14753
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The 'dominant' of two coinciding sortals is the one that entails the widest range of properties [Burke,M, by Sider]
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Full Idea:
Burke claims that the 'dominant' sortal is the one whose satisfaction entails possession of the widest range of properties. For example, the statue (unlike the lump of clay) also possesses aesthetic properties, and hence is dominant.
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From:
report of Michael Burke (Dion and Theon: an essentialist solution [1994]) by Theodore Sider - Four Dimensionalism 5.4
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A reaction:
[there are three papers by Burke on this; see all the quotations from Burke] Presumably one sortal could entail a single very important property, and the other sortal entail a huge range of trivial properties. What does being a 'thing' entail?
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16072
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'The rock' either refers to an object, or to a collection of parts, or to some stuff [Burke,M, by Wasserman]
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Full Idea:
Burke distinguishes three different readings of 'the rock'. It can be a singular description denoting an object, or a plural description denoting all the little pieces of rock, or a mass description the relevant rocky stuff.
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From:
report of Michael Burke (Dion and Theon: an essentialist solution [1994]) by Ryan Wasserman - Material Constitution 5
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A reaction:
Idea 16068 is an objection to the second reading. Only the first reading seems plausible, so we must just get over all the difficulties philosophers have unearthed about knowing exactly what an 'object' is. I offer you essentialism. Rocks have unity.
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16234
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Burke says when two object coincide, one of them is destroyed in the process [Burke,M, by Hawley]
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Full Idea:
Michael Burke argues that a sweater is identical with the thread that consitutes it, that both were created at the moment when they began to coincide, and that the original thread was destroyed in the process.
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From:
report of Michael Burke (Dion and Theon: an essentialist solution [1994]) by Katherine Hawley - How Things Persist 5.3
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A reaction:
[Burke's ideas are spread over three articles] It is the thread which is destroyed, because the sweater is the 'dominant sortal' (which strikes me as a particularlyd desperate concept).
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14750
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Two entities can coincide as one, but only one of them (the dominant sortal) fixes persistence conditions [Burke,M, by Sider]
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Full Idea:
Michael Burke has given an account that avoids distinguishing coinciding entities. ...The statue/lump satisfies both 'lump' and 'statue', but only the latter determines that object's persistence conditions, and so is that object's 'dominant sortal'.
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From:
report of Michael Burke (Dion and Theon: an essentialist solution [1994]) by Theodore Sider - Four Dimensionalism 5.4
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A reaction:
Presumably a lump on its own can have its own persistance conditions (as a 'lump'), but those would presumably be lost if you shaped it into a statue. Burke concedes that. Can of worms. Using a book as a doorstop...
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13165
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Geometrical proofs do not show causes, as when we prove a triangle contains two right angles [Proclus]
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Full Idea:
Geometry does not ask 'why?' ..When from the exterior angle equalling two opposite interior angles it is shown that the interior angles make two right angles, this is not a causal demonstration. With no exterior angle they still equal two right angles.
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From:
Proclus (Commentary on Euclid's 'Elements' [c.452], p.161-2), quoted by Paolo Mancosu - Explanation in Mathematics §5
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A reaction:
A very nice example. It is hard to imagine how one might demonstrate the cause of the angles making two right angles. If you walk, turn left x°, then turn left y°, then turn left z°, and x+y+z=180°, you end up going in the original direction.
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9569
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The origin of geometry started in sensation, then moved to calculation, and then to reason [Proclus]
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Full Idea:
It is unsurprising that geometry was discovered in the necessity of Nile land measurement, since everything in the world of generation goes from imperfection to perfection. They would naturally pass from sense-perception to calculation, and so to reason.
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From:
Proclus (Commentary on Euclid's 'Elements' [c.452]), quoted by Charles Chihara - A Structural Account of Mathematics 9.12 n55
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A reaction:
The last sentence is the core of my view on abstraction, that it proceeds by moving through levels of abstraction, approaching more and more general truths.
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