Counting Arithmetic - A New Foundational Approach

Explore a seminar on "Counting Arithmetic" presented by Dr. John Mumma from Cal State San Bernardino as part of the Orange County Inland Empire (OCIE) Seminar series in History and Philosophy of Mathematics. Delve into a new foundational approach to arithmetic that places counting at its core, challenging the traditional perspectives of Dedekind and Frege. Examine an alternative account of counting that diverges from the standard one-to-one correspondence model. Investigate the formal details of a first-order theory of arithmetic developed from this novel approach, known as CA (counting arithmetic). Learn how CA interprets arithmetical equations as equivalences rather than identities and achieves generality through the pigeonhole principle instead of mathematical induction. Gain insights into this innovative perspective on the foundations of arithmetic during this 1 hour and 55 minute presentation hosted by Chapman University's Schmid College of Science and Technology.