#
On Theoretical Incomprehensibility^{ †}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Incompleteness

- A complete and formal description of the relationships between the model state variables is available;
- A complete and explicit description of the interactions between the system and its environment is available; and
- The knowledge of the preceding two points allows the deduction of all possible states that the system can assume together with its structural characteristics.

## 3. Incomprehensibility

#### 3.1. Theoretical Incomprehensibility

#### 3.2. Theoretical Incomprehensibility of the Loop ‘Comprehensible—Incomprehensible’ Approaches

## 4. Conclusions

## Funding

## Conflicts of Interest

## References

- Carrier, M. The Completeness of Scientific Theories; Kluwer Academic Publisher: Dordrecht, The Netherlands, 1994. [Google Scholar]
- Minati, G. Knowledge to Manage the Knowledge Society: The Concept of Theoretical Incompleteness. Systems
**2016**, 4, 26. [Google Scholar] [CrossRef] - Maturana, H.R.; Varela, F. Autopoiesis and Cognition: The Realization of the Living; Reidel: Dordrecht, The Netherlands, 1980. [Google Scholar]
- Varela, F.; Maturana, H.R.; Uribe, R. Autopoiesis: The organization of living systems, its characterization and a model. BioSystems
**1974**, 5, 187–196. [Google Scholar] [CrossRef] - Maturana, H.R.; Varela, F. The Tree of Knowledge: The Biological Roots of Human Understanding; Shambhala: Boston, MA, USA, 1992. [Google Scholar]
- Heisenberg, W. Physics and Beyond; Harper & Row: New York, NY, USA, 1971. [Google Scholar]
- Bohr, N. The Quantum Postulate and the Recent Development of Atomic Theory. Nature
**1928**, 121, 580–590. [Google Scholar] [CrossRef] - Minati, G.; Pessa, E. Collective Beings; Springer: New York, NY, USA, 2006. [Google Scholar]
- De Wolf, T.; Holvoet, T. Emergence Versus Self Organisation: Different Concepts but Promising when Combined. In Engineering Self-Organising Systems: Methodologies and Applications; Brueckner, S.A., Di Marzo Serugendo, G., Karageorgos, A., Eds.; Springer: New York, NY, USA, 2005; pp. 1–15. [Google Scholar]
- Minati, G.; Licata, I. Emergence as Mesoscopic Coherence. Systems
**2013**, 1, 50–65. [Google Scholar] [CrossRef] - Sawyer, R.K. Social Emergence: Societies as Complex Systems; Cambridge University Press: Cambridge, UK, 2005. [Google Scholar]
- Vicsek, T.; Zafeiris, A. Collective motion. Phys. Rep.
**2012**, 517, 71–140. [Google Scholar] [CrossRef] [Green Version] - Licata, I. Logical openness in cognitive models. Epistemologia
**2008**, 31, 177–191. [Google Scholar] - Licata, I. Seeing by models: Vision as adaptive epistemology. In Methods, Models, Simulations and Approaches towards a General Theory of Change; Minati, G., Abram, M., Pessa, E., Eds.; World Scientific: Singapore, 2012; pp. 385–400. [Google Scholar]
- Licata, I.; Minati, G. Creativity as Cognitive design-The case of mesoscopic variables in Meta-Structures. In Creativity: Fostering, Measuring and Contexts; Corrigan, A.M., Ed.; Nova Publishers: New York, NY, USA, 2010. [Google Scholar]
- Minati, G.; Penna, M.P.; Pessa, E. Thermodynamic and Logical Openness in General Systems. Syst. Res. Behav. Sci.
**1998**, 15, 131–145. [Google Scholar] [CrossRef] - Minati, G.; Pessa, E. From Collective Beings to Quasi-Systems; Springer: New York, NY, USA, 2018. [Google Scholar]
- Von Foerster, H. Cybernetics of Cybernetics. In Communication and Control in Society; Krippendorff, K., Ed.; Gordon and Breach: New York, NY, USA, 1979; pp. 5–8. [Google Scholar]
- Magnani, L. Abduction, Reason and Science: Processes of Discovery and Explanation; Springer: New York, NY, USA, 2001. [Google Scholar]
