Schmid College, Chapman University Courses

Epistemic Logic of Crash Failures

Explore epistemic logic for distributed systems with crash failures using three-valued semantics and impure simplicial complexes to model agent knowledge and uncertainty.

• YouTube
• 1 hour 44 minutes
• Self-Paced
• Free Video

Fighting Fire with Fire - Applying Prescribed and Cultural Fire as a Tool for Proactive Forest Management

Explore how prescribed and cultural fire practices can restore forest resilience and support Indigenous-led stewardship with fire ecologist Dr. Kira Hoffman.

• YouTube
• 49 minutes
• Self-Paced
• Free Video

Proof Theoretic Pluralism and Harmony

Explore proof-theoretic pluralism through harmony conditions, examining how multiple notions of uniqueness create three-level logical variance while preserving balance.

• YouTube
• 1 hour 19 minutes
• Self-Paced
• Free Video

Computational Power and Model Selection

Explore the complex relationship between computational power, data, and background assumptions in scientific model selection through philosophical analysis of historical cases like Kepler's discovery.

• YouTube
• 1 hour 46 minutes
• Self-Paced
• Free Video

Dispensing with the Grounds of Logical Necessity

Explore Otávio Bueno's philosophical examination of logical necessity, its grounds, and why traditional conceptions may be problematic, ultimately proposing an alternative approach that dispenses with these grounds entirely.

• YouTube
• 1 hour 59 minutes
• Self-Paced
• Free Video

Point Set Topology is a Disease from Which the Human Race Will Soon Recover

Explore locale theory as an alternative to point set topology, examining its foundations, applications, and recent developments through Professor Moshier's comprehensive examination of spaces as lattices of parts rather than collections of points.

• YouTube
• 1 hour 46 minutes
• Self-Paced
• Free Video

On the Philosophy of Natural Numbers

Explore the philosophical foundations of natural numbers as Professor Vivanco develops a realist theory viewing numbers as cardinality properties of pluralities, examining their objective existence and foundational role in mathematics.

• YouTube
• 1 hour 57 minutes
• Self-Paced
• Free Video

A Reassessment of Gödel's Doctrine - The Necessity of Infinity

Delve into the philosophical examination of Gödel's Doctrine, exploring the necessity of infinity in mathematical proofs and its implications for finitary mathematics through multiple proof approaches.

• YouTube
• 1 hour 56 minutes
• Self-Paced
• Free Video

Interestingness in Mathematics - Exploring AI's Role in Mathematical Discovery

Explore the concept of interestingness in mathematics and its implications for AI-driven mathematical discoveries. Gain insights into defining proxies for mathematical interest using formal proof archives.

• YouTube
• 1 hour 27 minutes
• Self-Paced
• Free Video

A Possible Way to Read and Interpret Euclid's Elements

Explore a novel approach to reading Euclid's Elements, focusing on fundamental theorems in Books I and II as a guide to understanding Euclidean geometry and its philosophical implications.

• YouTube
• 2 hours 3 minutes
• Self-Paced
• Free Video

The Gödel Translation: History and New Directions

Explore the Gödel translation's history, its impact on intuitionistic and modal logic, and future research directions in this advanced mathematical seminar.

• YouTube
• 1 hour 13 minutes
• Self-Paced
• Free Video

Frege's Definition of Real Numbers is Consistent

Explore Frege's consistent definition of real numbers as ratios of magnitudes. Uncover how slight modifications to his original work could have preserved this groundbreaking mathematical concept.

• YouTube
• 1 hour 50 minutes
• Self-Paced
• Free Video

Geometric Inequalities Between Intrinsic and Extrinsic Curvature Invariants

Explore geometric inequalities between intrinsic and extrinsic curvature invariants in Riemannian manifolds, focusing on Nash's Theorem and recent developments in the field.

• YouTube
• 57 minutes
• Self-Paced
• Free Video

Formalization of Infinity Category Theory

Explore ∞-category theory's formalization, unifying mathematics, computer science, and physics. Learn synthetic reasoning and the Yoneda Lemma in this advanced mathematical seminar.

• YouTube
• 1 hour 51 minutes
• Self-Paced
• Free Video

From Mathematical Object to Philosophy of Culture - Lecture 8

Explore mathematical objects and their cultural significance with Prof. Salanskis. Delve into philosophy of science, culture, and etho-analysis in this thought-provoking seminar series.

• YouTube
• 1 hour 9 minutes
• Self-Paced
• Free Video