Constructivism (philosophy of mathematics)

In the philosophy of mathematics, intuitionism, or neointuitionism (opposed to preintuitionism), is an approach where mathematics is considered to be purely the result of the constructive mental activity of humans rather than the discovery of fundamental principles claimed to exist in an objective reality. That is, logic and mathematics are not considered analytic activities wherein deep properties of objective reality are revealed and applied, but are instead considered the application of internally consistent methods used to realize more complex mental constructs, regardless of their possibl

various systems of symbolic logic

mathematical viewpoint that existence proofs must be constructive

Finitism is a philosophy of mathematics that accepts the existence only of finite mathematical objects. It is best understood in comparison to the mainstream philosophy of mathematics where infinite mathematical objects (e.g., infinite sets) are accepted as existing.

bounded lattice that models intuitionistic propositional logic

method of proof that demonstrates the existence of a mathematical object by creating or providing a method for creating the object

lemma in infinite graph theory

any constructive definition of the real numbers

alternative foundation of mathematics

interpretation of intuitionistic logic

in constructive mathematics and computability theory, the axiom that given a decidable predicate on natural numbers, if it cannot be false for all numbers, then it is true for some number

In the philosophy of mathematics, ultrafinitism, ultraintuitionism, strict formalism, strict finitism, actualism, predicativism, and strong finitism are various philosophies of mathematics with aspects of finitism and intuitionism. Common to these philosophies is their objection to the totality of number theoretic functions like exponentiation over natural numbers.

function gauging the uniform continuity of a function

In mathematical logic, realizability is a collection of methods in proof theory used to study constructive proofs and extract additional information from them. Formulas from a formal theory are "realized" by objects, known as "realizers", in a way that knowledge of the realizer gives knowledge about the truth of the formula. There are many variations of realizability; exactly which class of formulas is studied and which objects are realizers differ from one variation to another.

axiomatization of arithmetic