Combining Philosophers

Ideas for David Wiggins, Michael Bratman and Protagoras

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3 ideas

6. Mathematics / A. Nature of Mathematics / 2. Geometry
No perceptible object is truly straight or curved [Protagoras]
     Full Idea: No perceptible object is geometrically straight or curved; after all, a circle does not touch a ruler at a point, as Protagoras used to say, in arguing against the geometers.
     From: Protagoras (fragments/reports [c.441 BCE], B07), quoted by Aristotle - Metaphysics 998a1
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / d. Counting via concepts
Maybe the concept needed under which things coincide must also yield a principle of counting [Wiggins]
     Full Idea: My thesis C says that to specify something or other under which a and b coincide is to specify a concept f which qualifies for this purpose only if it yields a principle of counting for fs. ...I submit that C is false, though a near miss.
     From: David Wiggins (Sameness and Substance [1980], 1.1)
The sortal needed for identities may not always be sufficient to support counting [Wiggins]
     Full Idea: My principle C seems unnecessary ...since it is one thing to see how many fs there are...but another to have a perfectly general method. ...One could answer whether this f-compliant is the same as that one, but there are too many ways to articulate it.
     From: David Wiggins (Sameness and Substance [1980], 2.8)
     A reaction: His famous example is trying to count the Pope's crown, which is made of crowns. A clearer example might be a rectangular figure divided up into various overlapping rectangles. Individuation is easy, but counting is contextual.