Scientia Salon recently published my article advocating that mathematics is best regarded as a part of science. In reply to “scientism week”, Massimo Pigliucci wrote an article criticising “the return of radical empiricism”. The collision of “scientism week” with “anti-scientism week” generated a lot of energy and comments!
Massimo Pigliucci’s article is well worth reading, being a clear exposition of the relevant ideas. He traces the issues back to Hume’s famous fork, in which Hume declares that:
All the objects of human reason or enquiry may naturally be divided into two kinds, to wit, Relations of Ideas, and Matters of fact and real existence.
The “relations of ideas” category is taken to include mathematics and logic, where knowledge is “discoverable by the mere operation of thought”, while the “matters of fact” category contains science, where knowledge derives from empirical data.
Kant rejected Hume’s empiricism and sought to establish the primacy of reason. He adopted the term “a priori” for knowledge that does not derive from experience, in contrast to “a posteriori” knowledge which does. A related concept is that of “analytic” statements, which follow from the definitions of the terms, contrasting with “synthetic” statements that describe how the world is.
This notion of a fundamental epistemological divide holds today, and is at the heart of resistance to the idea that mathematics, logic and science are a unified whole.
In reading Pigliucci’s article I agree with much of what he says, but, to me, he seems to miss the main arguments for the essential unity of the different domains of knowledge. I will thus outline how I see the roots of empiricism, and then consider the supposed divide between knowledge “from reasoning” versus knowledge “from observation”. Continue reading