**9. Conclusions**

According to Heidegger [81], the most profound and foundational metaphysical issue is to think the existent as the existent (*"das Seiende als das Seiende denken"*). Here the existent is metaphorically interpreted as an infinite sequence of bits, a Number World. Rather than answering the primary question [82] of why there is existence rather than nothingness, this paper has been mostly concerned with the formal consequences of existence under the least amount of extra assumptions [83].

As it turns out, existence implies that an intrinsic and sophisticated mixture of meaningful and (spurious) patterns—possibly interpreted as "laws"—can arise from xáos. The emergen<sup>t</sup> "laws" abound, they can be found almost everywhere. The axioms in mathematics find their correspondents in the "laws" of physics as a sort of "lógos" upon which the respective mathematical universe is "created by the formal system". By analogy, our own universe might be, possibly deceptively and hallucinatory, be perceived as based upon such sorts of "laws" of physics. The results in Sections 4 and 8 have corroborated the Humeanism view, later promoted by Exner and to some extend by the young Schrödinger, that at least some physical "laws" merely arise from xáos; a picture which is compatible with the unresolvable/irreducible lawless hypothesis. The analysis presented in this paper suggests that the "laws" discovered in science correspond merely to syntactical correlations, are local and not universal.

As in biological living systems, the dynamics described above is not a matter of stable or unstable equilibrium, but of far from equilibrium processes which are "structurally stable". This "duality" is supported in physics by the hierarchical layers theory [15,84]. The simultaneous structural stability and non-conservative behaviour in biology, which is a blend of stability and instability is due to the coexistence of opposite properties such as order/disorder and integration/differentiation [85].

Such an active and mindful (some might say self-delusional and projective) approach to order in and purpose of the universe may be interpreted in accord with the ancient Greek theogony [47] by saying that *lógos*, the Gods and the laws of the universe, originate from "the void," or, in a less certain interpretation, from *xáos.* Very similar concepts were developed in ancient China probably around the same time as Homerus and Hesiod: the *I Ching* utilises relational properties of symbols from sophisticated stochastic procedures providing inspiration, meaning and advice on what has been understood as divine intent and the way the universe operates.

**Author Contributions:** Conceptualization, C.S.C. and K.S.; methodology, C.S.C. and K.S.; writing—original draft preparation, C.S.C.; writing—review and editing, C.S.C. and K.S.

**Funding:** K. Svozil was supported in part by the John Templeton Foundation's *Randomness and Providence: An Abrahamic Inquiry Project*

**Acknowledgments:** We thank the anonymous referees for useful comments, criticism and suggestions which have significantly improved the paper

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **Appendix A. Causation and Correlation: Two Formal Models**

To understand better the difference between causation and correlation we present two simple models. In the first model we have two hypotheses, *x* and *y* which can true or false and we denote by *x y* the proposition "*x* is a cause for *y*" and by *<sup>C</sup>*(*<sup>x</sup>*, *y*) the proposition "*x* and *y* are correlated". The logical representations of the new propositions are enumerated in the following Table A1: Indeed, *x y* = 1 if *x* is true, then *y* is true, that is, *x* = *y* = 1. Note that *x y* is a "more restrictive" operator than the logical implication which is true also when 0 → *y* = 1, for every *y* ∈ {0, <sup>1</sup>}. We have *<sup>C</sup>*(*<sup>x</sup>*, *y* = 1) if and only if both *x* and *y* are either true or false, that is, *x* = *y*. If follows that *x y* implies *<sup>C</sup>*(*<sup>x</sup>*, *y*) = 1, but the converse is false.



The second model is inspired by the Fechner-Machian identification of causation with functional dependence [32,86]: suppose that data is represented by two sets *X* and *Y*. If *f* : *X* → *Y* is a function from *X* to *Y*, then we denote the graph of *f* by *Gf* = {(*<sup>x</sup>*, *f*(*x*)) ∈ *X* × *Y* | *f*(*x*) = *y*}. A relation *R* between *X* and *Y* is a set *R* ⊆ *X* × *Y*. We say that *x* ∈ *X* is an *f*-cause for *y* ∈ *Y* if *f*(*x*) = *y* and we write *x f y*. The elements *x*, *y* are correlated by the relation *R*, in writing, *CR*(*<sup>x</sup>*, *y*), if (*<sup>x</sup>*, *y*) ∈ *R*. Assume that *Gf*⊂ *R*; if *x fy*, then *CR*(*<sup>x</sup>*, *y*) but the converse implication is not true.

Both models show that correlation is symmetric, but causation is not. However, the models above do not reflect a crucial difference between causation and correlation: the former contributes to the understanding, in an imperfect way, of the phenomenon, but the second is just a syntactical observation. Causation invites testing, revision, even abandonment; correlation is static and without further analysis could be misleading, see [87,88].
