nuclear and Particle Science 53: 77-121.

Adler, Stephen L. (2003), “Why Decoherence Has Not Solved the Measurement Problem: A Response to P.W. Anderson”, Studies in History and Philosophy of Science Part B 34: 135-142.

Ahmad, Q.R., et al., SNO Collaboration (2001), “Measurement of the Rate of ne + d Æ p + p + e- Interactions Produced by 8B Solar Neutrinos at the Sudbury Neutrino Observatory”, Physical Review Letters 87: 071301.

Amelino-Camelia, Giovanni, et al. (1998), “Tests of Quantum Gravity from Observations of g-ray Bursts”, Nature 393: 763-765.

Amelino-Camelia, Giovanni (1999), “Gravity-Wave Interferometers as Quantum Gravity Detectors”, Nature 398: 216-218.

Anderson, L.H., et al. (2001), “Atomic and Condensed Matter Physics” in Nuclear Science: Impact, Applications, Interactions. Conference Paper, Nuclear Physics European Collaboration Committee (NUPECC) 2001 Conference, European Science Foundation. [Online Edition]: cited on 1 September 2004, ‹http://www.nupecc.org/iai2001›.

Arkani-Hamed, Nima, Savas Dimopoulos, and Gia Dvali (1998), “The Hierarchy Problem and New Dimensions at a Millimeter”, Physics Letters B 429: 263-272.

Aspect, Alain (1981), “Experimental Tests of Realistic Local Theories via Bell’s Theorem”, Physical Review Letters 47: 460-463.

__________ (1982), “Experimental Realization of Einstein-Podolsky-Rosen-Bohm Gedankenexperiment: A New Violation of Bell’s Inequalities”, Physical Review Letters 49: 91-94.

Babcock, Horace W. (1939), “The Rotation of the Andromeda Nebula”, Lick Observatory Bulletin 19 (498): 41-51.

Barrow, John D. (1991), Theories of Everything. Oxford: Clarendon Press.

__________ (1998), Impossibility: The Limits of Science and the Science of Limits. New York: Oxford University Press.

Barut, Asim O. (1995), “On the Status of Hidden Variable Theories in Quantum Mechanics”, Aperion 2: 97-98.

Baessler, S., et al. (1999), “Improved Tests of the Equivalence Principle for Gravitational Self-Energy”, Physical Review Letters 83: 3585-3588.

Bekenstein, Jacob (1974), “Generalized Second Law of Thermodynamics in Black-Hole Physics”, Physical Review D 9: 3292-3300.

__________ (1981), “Universal Upper Bound on the Entropy-to-Energy Ratio for Bounded Systems”, Physical Review D 23: 287-298.

Bell, John S. (1964), “On the Einstein-Podolsky-Rosen Paradox”, Physics 1: 195-200.

Bennett, C.L., et al. (2003), “First-Year Wilkinson Microwave Anistropy Probe (WMAP) Observations: Preliminary Maps and Basic Results”, The Astrophysical Journal Supplement Series 148: 1-27.

Bennett, G.W., et al., Muon (g-2) Collaboration (2004), “Measurement of the Negative Muon Anomalous Magnetic Moment to 0.7 ppm”, Physical Review Letters 92: 161802.

Bertotti, B., L. Iess, P. Tortora (2003), “A Test of General Relativity Using Radio Links with the Cassini Spacecraft”, Nature 425: 374-376.

Bird, Alexander (2003), “Kuhn, Nominalism, and Empiricism”, Philosophy of Science 70: 690-719.

Bitbol, Michel (2001), “Non-Representationalist Theories of Knowledge and Quantum Mechanics”, Nordic Journal of Philosophy 2: 37-61.

Bohm, David (1952), “A Suggested Interpretation of Quantum Theory in Terms of ‘Hidden Variables’, I [and II]”, Physical Review 85: 166-193.

