We have subjunctive conditionals of the form, If p were true, q would be true. We can abbreviate these as (p > q). Indicative conditionals admit of modus ponens, (If p is true, q is true; p is true; therefore q is true). So it seems natural that there would be something analogous for subjunctive conditionals. However, there are complications.
The antecedent of If p were true, q would be true is ambiguous. It could mean something like:
If p were true [rather than what is actually true], q would be true.
Call this the properly counterfactual interpretation. But it could also mean:
If p were true [as it may be], q would be true.
Call this the fortassic interpretation (from Latin fortasse). These are not at all the same thing, but subjunctive conditionals can be used in both ways. This matters a lot. The Supplement on Debates over Counteractual Principles at the SEP has the following example:
If George were caught, he would face years of prison.
Actually, George did get caught.
In that case, he will face years of prison.
This is clearly invalid on the properly counterfactual interpretation. It is at least defensible on the fortassic interpretation. Another example, from the same source:
If the soldier had shot the prisoner, then (even) if the captain hadn’t given the order to shoot, the prisoner (still) would have died.
Actually, the soldier did shoot the prisoner.
So, if the captain hadn’t given the order to shoot, the prisoner would have died.
Again, this is clearly invalid on the properly counterfactual interpretation. But if the main conditional is fortassic, then it is again defensible.
The essential thing is that when we construct a subjunctive conditional, we can do so in such a way as to rule out the possibility of the actual state of affairs from falling under the antecedent (properly counterfactual) or in such a way as to allow that it could (fortassic).
In both of the above examples, we need fortassic interpretations in order to allow the indicative second premise to be combinable with the . On the counterfactual interpretation, it becomes irrelevant and we have committed an equivocation, namely, treating the indicative p is true as if it were the same as were p to be true.
Thus, if we have a genuine counterfactual conditional, we can only get modus ponens if our ponens premise is shifted toward the same set of counterfactual situations as the antecedent of the counterfactual conditional:
If p were true [given some change to the actual], q would be true.
p were true [given the same change to the actual].
Therefore, q would be true [given the same change to the actual].
Colloquial English doesn't let us do anything directly like p were true on its own; the usual way we would say something like this is, 'p would be true'. Thus:
If George were caught, he would face years of prison.
George would be caught.
So he would face years of prison.
The shift in how it's stated is awkward, but I suppose it could be argued that it serves a function. In 'George were caught', we are, from the way things actually are, positing a counterfactual situation in which things would be different; with 'George would be caught', we are shifting to the perspective of that counterfactual situation. We then draw a conclusion from within that perspective.
The fortassic interpretation allows us to do the same thing; it just also allows us to treat the perspective of no-difference-from-the-actual as one of the options.
The abbreviation (p > q) unfortunately obscures this. If we say,
p > q
p
Therefore q,
there is nothing to indicate that the ponens premise (p) is to be taken subjunctively and not indicatively. Thus we should probably require something like an index in the antecedent of a subjunctive conditional, to let us indicate when we are in the same region of possibilities:
p1 > q
p1
Therefore q.
But this is not always adequate, either. When we have the fortassic conditional and an indicative ponens, the indicative does not cover the same region of possibilities; it's only a part of it. We could do something like p∈1, but this does not distinguish the indicative situation from the other situations that fall within that region of possibilities. Perhaps p@∈1? But we need something along such lines if we are to handle counterfactuals properly in a formal notation.
