The essay is not about formal vs. informal systems. In fact your example illustrates the very point that Arnold is making. In "F=ma" the symbols actually map-to

The essay is not about formal vs. informal systems. In fact your example illustrates the very point that Arnold is making. In "F=ma" the symbols actually map-to something in the real world. The "domain of discourse/interpretation" for the symbols is well known and there is no confusion on what the equation stands for. This article, Why “F = ma” is the most important equation in physics explains the nuances of the above equation - https://bigthink.com/starts-with-a-bang/most-important-equation-physics/ https://bigthink.com/starts-with-a-bang/most-important-equat... As the article points out it might be tempting to think of the above as a special case of the equation of a straight line (i.e. y=mx+c) but that would not be correct. Symbolic logic is concerned only with the "forms" of the argument and inference (hence the name "Formal" system) and not their meaning/context. It is the latter which brings mathematics "alive" else as the GEB book shows we are just playing games.