The quote suggests that among mathematicians who believe in Platonism—the idea that mathematical entities exist independently of human thought—there are few who accept the notion that there might be true mathematical facts that cannot be known. In other words, while many Platonist mathematicians believe that abstract mathematical objects have a real existence outside of our minds, they generally reject the possibility that these truths could remain forever beyond our grasp.
Delving deeper into this statement reveals its philosophical implications for mathematics and knowledge. Abraham Robinson's observation touches on the nature of truth and knowability within the field of mathematics. The idea that some truths might be unknowable challenges the notion that everything in mathematics can eventually be discovered or proven through rigorous methods. This perspective raises questions about the limits of human understanding and the potential existence of truths that are inherently beyond our cognitive reach. It also suggests a tension between the idealistic belief in mathematical Platonism and the practical reality of what we can actually prove or discover.
Abraham Robinson was an influential mathematician known for his work on non-standard analysis, a branch of mathematics that rigorously incorporates infinitesimal quantities, similar to those used by Isaac Newton and Gottfried Wilhelm Leibniz. His insights into mathematical logic and foundational aspects of calculus have had lasting impacts on the field. Through his statement about unknowable truths, Robinson reflects on broader philosophical questions within mathematics, underscoring the discipline's connection to abstract thinking and its inherent mysteries.