Bohm, David, and Jeffrey Bub (1966), “A Proposed Solution of the Measurement Problem in Quantum Mechanics by a Hidden Variable Theory”, Reviews of Modern Physics 38: 453-469.

Bohr, Niels (1949), “Discussions with Einstein on Epistemological Problems in Atomic Physics”, in Paul A. Schilpp (ed.), Albert Einstein: Philosopher-Scientist. Evanston, IL: Library of Living Philosophers.

Breuer, Thomas (1995), “The Impossibility of Accurate State Self-Measurements”, Philosophy of Science 62: 197-214.

Brown, H.N., et al., Muon (g-2) Collaboration (2000), “Improved Measurement of the Positive Muon Anomalous Magnetic Moment”, Physical Review D 62: 091101.

__________ (2001), “Precise Measurement of the Positive Muon Anomalous Magnetic Moment”, Physical Review Letters 86: 2227-2231.

Bub, Jeffrey (1995), “Fundamental Problems of Quantum Physics”, Aperion 2: 98-100.

Caldwell, Robert (2004), “Dark Energy”, Physics World May. [Online Edition]: cited on 1 September 2004, ‹http://physicsweb.org/articles/world/17/5/7/1›.

Campbell, L., et al. (1983), “The Sun’s Quadrupole Moment and Perihelion Precession of Mercury”, Nature 305: 508-510.

Cappellari, Michele, et al. (1999), “Objects in NGC Resolved into Stellar Associations by Hubble Space Telescope Ultraviolet Imaging”, The Astropysical Journal 515: L17-L20.

Cartwright, Nancy (2000), “Against the Completability of Science”, in M.W.F. Stone and J. Wolff (eds.), The Proper Ambition of Science. London: Routledge, 209-222.

Chaitin, Gregory (1970), “On the Difficulty of Computations”, IEEE Transactions on Information Theory 16: 5-9.

__________ (1971), “Computational Complexity and Gödel’s Incompleteness Theorem”, ACM SIGACT News No. 9: 11-12.

__________ (1974), “Information Theoretic Limitations of Formal Systems”, Journal of the ACM 21: 403-424.

__________ (1975), “Randomness and Mathematical Proof”, Scientific American 232, No. 5 (May): 47-52.

__________ (1990), Algorithmic Information Theory, 3rd Edition. Cambridge: Cambridge University Press. [Online Edition]: cited on 20 November 2004, ‹http://www.umcs.maine.edu/~chaitin/cup.pdf›

__________ (2000), “A Century of Controversy over the Foundations of Mathematics”, in C.S. Calude and G. Paun (eds.), Finite Versus Infinite. London: Springer-Verlag, 75-100.

Chen, Shaomin, et al., E949 Collaboration (2004), Rare Kaon Decay from E949 at BNL: K+ Æ pi + nunubar. Conference Paper, 32nd International Conference on High-Energy Physics, Beijing. [Online Edition]: cited on 15 October 2004, ‹http://www.arxiv.org/abs/hep-ex/0409064›.

Choi, S.-K., et al., Belle Collaboration (2003), “Observation of a Narrow Charmoniumlike State in Exclusive B± Æ K± π+ π- J/y Decays”, Physical Review Letters 91: 262001.

Church, Alonzo (1936), “An Unsolvable Problem of Elementary Number Theory”, American Journal of Mathematics 58: 345-363.

Churchland, Paul (1979), Scientific Realism and the Plasticity of Mind. Cambridge: Cambridge University Press.

__________ (1988), “Perceptual Plasticity and Theoretical Neutrality: A Reply to Jerry Fodor”, Philosophy of Science 55: 167-187.

Cimatti, A., et al. (2004), “Old Galaxies in the Young Universe”, Nature 430: 184-187.

Cohen, Paul J. (1963, 1964), “The Independence of the Continuum Hypothesis [and part II]”, Proceedings of the National Academy of Sciences of the U.S.A. 50: 1143-1148; 51: 105-110.

