“Mathematical Realism vs Mathematical Anti-Realism” Proposal Haley Pavlis and Kristin Rawlins What is mathematical realism? Mathematical realism is the idea that mathematical entities are not invented, they are discovered. Meaning, mathematical entities are independent from the human mind. What are the specific forms of mathematical realism? Platonism Mathematical Platonism is the most common form of mathematical realism, and shares an almost identical definition. The three most important pieces of mathematical Platonism are the following: existence, abstractness, and independence. Similarly to mathematical realism, mathematical Platonism considers the belief that mathematical entities are independent from humans to be true; they are independent from our thought and our language. In addition to this, it is assumed that there are mathematical objects, the piece of existence, and these objects are abstract, the piece of abstractness. Mathematically existence can be symbolized as “∃xMx”; here the “Mx” means “x is a mathematical object”. Therefore, the statements claims, “there exists an x that is a mathematical object” which is true for any sets studied by pure mathematics, which is mathematics that studies abstract concepts. Mathematical objects are considered independent on the basis that even without our intelligence, language, or thought, …show more content…
This philosophy supports the idea that all knowledge is acquired through experience, also, mathematics is essential to all empirical sciences. For example, because physicists must use numbers and calculations to make any legitimate explanations it is validated that numbers must exist. This can be further simplified by stating the empiricism thesis, “We have no source of knowledge in S or for the concepts we use in S other than sense experience.” (Stanford