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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

Topics:
Philosophy of Mind, Philosophy of Science

Year: 2004

OAI identifier:
oai:cogprints.org:3987

Provided by:
Cognitive Sciences ePrint Archive

Download PDF:- (2004). [Online Edition]: cited on 10
- (1983). A Modification of the Newtonian Dynamics as a Possible Alternative to the Hidden Mass Hypothesis”,
- (2002). Accelerated Universe from Gravity Leaking to Extra Dimensions”,
- (1983). and Furio Honsell
- (2001). Atomic and Condensed Matter Physics” in Nuclear Science:
- (1980). Autopoiesis and Cognition: The Realization of the Living. Dordrecht: Reidel. Realization of the Living.
- (1967). Biologie et Connaissance.
- (1983). Certain Philosophical Questions: Newton’s Trinity Notebook. Cambridge:
- (1989). Combining Stochastic Dynamical State-Vector Reduction with Spontaneous Localization”,
- (2004). Direct Sub-Angstrom Imaging of a Crystal Lattice”,
- (1998). Discovery of Supernova at Half the Age of the
- (1981). Experimental Tests of Realistic Local Theories via Bell’s Theorem”,
- (2004). Freezing on Heating of Liquid Solutions”,
- (2002). Fundamental Physics with GAIA”,
- (1999). Gravity-Wave Interferometers as Quantum Gravity Detectors”,
- (1999). Improved Tests of the Equivalence Principle for Gravitational Self-Energy”,
- (2003). Is the Low Cosmic Microwave Background Quadrupole a Signature of Spatial Curvature”,
- (2004). Modified Gravitational Theory as an Alternative to Dark Energy and Dark Matter. [Online Article]: cited on 15
- Muon (g-2) Collaboration (2002), “The Muon Anomaly: Experiment and Theory”,
- (1988). Non-Well-Founded Sets.
- (1984). Observation Reconsidered”,
- (1967). 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
- (1991). On Some Alleged Difficulties on the Interpretation of Quantum Mechanics”,
- (1929). 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
- (1995). On the Status of Hidden Variable Theories in Quantum Mechanics”,
- (1997). Phenomena and Patterns in Data Sets”,
- (1945). Phenomenology of Perception. Translated by Colin Smith. London: Routledge and Kegan Paul.
- (2003). Precision Measurements and New Physics”,
- (1970). Quantum Mechanics and Reality”,
- (1996). Relational Quantum Mechanics”,
- (1957). Relative State’ Formulation of Quantum Mechanics”,
- (2004). SELEX Collaboration (2004), First Observation of a Narrow Charm-Strange Meson DsJ(2632) → Ds eta and D0 K+. Fermilab-Pub-04/087-E, Submitted to Physical Review Letters. [Online Edition]: cited on 15
- (1996). Set Theory, Logic and Their Limitations. Cambridge:
- (2001). SNO Collaboration
- (2003). Suppressing the Lower Multipoles in the CMB Anisotropies”,
- (1967). The Character of Physical Law.
- (1938). The Evolution of Physics,
- (1998). The Hierarchy Problem and New Dimensions at a Millimeter”,
- (1963). The Independence of the Continuum Hypothesis [and part II]”,
- (1992). The Mind of God.
- (1992). The Quantum-State Diffusion Model Applied to Open Systems”,
- (1933). The Red Shift of Extragalactic Nebulas”,
- (1999). The Search for Non-Newtonian Gravity.
- (1994). The String Dilaton and a Least Coupling Principle”,
- (1991). Theories of Everything. Oxford: Clarendon Press. __________
- (1960). Truth and Method. Translated and edited by Garrett Barden and John Cumming.
- (1986). Unified Dynamics for Microscopic and Macroscopic Systems”,
- (1990). Unpredictability and Undecidability in Dynamical Systems”,
- (2003). Updated Estimate of the Muon Magnetic Moment Using Revised Results from e+e- Annihilation”,
- (1998). What is Quantum Mechanics Trying to Tell Us?”,
- (2003). Why Decoherence Has Not Solved the Measurement Problem: A Response to P.W.
- (1960). Word and Object. Cambride,

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