Contaldi, Carlo R., et al. (2003), “Suppressing the Lower Multipoles in the CMB Anisotropies”, Journal of Cosmology and Astroparticle Physics 7: 002.

Damour, T., and A.M. Polyakov (1994), “The String Dilaton and a Least Coupling Principle”, Nuclear Physics B 423: 532-558.

Davier, M., S. Eidelman, A. Hocker, and Z. Zhang (2003), “Updated Estimate of the Muon Magnetic Moment Using Revised Results from e+e- Annihilation”, The European Physical Journal C 31: 503-510.

Davies, Paul (1992), The Mind of God. New York: Touchstone.

de Witt, B.S. (1970), “Quantum Mechanics and Reality”, Physics Today 23: 30-55.

Deffayet, Cedric, Gia Dvali, and Gregory Gabadadze (2002), “Accelerated Universe from Gravity Leaking to Extra Dimensions”, Physical Review D 65: 044023.

Derrida, Jacques ([1967] 1974), Of Grammatology. Translated by Gayatri Spivak. Baltimore: The John Hopkins University Press.

__________ ([1967] 1973), Speech and Phenomena, and Other Essays on Husserl’s Theory of Signs. Translated by David B. Allison. Evanston, IL: Northwestern University Press.

__________ ([1992] 1995), The Gift of Death. Translated by David Wills. Originally published as Donner la mort in L’éthique du don, Jacques Derrida et la pensée du don (Paris: Métailié-Transition). Chicago: University of Chicago Press.

__________ (1994), “Nietzsche and the Machine: Interview with Jacques Derrida” (Interviewed by Richard Beardsworth), Journal of Nietzsche Studies, Issue 7.

Dieks, D. (1991), “On Some Alleged Difficulties on the Interpretation of Quantum Mechanics”, Synthese 86: 77-86.

Durrani, Matin, and Peter Rodgers (1999), “Physics: Past, Present, Future”, Physics World December. [Online Edition]: cited on 15 January 2004, ‹http://physicsweb.org/articles/world/12/12/14/1›.

Efstathiou, G. (2003), “Is the Low Cosmic Microwave Background Quadrupole a Signature of Spatial Curvature”, Monthly Notices of the Royal Astronomical Society 343: L95-L98.

Einstein, Albert, and Leopold Infeld ([1938] 1966), The Evolution of Physics, New Edition. New York: Simon & Schuster.

Evans, Denis J., E.G.D. Cohen, and G.P. Morriss (1993), “Probability of Second Law Violations in Shearing Steady States”, Physical Review Letters 71: 2401-2404.

Evdokimov, A.V., et al., SELEX Collaboration (2004), First Observation of a Narrow Charm-Strange Meson DsJ(2632) Æ Ds eta and D0 K+. Fermilab-Pub-04/087-E, Submitted to Physical Review Letters. [Online Edition]: cited on 15 October 2004, ‹http://www.arxiv.org/abs/hep-ex/0406045›.

Everett, H., III (1957), “‘Relative State’ Formulation of Quantum Mechanics”, Reviews of Modern Physics 29: 454-462.

Feynman, Richard (1967), The Character of Physical Law. Cambridge, MA: MIT Press.

__________ (1985), QED: The Strange Theory of Light and Matter. Princeton: Princeton University Press.

Fischbach, E., and C.L. Talmadge (1999), The Search for Non-Newtonian Gravity. New York: Springer Verlag.

Fodor, Jerry (1984), “Observation Reconsidered”, Philosophy of Science 51: 23-43.

__________ (1988), “A Reply to Churchland’s ‘Perceptual Plasticity and Theoretical Neutrality’”, Philosophy of Science 55: 188-198.

Forti, Marco, and Furio Honsell (1983), “Set Theory with Free Construction Principles”, Annali Scuola normale superiore 10: 493-522.

