Author Information: Peter Baumann, Swarthmore College, email@example.com.
Baumann, Peter. “Nearly Solving the Problem of Nearly Convergent Knowledge.” Social Epistemology Review and Reply Collective 7, no. 10 (2018): 16-21.
The pdf of the article gives specific page references. Shortlink: https://wp.me/p1Bfg0-41B
Contrastivism (see, e.g., Schaffer 2004) is the view that knowledge is not a binary relation between a subject and a proposition but a ternary relation between a subject S, a proposition p (the proposition attributed as known and thus entailed by the knowledge attribution; we can call it the “target proposition”) and an incompatible (cf. Rourke 2013, sec.2) and false contrast proposition q (a “contrast”).
The form of a knowledge attribution is thus not S knows that p but S knows that p rather than q. According to contrastivism, it’s elliptical, at least, to say that Chris knows that that bird is a goldfinch. Rather, we should say something like the following: Chris knows that that bird is a goldfinch rather than a raven. Chris might not know that that bird is a goldfinch rather than a canary. There can, of course be more than one contrasting proposition; in this case we can consider the disjunction of all the contrasting propositions to constitute the contrast proposition.
A Problem and Tweedt’s Proposed Solution
Chris Tweedt’s thought-provoking “Solving the Problem of Nearly Convergent Knowledge” discusses one kind of argument against the binary view and in favor of contrastivism. The argument (see Schaffer 2007) is based on the claim that knowing that p consists in knowing the answer to a question of the form Is p rather than q the case? (“Is this bird a goldfinch rather than a raven?”; “Is it a goldfinch rather than a canary?”). Put differently, knowing that p consists in knowing the correct answer to a multiple choice question (“What bird is this? A: A goldfinch; B: A raven”; What bird is this? A: A goldfinch; B: A canary”).
The binary account faces a problem because it has to claim that if one knows the answer to one such question (“Is it a goldfinch rather than a raven?”) then one also knows the answer to the other question (“Is it a goldfinch rather than a canary?”). However, one might only be able to answer one question but not the other. This is the problem of convergent knowledge. This, argues Schaffer, speaks in favor of contrastivism.
Some defenders of the binary view (see Jespersen 2008; Kallestrup 2009) have proposed the following way out: One does not know the same proposition when one knows the answers to different contrastive (multiple choice) questions which share a “target” (a target proposition). Rather, the corresponding knowledge has the form S knows that (p and not q). Our subject might know that that bird is a goldfinch and not a raven while it might not know that it is a goldfinch and not a canary.
Schaffer (2009) has a response to this: Even though there is no convergence of knowledge here there is “near convergence” which is still bad enough. Using the principle of closure of knowledge under known entailment one can easily acquire knowledge of the second proposition on the basis of knowledge of the first. If Chris knows that that bird is a goldfinch and not a raven, then Chris also knows or can easily come to know, according to the binary view, that that bird is a goldfinch.
Since Chris also knows that whatever is a goldfinch is not a canary, he also knows or can easily come to know that that bird is not a canary. So, he knows or can easily come to know that that bird is a goldfinch and not a canary. Given that this is implausible, the problem of convergent knowledge is reincarnated as the problem of “nearly convergent knowledge”.
Tweedt’s ingenuous reply in favor of the binary account (see also van Woudenberg 2008) proposes to analyze the known answer to a contrastive (multiple choice) question as having conditional form:
(0) If p or q, then p.
Question: Is that bird a goldfinch rather than a raven? Answer: If it is a goldfinch or a raven, then it is a goldfinch!
Tweedt claims that this solves the problem of convergent knowledge because the answer to the question “Is that bird a goldfinch rather than a raven?”, namely
(1) If that bird is a goldfinch or a raven, then it’s a goldfinch,
is not “a few quick closure steps away” (see Tweedt 2018, 220) from the answer to the question “Is that bird a goldfinch rather than a canary?”, namely
(2) If that bird is a goldfinch or a canary, then it’s a goldfinch.
A Problem with Tweedt’s Proposal
Tweedt does not add an explicit argument to his claim that (2) isn’t just a few easy closure steps away from (1). Here is an argument that (2) is indeed just a few easy closure steps away from (1). If that’s correct, then Tweedt’s proposal fails to solve the problem of nearly convergent knowledge.
Let “g”, “r” and “c” stand in for “That bird is a goldfinch”, “That bird is a raven”, and “That bird is a canary” respectively. We can then, following Tweedt, assume (about some subject S) that
(3) S knows that if g or r, then g.
