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Philosophy of mathematics is the branch of philosophy that deals with the nature of mathematics and its relationship with other human activities. Major themes that are dealt with in philosophy of mathematics include: Reality: The question is whether mathematics is a pure product of human mind or whether it has some reality by itself. Logic and ...
Although Popper mentions mathematics and logic, other writers focus on distinguishing science from metaphysics. A prominent question in meta-philosophy is that of whether or not philosophical progress occurs and more so, whether such progress in philosophy is even possible.
An Introduction to the Philosophy of Mathematics is a 2012 textbook on the philosophy of mathematics by Mark Colyvan. It has a focus on issues in contemporary philosophy , such as the mathematical realism – anti-realism debate and the philosophical significance of mathematical practice, and largely skips over historical debates.
This is a list of mathematical logic topics. For traditional syllogistic logic, see the list of topics in logic . See also the list of computability and complexity topics for more theory of algorithms .
In classical real analysis, one way to define a real number is as an equivalence class of Cauchy sequences of rational numbers.. In constructive mathematics, one way to construct a real number is as a function ƒ that takes a positive integer and outputs a rational ƒ(n), together with a function g that takes a positive integer n and outputs a positive integer g(n) such that
During Middle Ages, Euclid's Elements stood as a perfectly solid foundation for mathematics, and philosophy of mathematics concentrated on the ontological status of mathematical concepts; the question was whether they exist independently of perception or within the mind only (conceptualism); or even whether they are simply names of collection ...
This is a list of important publications in philosophy, organized by field. The publications on this list are regarded as important because they have served or are serving as one or more of the following roles: Foundation – A publication whose ideas would go on to be the foundation of a topic or field within philosophy.
Number theory is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions. German mathematician Carl Friedrich Gauss said, "Mathematics is the queen of the sciences—and number theory is the queen of mathematics." Number theory also studies the natural, or whole, numbers.