The physicist who states a law of nature with the aid of a mathematical formula is abstracting a real feature of a real material world, even if he has to speak of numbers, vectors, tensors, state-functions, or whatever to make the abstraction.
in What is Mathematics, in Hilary Putnam (1979). Mathematics, matter, and method. Cambridge University Press. p. 60. ISBN 0521295505.
No sane person should believe that something is 'subjective' merely because it cannot be settled beyond controversy.Hilary Putnam
[Oddly enough, Putnam believes part of the attraction of some of these formalisms is their obscurity]. "I think part of the appeal of mathematical logic is that the formulas look mysterious - you write backward Es!"Hilary Putnam
It was Rudolf Carnap’s dream for the last three decades of his life to show that science proceeds by a formal syntactic method; today no one to my knowledge holds out any hope for that project.Hilary Putnam