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2 ideas
| 10203 | We apprehend small, finite mathematical structures by abstraction from patterns [Shapiro] |
| Full Idea: The epistemological account of mathematical structures depends on the size and complexity of the structure, but small, finite structures are apprehended through abstraction via simple pattern recognition. | |
| From: Stewart Shapiro (Philosophy of Mathematics [1997], Intro) | |
| A reaction: Yes! This I take to be the reason why John Stuart Mill was not a fool in his discussion of the pebbles. Successive abstractions (and fictions) will then get you to more complex structures. |
| 12065 | Seeing a group of soldiers as an army is irresistible, in ontology and explanation [Wiggins] |
| Full Idea: It seems mandatory to an observer of soldiers to give 'the final touch of unity' to their aggregate entity (the army). ...Similar claims arise with the ontological and explanatory claims of other corporate entities. | |
| From: David Wiggins (Substance [1995], 4.13.3) | |
| A reaction: Wiggins must say (following Leibniz Essays II.xxiv,1) that we add the unity, but I take the view that an army has powers, and hence offers explanations, which are lacking in a merely group of disparate soldiers. So an army has an essence and identity. |