Einfluss

 

 

The Principia Mathematica by B. Russell and A. Whitehead (1913) is often put forward as a seminal work in the history of philosophy. It purported to show that mathematics could be derived from logic by doing so. The eventual three volume work did in fact achieve quite a bit, but the authors were visibly 'exhausted' with the endeavour and gave up short of achieving the whole project. Criticism, at the time, was partly directed to the formal apsects of the work, today stated as that it failed to follow the rules for designing a formal system. The overall evaluation was that it was cumbersome. The proof for 1+1 = 2 shows up in volume 2.

It is tempting to let this ride as it is historically far from us but there are aspects of the question which are troubling. For one, the title. Newton 's famous work introducing celestial mechanics was of that title: Philosophiae Naturalis Principia Mathematica (1687). This is usually translated as Mathematical Principles of Natural Philosophy. But the latin form is dative case, and could as easily be translated to the Mathematical Principles embedded in Natural Philosophy, or underpinning, or essential to, or a myriad of variants on the same idea. This is where the door was openend to natural science as mathematics.

So by 1912 Russell and Whitehead mean business, examining the mathematical tool itself as logic, short of making the actual claim. The second aspect worthy of note is what is coming down to us as the central error of the work: the little t on the side, indicating that the following is true. Now it is true that PM is the work of two people, and that Whitehead is a mathematician while Russell is not. Indeed it is a feature of language to come packing with its own claim to truth, as that infamous Snow is White from discussions on Tarki's formalism. This is why Tarki's work is known as a semantic theory of truth.

To those of the Vienna Circle who were in admiration of the work, Russel was an Einfluss, an influence, a fellow traveller. They felt PM might be wrong, but certainly not wrong-headed.