Platonism asserts that abstract mathematical objects, like numbers and sets, possess an objective existence independent of our minds. This view…
Neo-logicism revives the logicist project of grounding mathematics in logic. It addresses criticisms of traditional logicism with new insights and…
Neo-Fregeanism revives Frege's logicist project, aiming to base mathematics on logic. It utilizes Hume's Principle and other axioms to ground…
Mathematical abstractionism posits that mathematical concepts are derived from physical objects and their properties. These entities don't exist independently but…
Logicism is the philosophical view that mathematics is a branch of logic. Proponents believe all mathematical truths can be derived…
A logic designed for higher-order quantification and modalities. It emerged from discussions on the foundations of mathematics by Kreisel and…
Intuitionism is a philosophy of mathematics that questions the existence of the mathematical infinite and the completeness of mathematical truth.…
This argument posits that if mathematical entities are essential for our most successful scientific theories, we should accept their existence.…
Hume's principle states that two collections have the same number of objects if and only if a one-to-one correspondence can…
Frege's theorem establishes that arithmetic is reducible to logic. It demonstrates how basic arithmetic principles can be derived from logical…