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Explore an innovative internal approach to understanding meaning in mathematical language through this 44-minute conference talk. Discover how mathematical objects and structures can be organized into a nested hierarchy where each level internalizes the level below, starting with the fundamental hierarchy of n-categories including proof, truth, truth values, sets, and categories. Learn about the framework's attempt to internalize the process of definition itself at the level of truth values, effectively blurring the traditional boundaries between syntax and semantics. Examine how this approach challenges the notion of primitive terms by defining each object as an element of an object at the next hierarchical level, built inductively from lower levels. Understand the philosophical implications of how meaning can emerge internally from the act of definition itself, and consider how this framework addresses the syntax-semantics and analytic-synthetic dichotomies in mathematical discourse. Engage with the mathematical and philosophical questions raised by this perspective on the internal construction of meaning in mathematics.