Friedman, Jonathan R., et al. (2000), “Quantum Superposition of Distinct Macroscopic States”, Nature 406: 43-46.

Gadamer, Hans-Georg ([1960] 1975), Truth and Method. Translated and edited by Garrett Barden and John Cumming. New York: Seabury Press.

__________ ([1967] 1976), Philosophical Hermeneutics. Translated and edited by David E. Linge. Berkeley: University of California Press.

Ghirardi, G.C., A. Rimini, and T. Weber (1986), “Unified Dynamics for Microscopic and Macroscopic Systems”, Physical Review D 34: 470-491.

Gisin, N., and I.C. Percival (1992), “The Quantum-State Diffusion Model Applied to Open Systems”, Journal of Physics A 25: 5677-5691.

Glazebrook, Karl, et al. (2004), “A High Abundance of Massive Galaxies 3-6 Billion Years after the Big Bang”, Nature 430: 181-184.

Gleason, A. M. (1957), “Measures on the Closed Subspaces of a Hilbert Space”, Journal of Mathematics and Mechanics 6: 885-893.

Go, Apollo, Belle Collaboration (2004), “Observation of Bell Inequality Violation in B Mesons”, Journal of Modern Optics 51: 991-998.

Gödel, Kurt (1931), “Über Formal Unentscheidbare Sätze der Principia Mathematica und Verwandter Systeme, I”, Monatshefte für Mathematik und Physik 38: 173-198. English translation in Gödel (1962).

__________ (1940), Consistency of the Continuum Hypothesis. Princeton: Princeton University Press.

__________ (1962), On Formally Undecidable Propositions. New York: Basic Books.

Greene, Brian (2003), The Elegant Universe. New York: Vintage Books.

Griffiths, R.B. (1984), “Consistent Histories and the Interpretation of Quantum Mechanics”, Jorunal of Statistical Physics 36: 219-272.

Hall, Asaph (1894), “A Suggestion in the Theory of Mercury”, Astronomical Journal 14: 49-51.

Hawking, Stephen (1988), A Brief History of Time. New York: Bantam Books.

__________ (2002), Gödel and the End of Physics. Lecture, Dirac Centennial Celebration, Cambridge: University of Cambridge.

__________ (2003), Cosmology from the Top Down. Proceedings of the Davis Cosmic Inflation Meeting, Davis: University of California. [Online Edition]: cited on 1 February 2004, ‹http://www.arxiv.org/abs/astro-ph/0305562›.

Healy, R. (1989), The Philosophy of Quantum Mechanics. New York: Cambridge University Press.

Heavens, Alan, et al. (2004), “The Star-formation History of the Universe from the Stellar Populations of Nearby Galaxies”, Nature 428: 625-627.

Heidegger, Martin ([1927] 1962), Being and Time. Translated by John Macquarrie and Edward Robinson. New York: Harper & Row.

Hendry, John (1980), “Newton’s Theory of Colour”, Centaurus 23: 230-251.

Hoefer, Carl and Alexander Rosenberg (1994), “Empirical Equivalence, Underdetermination, and Systems of the World”, Philosophy of Science 61: 592-607.

Hofstadter, Douglas (1979), Gödel, Escher, Bach: An Eternal Golden Braid. New York: Basic Books.

Hollik, Wolfgang (2002), Electroweak Precision Analysis. Conference Paper, 10th International Conference on Supersymmetry and Unification of Fundamental Interactions, Hamburg. [Online Edition]: cited on 15 October 2004, ‹http://www-library.desy.de/preparch/desy/proc/proc02-02/Proceedings/pl.2/hollik_pr.pdf›.

Horgan, John (1996), The End of Science. Reading, Mass: Addison-Wesley.

Hoyle, C.D., et al. (2001), “Submillimeter Test of the Gravitational Inverse-Square Law: A Search for ‘Large’ Extra Dimensions”, Physical Review Letters 86: 1418-1421.