The proposition g is the target proposition here, not r (in the latter case our subject would know that if g or r, then r, instead). Since targets and contrasts are mutually incompatible, we may also assume that
(4a) S knows that if g, then not r;
(4b) S knows that if g, then not c.
Finally, we may assume that
(5) S knows that g or r.
To be sure, one can ask contrastive questions where both propositions are false: Is Einstein rather than Fido the dog the inventor of the telephone? One might want to answer that Einstein rather than Fido invented the telephone (whether one also believes falsely or doesn’t believe that Einstein invented the telephone).
However, this is a deviant case not relevant here because we are interested in cases where one of the contrasting propositions is true and particularly in knowledge that p (where p is the target). If that knowledge is construed in a binary way, then it involves knowledge of one of the contrasting propositions (p) that it is true; if it is construed as knowledge that p rather than q, then it still obeys the factivity principle for knowledge and thus entails that p. So, we can assume here that
g or r
is true. We may also assume that in standard cases the subject can know this. Hence:
(5) S knows that g or r.
A closure principle like (Closure) together with (3) and (5) entails
(6) S knows that g.
(Closure) together with (4b) and (6) entails
(7) S knows that not c.
So, there are only a few quick and easy “closure steps” to the implausible (7). And we can add that disjunction introduction will allow the subject to come to know (on the basis of (6)) that g or c
(8) S knows that g or c.
(We could also argue for (8) along the lines of the argument above for (5)). Conjunction introduction together with (6) and (8) will allow the subject to know that (g or c) and g:
(9) S knows that (g or c) and g.
Since whenever a conjunction is true, a corresponding conditional is true, the subject can also come to know that
If g or c, then g.
In other words:
(10) S knows that if g or c, then g.
There are then also quick and easy closure steps leading from Tweedt’s (1) to (2). So, the problem of nearly convergent knowledge remains unsolved.
There is more than one strategy for Tweedt to defend his proposal of a solution to the problem of nearly convergent knowledge. One would be to modify the closure principle in such a way that certain steps are not allowed any more. For instance, one could try to argue (4b) and (6) don’t lead to (7) because a valid closure principle doesn’t allow knowledge-producing inferences from easy-to-know propositions to hard-to-know propositions.
This kind of idea is well-known from discussions about skepticism: I might know that I have hands, and I might also know that if I have hands, then I am not merely hallucinating that I have hands, but I don’t know that I am not merely hallucinating that I have hands. Fred Dretske and Robert Nozick as well as some others have argued for such a view (see Dretske 2005 and Nozick 1981, ch.3). However, I am not sure whether Tweedt wants to choose this strategy. And it doesn’t seem easy to find a modification of the closure principle that is not ad hoc and has independent reasons in its favor.
Another strategy would be to identify other analyses of the answer to a contrastive (multiple choice) question. Perhaps one can improve on Tweedt’s response in a way similar to the one in which he attempts to improve on Kallestrup’s (and Jespersen’s) response to the original problem of convergent knowledge. I have to leave open here whether there is an analysis that does the trick, and what it could be (see, e.g., Steglich-Petersen 2015).
Could one take Tweedt’s conditional (0) not as a material conditional but rather as a subjunctive conditional? I am afraid that this would constitute a change of topic. Knowledge is factive and what would be the case (P) if something else (Q) were the case does not tell us anything about whether P or Q is the case, even if the corresponding subjunctive conditional is indeed true.
It might be more promising to explore the potential of a complaint about question begging: Isn’t Schaffer’s diagnosis that one can know (1) without knowing (2) already presupposing the truth of contrastivism? Why should one believe that there is a problem with knowing (2) but not with knowing (1) if not because one has already accepted contrastivism about knowledge?
One final side remark on an alleged advantage of binary accounts like Tweedt’s. He argues (see Tweedt 2018, 223) that contrastivism doesn’t take the skeptical problem seriously (enough) and rather deflates it; one might even want to say that contrastivism changes the topic. According to contrastivism I can know the Moorean proposition that I have hands rather than stumps even if I do not know the anti-skeptical proposition that I have hands rather than am merely hallucinating hands. Closure does not support any claim that if I know the one, then I know the other, too. Tweedt thinks this is a disadvantage of contrastivism. However, contrastivists like Schaffer would see this as an advantage. It seems to me that both ways of looking at the anti-skeptical potential of contrastivism have something going for them. In this context, it might be better to leave the question open whether skepticism can be deflated or not. (Similar points will apply to Tweedt’s remarks concerning the debate about expert disagreement; see Tweedt 2018, 223)
Ingenuous as Tweedt’s proposal is, it does not, I think, solve the problem of nearly convergent knowledge. However, this does not mean that a ternary account of knowledge has to be preferred to a binary account. I think that there are serious problems for contrastivism that make the binary account the better options. But this is something for another occasion.
