Combining Texts

All the ideas for 'Mahaprajnaparamitashastra', 'The Poetics' and 'Structuralism'

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5 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.

10. Modality / B. Possibility / 1. Possibility

22518	The actual must be possible, because it occurred [Aristotle]
	Full Idea: Actual events are evidently possible, otherwise they would not have occurred.
	From: Aristotle (The Poetics [c.347 BCE], 1451b18)
	A reaction: [quoted online by Peter Adamson] Seems like common sense, but it's important to have Aristotle assert it.

21. Aesthetics / B. Nature of Art / 8. The Arts / b. Literature

16566	Poetry is more philosophic than history, as it concerns universals, not particulars [Aristotle]
	Full Idea: Poetry is something more philosophic and of graver import than history, since its statements are rather of universals, whereas those of history are singulars.
	From: Aristotle (The Poetics [c.347 BCE], 1451b05)
	A reaction: Hm. Characters in great novels achieve universality by being representated very particularly. Great depth of mind seems required to be a poet, but less so for a historian (though there is, I presume, no upward limit on the possible level of thought).

23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues

7903	The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna]
	Full Idea: The six perfections are of giving, morality, patience, vigour, meditation, and wisdom.
	From: Nagarjuna (Mahaprajnaparamitashastra [c.120], 88)
	A reaction: What is 'morality', if giving is not part of it? I like patience and vigour being two of the virtues, which immediately implies an Aristotelian mean (which is always what is 'appropriate').