Fine-Tuning Our Distinctions

Thus far, I’ve framed the S&V literature in terms of "doing good science," viz.

1. A value is constitutive of science if and only if it is necessary for doing good science.
2. A value is contextual in science if and only if it is sometimes (but not always) useful for doing good science.
3. A value is invariant in science if and only if it is always useful for doing good science.

I think this is too loosely formulated. Since I’ll be focusing primarily on the theoretical virtues, I’m interested in a much narrower set of values, namely those that are predicated of theories as criteria of acceptance. It's my sense that the following fairly glosses what most have meant by the constitutive-contextual distinction:

1. A value V is constitutive of theory acceptance if and only if, for all theories T, correctly identifying V as a property of T is necessary for being justified in the acceptance of T. 
2. A value V is contextual in theory acceptance if and only if, for some (but not all) theories T, correctly identifying V as a property of T provides some justification for the acceptance of T.

If that's right, then we have two important dimensions by which to catalog values in science. The first is the scope of theories to which the value applies (which I've italicized), and the second is the value's justificatory role (in boldface). Minimally, invariant and constitutive values have the same scope: they apply to all theories. 

However, I want to suggest that we consider three justificatory roles: necessity (as illustrated by our new definition of constitutive values), contributing (as illustrated by our new definition of contextual values), and sufficiency (which provides a natural foil to necessity). This would then suggest a stronger and a weaker brand of invariantism about values:

3.  A value V is invariantly strong in theory acceptance if and only if, for all theories T, correctly identifying V as a property of T is sufficient for being justified in the acceptance of T. 

4. A value V is invariantly contributes to theory acceptance if and only if, for all theories T, correctly identifying V as a property of T provides some justification for the acceptance of T.

I note in passing that we can do the same thing with contextual values. In this case, i.e. 

2 (revised). A value V contextually contributes to theory acceptance if and only if, for some (but not all) theories T, correctly identifying V as a property of T provides some justification for the acceptance of T.

5.  A value V is contextually strong in theory acceptance if and only if, for some (but not all) sufficient for being justified in the acceptance of T. theories T, correctly identifying V as a property of T is

6. A value V is contextually necessary in theory acceptance if and only if, for some (but not all) necessary for being justified in the acceptance of T. theories T, correctly identifying V as a property of T is

These won't be part of my story, but it's useful to observe that we should have a six-part distinction instead of a bipartite one, as has been the norm. As for me, I'm leaning towards claiming that the virtues are invariantly strong, though I'll have to do more work before I make a firm decision on this. Otherwise, I'll claim that they're invariant contributors.