- Turing, A.M. On computable numbers, with an application to the Entscheidungsproblem. Proc. Lond. Math. Soc.
**1936**, 42, 230–265. [Google Scholar] - Soare, R.I. Turing oracle machines, online computing, and three displacements in computability theory. Ann. Pure Appl. Log.
**2009**, 160, 368–399. [Google Scholar] [CrossRef] [Green Version] - Gödel, K. On Formally Undecidable Propositions of Principia Mathematica and Related Systems; Dover Publications Inc.: Mineola, NY, USA, 1962. [Google Scholar]
- Nepomuceno, E.G.; Perc, M. Computational chaos in complex networks. J. Complex Netw.
**2019**, 2, 1–16. [Google Scholar] [CrossRef] - Nepomuceno, E.G.; Martins, S.A.M.; Silva, B.C.; Amaral, G.F.V.; Perc, M. Detecting unreliable computer simulations of recursive functions with interval extensions. Appl. Math. Comput.
**2018**, 329, 408–419. [Google Scholar] [CrossRef] - Ford, J. Chaos: Solving the Unsolvable, Predicting the Unpredictable. In Chaotic Dynamics and Fractals; Barnsley, M.F., Demko, S.G., Eds.; Academic Press: New York, USA, 1986; pp. 1–52. Available online: https://www.sciencedirect.com/science/article/pii/B9780120790609500072?via%3Dihub (accessed on 11 July 2019).
- Licata, I.; Minati, G. Emergence, Computation and the Freedom Degree Loss Information Principle in Complex Systems. Found. Sci.
**2016**, 21, 863–881. [Google Scholar] [CrossRef] - Mac Lennan, B.J. Natural computation and non-Turing models of computation. Theor. Comput. Sci.
**2004**, 317, 115–145. [Google Scholar] [CrossRef] - Goodfellow, I.; Bengio, Y.; Courville, A.; Bach, F. Deep Learning; MIT Press: Cambridge, MA, USA, 2017. [Google Scholar]
- Cabessa, J.; Villa, A.E.P. The super-Turing computational power of interactive evolving recurrent neural networks. In ICANN 2013; Mladenov, V., Koprinkova-Hristova, P., Palm, G., Villa, A.E.P., Appollini, B., Kasabov, N., Eds.; Lecture Notes in Computer Science (LNCS); Springer: Berlin/Heidelberg, Germany, 2013; Volume 8131, pp. 58–65. [Google Scholar]
- Siegelmann, H.T. Neural and super-Turing computing. Minds Mach.
**2003**, 13, 103–114. [Google Scholar] [CrossRef] - Syropoulos, A. Hypercomputation. Computing Beyond the Church–Turing Barrier; Springer: New York, NY, USA, 2008. [Google Scholar]
- Toby, O. Hypercomputation: Computing more than the Turing machine. Appl. Math. Comput.
**2006**, 178, 143–153. [Google Scholar] - Younger, A.S.; Redd, E.; Siegelmann, H. Development of Physical Super-Turing Analog Hardware. In Unconventional Computation and Natural Computation; Ibarra, O., Kari, L., Kopecki, S., Eds.; Lecture Notes in Computer Science; Springer: Cham, Switzerland, 2014; Volume 8553, pp. 379–392. [Google Scholar]
- Bonometti, P. Improving safety, quality and efficiency through the management of emerging processes: The Tenaris Dalmine experience. Learn. Organ.
**2012**, 19, 299–310. [Google Scholar] [CrossRef] - Janot, C. Quasicrystals: A Primer; Oxford University Press: Oxford, UK, 2012. [Google Scholar]
- Minati, G. Phenomenological structural dynamics of emergence: An overview of how emergence emerges. In The Systemic Turn in Human and Natural Sciences: A Rock in the Pond; Urbani Ulivi, L., Ed.; Springer: New York, NY, USA, 2019; pp. 1–39. [Google Scholar]
- Zenil, H. Compression is Comprehension, and the Unreasonable Effectiveness of Digital Computation in the Natural World. 2019. Available online: https://arxiv.org/abs/1904.10258 (accessed on 23 July 2019).
- McAllister, J.W. Algorithmic randomness in empirical data. Stud. Hist. Philos. Sci.
**2003**, 34, 633–646. [Google Scholar] [CrossRef] - Calude, C.S. Information and Randomness; Springer: Berlin/Heidelberg, Germany, 2002. [Google Scholar]
- Bermúdez, J.L. Cognitive Science: An Introduction to the Science of the Mind; Cambridge University Press: Cambridge, UK, 2014. [Google Scholar]
