Maths in Philosophy — Alexander Douglas

Alexander Douglas mounts a defense of rationalism against empiricism. 

Backgrounder to understanding the issues here. The Western intellectual tradition arose in ancient Greece with dissatisfaction with mythological explanation, the favorite form of explanation in the very ancient world — god and all that. The first "philosophers" in the sense of speculation based on reason attempted to provide a "rational" explanation of the world. The Greek terms are logikos and orthologikos (ortho signifies right, correct, straight), obviously the etymological root of "logic" in English. The corresponding Latin term is ratio, meaning "reason" as the faculty of understanding, or knowing in terms of universals rather than particulars. "Rational" in Latin is rationis ("of reason), rationalis, and rationalibus (akin to English "reasonable"). Thus, "rationalism" as an approach to gaining knowledge. 

Aristotle would extend this approach in his Metaphysics to causal explanation. This became the basis of the Western intellectual tradition. Aristotle also favored relying on observation with the senses where appropriate, e.g., the proto-science that was then developing. But Aristotle emphasized the rational over sense observation, and his approach would later be seen as an obstacle to the development and acceptance of scientific method owing to the influence of his philosophy in the Church after Aquinas. Plato was the other influence through Augustine and this was an even greater obstacle to the acceptance of science. Scientists have not forgotten this. 

The advantage of the rational approach at the outset was that it is not mythological, that is, explanation by story, i.e, allegory and analogy, but by reasoning based on principles that are, like the gods, immortal. But unlike the gods, these principles are unchanging. This was the great contribution of Pythagoras and the Pythagoreans in their emphasis on mathematics, as well as Plato's in the Academy. The Western intellectual tradition began as math-based. Aristotle extended this to logic in his Organon as a prerequisite to serious study.

The other end of the knowledge spectrum from the universal and unchanging is empiricism, which is based on observation and mediated by sense data, hence particular and subject to change. Sense data provide only secondary knowledge through phenomena (appearance) rather than being immediate (unmediated) knowledge of objects and events. Moreover, sense data are unreliable, unlike the objects of reason, numbers and concepts. So reason is preferable to sense observation.

Why is this relevant to economics? Because most conventional economists are rationalists that proceed on the basis of intuitive discovery for assumption identification and rely chiefly on formal argument using mathematical models. In other words, they are behaving like speculative philosophers instead of scientists that are guided by data in addition to mathematics, with observation having the final say.

As a philosopher I am a rationalist, and in matters where scientific method is applicable, I prefer to use it as most appropriate. The challenge is determining when those condition apply. Most of the enduring question are enduring because so far no way to apply scientific method to them has been devised in a way that compelling of acceptance.

The issue is fundamentally about criteria and how to identify and apply them. 

Returning to Alexander Douglas's post. I regard most of these issues as pseudo-problems. Philosophers have recognized for a long time that the chief procedural method of philosophy is logic and logic can be formalized. Not everything of interest philosophically is quantitive or can expressed quantitively, so mathematics is of limited use. That is not the issue. The is and has been the balance between rational and empirical in gaining true knowledge. Empiricism reduces the criteria to observational (sense data) and that excludes many if not most of the enduring issues.

Why is this significant? Because macroeconomics is policy science and policy presumes values, which are essentially qualitative rather than quantitate.

Alexander Douglas at Medium
Maths in Philosophy
Alexander Douglas | Lecturer in Philosophy, University of St. Andrews