**2. Physical/Universal/Natural Laws**

The notion of law in natural sciences, or law of the universe [28–33] has a long ambivalent history. It might not be overstated to claim that the conjecture that there are laws of nature is the core to what science is and how it was and is performed. Of course, one can refute this view and this lawless hypothesis has been discussed by various authors, see [12,34–40]. Contemplating a lawful universe usually amounts to assuming that the laws of nature are objective, have always existed and will exist,

<sup>2</sup> This physical-mathematical mapping assumption is essential for this paper.

<sup>3</sup> "Emergence is a notorious philosophical term of art." [16]. In this paper we will not use the term in the sense of the philosophical emergency theory, but with the signification given in physics [17]: *"The term emergent is used to evoke collective behaviour of a large number of microscopic constituents that is qualitatively different than the behaviours of the individual constituents."*

and they are written in the language of mathematics. Taken this for granted is an assumption which raises many problems, some of which will be discussed later. In this tradition science can be done in one way, the Galileo-Newton one; but if there are no laws, we can be freed to pursue other methodological options, some of which are not entirely unproblematic. Continuing to enrich the fundamental Greek practice of scientific observation, thinking and debating on different theoretical interpretations of phenomena with other methods, like the experimental methods (since Galileo) and the mathematical models (since Descartes and Newton) is obviously desirable. A step in this direction is to incorporate robust data analytics as a scientific method, see [41–44]. However, suggestions to narrow down the scientific methods to just a collection of "empirical evidences", to advance purely speculative theories (see [45] for physics) or to promote the "philosophy" according to which correlation supersedes causation and theorising (see [46]) are dangerous.<sup>4</sup>

The laws governing "physis" (nature) and those under which human societies are ruled have often been conflated and postulated to be of the same origin. At the dawn of western civilisation Heraclitus held that *lógos*<sup>5</sup> permeates everything, an arrangemen<sup>t</sup> common to all things ye<sup>t</sup> incomprehensible to man ([48,49] and [50]). However, there are crucial differences between these laws. As Aristotle argued, a law is "by nature" if it is justified by appeal to something other than an agreemen<sup>t</sup> or a decision; in contrast, the laws human societies are ruled by are agreed upon in the Agora. While the former laws have been considered "absolute", the latter are clearly conventional. For example, the laws of movement are natural in contrast with the institutional structure of Greek democracy which is the result of human consensus. In Rhetoric, I.13, Aristotle discusses also the compatibility between the natural and the conventional laws. a characteristic of human justice, in contrast to divine justice. Both these laws are different from the concept of "natural law" developed in the Greek (Aristotle) as well as the Roman (Cicero) philosophies. In this philosophical sense a "natural law" asserts certain rights inherent by virtue of *human nature*. Endowed by nature—by God or a transcendent source—such a law can be understood universally through human reason [51]. Two typical laws of Aristotelian "physis" are: (i) Nothing moves unless one pushes it (there must be a 'mover' in order to move it). (ii) Because motion does exist, the above law implies that there must be a self-moved mover, i.e., a 'Prime Mover'. Finally, according to the definition of "natural" found in the Nicomachean Ethics, V.7, God is both a lawgiver for humans and the governor of nature, a view which was inherited by Christianity.
