Mathematics Is About the World by Robert Knapp

The question of whether and  how mathematics connects with reality is an  important one which has occupied the attention of philosophers intermittently since the time of the pre-Socratics.   In his book Mathematics Is about the World, mathematician Robert Knapp attempts to answer it.

Along the way he makes some good points, particularly in his criticism. He is right that the “official” view of mathematics as an exercise in the formal analysis of undefined objects and  relationships  according to various lists of postulates and having no necessary connection to real things is  both intellectually faulty and operationally dishonest (the latter because mathematicians usually do not really  believe it).  He is right that the answer is not a return to some Pythagorean or Platonic notions of numbers as a higher or determinative sort of reality above the real world.   He is right  that the fact mathematics can be used to understand and predict things and events is not a lucky accident.  The sections on context determining needed, required, or possible precision are interesting as are some of his thoughts on Euclid and Greek mathematics. 

His solution to the main question is to tie mathematics to reality on the basis of objectivist epistemology,   in particular  on Rand’s theory of concepts and their formation. The book goes through a hypothetical development of mathematical ideas in geometry, analysis, algebra and other areas in terms of the integration/measurement omission process of that theory. The work is extensive  and well thought out, but I believe it is a case of someone using the wrong  tool. There are simpler, more thorough and  to the point, and to me better and more convincing ways to establish and describe  the connection between mathematical ideas and reality.  

However, it is surely worthwhile to stimulate people to think about the question and to look at  the standard  answers from the textbooks critically.  To the extent it would do that, the book might  be worth reading whether or not the reader had an interest in objectivist epistemology.  But it is not a book I would recommend to someone wanting to get started thinking about its main topic.