Schaffer on Knowing the Answer

Been re-reading this very fine paper recently (in order to be a responsible dissertation director!), and noticed something puzzling. Schaffer aims to discredit the reductive view that knowledge-wh constructions are reducible to knowledge that constructions. The basic idea of the reductive view is that the former construction encodes a question, and the reduction can go through correct answers to such questions. So, you know whether the caged bird sings, when the caged bird sings, iff you know that the caged bird sings.

The fundamental problem Schaffer raises for this reductive view is the problem of convergent knowledge: where two different questions have a common correct answer. As in: S knows whether it is a wolf or german shepherd vs. S knows whether it is a poodle or german shepherd. When it is a german shepherd, a correct answer to the two embeddded questions is: it is a german shepherd. But the first knowledge is hard and the second is easy, so a reductive view that replaces both knowledge-wh attributions with knowledge that it is a german shepherd is in trouble.

It strikes me that this argument plays off a too simplistic version of the reductive view. Some versions of it allow the reduction through any correct answer to the question (see, e.g., Higginbotham), but that’s a special case.

To see alternatives, note that there are lots of correct answers to the questions “is it a GS or W?”, “is it a GS or P?”. Among them are: “it is a GS”, “it is a GS and not a W”, “it is a GS and not a P”, and (a favorite among logicians) “yes”. There is no answer such that it is the correct answer to these questions. There are multiple correct answers. So which answers should the reductive view exploit in trying to reduce knowledge-wh to knowledge that?

I would think one would begin with the idea of informative and responsive answers to the question. So if the question is “is it a GS or a W?”, the answer that it is a GS and not a W is more informative and responsive an answer to the question than the answer that it is a GS. In short, I would think that a reductive view would want to exploit answers to questions that involve all the central conceptual elements involved in the question.

I don’t pretend that this is formally precise or an adequate form of a reductive view as it stands. It’s more like a pointing in the direction that I expect the best reductive view to be found. If so, however, it looks like the problem of convergent knowledge is going to have to be formulated differently, if it is to raise a problem for the reductivist view. For knowing that it is a german shepherd and not a wolf is knowing something different from knowing that it is a german shepherd and not a poodle.


Schaffer on Knowing the Answer — 6 Comments

  1. I have been fascinated with this area of thought since Hofstadter wrote the Pulitzer Prize winning “Goedel, Escher and Bach” which points to Copycat with Melanie Mitchell, his old analogical reasoning approach to AI.

    Take a fairly easy question on an IQ test: A bird is most like,
    a)flying squirrel b) flying fish c)airplane d)bat e) butterfly

    Analogical reasoning compares one conceptual space to another plus the relative intensities of the various connections. So some knowledge is required to answer the above question. Flying fish and squirrels glide, and so don’t fly like a bird. An airplane is not living. Although the important taxonomic consideration of reproduction by laying eggs is shared between the bird and butterfly, the combined weight of other similarities (such as how and what they eat) produces “d) bat” as the correct answer.

    As questions on the test become more difficult (we know what that means but it is defined in a circular fashion) the answers people with an average IQ give become more random. So if there are five possible answers to a difficult question, the answers given by the 100 IQs tend to spread out at 20% for each answer. This is true for people in the same socioeconomic status independent of the well known cultural biases inherent in IQ tests.

    People who typically score 140 on an IQ test do so because they have in common recognizing a rule or a pattern in comparison to those of IQ 100, whose answers are random because they do not discriminate matching distinguishing features. OTOH, people with estimated IQs can’t be measured by a standardized test. That’s because there is no consensus among the people who devise the test, what the right answers actually are. This inability to discern an absolute right answer is mirrored by our perception of reality and our analogically acquired knowledge -> our tool to reason/know reality.
    The justified true belief attempt to define knowledge rests upon a foundation of commonly shared perceptions and common understandings reached by reasoning about those shared perceptions.