Hughes, R.I.G. (1989), The Structure and Interpretation of Quantum Mechanics. Cambridge, MA: Harvard University Press.

Ilic, B., et al. (2004), “Attogram Detection Using Nanoelectromechanical Oscillators”, Journal of Applied Physics 95: 3694-3703.

Jaki, Stanley (1966), The Relevance of Physics. Chicago: University of Chicago Press.

Klee, Robert (1997), Introduction to the Philosophy of Science: Cutting Nature at its Seams. New York: Oxford University Press.

Knecht, Marc, and Andreas Nyffeler (2002), “Hadronic Light-by-Light Corrections to the Muon g-2: The Pion-Pole Contribution”, Physical Review D 65: 073034.

Knecht, Marc (2003), The Anomalous Magnetic Moment of the Muon: A Theoretical Introduction. CPT-2003/P.4525. [Online Edition]: cited on 15 October 2004, ‹http://www.arxiv.org/abs/hep-ph/0307239›.

Kochen, S., and E.P. Specker (1967), “The Problem of Hidden Variables in Quantum Mechanics”, Journal of Mathematics and Mechanics 17: 59-87.

Kochen, S. (1985), “A New Interpretation of Quantum Mechanics”, in P. Lahti and P. Mittelstaedt (eds.), Symposium on the Foundations of Modern Physics. Singapore: World Scientific, 151-170.

Kracht, Marcus (2003), The Mathematics of Language. Berlin: Mouton de Gruyter.

Kuhn, Thomas (1970), The Structure of Scientific Revolutions, 2nd Edition. Chicago: University of Chicago Press.

Laudan, L., and J. Leplin (1991), “Empirical Equivalence and Underdetermination”, Journal of Philosophy 88: 449-472.

LeBach, D.E., et al. (1995), “Measurement of the Solar Gravitational Deflection of Radio Waves Using Very-Long Baseline Interferometry”, Physical Review Letters 75: 1439-1442.

Leggett, A.J. (2002), “Testing the Limits of Quantum Mechanics: Motivation, State of Play, Prospects”, Journal of Physics: Condensed Matter 14: R415-R451.

Linde, Andrei (1994), “The Self-Reproducing Inflationary Universe”, Scientific American 271, No. 5 (November): 48-55.

Long, J.C., H.W. Chan, and J.C. Price (1999), “Experimental Status of Gravitational-Strength Forces in the Sub-Centimeter Regime”, Nuclear Physics B 539: 23-34.

Lindley, David (1993), The End of Physics: The Myth of a Unified Theory. New York: Basic Books.

Luminet, Jean-Pierre, et al. (2003), “Dodecahedral Space Topology as an Explanation for Weak Wide-Angle Temperature Correlations in the Cosmic Microwave Background”, Nature 425: 593-595.

Machover, Moshe (1996), Set Theory, Logic and Their Limitations. Cambridge: Cambridge University Press.

Marciano, W.J. (2003), “Precision Measurements and New Physics”, Journal of Physics G 29: 225-234.

Maturana, Humberto R., and Francisco Varela (1980), Autopoiesis and Cognition: The Realization of the Living. Dordrecht: Reidel.

McAllister, James W. (1997), “Phenomena and Patterns in Data Sets”, Erkenntnis 47: 217-228.

__________ (2003), “Effective Complexity as a Measure of Information Content”, Philosophy of Science 70: 302-307.

McGuire, John E., and Martin Tamny (1983), Certain Philosophical Questions: Newton’s Trinity Notebook. Cambridge: Cambridge University Press.

Merleau-Ponty, Maurice ([1945] 1962), Phenomenology of Perception. Translated by Colin Smith. London: Routledge and Kegan Paul.

Mermin, David (1998), “What is Quantum Mechanics Trying to Tell Us?”, American Journal of Physics 66: 753-767.

Mester, J., et al. (2001), “The STEP Mission: Principles and Baseline Design”, Classical and Quantum Gravity 18: 2475-2486.

