"To say that mathematics in general has been reduced to logic hints at some new firming up of mathematics at its foundations. This is misleading. Set theory is less settled and more conjectural than the classical mathematical superstructure than can be founded upon it." (Willard v O Quine," Elementary Logic", 1941)
"We must not leap to the fatalistic conclusion that we are stuck with the conceptual scheme that we grew up in. We can change it, bit by bit, plank by plank, though meanwhile there is nothing to carry us along but the evolving conceptual scheme itself. The philosopher's task was well compared by Neurath to that of a mariner who must rebuild his ship on the open sea." (Willard v O Quine, "The Journal of Philosophy", 1950)
"Meaning is what essence becomes when it is divorced from the object of reference and wedded to the word." (Wïllard v O Quine, "Two dogmas of empiricism" , Philosophical Review Vol. 60, 1951)
"As an empiricist I continue to think of the conceptual scheme of science as a tool, ultimately, for predicting future experience in the light of past experience. Physical objects are conceptually imported into the situation as convenient intermediaries - not by definition in terms of experience, but simply as irreducible posits comparable, epistemologically, to the gods of Homer."(Willard v O Quine, "From a Logical Point of View", 1953)
"Our acceptance of an ontology is, I think, similar in principle to our acceptance of a scientific theory, say a system of physics; we adopt, at least insofar as we are reasonable, the simplest conceptual scheme into which the disordered fragments of raw experience can be fitted and arranged." (Willard v O Quine, "From a Logical Point of View", 1953)
"Science is not a substitute for common sense, but an extension of it." (Willard v O Quine, "The Scope and Language of Science", 1954)
"It is one of the consolations of philosophy that the benefit of showing how to dispense with a concept does not hinge on dispensing with it." (Willard v O Quine, "Word and Object", 1960)
"Scientific method is the way to truth, but it affords, even in principle, no unique definition of truth. Any so-called pragmatic definition of truth is doomed to failure equally." (Willard v O Quine, "Word and Object", 1960)
"It makes no sense to say what the objects of a theory are, beyond saying how to interpret or reinterpret that theory in another." (Willard v O Quine, "Ontological Relativity and Other Essays", 1969)
"At root what is needed for scientific inquiry is just receptivity to data, skill in reasoning, and yearning for truth. Admittedly, ingenuity can help too." (Willard v O Quine, "The Web of Belief", 1970)
"Implication is thus the very texture of our web of belief, and logic is the theory that traces it." (Willard v O Quine, "The Web of Belief", 1970)
"It is within science itself, and not in some prior philosophy, that reality is to be identified and described." (Willard v O Quine, "Theories and Things", 1981)
"Physics investigates the essential nature of the world, and biology describes a local bump. Psychology, human psychology, describes a bump on the bump" (Willard v O Quine, "Theories and Things", 1981)
"It is the tension between the scientist's laws and his own attempted breaches of them that powers the engines of science and makes it forge ahead." (Willard v O Quine, "Quiddities" , 1987)
Quotes and Resources Related to Mathematics, (Mathematical) Sciences and Mathematicians
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