1. Kant & Mill on Mathematics

2. Overview

3. 2.1. Kant: Key Concepts

4. Example of “conceptual analysis” & analytic truths 1.All vixens are foxes. 2.For all x, x is a vixen if and only if x is a female fox. 3.  All female foxes are foxes. For all x, if x is F and x is G, then x is G.

5. 2.2. Kant’s epistemology 2.2.1. How is mathematical knowledge synthetic?

6. Intuition and counting Enunciation: 7+5 = 12 Ecthesis/setting-out: |||||||||||| Auxiliary construction – Step 1: |||||||| |||| – Step 2: ||||||||| ||| … – Step 5: ||||||||||||

7. 2.2. Kant’s epistemology, continued

8. The rest of Kant’s philosophy of math 2.3. Ontology 2.4. Semantics 2.5. Applicability

9. 3. Mill 3.1. Epistemology 3.2. Ontology 3.3. Semantics 3.4. Applicability