Mignard, François (2002), “Fundamental Physics with GAIA”, in O. Bienayme and C. Turon (eds.), EAS Publication Series, Volume 2, GAIA: A European Space Project.

Miller, J.P., Muon (g-2) Collaboration (2002), “The Muon Anomaly: Experiment and Theory”, International Journal of Modern Physics A 17: 3318-3335.

Milgrom, Mordehai (1983a), “A Modification of the Newtonian Dynamics as a Possible Alternative to the Hidden Mass Hypothesis”, The Astrophysical Journal 270: 365-370.

__________ (1983b), “A Modification of the Newtonian Dynamics: Implications for Galaxies”, The Astrophysical Journal 270: 371-383.

Milgrom, Mordehai, and Robert H. Sanders (2003), “Modified Newtonian Dynamics and the ‘Dearth of Dark Matter in Ordinary Elliptical Galaxies”, The Astrophysical Journal 599: L25-L28.

Moffat, J.W. (2004), Modified Gravitational Theory as an Alternative to Dark Energy and Dark Matter. [Online Article]: cited on 15 October 2004, ‹http://www.arxiv.org/abs/astro-ph/0403266›.

Moore, Cristopher (1990), “Unpredictability and Undecidability in Dynamical Systems”, Physical Review Letters 64: 2354-2357.

Nellist, P.D., et al. (2004), “Direct Sub-Angstrom Imaging of a Crystal Lattice”, Science 305: 1741.

Nesvizhevsky, Valery, et al. (2002), “Quantum States of Neutrons in the Earth’s Gravitational Field”, Nature 415: 297-299.

Newton, Isaac ([1730] 1952), Optiks, 4th Edition. New York: Dover.

Paredes, Belén, et al. (2004), “Tonks-Girardeau Gas of Ultracold Atoms in an Optical Lattice”, Nature 429: 277-281.

Pearle, Philip (1989), “Combining Stochastic Dynamical State-Vector Reduction with Spontaneous Localization”, Physical Review A 39: 2277-2289.

Perlmutter, S., et al. (1998), “Discovery of Supernova at Half the Age of the Universe”, Nature 391: 51-54.

Piaget, Jean (1967), Biologie et Connaissance. Paris: Gallimard.

Plazanet, M. et al. (2004), “Freezing on Heating of Liquid Solutions”, The Journal of Chemical Physics 121: 5031-5034.

Presburger, Mojzesz ([1929] 1991), “On the Completeness of a Certain System of Arithmetic of Whole Numbers in Which Addition Occurs as the Only Operation”, Translated by Dale Jacquette, History and Philosophy of Logic 12: 225-233. Originally published as “Über die Vollständigkeit eines gewissen Systems der Arithmetik ganzer Zahlen, in welchem die Addition als einzige Operation hervortritt”, Sparawozdanie z I Kongresu matematyków krajów slowianskich, Warszawa: 92-101.

Quine, W.V. (1960), Word and Object. Cambride, MA: MIT Press.

__________ (1992), Pursuit of Truth, Revised Edition. Cambridge, MA: Harvard University Press.

Rovelli, Carlo (1996), “Relational Quantum Mechanics”, International Journal of Theoretical Physics 35: 1637-1678.

Rowe, M.A., et al. (2001), “Experimental Violation of Bell’s Inequality with Efficient Detection”, Nature 409: 791-794.

Rubin, Vera C., and W. Kent Ford, Jr. (1970), “Rotation of the Andromdea Nebula from a Spectroscopic Survey of Emission Regions,” The Astrophysical Journal 159:379-404.

Ruphy, Stéphanie (2003), “Is the World Really ‘Dappled’? A Response to Cartwright’s Charge against ‘Cross-Wise Reduction’”, Philosophy of Science 70: 57-67.

