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Towards the (Cognitive) Reality of Mathematics and the Mathematics of (Cognitive) Reality

In: Artificial Mathematical Intelligence

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  • Danny A. J. Gómez Ramírez

    (Instituto Tecnológico Metropolitano (ITM), Research’s Labs Center Parque i)

Abstract

We show that mathematical structures are implicitly present in nature as structural (quantitative) commonalities of different, totally possible physical scenarios. Thus, the ontological reality of mathematics is supported, at least partially, in the physical realm. On the other hand, we claim that mathematics plays an existential structural role within the whole (meta-)physical reality, which is supported by the meta-cosmological fact that one of the most important conceptual frameworks for describing our universe is a mathematical one. We deduce that the (external) reality has (at least) mathematical precision at any level of observation. In addition, we show that natural will offers an explicit example of a (meta-)physical phenomenon that structurally delimits the accuracy of any predictive model, as we know them today in modern physics. In this way an unpredictability principle of natural human emerges. Finally, we explore, by means of a couple of thought experiments, under which conditions and hypothesis we could be able to “produce” explicit mathematical objects.

Suggested Citation

  • Danny A. J. Gómez Ramírez, 2020. "Towards the (Cognitive) Reality of Mathematics and the Mathematics of (Cognitive) Reality," Springer Books, in: Artificial Mathematical Intelligence, chapter 0, pages 53-66, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-50273-7_4
    DOI: 10.1007/978-3-030-50273-7_4
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