# Equivalence of the Symbol Grounding and Quantum System Identification Problems

## Abstract

**:**

## 1. Introduction

How can the semantic interpretation of a formal symbol system be made intrinsic to the system, rather than just parasitic on the meanings in our heads? How can the meanings of the meaningless symbol tokens, manipulated solely on the basis of their (arbitrary) shapes, be grounded in anything but other meaningless symbols?[1] (p. 335)

## 2. Preliminaries

#### 2.1. Symbols and Grounds

#### 2.2. Systems, States and Observables

#### 2.3. Quantum and Classical

#### 2.4. Summary

## 3. Solving the QSIP Requires Solving the SGP

- (1)
- The state $|\mathbf{U}\rangle $ of any isolated quantum system $\mathbf{U}$ may be represented as a unit vector in a Hilbert space ${\mathcal{H}}_{\mathbf{U}}$.
- (2)
- The time evolution of $|\mathbf{U}\rangle $ is unitary, and may be represented by a propagator ${e}^{-(i/\hslash ){H}_{\mathbf{U}}\mathit{t}}$ where ${H}_{\mathbf{U}}$ is the Hamiltonian operator characterizing $\mathbf{U}$.
- (3)
- Measurements of $|\mathbf{U}\rangle $ may be represented as actions by a positive operator-valued measure (POVM), a collection $\left\{{E}_{i}^{\mathbf{U}}\right\}$ of positive semi-definite Hilbert-space automorphisms that sum to the Identity, on ${\mathcal{H}}_{\mathbf{U}}$.
- (4)
- The components of an isolated composite system $\mathbf{U}$ may be represented by a tensor-product structure (TPS) of ${\mathcal{H}}_{\mathbf{U}}$.

## 4. Solving the SGP Requires Solving the QSIP

^{rd}and higher-order terms are neglected, as a sum ${H}_{\mathbf{U}}={\sum}_{\mathit{ij}}{\mathit{H}}_{\mathit{ij}}$, where ${H}_{ij}$ describes the pairwise interaction between two physical degrees of freedom i and j of $\mathbf{U}$, and that allows alternative TPSs ${\mathcal{H}}_{\mathbf{S}}\otimes {\mathcal{H}}_{\mathbf{E}}$ and ${\mathcal{H}}_{{\mathbf{S}}^{\prime}}\otimes {\mathcal{H}}_{{\mathbf{E}}^{\prime}}$ to describe the same universe [18,19]. Any assumption that particular systems, and hence particular TPSs, are “preferred” by physical dynamics violates decompositional equivalence. It cannot, therefore, be assumed that the “environment” only encodes information about the states of particular systems; if the environment is assumed to encode information about the states of systems embedded in it, it must be assumed to encode information about the states of all such systems. In this case, however, observers must be regarded as choosing which encoded information to extract from the environment, which is precisely the assumption of relevance that the environment as witness formulation was designed to avoid [52].

