1. 1. Posted by Geoff Ferrari | October 23, 2007 9:30 am

   Thanks Bart for a good discussion of Jackon’s argument. I have yet another proposed counterexample to the identity of necessarily co-extensive properties” (INCP).

   Suppose there are disjunctive properties. Suppose also that these properties are not metaphysically basic. Instead, they are composed or constituted by their properties that appear as their disjuncts. Suppose finally that it is a necessary condition of a disjunctive property A being identical to a disjunctive property B that A and B have the same constituents.

   Take any disjunctive property you like and call it F. And now consider the property F*: (being F or (being F and such that 2+2=4)). I take it that F and F* are necessarily co-extensive. But they have distinct constituents and hence, on my previous assumptions, cannot be identical.

2. 2. Posted by Bart Streumer | October 26, 2007 12:40 pm

   Thanks for this example, Geoff, and sorry for this late reply. As I said on Monday, if necessarily co-extensive predicates ascribe the same property, a disjunctive predicate and a non-disjunctive predicate can ascribe the same property, and properties themselves therefore do not seem to be disjunctive or non-disjunctive. However, if there were disjunctive properties, I’m not sure if it would be plausible to say that these properties are constituted by the properties that appear as their disjuncts. For, surely, if there were disjunctive properties, an object could have a disjunctive property without having all the properties that appear as its disjuncts. In that case, if disjunctive properties were constituted by the properties that appear as their disjuncts, it would follow that an object could have a property without having all the properties that constitute this property, which doesn’t seem plausible.

   It would perhaps be more plausible to say that there are conjunctive properties, and that such properties are constituted by the properties that appear as their conjuncts. You could then say that necessarily co-extensive predicates ascribe different properties if at least one of these properties contains a conjunct that the other property does not contain. Changing your example a bit, you could say that the predicate ‘is F’ and the predicate ‘is F and such that 2+2=4′ are necessarily co-extensive but ascribe different properties, since the second predicate ascribes a property that contains a conjunct (‘such that 2+2=4′) that the property ascribed by the first predicate does not contain.

   However, if you said this, you would presuppose that the predicate ‘is F and such that 2+2=4′ ascribes a property. In that case, I’d like to know more about which view of properties you are relying on, since the two views of properties that most obviously allow this are either irrelevant to this debate or cannot support this example. The first of these is the view that identifies properties with the meanings of predicates. As I said on Monday, this view is irrelevant to the debate about whether there are irreducibly normative properties, since the parties in this debate agree that normative and descriptive predicates have different meanings but nevertheless disagree about whether there are irreducibly normative properties. The second of these is the view that identifies properties with sets of actual and possible objects. But this view cannot support this example, since it entails that necessarily co-extensive predicates ascribe the same property.

   It seems to me that similar remarks may apply to the example that Ralph offered on Monday, which (if I remember it correctly) was that the predicates ‘is red’ and ‘is red and a member of the set of red things and natural numbers’ are necessarily co-extensive but ascribe different properties. This example presupposes that the predicate ‘is red and a member of the set of red things and natural numbers’ ascribes a property. Again, the views of properties that most obviously allow that this predicate ascribes a property are the view that identifies properties with meanings of predicates, which is irrelevant to this debate, and the view that identifies properties with sets of actual and possible objects, which cannot support this example since it entails that necessarily co-extensive predicates ascribe the same property.

   More generally, I think that a convincing example of necessarily co-extensive predicates that ascribe different properties should probably not appeal to gerrymandered predicates like ‘is F or (is F and such that 2+2=4)’ or ‘is red and is a member of the set of all red things and natural numbers’. For most of us probably do not have very clear intuitions about whether such gerrymandered predicates ascribe properties or not and, if they do, about whether these properties are identical to the properties that certain other predicates ascribe (at any rate, I don’t). Of course, predicate D* is a highly gerrymandered predicate too, but in the paper I do not appeal to predicate D* to defend the view that necessarily co-extensive predicates ascribe the same property (I don’t think that would convince anyone). Instead, I appeal to predicates of which it is far less controversial that they ascribe a property and which are often put forward as counterexamples to the claim that necessarily co-extensive predicates ascribe the same property (‘is a closed figure that has three angles’, ‘is a closed figure that has three sides’, ‘is a triangle’, etc.), and I argue that, on reflection, we should admit that these predicates do not ascribe different properties.

3. 3. Posted by Paul Healey | September 16, 2008 11:46 pm

   Hello Bart,

   hoping it is not to late to challenge you on what I find to be a very interesting subject:

   when you write ‘is a closed figure that has three sides’ and ‘is a closed figure that has three angles’, one objection it appears you didn’t consider is that predicates can be equal or unequal in number. I.e., the predicates are not the same for a circle.

   In the example you give of water ascribing the same property as H20, could it not also be argued that water can also be thought of as predicating something that is drinkable, but not as pure as H20, which is also drinkable but doesn’t have anything else that could be included in its concept?

   More significantly perhaps, can laws not be thought of as satisfying instances(contingent particulars) of entities that have the properties of elements within a composition;and the properties of those entities within a composition can be thought of as universal particulars?

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