Combining Texts

All the ideas for 'Commentary on 'De Anima'', 'Geometrical Method and Metaphysics' and 'Structuralism'

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4 ideas

6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism

8921	Structuralism is now common, studying relations, with no regard for what the objects might be [Hellman]
	Full Idea: With developments in modern mathematics, structuralist ideas have become commonplace. We study 'abstract structures', having relations without regard to the objects. As Hilbert famously said, items of furniture would do.
	From: Geoffrey Hellman (Structuralism [2007], §1)
	A reaction: Hilbert is known as a Formalist, which suggests that modern Structuralism is a refined and more naturalist version of the rather austere formalist view. Presumably the sofa can't stand for six, so a structural definition of numbers is needed.

6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism

8922	Maybe mathematical objects only have structural roles, and no intrinsic nature [Hellman]
	Full Idea: There is the tantalizing possibility that perhaps mathematical objects 'have no nature' at all, beyond their 'structural role'.
	From: Geoffrey Hellman (Structuralism [2007], §1)
	A reaction: This would fit with a number being a function rather than an object. We are interested in what cars do, not the bolts that hold them together? But the ontology of mathematics is quite separate from how you do mathematics.

14. Science / D. Explanation / 2. Types of Explanation / g. Causal explanations

19398	Minds are best explained by their ends, and bodies by efficient causes [Leibniz]
	Full Idea: Whatever concerns reasonable substances (the minds of men) is more naturally explained by the consideration of ends, whereas other substances (bodies) are better explained by efficient causes.
	From: Gottfried Leibniz (Geometrical Method and Metaphysics [1712], p.89)
	A reaction: That is, I take it, that the type of causal explanation considered most appropriate is the one that leads to the greatest understanding. So there is no absolute or correct answer as to which type of causation is the more important.

22. Metaethics / B. Value / 2. Values / e. Death

16764	The soul conserves the body, as we see by its dissolution when the soul leaves [Toletus]
	Full Idea: Every accident of a living thing, as well as all its organs and temperaments and its dispositions are conserved by the soul. We see this from experience, since when that soul recedes, all these dissolve and become corrupted.
	From: Franciscus Toletus (Commentary on 'De Anima' [1572], II.1.1), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 24.5
	A reaction: A nice example of observing a phenemonon, but not being able to observe the dependence relation the right way round. Compare Descartes in Idea 16763.