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The belief that mathematical entities exist, but their existence is dependent upon physical objects and their properties.

A theory that focuses on the positions that elements occupy within a structure over the nature of the elements themselves.

An argument claiming that since mathematical entities are indispensable to the best scientific theories, they must be accepted as real.

Numbers that are greater than all finite numbers, often discussed in the context of set theory and the work of Georg Cantor.

The philosophical doctrine that mathematics can be reduced to logic and that all mathematical truths are logical truths.

A philosophy of mathematics that holds that mathematics is a creation of the human mind and that mathematical truths are derived from intuition.

A view that mathematics is not about numbers and other abstract objects, but rather about the manipulation of symbols according to prescribed formal rules.

A speculative idea that the universe itself is mathematical in nature, and that every physical object is an abstract mathematical structure.

The philosophical position that abstract mathematical objects do not exist in any sense outside of human language and thought.

A theory that mathematical knowledge is derived from sensory experience and is not innate or a priori.

The view that sets can be constructed in a step-by-step process, starting with the most basic sets and building up to more complex ones.

The perspective that mathematical entities do not exist, and mathematical statements are akin to fiction.

The view that mathematical entities are abstract, non-physical objects that exist in a non-spatial, non-temporal realm.

The phenomenon that mathematics is unexpectedly effective in describing and predicting the physical world.