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Dretske, Fred I. 2005, The Case against Closure, Matthias Steup and Ernest Sosa (eds.) Contemporary Debates in Epistemology, Malden, MA: Blackwell, 13-26.
Jespersen, Bjørn 2008, Knowing that p rather than q, Sorites 20, 125-134.
Kallestrup, Jesper 2009, Knowledge-wh and the Problem of Convergent Knowledge, in: Philosophy and Phenomenological Research 78, 468-476.
Nozick, Robert 1981, Philosophical Explanations, Cambridge, MA: Harvard University Press.
Rourke, Jason 2013, A Counterexample to the Contrastive Account of Knowledge, Philosophical Studies 162, 637-643.
Schaffer, Jonathan 2004, From Contextualism to Contrastivism, Philosophical Studies 119, 73-103.
Schaffer, Jonathan 2007, Knowing the Answer, Philosophy and Phenomenological Research 75, 383-403.
Steglich-Petersen, Asbjørn 2015, Knowing the Answer to a Loaded Question, in: Theoria 81, 97-125.
Tweedt, Chris 2018, Solving the Problem of Nearly Convergent Knowledge, Social Epistemology 32, 219-227.
van Woudenberg, René 2008, The Knowledge Relation: Binary or Ternary?, Social Epistemology 22, 281-288.
 We can allow for a different kind of contrastive knowledge relation where the contrast can also be true. Suppose I know of Jo, the president of the cheese club and also my dentist, that Jo is my dentist. Since I have no clue who might be the president of the cheese club, it could be appropriate to express all this by saying that I know that Jo is my dentist rather than the president of the cheese club. However, against this speaks that the latter is best understood as saying that I know that Jo is my dentist rather than that I know that Jo is the president of the cheese club. But even if there was such an alternative kind of contrastivity of knowledge, we can leave it aside here.
 Here is a basic version: (Closure) If S knows that p, and if S knows that p entails q, then S knows that q. Whistles and bells should be added but nothing depends on these here; we can use (Closure) or other simple variants of it here.
 Tweedt adds that not all knowledge or all answers to questions are conditional in form (see Tweedt 2018, 222).
 See also Tweedt 2018, 224, fn.11 and 225, fn.14. Given (4a) and therefore also given that if g, then not r, we can also rule out that both propositions are true. Could r be true and g be false? Sure, but then r would be the target proposition, not g. This would not constitute a different case.
 Even if one insists that knowledge of the answer to a contrastive question is compatible with the lack of truth of any of the contrasting propositions, one still has to accept that there are other cases where there is a true target. And for such cases one still needs a convincing solution of the problem of nearly convergent knowledge.
 A different route to (6) uses (5) and (8) below together with the claim that all contrasting propositions are mutually incompatible. However, one might have doubts about the latter assumption and allow for propositions in the contrast set to be mutually compatible (as long as they are incompatible with the target proposition). I want to leave this issue open here and will thus not put weight on this alternative route to (6). – Here is still another route to (6). If it is true (following (3)) that if g or r, then g, (thus ruling out the case in which g is false and r is true) and if it is also true (following (4a)) that if g, then not r (thus ruling out the case in which both g and r are true), and if, finally, r is the disjunction of all the propositions contrasting with g (thus ruling out the case in which both g and r are false), then we are left with only one case: the case in which g is true and r is false. Since this is a case where g is true, S can come to know g on the basis of the considerations just given. However, in many cases the contrast set does not contain all propositions except the target proposition. In all these cases, we need to use another route to (6).
 If one replaces c by some proposition about the obtaining of a skeptical scenario (like An evil demon makes me hallucinate goldfinches), then one gets to even more drastic cases and implications.
 Again, if one replaces c by some proposition about the obtaining of a skeptical scenario (like An evil demon makes me hallucinate goldfinches), then one gets to even more drastic conclusions like the following one: S knows that if he is looking at a goldfinch or is suffering from a demon-induced hallucination of a goldfinch, then he is looking at a goldfinch. Hence, given the above, S can also come to know he is looking at a goldfinch and not suffering from a demon-induced hallucination of a goldfinch.