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Another Book to Cross Off One's list

Julian Friedlander, the editor of Doing Well and Good: The Human Face of the New Capitalism, a visiting Professor of Ethics at a business school, is telling the punters at the New York Times  that

  • we [philosophers] should underscore the fact that various disciplines we ordinarily treat as science are at least as — if not more —philosophical than scientific. Take for example mathematics, theoretical physics, psychology and economics. These are predominately rational conceptual disciplines. That is, they are not chiefly reliant on empirical observation. For unlike science, they may be conducted while sitting in an armchair with eyes closed.

but they yield objective knowledge; therefore philosophy doesn't have to be science either. Thus Friedlander.  

Mathematics consists of analytic statements; insofar as it is mathematics, it says nothing about the observable world, and what it says about itself  depends on an arbitrary choice of axioms . (Whether 5+7 = 12 depends on which field of mathematics one is working in; in the ring Z/(11), 5+7 = 1.) Of course, it can be done with the eyes shut.  Insofar as theoretical physics is analytic - insofar as it merely derives consequences of  some given set of assumptions - it doesn't have anything to do with the real world either ; when it interacts with the real world, through  comparison with experimental physics, the physicist must open his eyes and read the physical journals. This distinction goes back to David Hilbert and Ernst Mach, a century ago; it would be nice if our dogmatists would catch up with the literature. 

The sort of psychology and economics that can be done with closed eyes aren't science at all; a priori claims about the observable world are prejudice and superstition. (Introspective psychology, which is observable with closed eyes, is not prejudice; but it is neither objective nor verifiable, so not science either.) We get, therefore, extra helpings of them in an election year.

It's always nice to know which books one does not have to read.


Jul. 7th, 2012 05:07 am (UTC)
The analytic-synthetic dichotomy has been with us since Kant (and Hume's relations of ideas and matters of fact are practically the same idea), and is the basis of logical positivist philosophy of science. But I don't think it's valid. For a long time I've thought of analyticity as a kind of myth of the philosophers.

The formal manipulation of uninterpreted symbol strings may be useful occasionally as a technique for checking the validity of arguments. But I don't think it has much to do with actual human cognition. The human nervous system didn't evolve to manipulate abstract terms by formal rules, but to steer the human body around the physical (and social) environment. So I think that all actual conceptual systems—even those of mathematics—originate in perception of the physical world. Of course that entails rejection of the Hilbertian program for formalist mathematics, but then I've leaned toward constructivism ever since a memorable lecture by Errett Bishop, who was one of my math professors back around 1971-1973.
Jul. 7th, 2012 04:26 pm (UTC)
The origin of mathematical questions is part of the history of mathematics - a different discipline. The evolutionary pre-adaption for the art of mathematics is also a different discipline; just so, the reason that several species of primate like to splash paint around is not part of the art of painting. Causes may equal effects; they are not identical.

I prefer not to adopt the narrow and arbitrary tenents of constructivism; I am not convinced it is talking about anything. "We must know; we shall know."
Jul. 7th, 2012 07:35 pm (UTC)
Ironically, I am convinced that constructivism is talking about something; I am not convinced that either formalist mathematics or the analytic statements postulated by logical positivism are talking about anything.