By Axel Arturo Barceló Aspeitia
In 2013, Ralf M. Bader argues that not all necessary properties are intrinsic. Some are, but not all. His examples are as follows: Let I(x) be an intrinsic property and E(x) and extrinsic one. Then I(x)v¬I(x) is intrinsic while E(x)v¬E(x) is extrinsic.
- Let a be an object that is I. [Hypothesis]
- If P and not Q, then PvQ in virtue of P or whatever P is in virtue of. [Grounding Closure]
- If I(a) then not ¬I(a). [Logical truth]
- If I(a) and not ¬I(a)then I(a)v¬I(a) in virtue of I(a) or whatever grounds I(a). [From 3 and 2]
- Since I(x) is intrinsic, it is always had intrinsically, i.e., if a has it, it has it in virtue only of how a is, regardless of what happens outside of it. [By hypothesis]
- I(a) in virtue only of what a is, regardless of what happens outside of it. [5 & 1]
- I(a)v¬I(a) in virtue of what a is, regardless of what happens outside of it. [Transitivity of Grounding 4 & 6]
- If a is I, then I(a)v¬I(a) intrinsically. [Hypothetical proof from 1 to 7]
- If a is not I, then I(a)v¬I(a) intrinsically. [From a symmetrical argument]
- I(x)v¬I(x) is intrinsic. [Universal Instantiation and constructive dilemma from 8 and 9]
Mutatis Mutandi for E(x)v¬E(x) being extrinsic.
As appealing as Bader argument is, it is still incompatible with a very popular account of the grounds of necessity: essentialism, i.e., the hypothesis that necessary truths are true in virtue of essences.
If essentialism is right, then Bader is wrong. From an essentialist perspective, it is true that not all necessary properties are intrinsic, but not for the reasons Bader presents. After all, even if necessary properties are had by all entities, they are nevertheless true only in virtue of the essence of some of them.
This means that premise 2 is false.
Remember that a property is intrinsic if it is had in virtue of how the thing itself is, i.e. the grounding fact involves only the object having the property. Still, not all essences are intrinsic (consider, for example, necessity of origin cases), so even if an object had a necessary property in virtue of its essence, it might still have it externally. Furthermore, even when essences are intrinsic, the objects whose essence may be responsible for the necessity of a truth may not be the ones having the property. For example, one can hold that logical truths are true in virtue of the essence of their logical constants. This would make a logical truth like I(a)v¬I(a) be true in virtue of the essence of “v” not of a, thus making property I(x)v¬I(x) extrinsic. Thus, premise 2 is false.