Kant & Mill on Mathematics. Overview 2.1. Kant: Key Concepts.

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  • Slide 1
  • Kant & Mill on Mathematics
  • Slide 2
  • Overview
  • Slide 3
  • 2.1. Kant: Key Concepts
  • Slide 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.
  • Slide 5
  • 2.2. Kants epistemology 2.2.1. How is mathematical knowledge synthetic?
  • Slide 6
  • Intuition and counting Enunciation: 7+5 = 12 Ecthesis/setting-out: |||||||||||| Auxiliary construction Step 1: |||||||| |||| Step 2: ||||||||| ||| Step 5: ||||||||||||
  • Slide 7
  • 2.2. Kants epistemology, continued
  • Slide 8
  • The rest of Kants philosophy of math 2.3. Ontology 2.4. Semantics 2.5. Applicability
  • Slide 9
  • 3. Mill 3.1. Epistemology 3.2. Ontology 3.3. Semantics 3.4. Applicability