Samuelsson, P., and M. Büttiker (2002), “Chaotic Dot-Superconductor Analog of the Hanbury Brown-Twiss Effect”, Physical Review Letters 89: 046601.

Sankey, Howard (1997), “Incommensurability: The Current State of Play”, Theoria 12: 425-445.

Skolem, Thoralf (1930), “Über einige Satzfunktionem in der Arithmetik”, Skrifter Utgitt av Det Norske Videnskaps-Akademi i Oslo, I. Mat.-Naturv.

Smith, Sinclair (1936), “The Mass of the Virgo Cluster”, The Astrophysical Journal 83: 23-30.

Smolin, Lee (1995), The Beckenstein Bound, Topological Quantum Filed Theory and Pluralistic Quantum Field Theory. [Online Article]: cited on 20 November 2004, ‹http://arxiv.org/abs/gr-qc/9508064›.

__________ (1997), The Life of the Cosmos. New York: Oxford University Press.

__________ (2003), How Far Are We from the Quantum Theory of Gravity? [Online Article]: cited on 10 November 2004, ‹http://arxiv.org/abs/hep-th/0303185›.

Solomonoff, Ray (1964), “A Formal Theory of Inductive Inference, Part 1 [&2]”, Information and Control 7: 1-22 & 224-254.

Sommerer, John C., and Edward Ott (1996), “Intermingled Basins of Attraction: Uncomputability in a Simple Physical System”, Physics Letters A 214: 243-251.

Soussa, M.E., and R. P. Woodard (2003), “A Nonlocal Metric Formulation of MOND”, Classical and Quantum Gravity 20: 2737-2751.

Spergel, D., et al. (2003), “First-Year Wilkinson Microwave Anistropy Probe (WMAP) Observations: Determination of Cosmological Parameters”, The Astropysical Journal Supplement Series 148: 175-194.

Suppes, Patrick (1962), “Models of Data”, in E. Nagel, P. Suppes, and A. Tarski (eds.), Logic, Methodology, and Philosophy of Science. Stanford: Stanford University Press, 252-261.

__________ (1978), “The Plurality of Science”, in P.D. Asquith and I. Hacking (eds.), PSA 1978, Volume 2. Philosophy of Science Association, 3-16.

Susskind, Leonard (2003), The Anthropic Landscape of String Theory. [Online Article]: cited on 10 November 2004, ‹http://arxiv.org/abs/hep-th/0302219›.

Tarski, Alfred (1933), “The Concept of Truth in the Deductive Sciences”, Prace Towarzystwa Naukowego Warszawskiego, Wydzial III Nauk Matematyczno-Fizycznych 34. Expanded English translation in Tarski (1956).

__________ (1956), Logics, Semantics, Metamathematics. Oxford: Clarendon Press.

__________ (1969), “Truth and Proof”, Scientific American 220, No. 6 (June): 63-77.

Touboul, Pierre, and Manuel Rodrigues (2001), “The MICROSCOPE Space Mission”, Classical and Quantum Gravity 18: 2487-2498.

Traub, Joseph F. (1996), “On Reality and Models”, in J. Casti and A. Karlqvist (eds.), Boundaries and Barriers: On the Limits to Scientific Knowledge. Reading, MA: Addison-Wesley.

__________ (1997a), “Do Negative Results from Formal Systems Limit Scientific Knowledge?” Complexity 3: 29-31.

__________ (1997b), Non-Computability and Intractability: Does it Matter to Physics? Technical Report, Columbia University Department of Computer Science.

Turing, Alan (1936), “On Computable Numbers, with an Application to the Entscheidungsproblem”, Proceedings of the London Mathematical Society 42: 230-265.

