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8921
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Structuralism is now common, studying relations, with no regard for what the objects might be [Hellman]
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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.
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From:
Geoffrey Hellman (Structuralism [2007], §1)
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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.
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13083
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The essence is the necessary properties, and the concept includes what is contingent [Leibniz]
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Full Idea:
Of the essence of a particular thing is what pertains to it necessarily and perpetually; of the concept of an individual thing on the other hand is what pertains to it contingently or per accidens.
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From:
Gottfried Leibniz (Human Freedom and Divine choice [1690], Grua 383), quoted by Cover,J/O'Leary-Hawthorne,J - Substance and Individuation in Leibniz 3.3.1
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A reaction:
This arbitrates on the apparent conflict between his remarks in Idea 13077 and Idea 10382. There seems to be a distinction between the 'concept' of a thing, and the 'complete concept', the latter including the contingent properties.
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