## 5. The Unsolvability of the QSIP Renders the SGP Unsolvable

## 6. So What?

## 7. Conclusions

## Acknowledgments

## Conflict of Interest

## References

- Harnad, S. The symbol grounding problem. Physica D
**1990**, 42, 335–346. [Google Scholar] [CrossRef] - Searle, J.R. Minds, brains and programs. Behav. Brain Sci.
**1980**, 3, 417–457. [Google Scholar] [CrossRef] - Newell, A.; Simon, H.A. Computer science as empirical inquiry: Symbols and search. Comm. ACM
**1976**, 19, 113–126. [Google Scholar] [CrossRef] - Fodor, J.A. Methodological solipcism considered as a research strategy in cognitive psychology. Behav. Brain Sci.
**1980**, 3, 63–109. [Google Scholar] [CrossRef] - Newell, A. Physical symbol systems. Cogn. Sci.
**1980**, 4, 135–183. [Google Scholar] [CrossRef] - Pylyshyn, Z.W. Computation and cognition. Behav. Brain Sci.
**1980**, 3, 111–169. [Google Scholar] [CrossRef] - Taddeo, M.; Floridi, L. Solving the symbol grounding problem: A critical review of fifteen years of research. J. Expt. Theor. Artif. Intell.
**2005**, 17, 419–445. [Google Scholar] [CrossRef] - Floridi, L. Open problems in the philosophy of information. Metaphilosophy
**2004**, 35, 554–582. [Google Scholar] [CrossRef] - Dodig Crnkovic, G.; Hofkirchner, W. Floridi’s ‘Open problems in the philosophy of information’, ten years later. Information
**2011**, 2, 327–359. [Google Scholar] [CrossRef] - Gallese, V.; Lakoff, G. The brain’s concepts: The role of sensory-motor systems in conceptual knowledge. Cogn. Neuropsychol.
**2005**, 22, 455–479. [Google Scholar] [CrossRef] [PubMed] - Barsalou, L. Grounded cognition. Ann. Rev. Psychol.
**2008**, 59, 617–645. [Google Scholar] [CrossRef] [PubMed] - Taddeo, M.; Floridi, L. A praxical solution of the symbol grounding problem. Minds Mach.
**2007**, 17, 369–389. [Google Scholar] [CrossRef] - Kramer, O. On machine symbol grounding and optimization. Int. J. Cogn. Inform. Nat. Intell.
**2011**, 5, 73–85. [Google Scholar] [CrossRef] - Farkaš, I.; Malik, T.; Rebrová, K. Grounding the meanings in sensorimotor behavior using reinforcement learning. Front. Neurorobot.
**2012**, 6. [Google Scholar] [CrossRef] [PubMed] - Ashby, W.R. An Introduction to Cybernetics; Chapman & Hall: London, UK, 1956. [Google Scholar]
- Moore, E.F. Gedanken-experiments on sequential machines. In Automata Studies; Shannon, C.W., McCarthy, J., Eds.; Princeton University Press: Princeton, NJ, USA, 1956; pp. 129–155. [Google Scholar]
- Fields, C. If physics is an information science, what is an observer? Information
**2012**, 3, 92–123. [Google Scholar] [CrossRef] - Fields, C. A model-theoretic interpretation of environment-induced superselection. Int. J. Gen. Syst.
**2012**, 41, 847–859. [Google Scholar] [CrossRef] - Fields, C. Implementation of classical communication in a quantum world. Information
**2012**, 3, 809–831. [Google Scholar] [CrossRef] - Schlosshauer, M. Experimental motivation and empirical consistency of minimal no-collapse quantum mechanics. Annals Phys.
**2006**, 321, 112–149. [Google Scholar] [CrossRef] - Bohm, D.; Hiley, B.J.; Kaloyerou, P.N. An ontological basis for the quantum theory. Phys. Rep.
**1987**, 144, 321–375. [Google Scholar] [CrossRef] - Weinberg, S. Collapse of the state vector. Phys. Rev. A
**2012**, 85, 062116. [Google Scholar] [CrossRef] - Fields, C. Bell’s theorem from Moore’s theorem. Int. J. Gen. Syst.
**2013**, 42, 376–385. [Google Scholar] [CrossRef] - Bennet, A.J.; Evans, D.A.; Saunders, D.J.; Branciard, C.; Cavalcanti, E.G.; Wiseman, H.M.; Pryde, G.J. Arbitrary loss-tolerant Einstein-Podolsky-Rosen steering allowing a demonstration over 1 km of optical fiber with no detection loophole. Phys. Rev. X
**2012**, 2, 031003. [Google Scholar] - Christensen, B.G.; McCusker, K.T.; Altepeter, J.B.; Calkins, B.; Gerrits, T.; Lita, A.E.; Miller, A.; Shalm, L.K.; Zhang, Y.; Nam, S.W.; et al. Detection-loophole-free test of quantum nonlocality, and applications.
**2013**. Preprint arxiv:1306.5772 [quant-ph]. [Google Scholar] [CrossRef] - Inagaki, T.; Matsuda, N.; Tadanaga, O.; Asobe, M.; Takesue, H. Entanglement distribution over 300 km of fiber. Opt. Express
**2013**, 21, 23241–23249. [Google Scholar] [CrossRef] [PubMed] - Kaiser, F.; Coudreau, T.; Milman, P.; Ostrowsky, D.B.; Tanzilli, S. Entanglement-enabled delayed choice experiment. Science
**2012**, 338, 637–640. [Google Scholar] [CrossRef] [PubMed][Green Version] - Peruzzo, A.; Shadbolt, P.; Brunner, N.; Popescu, S.; O’Brien, J.L. A quantum delayed-choice experiment. Science
**2012**, 338, 634–637. [Google Scholar] [CrossRef] [PubMed] - Saeedi, K.; Simmon, S.; Salvail, J.Z.; Dluhy, P.; Riemann, H.; Abrosimov, N.V.; Becker, P.; Pohl, H.-J.; Morton, J.J.L.; Thewalt, M.L.W. Room-temperature quantum bit storage exceeding 39 minutes using ionized donors in Silicon-28. Science
**2013**, 342, 830–833. [Google Scholar] [CrossRef] [PubMed] - Bartlett, S.D.; Rudolph, T.; Spekkens, R.W. Reference frames, superselection rules, and quantum information. Rev. Mod. Phys.
