Question

The demarcation problem in the context of philosophy is usually used to mean the demarcation problem of science, the problem of separating science from non-science. However, what about the demarcation problem of mathematics, that is, the problem of separating mathematics from non-mathematics? Has any philosopher talked about that? And if so, can I see some references for their discussion? I am particularly interested in the question of how to decide whether some statement is mathematical or not, and also how to decide whether some entity is mathematical or not. For instance, most people agree that the number 3 is a mathematical entity, and that a wooden desk is not a mathematical entity, but how exactly does one demarcate the boundaries of math?

Answer 1

The demarcation problem in mathematics refers to the challenge of distinguishing between mathematical and non-mathematical entities and statements. Philosophers such as Imre Lakatos and Hilary Putnam have written about this problem and proposed various criteria for identifying mathematical entities.

Step-by-step explanation:

The demarcation problem in mathematics, similar to the demarcation problem in science, refers to the challenge of distinguishing between mathematical and non-mathematical entities and statements. While there is ongoing debate among philosophers, several scholars have discussed the demarcation problem of mathematics and proposed various criteria for identifying what is considered mathematical.

One philosopher who has written extensively on this topic is Imre Lakatos. In his book 'Proofs and Refutations,' Lakatos examines the process of mathematical discovery and argues that the boundaries of mathematics are not fixed but evolve over time through the exploration of mathematical proofs and counterexamples.

Another philosopher who has addressed the demarcation problem of mathematics is Hilary Putnam. In 'Mathematics, Matter, and Method,' Putnam suggests that mathematical entities have a certain level of indispensability and that their existence can be justified based on their explanatory power in scientific theories.