Consider a view on which all modality is grounded in property entailment: the relation between properties F and G expressed by "having F entails having G". Jubien has defended a view that might sound like this (though see comments at the end). One way to make this precise is to say that the theory of necessity is generated by the axiom schema
- from a subproof of p that reiterates no assumptions other than instances of (1), we can derive Necessarily(p).
Here is one quick problem. This fits best with a Platonic metaphysics of properties (Jubien certainly does that). On a Platonic metaphysics of properties:
- Necessarily(a is a circle → circularity exists).
One might think that something could be done if existence is a property and there are entailment relations like that being a property entails existence. But that won't help unless we add to the axioms that circularity is a property. But the axioms are automatically necessary by (2), so now we are no longer just giving a property entailment account. We are adding axioms that directly force cerain essentialist claims, like that any property is essentially a property.
Alright, maybe that's unfair. Maybe any Platonist who has a property entailment view of modality will also have among the axioms the schema:
- Necessarily(circle(a) → circularity is a property).
Of course, we can add things like (5) to our axiom scheme. But the theory is now really swelling, and it is no longer true that it grounds modality in property entailment. It grounds modality in provability from a whole bunch of axiom schemata, one of which is the property entailment one.
My fairly quick glance at Jubien doesn't show him discussing this. But it does show him discussing a related issue, Kripkean arguments that a certain particular table must be made of wood. Jubien says that the table has a "table-essence" being this table and being this table entails being made of wood. So he could handle (5) by saying that circularity has an "object-essence" (I think it had better be an obejct essence, in his terminology), being circularity, and that being circularity entails being a property. Fine so far, but what about the following necessities:
- Necessarily(exists(circularity) → circularity has being circularity).
Here is a different kind of problem. Consider this claim:
- Necessarily(wrongs(x,y) → agent(x)).
So, it seems, the system needs to be extended to include entailments between relations of different adicities. Moreover, it needs to be extended to include entailments between relations of the same adicity but with the relata reorganized:
- Necessarily(wrongs(x,y) → iswrongedby(y,x)).
- Necessarily(A(x1,...,xn) → B(xf(1),...,xf(m))),
The view is still non-trivial. But it is messy, and it is difficult to see what motive one has for believing it rather than just giving up on the grounding project altogether—or going for my view. :-) After all, f-twisted-entailment is not such a natural property as entailment.
[Fixed definition of twisted entailment.]