Here is a problem I have been struggling with for the last couple of weeks. Suppose we assign the following truth-conditions to 'for all S knows, p might be the case'.
'For all S knows, p might be the case' is true iff there is a scenario v such that v is compatible with what S knows, and the 1-intension of 'p' is true at v.
For simplicity's sake, suppose scenarios are sets of enriched propositions, and suppose a scenario v is compatible with what S knows iff every enriched proposition in v has a 1-intension that is compatible with the 1-intensions of S's knowledge mental states.
This account seems to give us the right result in the simple cases. Suppose I don't know that water is H20. Then there is a scenario, namely the XYZ scenario, which is compatible with what I know and in which the 1-intension of 'water is not H20' is true.
But, now, here is the problem. Suppose I use 'water' and 'H20' interchangeably but fail to know that this is so. Then, since I do not know that I use 'water' and 'H20' interchangeably, it is plausible that I do not know that water is H20. So, it is strictly epistemically possible for me that water is not H20. But, as I use 'water' and 'H20' interchangeably, it is not deeply epistemically possible for me that water is not H20. In other words, 'water is not H20' is compatible with what I know but not compatible with my use of the words 'water' and 'H20'.
The problem now is this. The account of strict epistemic possibility just offered makes use of the notion of 1-intension. However, the 1-intension of a sentence S is a function from deeply epistemically possible scenarios to truth-values (see David Chalmers' work on this). As strictly epistemically possible propositions may be deeply epistemically impossible, the notion of 1-intension should not play a role in an account of strict epistemic possibility. But how then do we deal with strict epistemic possibility? I am pretty much stuck here. Any suggestions?
Monday, March 05, 2007
1-Intensions and Strict Epistemic Possibility
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12 comments:
Hi Colin. Thanks for the suggestion! I don't think it's going to work, though.
'For all Twin Oscar knows, water might be odorless' is true if uttered by me, but it doesn't seem to Twin-Oscar that there is a scenario v such that v is compatible with what he knows and the 1-intension of 'p' is true at v. Twin-Oscar has no water-thoughts.
Hi Brit,
It looks like you don't really use 'water' and 'H2O' interchangably here, since you say 'water is water' but not 'water is H2O'. But maybe you mean something like, you use them with the same 1-intension, or that it is knowable a priori for you that water is H2O, even though you don't currently know it. If so, then I'd be inclined to assimilate this case to others where something is a priori knowable without being known -- e.g. mathematical theorems. In these cases we are sufficiently nonideal that we haven't done the relevant a priori reasoning. So the negations are deeply (ideally) epistemically impossible, but strictly epistemically possible (for the relevant nonideal agent).
I think that to handle strict epistemic possibility in these cases, for nonideal reasonerss, within a possible-worlds framework, one needs to go beyond standard two-dimensionalism (which assumes idealized reasoning). The most obvious thing to do, which I discuss at the end of "The Nature of Epistemic Space", is to introduce more fine-grained scenarios, akin to impossible worlds. Then one can have fine-grained 1-intensions over these spaces, and so on. My student Jens Christian Bjerring is working on this project at the moment for his Ph.D. thesis.
Hi Dave,
Thanks for this! Right, suppose I use 'water' and 'H2O' with the same 1-intension, and suppose there are deeply epistemically impossible scenarios. The analysis I offered still won't do the trick. For it says:
'for all s knows, p might be the case' is true iff there is a scenario v such that v is compatible with what s knows, and the 1-intension of 'p' is true at v.
If a scenario v is deeply epistemically impossible, then the 1-intension of 'p' is not true there, since 1-intensions are functions from deeply epistemically possible scenarios to 1-extensions.
We might try: 'for all s knows, p might be the case' is true iff there is a scenario v such that v is compatible with what s knows, and the 1-EXTENSION of 'p' is the truth-value true at v.
But what determines the 1-extension of 'p' at a deeply epistemically impossible scenario? Not my use of the expressions (ex hypothesi). So, what makes it the case that 'p' has the truth-value true rather than false at such deeply epistemically impossible scenarios? (PS: I am not worried about the mathematical cases anymore -- just about this one)
Hi Brit,
Well, if we introduce fine-grained scenarios (i.e. deeply epistemically impossible scenarios), then we'll also have fine-grained 1-intensions defined over these scenarios. Then the model of strict epistemic possibility for nonideal reasoners will say something like: 'for all s knows p might be the case' is true iff there is a fine-grained scenario v such that v is epistemically possible for s and such that the fine-grained 1-intension of p is true at v.
