What do we learn from experience?
Looking out of the window, I come to believe that it's snowing outside. I don't just add this single belief to my stock of beliefs; I conditionalize on something. On what?
It doesn't seem to be the proposition that the scene before my eyes contains the very features that caused my perception. Arguably, what caused my perception is H2O falling from the sky. If that was what I conditionalize on, I would take my present experience as evidence that snow is made of H2O, rather than XYZ. But I don't.
So how about the proposition that snowy stuff is falling from the sky? If that is what I conditionalize on, my experience would lower my (already quite low) credence in the hypothesis that someone goes out of his way to make it look like it's snowing even though it isn't really snowing. But on the contrary, my credence in this hypothesis is increased: if it did not look like it's snowing, that would descrease the probability that someone goes out of his way to make it look like it's snowing. So the fact that it does look like it's snowing increases the probability of that hypothesis.
In general, my experience supports any hypothesis H of which I believe that if H obtained then I'd have this kind of experience, including the hypothesis that H2O falls from the sky, that XYZ falls from the sky, that I'm halluzinating that it is snowing, and that this window is a sophisticated computer screen with a "snow" program running. So whatever it is that I conditionalize on, it must not rule out any of these hypotheses.
So perhaps the proposition I conditionalize on is just the proposition that I'm having this kind of experience. Let's call this proposition the minimal content of my perception.
In principle, conditionalizing on minimal content could lead to all kinds of weird beliefs. If I thought an evil demon deceived me in such a way that I halluzinate snow iff a tiger walks by, my current visual experience would cause me to believe that a tiger walks by.
Could someone infer that a tiger walks by from this kind of experience without believing anything like the demon hypothesis? Could someone find it just as natural to take this experience as evidence for tigers as I naturally take it as evidence for snow? That sounds odd.
So either the content I conditionalize on goes beyond minimal content, or folk psychology assumes a certain distribution of priors so that everyone draws certain 'inferences' from their experiences. I suspect this is a distinction without a difference.
Anyway, what is the resulting, not-quite-minimal content of my perception? Like the minimal content, it excludes (or at least assigns very low probability) to situations where I don't have this kind of experience. But unlike the minimal content, it also excludes, say, the possibility that a) I have this experience while b) the world is roughly as I think it is -- no deceiving demons or windows etc. --, c) my eyes are working properly, and yet d) the weather is clear.
Let's call this the raw content of my experience. I'm not sure how best to define this notion. Roughly, a possibility belongs to the raw content of an experience if I cannot coherently imagine someone having the experience who does not thereby increase his credence in this possibility. That snowy stuff is falling from the sky is still not part of the raw content of my experience, as I can easily imagine situations where it would be rational not to take this experience as evidence that snowy stuff is falling from the sky.
Minumal and raw content are not our everyday notions of content: it would be strange to say that I see that I am having a certain kind of visual experience. What I see (or quasi-see) is rather that it is snowing, or that snowy stuff is falling from the sky. Our everyday conception of perceptual content says that when people halluzinate, the content of their perception is usually false.
In fact, there are probably different everyday notions of content. Some are narrow: narrow everyday content is like raw content except that it also rules out certain skeptical possibilities like halluzinations. I don't know where to draw the line here: does the narrow everyday content of my experience exclude that I'm looking at a sophisticated computer screen, or -- to change the example -- at a donkey painted like a zebra? Then there are various kinds of wide everyday content, in which the nature of the things causing my perception figure: I see crystallized H2O, my twin sees crystallized XYZ; crystallized H2O is part of the content of my perception and not part of the content of my twin's perception.
There's nothing wrong these kinds of content, except that they are not what we conditionalize on when we look around us. Narrow everyday content at least comes close: for people who assign zero credence to skeptical alternatives, it probably coincides with raw content.
Two relevant sorts of content: (i) What you would conditionalize on in virtue of *endorsing* the experience; (ii) What you would conditionalize on in virtue of accepting that you *have* the experience. I think the ordinary notion of content of experience is closer to (i). I think that both sorts of content should be understood as narrow content -- at least on my view, content that one conditionalizes on is always narrow. In the case of (i), there are various proposals in the literature about what that narrow content might be.
As for (ii), I'd be inclined to say that it's a content true just in scenarios (centered worlds) where the person at the center has an experience of the relevant sort. The rest of the work of excluding weird scenarios is done by priors. Is this a distinction between saying this and saying those worlds are excluded by the content? Well, intuitively it seems consistent to suppose that the minimal content is correct and that one is in a weird scenario. If so, it's natural to say that the minimal content doesn't exclude these scenarios.
But following up your suggestion, maybe there are two notions of content here, depending on whether one ties the content to what one can infer *conclusively* from accepting that one has the experience (the minimal content), and one what can infer defeasibly but on a priori grounds (the not-quite-minimal or raw content). I think one comes up with a cleaner picture of content in general if one ties it to conclusive a priori inference. Otherwise inductive and abductive inferences get into content, which seems odd, and one can't draw the distinction between deductive and inductive inference in virtue of content. But a pluralist can allow both notions.
In any case, it's interesting to see that the multiple notions of content here are all tied to inferential role, but based on different ways of conceiving of the inferential role of an experience. I.e. (i) what one infers a priori from endorsing the experience, (ii) what one infers conclusively and a priori from accepting that one has the experience, and (iii) what one infers a priori (conclusively or nonconclusively) from accepting that one has the experience. No doubt there are more.