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This seminar presentation by Professor Melisa Vivanco from the University of Texas Rio Grande Valley explores the philosophy of natural numbers as part of the Orange County Inland Empire (OCIE) Seminar series in History and Philosophy of Mathematics. Delve into a realist theory of natural numbers that positions them as objectively existing mathematical objects independent of human cognition. Discover how natural numbers are conceptualized as cardinality properties of pluralities rather than sets or aggregates of individual entities. Learn how this philosophical framework provides explanations for arithmetic sentences, their necessity, and their a priori character, while examining connections to language and epistemology. The presentation also contrasts this proposal with other realist theories and addresses Benacerraf's epistemological challenge, suggesting that mathematical and non-mathematical knowledge share homogeneous properties when numbers are properly conceived as properties. The nearly two-hour talk was hosted at Chapman University's Keck Center within Schmid College of Science and Technology.