The residual questions are: what is a fine-grained scenario and what is it for a sentence to be true at such a scenario? There are various different ways to model these things, a number of which are being explored by JC Bjerring in his thesis on "Epistemic Modality for Nonideal Agents".
One natural idea is that we can start with a notion of epistemic necessity that is more demanding than apriority: e.g. S is epistemically necessary if it can be known apriori via such-and-such small amount of reasoning. Then we can say a set of sentences is epistemically consistent if no conjunction of them is epistemically necessary in this sense. Then a fine-grained scenario can be modeled as a maximal epistemically consistent set of sentences (or an equivalence class thereof), and a sentence will be true at such a scenario if it is in the set, or perhaps if it is epistemically necessitated by some sentences in the set.
The construction is quite similar to the epistemic construction of scenarios in "The Nature of Epistemic Space", except that we start with a stronger notion of epistemic necessity. Then as long as 'water is H2O' in your case is not epistemically necessary in this sense, 'water' and 'H2O' will have different fine-grained epistemic intensions.
Thanks, Dave! This is great. A couple of questions remain (in my mind). I don't see how the problem goes away if fine-grained scenarios are defined in terms of a stronger notion of a priori. For we can just set up a new problem: while it is a priori known by me by such and such a small amount of reasoning that water is H2O, I don't know that it is. In other words, suppose I use 'water' and 'H2O' with the same fine-grained 1-intensions but suppose I don't know that I use them that way. Then prima facie at least 'for all I know, water might not be H2O' is true. So it is strictly epistemically possible that water is not H2O but there is no fined-grained scenario compatible with what I know in which the fine-grained intension of 'water is not H2O' is true. For there is no fine-grained scenario in which the fine-grained intension of 'water is not H2O' is true.
To solve the problem one would need to introduce "strict epistemic intensions" (or some such thing). (and scenarios defined on strict epistemic intensions). Now, I am not willing to do that, because I want the very same scenarios (and intensions) to play a role in the analysis of claims such as 'for all s knows, p might be the case', 'for all s knows a priori, p might be the case', and some other stuff that I am working on.
Besides it would be odd if there are different kinds of scenarios in play depending on the operator considered.
For this reason, I am now tempted to say that 'for all s knows, p might be the case' is false when s and the ascriber are me, and the situation is as envisaged. The reason I am tempted to say this (at this point) is that I think that if I am the ascriber, then I am using 'p' with such and such a 1-intension, and so, given that I am using the terms that way, it is simply false that for all I know, water might not be H2O.
I am not totally happy with this conclusion, though. But the conclusion is slightly less odd for analogous cases. If I say: 'For all Twin Oscar knows, water might not be H2O' and I use 'water' and 'H2O' with the same 1-intension, then it is obvious that what I said is simply incorrect.
Anyway, this is what I am now tempted to say. Fine-grained scenarios are great for all kinds of other purposes, though.
Hi Brit,
I don't think I get your case. You stipulate that is a priori known by you by the relevantly small amount of reasoning that water is H2O. From this, it follows that you know that water is H2O, and from this, it seems to follow that your utterance of 'For all I know, water might not be H2O' is false, contrary to what you suggest.
Of course maybe you don't have reflective knowledge of your intensions (most speakers don't!), but I think one can handle this issue separately from handling your first-order knowledge about water and H2O.
Hi Dave,
Just as I can use 'water' and 'H2O' with the same 1-intension without knowing it, so I am assuming I can use 'water' and 'H2O' with the same fine-grained 1-intension without knowing it. My use of my terms need not be known to me. As you yourself have pointed out, I might think I use 'Godel' to refer to the discoverer of the incompleteness of arithmetic when in fact I am using it to refer to someone who didn't prove this. Likewise, I am assuming I can use 'water' and 'H2O' with the same fine-grained 1-intension without knowing it. If so, then it is plausible that I don't know 'water is H2O', even though I use them in the same way. At the end of my previous comment I suggested that one could (and I said I would) bite the bullet and say that 'for all I know, water might not be H2O' is false in these circumstances. But intuitively it is true. I still find it puzzling.
