This essay looks at the logicist idea that math can be made into pure logic. It pays special attention to strong criticisms from intuitionism. First, it splits logicism into two types. Strong logicism wants to turn all math into logic rules. Weak logicism, or neo-logicism, tries a smaller goal. It uses ideas like Hume's Principle to handle only part of math. Then, the essay explains the intuitionist attack. Thinkers like Brouwer and Heyting say math is not about formal rules. Instead, it is about building ideas in the mind. This view says common logic does not always work in math. It pushes for proofs that build things step by step. It also prefers endless possibilities over finished endless sets. The essay ends by saying neo-logicism gives a smart answer. It gets math from logic ideas. But intuitionism shows big problems for logicism. A full turn of math into logic is not possible without looking deeper into what math truth and practice really are.
Yule Yan (Thu,) studied this question.