- Fodor, J.A. Representations: Philosophical Essays on the Foundations of Cognitive Science; MIT Press: Cambridge, MA, USA, 1981. [Google Scholar]
- Varela, F.; Thompson, E.; Rosch, E. The Embodied Mind: Cognitive Science and Human Experience; MIT Press: Cambridge, MA, USA, 1991. [Google Scholar]
- Macdonald, C.; Macdonald, G. Emergence in Mind; Oxford University Press: Oxford, UK, 2010. [Google Scholar]
- Gerstner, W.; Kistler, W.M.; Naud, R. Neuronal Dynamics: From Single Neurons to Networks and Models of Cognition; Cambridge University Press: Cambridge, UK, 2014. [Google Scholar]
- Banathy, B.H. The Story of the Evolution of Homo sapiens sapiens. In Guided Evolution of Society: A System View; Contemporary Systems Thinking; Springer: Boston, MA, USA, 2000; pp. 89–142. [Google Scholar]
- Harari, Y.N. Sapiens: A Brief History of Human Kind; HarperCollins: New York, NY, USA, 2015. [Google Scholar]
- Von Foerster, H. Understanding Understanding: Essays on Cybernetics and Cognition; Springer: New York, NY, USA, 2003. [Google Scholar]
- Von Foerster, H. Notes pour une épistémologie des objets vivants. In L’unité de L’homme: Invariants Biologique and Universaux Culturels; Morin, E., Piattelli-Palmerini, M., Eds.; Seuil: Paris, France, 1974; pp. 139–155. [Google Scholar]
- Andreewsky, E.; Bourcier, D. Abduction in Language interpretation and Law making. Kybernetes
**2000**, 29, 836–845. [Google Scholar] [CrossRef] - Mathen, J. On the Inherent Incompleteness of Scientific Theories. Act. Nerv. Super.
**2011**, 53, 44–100. [Google Scholar] [CrossRef] [Green Version] - Susskind, L.; Lindesay, J. An Introduction to Black Holes, Information and the String Theory Revolution: The Holographic Universe; World Scientific: Singapore, 2002. [Google Scholar]
- Blasone, M.; Jizba, P.; Vitiello, G. Quantum Field Theory and Its Macroscopic Manifestations; Imperial College Press: London, UK, 2011. [Google Scholar]
- Itzykson, C.; Zuber, J.B. Quantum Field Theory; McGraw-Hill: Singapore, 1986. [Google Scholar]
- Hobson, A. There are no particles, there are only fields. Am. J. Phys.
**2013**, 81, 211–223. Available online: https://arxiv.org/ftp/arxiv/papers/1204/1204.4616.pdf (accessed on 28 May 2019). [CrossRef] [Green Version] - Gühne, O.; Toth, G. Entanglement detection. Phys. Rep.
**2009**, 474, 1–75. [Google Scholar] [CrossRef] [Green Version] - Koksma, J.F.; Prokopec, T.; Schmidt, M.G. Decoherence in an interacting quantum field theory: The vacuum case. Phys. Rev. D
**2010**, 81, 65030. [Google Scholar] [CrossRef] - Bain, J. Against particle/field duality: Asymptotic particle states and interpolating fields in interacting QFT (or: Who is afraid of Haag’s theorem?). Erkenntnis
**2000**, 53, 375–406. [Google Scholar] [CrossRef] - Peskin, M.E.; Schroeder, D.V. An Introduction to Quantum Field Theory; Addison-Wesley: Reading, MA, USA, 1995. [Google Scholar]
- Teller, P. An Interpretive Introduction to Quantum Field Theory; Princeton University Press: Princeton, NJ, USA, 1995. [Google Scholar]
- Pessa, E. The concept of particle in quantum field theory. In Vision of Oneness; Licata, I., Sakaji, A., Eds.; Aracne: Rome, Italy, 2011; pp. 13–40. [Google Scholar]
- Parisi, G. Statistical Field Theory; Perseus Books: New York, NY, USA, 1998. [Google Scholar]
- Foucault, M. Histoire de la Folie à L’âge Classique; Gallimard: Paris, France, 1972. [Google Scholar]
- Beltrami, E. Essay of interpretation of non-Euclidean geometry. G. Mat.
**1868**, 4, 285–315. [Google Scholar] - Beltrami, E. Fundamental theory of the spaces of constant curvature. Ann. Mat.
**1868**, 2, 232–255. [Google Scholar] [CrossRef] - Stinson, D.R.; Paterson, M. Cryptography: Theory and Practice; CRC Press: Boca Raton, FL, USA, 2018. [Google Scholar]
- Watzlawick, P. (Ed.) The Invented Reality; Norton: New York, NY, USA, 1983. [Google Scholar]
