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Single Idea 8970
[filed under theme 9. Objects / F. Identity among Objects / 1. Concept of Identity
]
Full Idea
Our conceptual grip on the notion of a set is founded on the axiom of extensionality: a set x is the same as a set y iff x and y have the same members. But this axiom deploys the notion of absolute identity ('same members').
Gist of Idea
Our notion of identical sets involves identical members, which needs absolute identity
Source
John Hawthorne (Identity [2003], 3.1)
Book Ref
'The Oxford Handbook of Metaphysics', ed/tr. Loux,M /Zimmerman,D [OUP 2005], p.112
A Reaction
Identity seems to be a primitive, useful and crucial concept, so don't ask what it is. I suspect that numbers can't get off the ground without it (especially, in view of the above, if you define numbers in terms of sets).
The
17 ideas
from John Hawthorne
14588
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Modern metaphysicians tend to think space-time points are more fundamental than space-time regions
[Hawthorne]
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14589
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A modal can reverse meaning if the context is seen differently, so maybe context is all?
[Hawthorne]
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14590
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If we accept scattered objects such as archipelagos, why not think of cars that way?
[Hawthorne]
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14591
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Four-dimensionalists say instantaneous objects are more fundamental than long-lived ones
[Hawthorne]
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19551
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How can we know the heavyweight implications of normal knowledge? Must we distort 'knowledge'?
[Hawthorne]
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19552
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We wouldn't know the logical implications of our knowledge if small risks added up to big risks
[Hawthorne]
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19554
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Denying closure is denying we know P when we know P and Q, which is absurd in simple cases
[Hawthorne]
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19553
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Commitment to 'I have a hand' only makes sense in a context where it has been doubted
[Hawthorne]
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15121
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An individual essence is a necessary and sufficient profile for a thing
[Hawthorne]
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15123
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Is the causal profile of a property its essence?
[Hawthorne]
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15122
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Could two different properties have the same causal profile?
[Hawthorne]
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15124
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If properties are more than their powers, we could have two properties with the same power
[Hawthorne]
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15126
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Maybe scientific causation is just generalisation about the patterns
[Hawthorne]
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15127
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A categorical basis could hardly explain a disposition if it had no powers of its own
[Hawthorne]
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15128
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We can treat the structure/form of the world differently from the nodes/matter of the world
[Hawthorne]
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15125
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We only know the mathematical laws, but not much else
[Hawthorne]
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8970
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Our notion of identical sets involves identical members, which needs absolute identity
[Hawthorne]
|