The enigma of the natural order

In 2019 a book I wrote was published and distributed with the Spanish newspaper El País in a collection dedicated to the popularization of mathematics. The translation into English of my book title is Everything is Number: Is Reality Mathematical?

I addressed the problem of whether mathematical ideas correspond to an external reality, or if on the contrary they are arbitrary and vary with our current mentality. In other words, the question is whether mathematics is discovered, or invented. In one of the posts in this blog I dealt with this issue in relation to the real existence (or not) of the digits of number π (pi).

In the last chapter of that book I addressed a related issue: whether scientific theories, especially those proposed by physicists, are true (in the sense that they represent an underlying reality independent of us), or if are they mental or social constructs unrelated to a reality that could be unknowable (such as Kant's noumena) or even non-existent. I suppose my readers won't be surprised if I say that my personal position is clearly realistic, as is that of many physicists, while supporters of the anti-realist hypothesis tend to be predominantly philosophers.

In this context, we must welcome the appearance of a new book by Francisco José Soler Gil, a doctor of philosophy specialized in the philosophy of physics, with whom I have often collaborated, who defends in this book his clearly realistic position in this debate. I have used the English translation of the Spanish title of the book (The enigma of the natural order) to title this post. Of the two parts of the book, I am going to comment on the second, which reviews the classical realist analysis of the natural order and its modern alternatives, which are totally or partially anti-realist.

The classical analysis of the natural order can be defined as follows, in the words of Soler Gil:

We find, therefore, a line of reflection on the experience of the security, stability and regularity of natural dynamisms, which starts from the generalization and mathematical interpretation... of this experience of natural patterns in the Pythagorean idea of ​​"order" ("cosmos"); which is then developed by associating that order with the idea of ​​design of a primordial Mind, in the thought of Socrates and Plato; and that it evolves from there towards modern scientific activity through the legislative approach to order developed in medieval thought. Seeking the mathematical laws of nature promulgated by God will therefore become the objective of scientific activity... We can call this line of reflection the "classical analysis of the natural order."

Hillary Putnam

Seen this way, it is not surprising that the nineteenth-century materialist and atheistic philosophy, which has reached a certain dominance, has reacted by directly opposing the classical analysis of the natural order, resorting to anti-realist options such as the following:

1. Scientism, according to which the natural order arises spontaneously by natural selection, which would apply, not just to biological evolution, but also to cosmology. Unfortunately for this position, at the end of the 20th century it was discovered that the whole of this building of the natural order rests on some laws of physics and some constants and parameters associated with these laws, which support it thanks to a series of very precise balances between the operating forces. For this reason, perhaps never in history have we been further from understanding how the order of nature could arise spontaneously than today. For, as we know it in more detail, the less spontaneous it seems.
2. Social constructivism, which asserts that scientific theories [are] cultural constructions that arise from negotiations between various academic groups... [and] cannot reveal anything similar to an "objective structure" or a "real structure" of the world. According to this position, The history of science would not be... a progressive unveiling of the natural order, but... a series of stories about nature, which codify the balances of interests between the different social groups that participate... in the establishment of the dominant narrative at a given moment. Which... means that there is no true progress in the knowledge of nature, but rather that the different theories... succeed each other as a reflection of changes in the balance between the social groups that participate in the scientific task. But this would lead us to a Ptolemaic-style way of doing science: saving the theory at all costs by introducing the necessary modifications (such as epicycles and deferents). A way of doing science opposite to that of Copernicus, Kepler, Galileo, Newton and Einstein.
3. Hilary Putnam's internal realism, an apparently realistic position, but with an anti-realist background, about a part of which I spoke in three consecutive posts on this blog, the first of which is Abduction and the no-miracles argument.
4. Larry Laudan's pessimistic meta-induction, which I spoke about in the second of the three posts mentioned.

After a detailed analysis of all these positions, Soler's conclusion is that the objective natural order reappears, again and again, behind all attempts to explain it or to cancel it... And what is thus revealed is... a new enigmatic facet in the very enigmatic question of the natural order: the impossibility of seeing it from outside. The impossibility of not presupposing it in one way or another, whenever we want to explain it away.

The same post in Spanish

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Manuel Alfonseca