- Butts, R.; Brown, J. (Eds.) Constructivism and Science; Kluwer: Dordrecht, The Netherlands, 1989. [Google Scholar]
- Gash, H. Constructing constructivism. Constr. Found.
**2014**, 9, 302–310. [Google Scholar] - Von Glasersfeld, E. Radical Constructivism: A Way of Knowing and Learning; Falmer Press: London, UK, 1995. [Google Scholar]
- Segal, L. The Dream of Reality: Heinz Von Foerster’s Constructivism; Springer: New York, NY, USA, 2013. [Google Scholar]
- Galavotti, M.C. (Ed.) Bruno de Finetti Radical Probabilist; College Publications: London, UK, 2008. [Google Scholar]
- Minati, G. Big Data: From Forecasting to Mesoscopic Understanding. Meta-Profiling as Complex Systems. Meta-Profiling as Complex Syst. Syst.
**2019**, 7, 8. [Google Scholar] [Green Version] - Anderson, C. The End of Theory: The Data Deluge Makes the Scientific Method Obsolete. 2008. Available online: https://www.wired.com/2008/06/pb-theory/ (accessed on 21 May 2018).
- Minati, G. Does Systemics still need theories? Theory-less knowledge. In Systemics of Incompleteness and Quasi-Systems; Minati, G., Abram, G., Pessa, E., Eds.; Springer: New York, NY, USA, 2019; pp. 87–92. [Google Scholar]
- Minati, G.; Licata, I. Meta-Structural properties in Collective Behaviours. Int. J. Gen. Syst.
**2012**, 41, 289–311. [Google Scholar] [CrossRef] - Zadeh, L.A.; Klir, G.J.; Yuan, B. (Eds.) Fuzzy Sets, Fuzzy Logic, and Fuzzy Systems: Selected Papers by Lotfi A. Zadeh; World Scientific: Singapore, 1996. [Google Scholar]
- Transtrum, M.K.; Machta, B.B.; Brown, K.S.; Daniels, B.C.; Myers, C.R.; Sethna, J.P. Perspective: Sloppiness and Emergent Theories in Physics, Biology, and beyond. J. Chem. Phys.
**2015**, 143, 010901. [Google Scholar] [CrossRef] - Merelli, E.; Rucco, M. Topological characterization of complex systems: Using persistent entropy. Entropy
**2015**, 17, 6872–6892. [Google Scholar] [CrossRef] - Li, M.; Vitányi, P. An Introduction to Kolmogorov Complexity and Its Applications, 3rd ed.; Springer: New York, NY, USA, 2008. [Google Scholar]
- Zeno, C. Our Way to Certitude: An Introduction to Newman’s Psychological Discovery: The Illative Sense, and His Grammar of Assent; E. J. Brill: Leiden, The Netherlands, 1957; pp. 114–148. [Google Scholar]
- Newman, J.H. An Essay in Aid of a Grammar of Assent; Assumption Press: New York, NY, USA, 2013; pp. 343–383. [Google Scholar]
- Minati, G.; Vitiello, G. Mistake Making Machines. In Systemics of Emergence: Applications and Development; Minati, G., Pessa, E., Abram, M., Eds.; Springer: New York, NY, USA, 2006; pp. 67–78. [Google Scholar]
- Minati, G.; Abram, M.; Pessa, E. (Eds.) Towards a Post-Bertalanffy Systemics; Springer: New York, NY, USA, 2016. [Google Scholar]
- Kumar, K. From Post-Industrial to Post-Modern Society: New Theories of the Contemporary World; Blackwell Publishers: Oxford, UK, 2004. [Google Scholar]
- Haunss, S. Conflicts in the Knowledge Society; Cambridge University Press: Cambridge, UK, 2015. [Google Scholar]
- Minati, G. Some new theoretical issues in Systems Thinking relevant for modelling corporate learning. Learn. Organ.
**2007**, 14, 480–488. [Google Scholar] [CrossRef] - Minati, G. Knowledge to Manage the Knowledge Society. 2012. Available online: https://www.emerald.com/insight/content/doi/10.1108/09696471211226707/full/html (accessed on 13 August 2019).
- Minati, G. (Ed.) Special Issue: Knowledge to Manage the Knowledge Society. 2012. Available online: https://www.emerald.com/insight/content/doi/10.1108/09696471211226725/full/html (accessed on 13 August 2019).

