While one is not forced to hold that causality is ultimately defined in terms of counterfactuals, the question of which notion is “more primitive” still emerges.
One might therefore wonder how, and in what sense, causality is linked to the notion of the generation relations. There is an obvious part of this re- lation that resembles causality. For instance, when we say that bad weather always makes Jones wear his hat are we not saying that bad weathercauses him to wear his hat? It would seem so, but the counterfactual ‘no bad weather; no hat’ is not true relative to the relevant state. So, the notion of causality involved cannot be the simple notion of ‘no cause; no effect’ being true. It is of course also very dubious whether anyone would ever ac- cept such a reduction of causality to counterfactuals; it does not seem that the proposed condition is necessary for establishing a causal relationship.
Even so, what are we saying about the situation of evaluation when we propose that gen({bad},{hat}) holds true of it? It seems we are saying nothing more than the knowledge we presently have of the situation is such that bad weather brings about Jones wearing his hat. This is simply what we know about the world, it is given by the description of the example, and as such it is no wonder that we pay special attention to this when evaluating the counterfactual in question.
edge that the evaluator of the counterfactual possesses about the world. This is well in tune with how we have set up our semantics. We defined a state of an agent to reflect exactly the generation relations that the agent takes to hold true of the world, and we said that a counterfactual is acceptable by an agentiff the state of the agent supports the counterfactual in question. The knowledge represented by these generation relations can be causal or it can be of another kind. The good thing is that right now we do not need to say anything more about what it is, we need only observe that under such a treatment of counterfactuals the predictions of the theory coincide with our intuitions.
There does seem to be two different kinds of generation relations at work though. One is more accurately described by notions such ascausality, while the second could plausibly be better described by using the term analytic relation. It does not seem that we can say that John being a bachelorcauses him to be an unmarried man. It is true that whenever we have the former, we also have the latter, but it does not seem that the relation is accurately described by using the concept of causality. When John is a bachelor, the fact that he is an unmarried man follows purely by the meaning of the terms involved. We might therefore choose to call such relations analytic.
So, it is clear that there are two kinds of relations falling under the category of generation relation. One might be described as causal relations, while the other would more accurately be described by the term analytic. However, since their relevant properties as relations, that is, that by settling on the “input”we know exactlywhat the “output” is, are the same, it seems there is no reason to work with two different notions of relations.
If we do wish to make a distinction between the relations that are analytic and the relations that are not, we seem to have an obvious way of doing so. The state US is defined as a subset of the set of all possible worlds W.
However, if we take serious the claim that in no possible world can someone be a bachelor and not an unmarried man, and vice versa — a claim that, as long as we are working relative to the meaning wein this world ascribe to the term bachelor, seems reasonable — it seems the analytic relations do not need to be presented as generation relations. This is so because these relations will hold throughout all members of the set W and worlds where these relations do not hold will therefore not be able to enter into the state US. This is a solution very similar to that of Schulz (2007). In
that framework we work with a set of possible worlds where the relations that we have called analytic all hold true. On this set of worlds we then impose a causal structure, which is just another name for a dynamics. The
approach of Schulz (2007) thus also has this two step procedure that we are proposing for our semantics. First we sort through all worlds to get rid of the worlds that are impossible.1 Then, on the remaining worlds we impose
the relations that we take ourselves to know about the world; in Schulz case these are the relations represented by a dynamics, whereas in our case these are the relations represented by the generation relations.
However, in the case of our semantics this represents a problem in case the agent does not know the analytic relations in question. We have defined the truth of a counterfactual relative to a state of an agent; which we have also called acceptability/assertability of a counterfactual. But, it seems clear that an agent to whom it is unknown that all bachelors are unmarried men should not straightforwardly accept the counterfactual ‘if John had been a bachelor, he would have been an unmarried man’. But, if we exclude all worlds where something is a bachelor yet not an unmarried man, and vice versa, from the set W we are unable to predict this. So we might want to make the set W relative to the agent in question, but then we need the following procedure; first we take the set W, then we impose the analytic relations that the agent takes to hold on these worlds, and then we impose thegeneration relations that the agent takes to hold on this set. We could of course do this by having two different kind of relations in our semantics; generation relations, which we have already presented and discussed, and then analytic relations, which we could abbreviate as ana(X, Y) when the literals in X and Y are in such a relation.
There are thus many ways one can build a semantics which will make the same predictions as the one we have proposed, but where we are more clear on what is an analytic relation and what is a relation ofbringing about, that is, a generation relation. For matters of simplicity and ease of exposition we have chosen not to make this distinction in the presentation of the semantics.