Post on 25-Dec-2015
transcript
Kant & Mill on Mathematics
Kareem KhalifaPhilosophy Department
Middlebury College
Overview
1. Historical background (let’s skip this)
2. Kant3. Mill
2.1. Kant: Key Concepts
2.1.1. Analytic vs. synthetic statements2.1.2. Concepts vs. intuitions2.1.3. The a priori
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.
2.2. Kant’s epistemology
2.2.1. How is mathematical
knowledge synthetic?
Intuition and counting
• Enunciation: 7+5 = 12• Ecthesis/setting-out:
||||||| |||||• Auxiliary construction– Step 1: |||||||| ||||– Step 2: ||||||||| |||
…– Step 5: ||||||||||||
2.2. Kant’s epistemology, continued
2.2.2. Why is mathematical knowledge a priori?2.2.3. What are objective structures of space &
time?2.2.4. Why isn’t mathematical knowledge
analytic?
The rest of Kant’s philosophy of math
2.3. Ontology2.4. Semantics2.5. Applicability
3. Mill
3.1. Epistemology3.2. Ontology3.3. Semantics3.4. Applicability