**2007**, 79, 555–609. [Google Scholar] [CrossRef] - Fuchs, C. QBism: The perimeter of quantum Bayesianism.
**2010**. Preprint arXiv:1003.5209v1 [quant-ph]. [Google Scholar] - Wheeler, J.A. Recent thinking about the nature of the physical world: It from bit. Ann. N. Y. Acad. Sci.
**1992**, 655, 349–364. [Google Scholar] [CrossRef] - Floridi, L. A defence of informational structural realism. Synthese
**2008**, 161, 219–253. [Google Scholar] [CrossRef] - Floridi, L. Against digital ontology. Synthese
**2009**, 168, 151–178. [Google Scholar] [CrossRef][Green Version] - Von Neumann, J. Mathematische Grundlagen der Quantenmechanik; Springer: Berlin, Germany, 1932. (in German) [Google Scholar]
- Joos, E.; Zeh, D. The emergence of classical properties through interaction with the environment. Z. Phys. B
**1985**, 59, 223–243. [Google Scholar] [CrossRef] - Zurek, W.H. Decoherence, einselection and the existential interpretation (the rough guide). Phil. Trans. R. Soc. A
**1998**, 356, 1793–1821. [Google Scholar] [CrossRef] - Joos, E.; Zeh, D.; Kiefer, C.; Giulini, D.; Kupsch, J.; Stamatescu, I.-O. Decoherence and the Appearance of a Classical World in Quantum Theory, 2nd ed.; Springer: Berlin, Germany, 2003. [Google Scholar]
- Zurek, W.H. Decoherence, einselection, and the quantum origins of the classical. Rev. Mod. Phys.
**2003**, 75, 715–775. [Google Scholar] [CrossRef] - Schlosshauer, M. Decoherence and the Quantum to Classical Transition; Springer: Berlin, Germany, 2007. [Google Scholar]
- Nielsen, M.A.; Chaung, I.L. Quantum Information and Quantum Computation; Cambridge University Press: Cambridge, UK, 2000. [Google Scholar]
- Clifton, R.; Bub, J.; Halvorson, H. Characterizing quantum theory in terms of information-theoretic constraints. Found. Phys.
**2003**, 33, 1561–1591. [Google Scholar] [CrossRef] - Chiribella, G.; D’Ariano, G.M.; Perinotti, P. Informational derivation of quantum theory. Phys. Rev. A
**2011**, 84, 012311. [Google Scholar] [CrossRef] - Lee, J.-W. Quantum mechanics emerges from information theory applied to causal horizons. Found. Phys.
**2011**, 41, 744–753. [Google Scholar] [CrossRef] - Masanes, L.; Müller, M.P. A derivation of quantum theory from physical requirements. New J. Phys.
**2011**, 13, 063001. [Google Scholar] [CrossRef] - De la Torre, G.; Masanes, L.; Short, A.J.; Müller, M.P. Deriving quantum theory from its local structure and reversibility. Phys. Rev. Lett.
**2012**, 109, 090403. [Google Scholar] [CrossRef] [PubMed] - Karmiloff-Smith, A. Beyond Modularity: A Developmental Perspective on Cognitive Science; MIT Press: Cambridge, MA, USA, 1995. [Google Scholar]
- Zanardi, P. Virtual quantum subsystems. Phys. Rev. Lett.
**2001**, 87, 077901. [Google Scholar] [CrossRef] [PubMed] - Lombardi, O.; Fortin, S.; Castagnino, M. The problem of identifying the system and the environment in the phenomenon of decoherence. In EPSA Philosophy of Science: Amsterdam 2009; de Regt, H.W., Hartmann, S., Okasha, S., Eds.; Springer: Dordrecht, The Netherlands, 2012; pp. 161–174. [Google Scholar]
- Ollivier, H.; Poulin, D.; Zurek, W.H. Objective properties from subjective quantum states: Environment as a witness. Phys. Rev. Lett.
**2004**, 93, 220401. [Google Scholar] [CrossRef] [PubMed] - Ollivier, H.; Poulin, D.; Zurek, W.H. Environment as a witness: Selective proliferation of information and emergence of objectivity in a quantum universe. Phys. Rev. A
**2005**, 72, 042113. [Google Scholar] [CrossRef] - Fields, C. On the Ollivier-Poulin-Zurek definition of objectivity. Axiomathes
**2014**, 24, 137–156. [Google Scholar] [CrossRef] - Fields, C. The very same thing: Extending the object token concept to incorporate causal constraints on individual identity. Adv. Cogn. Psychol.
**2012**, 8, 234–247. [Google Scholar] [CrossRef] [PubMed] - Bohr, N. The quantum postulate and the recent development of atomic theory. Nature
**1928**, 121, 580–590. [Google Scholar] [CrossRef] - Hobson, A. There are no particles, there are only fields. Am. J. Phys.
**2013**, 81, 211–223. [Google Scholar] [CrossRef] - Quine, W.V.O. Word and Object; MIT Press: Cambridge, MA, USA, 1960. [Google Scholar]
- Quine, W.V.O. Ontological relativity. In Ontological Relativity and Other Essays; Columbia University Press: New York, NY, USA, 1969; pp. 26–68. [Google Scholar]
- Wettstein, H. A father of the revolution. Philos. Perspect.
**1999**, 13, 443–457. [Google Scholar] [CrossRef] - Landsman, N.P. Between classical and quantum. In Handbook of the Philosophy of Science: Philosophy of Physics; Butterfield, J., Earman, J., Eds.; Elsevier: Amsterdam, The Netherlands, 2007; pp. 417–553. [Google Scholar]
- Everett, H., III. “Relative state” formulation of quantum mechanics. Rev. Mod. Phys.
**1957**, 29, 454–462. [Google Scholar] [CrossRef]

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Fields, Chris. 2014. "Equivalence of the Symbol Grounding and Quantum System Identification Problems" *Information* 5, no. 1: 172-189.
https://doi.org/10.3390/info5010172