Hilary Putnam: Real

Hilary Putnam was American philosopher. Explore interesting quotes on real.
Hilary Putnam: 16   quotes 1   like

“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.”

Hilary Putnam

in What is Mathematics, in [Hilary Putnam, Mathematics, matter, and method, Cambridge University Press, 1979, 0521295505, 60]

World , Law , Mathematics , Nature

“The real significance of the Russell paradox, from the standpoint of the modal-logic picture, is this: it shows that no concrete structure can be a standard model for the naive conception of the totality of all sets; for any concrete structure has a possible extension that contains more 'sets.'”

Hilary Putnam

"Mathematics without foundations"
Source: Philosophical Papers Volume 1: Mathematics, Matter, and Method (1975, 1979)
Context: (If we identify sets with the points that represent them in the various possible concrete structures, we might say: it is not possible for all possible sets to exist in any one world!) Yet set theory does not become impossible. Rather, set theory becomes the study of what must hold in, e.g. any standard model for Zermelo set theory.

“To require that all of these must be reducible to a single version is to make the mistake of supposing that 'Which are the real objects?' is a question that makes sense independently of our choice of concepts.”

Hilary Putnam

Lecture I: Is There Still Anything to Say about Reality and Truth?
The Many Faces of Realism (1987)

Question , Sense