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2. Claim (philosophy) - Wikipedia

   en.wikipedia.org/wiki/Claim_(philosophy)

   A claim is a substantive statement about a thing, such as an idea, event, individual, or belief. It's truth or falsity is open to debate. It's truth or falsity is open to debate. Arguments or beliefs may be offered in support, and criticisms and challenges of affirming contentions may be offered in rebuttal.

3. Intuitionism - Wikipedia

   en.wikipedia.org/wiki/Intuitionism

   The fundamental distinguishing characteristic of intuitionism is its interpretation of what it means for a mathematical statement to be true. In Brouwer's original intuitionism, the truth of a mathematical statement is a subjective claim: a mathematical statement corresponds to a mental construction, and a mathematician can assert the truth of a statement only by verifying the validity of that ...

4. Definitions of mathematics - Wikipedia

   en.wikipedia.org/wiki/Definitions_of_mathematics

   The preceding kinds of definitions, which had prevailed since Aristotle's time, [4] were abandoned in the 19th century as new branches of mathematics were developed, which bore no obvious relation to measurement or the physical world, such as group theory, projective geometry, [3] and non-Euclidean geometry.

5. Philosophy of mathematics - Wikipedia

   en.wikipedia.org/wiki/Philosophy_of_mathematics

   Philosophy of mathematics is the branch of philosophy that deals with the nature of mathematics and its relationship to other areas of philosophy, particularly epistemology and metaphysics. Central questions posed include whether or not mathematical objects are purely abstract entities or are in some way concrete, and in what the relationship ...

6. Formalism (philosophy of mathematics) - Wikipedia

   en.wikipedia.org/wiki/Formalism_(philosophy_of...

   David Hilbert. A major figure of formalism was David Hilbert, whose program was intended to be a complete and consistent axiomatization of all of mathematics. [8] Hilbert aimed to show the consistency of mathematical systems from the assumption that the "finitary arithmetic" (a subsystem of the usual arithmetic of the positive integers, chosen to be philosophically uncontroversial) was ...

7. Principles and Standards for School Mathematics - Wikipedia

   en.wikipedia.org/wiki/Principles_and_Standards...

   The Principles and Standards for School Mathematics was developed by the NCTM. The NCTM's stated intent was to improve mathematics education. The contents were based on surveys of existing curriculum materials, curricula and policies from many countries, educational research publications, and government agencies such as the U.S. National Science Foundation. [3]

8. Judgment (mathematical logic) - Wikipedia

   en.wikipedia.org/wiki/Judgment_(mathematical_logic)

   For example, typical judgments in first-order logic would be that a string is a well-formed formula, or that a proposition is true. Similarly, a judgment may assert the occurrence of a free variable in an expression of the object language, or the provability of a proposition .

9. Premise - Wikipedia

   en.wikipedia.org/wiki/Premise

   An example of this is the use of the rules of inference found within symbolic logic. Aristotle held that any logical argument could be reduced to two premises and a conclusion. [2] Premises are sometimes left unstated, in which case, they are called missing premises, for example: Socrates is mortal because all men are mortal.