    There are patterns or rules displayed by reality which transcend the human ability to grasp them, and likely go beyond any algorithmic process to encompass them. Reality, systems of events unfolding may show random processes which appear patterned, or patterned processes which appear random, and we don’t know which are which, or indeed, if there are any genuine foundational random processes, or if various discussions about those concepts are artifacts of our analogical reasoning. I think the basic predicament reached in attempts to define Causality is the inability to distinguish or discriminate one event being the direct cause of another, from those events which have a common cause but appear in close succession, so that they appear to have a common cause. So at this level of abstraction it is similar to the difficulty in analogical reasoning, it’s a problem in pattern recognition or lack thereof.

  2. Perfect opportunity for shameless self-promotion!

    I’ve just finished a draft for _Philosophy Compass_ on knowing-wh. Section 2 of the paper covers Schaffer’s convergent knowledge problem, and some of your responses are confirmed by the literature. The draft is available on my website (and comments from any and all are very welcome).

    Your point about multiple answers to a question is absolutely right, though it seems that whichever answer takes priority in a context is interest-relative (in an almost trivial sense). Section 3 of the paper covers this sort of issue.

    Still, Schaffer may not care if a question admits of multiple answers. His point is: Take a case where someone knows that it’s a GS and not a P. Then, they know it’s a GS. This last bit of knowledge is *one* answer to the question “Is that a GS or a W?” But then, orthodox reductionism says the person knows-whether it is a GS or W in virtue of knowing *an* answer to the question.

    Still, you’re right that most reductionists need not be committed to such a simplistic view on the case. For instance, reductionists like Groenendijk & Stokhof and Jason Stanley distinguish between “mention some” cases, where knowing one answer is necessary and sufficient–versus “mention all” cases, where knowing all answers is necessary and sufficient (though ‘all’ can be contextually restricted). So these folks might just say that “GS or W?” is a “mention all” case…it’s the kind of case where knowing one answer isn’t sufficient for knowing-wh.

  3. Hey Jon,

    In the case above — S knows whether it is a wolf or german shepherd vs. S knows whether it is a poodle or german shepherd — you mention that knowledge of the first is “hard”, while knowledge of the second is “easy”. I’m unsure that this is correct.

    Intuitively, this does seem correct and I take the guiding insight to be this: It’s easier to tell the difference between a poodle and a German Shepard than it is to tell the difference between a wolf and a German Shepard and therefore knowledge of the first question — whether it’s a GS or a W — is more difficult to come by (harder) than knowledge of the second question — whether it’s a GS or P. I think that this is probably right, but I think that, at least in this case, it is somewhat of a red herring.

    Imagine asking someone the first question. The following responses would all be acceptable answers — 1.) “I know it’s not a wolf, therefore it must be a German Shepard”; 2.) “It’s a German Shepard”; 3.) “I know it’s a German Shepard, but I don’t know what wolves are, so, as long as wolves and German Shepherds aren’t the same thing, it must be a German Shepperd.” Of course, there are many other possible answers as well, but these three will illustrate the point fine.

    Notice, that all three of these responses illustrate different sorts of knowledge — the first illustrates knowledge ‘that it’s not a wolf'(and since the question implies it’s either a W or a GS, one can infer that it’s a GS) the second illustrates knowledge ‘that it’s a GS’ (implying that the responder also knows ‘that it’s not a W’) and the third illustrates knowledge ‘that it’s a GS’ and a lack of knowledge about what wolves are.

    Now, imagine each of these three answers in response to the question — “What is that?”. It seems that only the second and third answer would be acceptable; if someone said “Well, it’s not a wolf” that wouldn’t answer my question.
    The point is that both the second and third answer above have the form “that is a GS and not anything else (unless it’s the same thing as a GS)”.

    Now, I’ve rambled a little bit, but here is the main point. Shaffer argues that knowledge of the first – GS v W — is harder than knowledge of the second — GS v P — but this is NOT the case if the answer given is ‘That is a GS’ because if I know that it’s a GS (and nothing else) than why should it be more difficult for me to answer the first question than the second? It doesn’t seem to me that it is. On the other hand, if the answer given is something like ‘It’s not a Wolf/poodle, so it must be a GS’ then there may be an argument that the first is more difficult than the second. However, even on this interpretation I’m not sure that the first knowledge is “harder” just because W’s and GS’s are more similar than P’s and GS’s. So, I’m not sure that I understand where the convergent knowledge problem arises at all.