**Table 1.**A schematic comparison between aspects of logically closed systems and logically open systems.

Logically Closed Systems | Logically Open Systems |
---|---|

Deductive and inductive | Deductive, inductive, and abductive |

Avoids contradictions | Use contradictions |

Insensitive to context | Context-sensitive |

Does not change the rules, at most the parameters | Change the Rules |

Non-Flexible | Changes its structure but maintains consistency |

Does not learn | Learn |

Work on the basis of mono-strategies | Work on the basis of multiple strategies, such as DYSAM * |

Object-oriented | Process-oriented |

Observer considered external, generator of relativism | The observer is an integral part of the system and generator of cognitive existence |

Passive | Active |

Conceptual framework of objectivism | Use of objectivism and constructivism |

The theoretically incomprehensibility of inexhaustibility of the multiplicity of constructivist reality |

The theoretically incomprehensible endless loop Incomprehensible-comprehensible and incompressibility |

The theoretically incomprehensibility of existential questions |

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Minati, G.
On Theoretical Incomprehensibility. *Philosophies* **2019**, *4*, 49.
https://doi.org/10.3390/philosophies4030049

**AMA Style**

Minati G.
On Theoretical Incomprehensibility. *Philosophies*. 2019; 4(3):49.
https://doi.org/10.3390/philosophies4030049

**Chicago/Turabian Style**

Minati, Gianfranco.
2019. "On Theoretical Incomprehensibility" *Philosophies* 4, no. 3: 49.
https://doi.org/10.3390/philosophies4030049