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

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Presentation transcript:

Kant & Mill on Mathematics

Overview

2.1. Kant: Key Concepts

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 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

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

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