Appealing to Intuitions - The Necessity and Limitations in Mathematics and Ethics

Explore the complex role of intuitions in human reasoning and decision-making in this thought-provoking lecture by Rebecca Goldstein, Miller Scholar at the Santa Fe Institute. Delve into the philosophical and mathematical challenges surrounding intuitions, from their variability between individuals to their potential to lead us astray. Examine historical attempts to formalize mathematics without relying on intuitions, and discover how Gödel's Incompleteness Theorems demonstrate the impossibility of eliminating them entirely. Investigate the implications of intuitions across various fields, including epistemology, psychology, ethics, and the nature of time. Analyze paradoxes in set theory, non-Euclidean geometry, and formal systems to gain a deeper understanding of the limits and necessities of intuitive reasoning. Engage with concepts such as the Moral Sense Test, free will, and determinism to challenge your own intuitions and expand your perspective on human cognition and decision-making processes.

Introduction
Intuition of a proposition
Epistemology
Problems with Intuitions
Religious Wars
Psychology and Rationalism
Nature of Intuitions
Mathematics is Cheap
Implications of Intuitions
NonEuclidean Geometry
Russells Paradox
Liars Paradox
David Hilbert
Formal Systems
Hilberts Program
Incompleteness Theorem
The Emperors New Mind
Ethics
The Moral Sense Test
The Little Question
The Nature of Time
Free Will and Determinism
Intuitions Performance