8920
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Equivalence relations are reflexive, symmetric and transitive, and classify similar objects [Lipschutz]
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Full Idea:
A relation R on a non-empty set S is an equivalence relation if it is reflexive (for each member a, aRa), symmetric (if aRb, then bRa), and transitive (aRb and bRc, so aRc). It tries to classify objects that are in some way 'alike'.
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From:
Seymour Lipschutz (Set Theory and related topics (2nd ed) [1998], 3.9)
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A reaction:
So this is an attempt to formalise the common sense notion of seeing that two things have something in common. Presumably a 'way' of being alike is going to be a property or a part
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18431
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Internal relations combine some tropes into a nucleus, which bears the non-essential tropes [Simons, by Edwards]
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Full Idea:
Simons's 'nuclear' option blends features of the substratum and bundle theories. First we have tropes collected by virtue of their internal relations, forming the essential kernel or nucleus. This nucleus then bears the non-essential tropes.
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From:
report of Peter Simons (Particulars in Particular Clothing [1994], p.567) by Douglas Edwards - Properties 3.5
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A reaction:
[compression of Edwards's summary] This strikes me as being a remarkably good theory. I am not sure of the ontological status of properties, such that they can (unaided) combine to make part of an object. What binds the non-essentials?
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13804
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A property is essential iff the object would not exist if it lacked that property [Forbes,G]
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Full Idea:
A property P is an essential property of an object x iff x could not exist and lack P, that is, as they say, iff x has P at every world at which x exists.
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From:
Graeme Forbes (In Defense of Absolute Essentialism [1986], 1)
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A reaction:
This immediately places the existence of x outside the normal range of its properties, so presumably 'existence is not a predicate', but that dictum may be doubted. As it stands this definition will include trivial and vacuous properties.
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13806
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Trivially essential properties are existence, self-identity, and de dicto necessities [Forbes,G]
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Full Idea:
The main groups of trivially essential properties are (a) existence, self-identity, or their consequences in S5; and (b) properties possessed in virtue of some de dicto necessary truth.
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From:
Graeme Forbes (In Defense of Absolute Essentialism [1986], 2)
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A reaction:
He adds 'extraneously essential' properties, which also strike me as being trivial, involving relations. 'Is such that 2+2=4' or 'is such that something exists' might be necessary, but they don't, I would say, have anything to do with essence.
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13809
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One might be essentialist about the original bronze from which a statue was made [Forbes,G]
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Full Idea:
In the case of artefacts, there is an essentialism about original matter; for instance, it would be said of any particular bronze statue that it could not have been cast from a totally different quantity of bronze.
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From:
Graeme Forbes (In Defense of Absolute Essentialism [1986], 3)
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A reaction:
Forbes isn't endorsing this, and it doesn't sound convincing. He quotes the thought 'I wish I had made this pot from a different piece of clay'. We might corrupt a statue by switching bronze, but I don't think the sculptor could do so.
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