Confirmation and singular propositions
In discussions of the raven paradox, it is generally assumed that the (relevant) information gathered from an observation of a black raven can be regimented into a statement of the form Ra & Ba ('a is a raven and a is black'). This is in line with what a lot of "anti-individualist" or "externalist" philosophers say about the information we acquire through experience: when we see a black raven, they claim, what we learn is not a descriptive or general proposition to the effect that whatever object satisfies such-and-such conditions is a black raven, but rather a "singular" proposition about a particular object -- we learn that this very object is black and a raven. It seems to me that this singularist doctrine makes it hard to account for many aspects of confirmation.
One case in point concerns the confirmation of hypotheses about identity. The point is well made in Chalmers 2011. The point I want to make doesn't involve identities. It doesn't exploit the non-singularist's modes of presentations at all.
Let's begin with a scenario (due to I.J. Good) in which the observation of a black raven disconfirms the hypothesis that all ravens are black. Suppose we have good reason to believe that on a certain island there are either (1) very few ravens all of which are black, or (2) a lot of ravens 80 percent of which are black. When we arrive at the island, the first thing we see is a black raven. Arguably, this supports hypothesis (2) over hypothesis (1), and thus disconfirms the hypothesis that all ravens on the island are black.
We can make sense of this effect by noting that the universal statement 'all Rs are Bs' does not entail any particular instance 'Ra & Ba'; it only entails the conditional if Ra then Ba. The instance therefore goes beyond the universal hypothesis. It contains the additional information Ra. In Good's scenario, this additional information is what disconfirms the univeral hypothesis, because the probability of Ra is much greater conditional on hypothesis (2) than conditional on hypothesis (1).
(Incidentally, Hempel 1945 observed that a universal hypothesis can even be inconsistent with any instance. The observation is in footnote 1 on page 13 of Hempel's paper, and a little hard to understand because of some typos. The example Hempel has in mind (I think) is the universal statement
∀x∀y(¬(Rxy & Ryx) → (Rxy & ¬Ryx)).
As you can check, this entails -- in fact, is equivalent to -- the statement that nothing satisfies the instance condition ¬(Rxy & Ryx):
¬∃x∃y¬(Rxy & Ryx).
Thus observing any instance of the universal hypothesis refutes the hypothesis.)
Anyway, back to the above diagnosis of Good's scenario. I think the diagnosis is essentially right, but there is something odd about the way I expressed it. It's true that when we arrived at the island and saw the raven, our evidence supported the hypothesis that there are a lot of ravens on the island and thereby disconfirmed the hypothesis that all ravens on the island are black. But is the relevant evidence really captured by the singular proposition Ra, attributing ravenhood to a particular individual a?
The problem is that it's hard to assign a sensible prior probability to that proposition. For the same reason it is hard to assign a prior probability to that proposition conditional on hypothesis (1) or hypothesis (2). But without such prior probabilities, we cannot make sense of the example as a case of Bayesian reasoning.
A natural and popular idea among friends of singular propositions is that one can only have singular thoughts about an individual if one stands in a suitable kind of causal contact to that individual. On that account, we could not have had any beliefs involving the raven a before seeing it on the island. But when we saw the raven, we immediately saw that it is a raven. We never gave significant credence to the possibility that it might be a shoe or a fish or a crocodile. The probability of Ra went straight from undefined to near 1. But then how did this information disconfirm hypothesis (1)?
To make sense of the inference, we have to assume that before learning Ra, we gave significant credence to various other hypotheses concerning a. If our prior credence in hypothesis (1) was fairly high, our prior credence in Ra should in fact have been quite low. So most of our credence should have gone to scenarios in which a is not a raven. But that not only runs into problems with the idea that singular thoughts require causal contact, it is also implausible on its own. Look at that raven. Before you saw it, how confident were you that it is a fish? It would be fair to respond that you never gave serious credence to the hypothesis that this raven is a fish. It would certainly be very odd to say, upon encountering the raven, "oh look, it's a raven! I had thought it's a fish (or a shoe, or whatever)."
Things might get even worse for the singularist doctrine if we consider cases where the evidential relevance comes not from the fact that a particular individual is a raven, but from the fact that it exists.
Consider two hypotheses about the universe. Hypothesis (1) says that the universe is fairly empty, inhabited only by a few hundred widely scattered individuals, including two ravens both of which are black. Hypothesis (2) says that there are trillions of individuals in the universe, among them ravens of all colour. Imagine an ideal reasoner who has learned very little about the world up to now and gives positive credence to those two hypotheses. At this point the reasoner opens their eyes for a split second and sees a black raven (or a hundred ravens, if you prefer). Arguably this confirms hypothesis (2) over hypothesis (1), because if hypothesis (1) were true one would mostly see nothing. What does the confirmatory work here is not so much that the observed object is a raven: observing a white shoe would likewise have confirmed hypothesis (2) over hypothesis (1). What does the work is that any objects were observed at all.
Now suppose the singularist doctrine is right and the content of the reasoner's observation is something like Ra & Ba. In order for this to confirm the hypothesis that the universe contains many objects, we would have to say that Ra & Ba is more probable conditional on the hypothesis that there are many objects than conditional on the hypothesis that there are few. More generally, we would have to say that for any (ordinary) predicate F, Fa supports the hypothesis that there are many objects. But then significant prior probability must have gone to worlds where a does not exist. So our reasoner must have singular credences not only about individuals with whom she is not in causal contact, but also about individuals that may not even exist! It should make sense for her to say: "Look, a raven! What a surprise to find that it exists. I was confident that this very raven wouldn't exist."
All these problems disappear on the non-singular conception of evidence. On that conception, what we learn is always given by a descriptive proposition. When we arrived on the island, we learned that there is a black raven presented to us in such-and-such a way. The identity of the raven doesn't matter. What we would have learned is exactly the same if it had been raven b rather than raven a, provided they had looked and sounded the same from our point of view. Accordingly, we don't have to struggle assigning prior probabilities to hypotheses in which this raven is a fish or doesn't exist. What matters is only the prior probability of the hypothesis that there won't be raven presented to us in such-and-such a way, and that's unproblematic and straightforward.