    To my mind, the reductivist should say that you know whether it’s a W or a GS, when it’s a GS iff you know a.) that it’s a GS b.) that it’s not a GS c.) that it’s a wolf OR d.) that it’s not a wolf. Further, you could transfer this to the poodle case and then I don’t see where the problem arises at all? If anything, it seems you could only say that knowing A or C are more difficult than B and D because they are cases of positive identification.

    As a caveat, I am running out the door to get a haircut and I haven’t read Schaffer’s paper, so if I apologize if I have completely flubbed this up or taken a page to answer what should have taken a couple sentences! 🙂

  4. Start with, on the hard/easy issue, the obvious point that it is harder to tell whether something is a german shepherd rather than a wolf than it is to tell that something is a german shepherd rather than a poodle. The rest he’ll have to argue for, but it would be a head-scratcher to be told that this point is mistaken.

  5. Making knowledge question-relative, as Schaffer does, feels quite radical. And he goes to some trouble to make us comfortable with the idea. How would it be if we did something else, that may be just as radical, but that would save knowledge from question-relativity? What I have in mind moves the relativity into the proposition that is known (I do like the idea of reducing knowledge-wh to knowledge-that).

    (What follows may well be somewhere in the literature, in which case, my apologies to whomever I have failed to cite. It certainly bears a relationship to the KAL proposal, which Schaffer discusses at pp 491ff of “Knowing the Answer Redux: Replies to Brogaard and Kallestruppp” Philosophy and Phenomenological Research, March 2009.)

    Suppose you present me with a quadruped in fog. The fog slowly clears, and we may check my knowledge at any time as this happens. (The degree of fogginess is a stand-in for the customary assumption of limited ability to distinguish between breeds even in perfect conditions, and there may be a separate debate to be had about whether it is an adequate stand-in, or whether it skews the philosophical debate.)

    Here are different things I might know at any given time:

    (1) If it is a German shepherd (GS) or a wolf (W), it is a GS.
    (2) If it is a GS or a poodle (P), it is a GS.
    (3) It is a GS.

    If I know (3), then I know both (1) and (2), simply because the truth of (3) makes the consequents in (1) and (2) true. That result looks intuitively correct.

    If I know either, or even both, of (1) and (2), I may not know (3). As the fog clears, I probably get to know (2) first. By the time I get to know (1), I am probably only a few moments away from knowing (3) – assuming that (3) is true, and that I can in general distinguish between Ws and GSs under perfect conditions.

    The point of this is that each of (1), (2) and (3) is a proposition, appropriate to the non-question-relative “I know that p” locution.

    I have shunted the question-relativity into the answers. Moreover, my response to “Do you know whether it is a GS or a P?” is “I am not going to answer your question directly, but here is something closely related to your question that I do know: (2)”. But I do not think there is anything wrong with that. There are questions, direct answers to which can be inappropriate: “Have you stopped blackmailing the mayor?”, for example.

    The proposed move may be worth making, simply because it gets us away from question-relativity, and also makes a slightly more obvious connection than does question-relativity with possible worlds. “I know that (2)” can very directly be re-worded as “I know that if we are in one of the GS-worlds or one of the P-worlds, we are in one of the GS-worlds”. (See Schaffer, “Knowing the Answer Redux”, pp 498-499 on possible worlds.)

    There is also a straightforward application to the likely fact that I know (4) but not (5):

    (4) If it is a zebra or a giraffe, it is a zebra.
    (5) If it is a zebra or a cleverly disguised mule, it is a zebra.

  6. Jon, I scanned the thread and the Schaffer papers, and then wrote my comment, and then neglected to review the thread before posting. Looking back over the thread, I see that all I have done is go a little way down the path that you indicated in your original post. My apologies for accidentally not acknowledging this in my comment.

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