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.

Pierre Duhem: Realist or anti-realist?

Pierre Duhem

Pierre Duhem (1861-1916) can be considered one of the last nineteenth-century physicists. Specialist in Thermodynamics, the branch of physics that dominated the second half of the nineteenth century, introduced the idea of the ​​chemical potential at the same time as William Gibbs, expressed in the Gibbs-Duhem equation, which connects the chemical potential with magnitudes such as the volume, pressure, entropy and temperature of a chemical mixture. He is considered one of the creators of physical chemistry and was nominated twice for the Nobel Prize in Physics.

In his scientific work, Duhem confronted Marcellin Berthelot, whose principle of maximum work he opposed. This led to his doctoral thesis being rejected, and he was denied a teaching position at the University of Paris. Duhem was finally shown to be right, as Berthelot’s principle is not generally applicable, for it has many exceptions.

Anti-realist answers to the no-miracles argument

Hilary Putnam

The previous post described the no-miracles argument, proposed by Hilary Putnam. The article ended thus:

What do anti-realists answer to this argument? Are they convinced?

I guess the readers have deduced that the answer to the second question must be negative, otherwise the debate between realism and anti-realism would have ended. Let us look, therefore, at the answer to the first question. Faced with the abductive argument of no-miracles, anti-realists answer in two different ways:

1.      Bas van Fraassen is an anti-realist American philosopher who criticizes Putnam’s argument, arguing that scientific theories are successful because unsuccessful theories have been eliminated by natural selection (i.e. scientists have ruled them out). Therefore, asking why science is successful is similar to asking why basketball players are tall: because they have been selected. Let us see how Fraassen describes his theory, which is called constructive empiricism:

Abduction and the no-miracles argument

The Cheshire cat,
famous invisible cat

In an earlier post in this blog, I explained with an example the mode of reasoning based on abduction. Although not as strong as deduction and induction, abduction reaches high degrees of confidence in fields such as history, art criticism and others, less scientific than mathematics or natural science.

In another post published in March 2016, I described the fallacy of the invisible cat, which confuses a sufficient condition with a necessary condition for something to happen. This situation occurs when there are several possible causes that may have given rise to the same phenomenon.

In some cases, if we apply abduction to a situation where the fallacy of the invisible cat could occur, a conclusion can be reached. Think of the example I proposed to describe this fallacy: