In “Epistemic oughts in Stit Semantics” Horty’s main argument is that an epistemic logic must be integrated in a satisfactory deontic logic. This is needed in order to account for a sense of what an agent ought to do hinges on a role for knowledge (“epistemic oughts”).
That argument occupies the second part of his paper, and I hope to explore it in a later post. But the first part of the paper, which focuses on a general concept of what an agent ought to do (ought to see to) is interesting in itself, and crucial for what follows. I will limit myself here to that part.
I agree with a main conclusion reached there, which is that the required value ordering is not of the possible outcomes of action but of the choices open to the agent.
However, I have a problem with the specific ordering of choices that Horty defines, which it seems to me faces intuitive counterexamples. I will propose an alternative ordering principle.
At a given instant t an agent has a variety V(h, t) of possible futures in history h. I call V(h, t) the future cone of h at t. But certain choices {K, K’, …} are open to the agent there, and by means of a given choice K the agent may see to it that the possible futures will be constrained to be in a certain subset V(K, h, t) of V(h, t).
The different choices are represented by these subsets of V(h, t), which form a partition. Hence the following is well defined for histories in V(m): the choice made in history h at t is the set V(K, h, t) to which h belongs; call it CA(h, t), thinking of “CA” as standing for “actual choice”.
In the diagram K1 is the set of possible histories h1 and h2, and so CA(h1,t) = K1 = CA(h2, t). (Note well: I speak in terms of instants t of time, rather than Horty’s moments.
And the statement that the agent sees to it that A is true in in h at t exactly if A is true in all the possible futures of h at t that belong to the choice made in history h at t. Briefly put: CA(h, t) ⊆ A.
The Chisholm/Meinong analysis of what ought to be is precisely what it is maximally good to be the case. Thus, at a given time, it ought to be that A if A is the case in all the possible future whose value is maximal among them. So applied to a statement about action, that means: It ought to be that the agent sees to it that A is true in h at t exactly if all the histories in the choice made in history h at t are of maximal value. That is, if h is in CA(h, t) and h’ is in V(h, t) but outside CA(h, t) then h’ is no more valuable than h.
But this analysis is not correct, as Horty shows with two examples of gambles. In each case the target proposition is G: the agent gambles, identified with the set of possible histories in which the agent takes the offered gamble. This is identified with: the agent sees to it that G. Hence the two choices, K1 and K2, open to the agent in h at t are represented by the intersection of V(h, t) with G and with ~G respectively.
In the first example the point made is that according to the above analysis, it is generally the case that the agent ought to gamble, since the best possible outcome is to win the gamble, and that is possible only if you gamble. That is implausible on the face of it — and in that first example, we see that the gambler could make sure that gets 5 units by not gambling, which looks like a better option than the gamble, which may end with a gain of 10 or nothing at all. While someone who values gambling for its own risk might agree, we can’t think that this is what he ought to do. The second example is the same except that winning the gamble would only bring 5 units, with a risk of getting 0, while not gambling brings 5 for sure. In this case we think that he definitely ought not to gamble, but on the above analysis it is not true either that he ought to gamble or ought not to gamble.
Horty’s conclusion, surely correct, is that what is needed is a value ordering of the choices rather than of the possible outcomes (though there may, perhaps should, be) a connection between the two.
Fine, but Horty defines that ordering as follows: choice K’ (weakly) dominates choice K if none of the possible histories in K are better than any of those in K’. (See NOTES below, about this.) The analysis of ‘ought’ is then that the agent ought to see to it that A exactly if all his optimal choices make A definitely true.
Suppose the choice is between two lotteries, each of which sells a million tickets, and has a first prize of a million dollars, and a second prize of a thousand dollars. But only the second lottery has many consolation prizes worth a hundred dollars each. Of course there are also many outcomes of getting no prize at all. There is no domination to tell us which gamble to choose, but in fact, it seems clear that the choice should be the second gamble. That is because the expectation value of the second gamble is the greater.
This brings in the agent’s opinion, his subjective probability, to calculate the expectation value. It leads in this case to the right solution. And it does so too in the two examples above that Horty gave, if we think that the individual outcomes were in each case equally likely. For then in the first example the expectation value is 5 in either case, so there is no forthcoming ought. In the second example, the expectation value of gambling is 2.5, smaller than that of not gambling which is 5, so the agent ought not to gamble.
So, tentatively, here is my conclusion. Horty is right on three counts. The first is that the Chisholm/Meinong analysis, with its role for the value ordering of the possible outcomes, is faulty. The second is that the improvement needed is that we rely, in the analysis of ought statements, on a value ordering of the agent’s choices. And the third is that an integration with epistemic logic is needed, ….
…. but — I submit — with a logic of opinion rather than of knowledge.
NOTES
John Horty “Epistemic Oughts in Stit Semantics”. Ergo 6 (2019): 71-120
Horty’s definition of dominance is this:
K ≤ K’ (K’ weakly dominates K) if and only if Value(h) ≤ Value(h’) for each h in K and h’ in K’; and K < K’ (K’ strongly dominates K) if and only if K ≤ K’ and it is not the case that K’ ≤ K.
This ordering gives the right result for Horty’s second example (Ought not to gamble), while in the first example neither choice dominates the other. But the demand that all possible outcomes of choice K’ should be better than any in K seems to me too strong for a feasible notion of dominance. For example if the values of outcomes in one choice are 100 and 4, while in the other they are 5 and 4, this definition does not imply that the first choice weakly dominates the other, since 5 (in the second) is larger than 4 (in the first) — while intuitively, surely, the first choice should be advocated.
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