Hi Brit,
I think we can set aside the complicated issue of knowledge of intensions and focus on knowledge of water and H2O. It seems to me that either you are in a position to easily know 'water is H2O' a priori (i.e. know it by a small amount of a priori reasoning) or you are not. If you are not in such a position, then 'water' and 'H2O' will have different fine-grained 1-intensions, and the issue you mention won't arise. If you are in such a position, then 'water' and 'H2O' will have the same fine-grained 1-intensions, but 'water is H2O' will not be strictly epistemically possible for you. Here I use the common observation that if one can easily deduce p based on one's current knowledge, then p is not strictly epistemically possible for one (i.e. it's not the case that for all one knows, p might be the case). So it looks like either way, the analysis is OK.
Hi Dave,
I don't understand this: 'if one can easily deduce p based on one's current knowledge, then p is not strictly epistemically possible for one (i.e. it's not the case that for all one knows, p might be the case).' I can easily deduce that 2 + 2 = 4 based on my current knowledge, but it *is* strictly epistemically possible for me that 2 + 2 = 4. (i.e., for all I know, 2 + 2 = 4 might be the case, because I know it is the case).
I would agree with 'if one can easily deduce p based on one's current knowledge, then not-p is not strictly epistemically possible for one (i.e. it's not the case that 'for all one knows, not-p might be the case'). Though I agree with this, I still find it puzzling. What is puzzling is that even if you are in a *position* to know 'water is H2O' a priori, then it *seems* that you might not know that you are in such a position. And so it *seems* that you might not know that water is H2O, and so for all you know, water might not be H20 (or so it seems).
To summarize: I agree with this: if I can easily deduce that water is H20 based on my current knowledge, then it is not the case that for all I know, water might not be H20. But for the reasons stated, this seems somewhat counterintuitive.
Hi Brit,
Sorry, I messed up a negation. Your version works, or alternatively: If one can easily deduce ~p based on one's current knowledge, then p is not strictly epistemically possible for one. Of course this is a slightly weaker condition that one that says "If one knows ~p, then p is not strictly epistemically possible for one". The difference is to handle cases where e.g. someone doesn't know ~p because they haven't thought about it, but if they were to think about it they would very easily come to know it. In such cases it's natural to hold that ~p is not epistemically possible for the subject.
So in your case, one can't infer from lack of knowledge of 'water is H2O' to the epistemic possibility claim. What matters is whether you're in a position to know it easily if you think about it. If you are, then 'water is not H2O' is not epistemically possible for you. If you are not, then 'water is not H2O' is epistemically possible for you. I think this applies whatever your higher-order beliefs and knowledge are about this lower-order knowledge. E.g. even if you're not in a position to know that you're in a position to know that water is H2O (maybe because your introspective faculties are not too good), then as long as you're in a position to know that water is H2O, 'water is not H2O' is not epistemically possible for you.
Hi Dave,
Thanks! I agree with this. A couple of further thoughts. First, if we admit that we cannot infer 'I know p' from 'I can easily deduce p based on my current knowledge', and that 'if I can easily deduce p based on my current knowledge, then not-p is not strictly epistemically possible for me' is true, then one might wonder whether 'for all I know, not-p might be the case' means exactly the same as 'not-p is strictly epistemically possible for me'.
Second, if I use 'water' and 'H2O' with the same fine-grained 1-intension, then it would seem that my utterance of 'it is strictly epistemically possible for Twin Oscar that water is not H2O' comes out false. For there is no fine-grained scenario v (relative to me -- the utterer) in which water is not H2O. A fortiori, there is no fine-grained scenario v (relative to me -- the utterer) such that v is compatible with what Twin Oscar knows, and water is not H2O in v.
The problem: my utterance of 'for all Twin Oscar knows, water might not be H2O' seems true (even if I use 'water' and 'H2O' with the same fine-grained 1-intension). [notice that it won't help to say that the fine-grained scenarios are to be partially determined by Twin Oscar's uses of 'water' and 'H2O', for he may not have both of these expressions in his vocabulary]
Hi Brit,
Re your first point: Actually, my intuition is that in these cases where p is easily deducible from current knowledge, 'For all I know, ~p might be the case' is false. Which suggests that even this locution should not be analyzed as 'I don't know p'.
Re your second point: anyone for whom 'water' and 'H2O' have the same 1-intension is a very unusual user of 'water', basically using it to pick out whatever plays a highly specific chemical role. So I don't think our Twin Earth intuitions involving the ordinary use of 'water' apply here. For example, Twin Oscar's term 'water' will pick out H2O, not XYZ. And my intuition is that in this case, 'For all Twin Oscar knows, water might not be H2O' is false.
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