Turneaure, J.P., et al. (2003), “Development of the Gravity Probe B Flight Mission”, Advances in Space Research 32: 1387-1396.

van den Bergh, Sidney (1999), “The Early History of Dark Matter”, Publications of the Astronomical Society of the Pacific 111: 657-660.

van der Wal, Caspar H., et al. (2000), “Quantum Superposition of Macroscopic Persistent-Current States”, Science 290: 773-777.

van Dyck, Robert S. Jr., Paul B. Schwinberg, and Hans G. Dehmelt (1987), “New High-Precision Comparison of Electron and Positron g Factors”, Physical Review Letters 59: 26-29.

van Fraassen, B.C. (1989), “The Charybdis of Realism: Epistemological Implications of Bell’s Inequality”, in J. Cushing and E. McMullin (eds.), Philosophical Consequences of Quantum Theory. Notre Dame: University of Notre Dame Press.

__________ (1991), Quantum Mechanics: An Empiricist View. Oxford: Clarendon Press.

von Baeyer, Hans Christian (2003), Information: The New Language of Science. Cambridge, MA: Harvard University Press.

von Neumann, John ([1932] 1955), Mathematical Foundations of Quantum Mechanics. Translated by R.T. Beyer. Princeton: Princeton University Press.

__________ (1966), Theory of Self-Reproducing Automata. Urbana, IL: University of Illinois Press.

Wang, G.M., et al. (2002), “Experimental Demonstration of Violations of the Second Law of Thermodynamics for Small Systems and Short Time Scales”, Physical Review Letters 89: 050601.

Weinberg, Steven (1992), Dreams of a Final Theory. New York: Pantheon.

Weinstein, Steven (2003), “Objectivity, Information, and Maxwell’s Demon”, Philosophy of Science 70: 1245-1255.

Weiss, Peter (2003), “A Spin through Space-Time”, Science 164: 280.

Wigner, E.P. (1961), “Remarks on the Mind-Body Question”, in I.J. Good (ed.), The Scientist Speculates. London: Heinemann.

Wiles, Andrew (1995), “Modular Elliptic Curves and Fermat’s Last Theorem”, Annals of Mathematics 142: 443-551.

Will, Clifford M. (2001), “The Confrontation between General Relativity and Experiment”, Living Reviews in Relativity 4: 4. [Online Article]: cited on 1 October 2004, ‹http://www. livingreviews.org/lrr-2001-4›.

Williams, J.G., X.X. Newhall, and J.O. Dickey (1996), “Relativity Parameters Determined from Lunar Laser Ranging”, Physical Review D 53: 6730-6739.

Winograd, Terry, and Fernando Flores (1986), Understanding Computers and Cognition. Norwood, NJ: Ablex Publishing Corporation.

Wittgenstein, Ludwig (1953), Philosophical Investigations. Translated by G.E.M Anscombe and edited by G.E.M Anscombe and R. Rhees. Oxford: Blackwell.

Wolfram, Stephen (1985), “Undecidability and Intractability in Theoretical Physics”, Physical Review Letters 54: 735-738.

__________ (2002), A New Kind of Science. Champaign: Wolfram Media.

Zeh, H.D. (2003), “Basic Concepts and their Interpretation”, in E. Joos (ed.), Decoherence and the Appearance of a Classical World in Quantum Theory, 2nd Edition. Heidelberg: Springer-Verlag. [Online Edition]: cited on 10 November 2004, ‹http://arxiv.org/abs/quant-ph/9506020›.

Zehavi, Idit, and Avishai Dekel (1999), “Evidence for a Positive Cosmological Constant from Flows of Galaxies and Distant Supernovae”, Nature 401: 252-254.

Zeilinger, Anton (1998), “Fundamentals of Quantum Information”, Physics World March. [Online Edition]: cited on 10 November 2004, ‹http://physicsweb.org/articles/world/11/3/9/1›.

__________ (1999), “A Foundational Principle for Quantum Mechanics”, Foundations of Physics 29: 631-643.

Zwicky, Fritz (1933), “The Red Shift of Extragalactic Nebulas”, Helvetica Physica Acta 6: 110-127.

Metadata

Repository Staff Only: item control page