The Fragility of Knowledge

A recent addition to the collection of essays at “Einstein’s Errors” relies mainly on Christoph von Mettenheim’s Popper versus Einstein. One of Mettenheim’s key witnesses for the prosecution of Einstein’s special theory of relativity (STR) is Alfred Tarski, a Polish-born logician and mathematician. According to Mettenheim, Tarski showed

that all the axioms of geometry [upon which STR is built] are in fact nominalistic definitions, and therefore have nothing to do with truth, but only with expedience. [p. 86]


Tarski has demonstrated that logical and mathematical inferences can never yield an increase of empirical information because they are based on nominalistic definitions of the most simple terms of our language. We ourselves give them their meaning and cannot,therefore, get out of them anything but what we ourselves have put into them. They are tautological in the sense that any information contained in the conclusion must also have been contained in the premises. This is why logic and mathematics alone can never lead to scientific discoveries. [p. 100]

Mettenheim refers also to Alfred North Whitehead, a great English mathematician and philosopher who preceded Tarski. I am reading Whitehead’s Science and the Modern World thanks to my son, who recently wrote about it. I had heretofore only encountered the book in bits and snatches. I will have more to say about it in future posts. For now, I am content to quote this relevant passage, which presages Tarski’s theme and goes beyond it:

Thought is abstract; and the the intolerant use of abstractions is the major vice of the intellect. this vice is not wholly corrected by the recurrence to concrete experience. For after all, you need only attend to those aspects of your concrete experience which lie within some limited scheme. There are two methods for the purification of ideas. One of them is dispassionate observation by means of the bodily senses. But observation is selection. [p. 18]

More to come.