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It is not the case that Extensionalist identity conditions for properties — two properties are identical iff they are co-extensional — cannot work as a general criterion.
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Reasons For
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Reason for
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1.
There are seemingly distinct properties that share the same extension, such as having a heart and having kidneys.
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2.
Wildly different properties such as being spherical and weighing 2 kilos could by accident be co-extensive.
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3.
If two distinct properties can share an extension, then co-extension is insufficient to establish property identity.
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Reasons Against
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Reason against 1 of 2
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1.
Necessarily co-extensional properties can still be distinct: 'triangular' and 'trilateral' differ in inferential role despite sharing all possible instances.
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2.
Chalmers and Jackson's two-dimensional semantics shows properties have both primary and secondary intensions, making modal profile part of property individuation.
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3.
A criterion that fails in even one possible world fails as a general criterion, and accidental co-extension is nomologically possible in the actual world.
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Reason against 2 of 2
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1.
Shoemaker's causal theory of properties individuates them by causal powers, so 'renate' and 'cordate' are distinct because they ground different counterfactual dependencies.
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2.
Armstrong's truthmaker principle requires that distinct causal roles in nature correspond to distinct universals, independent of actual extension.
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