Solving the Problem of Nearly Convergent Knowledge

ABSTRACT

The Problem of Nearly Convergent Knowledge is an updated and stronger version of the Problem of Convergent Knowledge, which presents a problem for the traditional, binary view of knowledge in which knowledge is a two-place relation between a subject and the known proposition. The problem supports Knowledge Contrastivism, the view that knowledge is a three-place relation between a subject, the known proposition, and a proposition that disjoins the alternatives relevant to what the subject knows. For example, if knowledge is contrastive, I do not simply know that the bird in front of me is a goldfinch; instead, I know that the bird in front of me is a goldfinch rather than a raven or eagle or falcon. There is, however, a binary view of knowledge that overcomes even the Problem of Nearly Convergent Knowledge. I will give this binary view, show that it is motivated by the same considerations that motivate Knowledge Contrastivism, and argue that it avoids problematic consequences for our epistemic lives that Knowledge Contrastivism cannot.

KEYWORDS:

• Contrastive knowledge
• Contrastivism
• convergent knowledge
• disagreement

Acknowledgments

Special thanks to Jonathan Schaffer, Jonathan Kvanvig, Alexander Pruss, Allison Krile Thornton, Peter van Elswyk, and many others who offered written comments on previous versions of this article and verbal comments at the Eastern meeting of the American Philosophical Association and at Baylor University’s graduate colloquium. 

Disclosure statement

No potential conflict of interest was reported by the author.

Notes

1. Contrastivism is defended by Schaffer (2004, 2005, 2007a, 2007b, 2008a, 2008b, 2012), Schaffer and Szabo (2013), Sinnott-Armstrong (2008), and Karjalainen and Morton (2003), and the view is applied in various ways to knowledge of oneself (Sawyer 2014) and other propositional attitudes (Morton and Karjalainen 2008). Criticisms of the view can be found in Baumann (2008), Buenting (2010), Kallestrup (2009), Neta (2008), Pritchard (2008), Rourke (2013), and Steglich-Petersen (2015).

2. Although Jonathan Schaffer is the primary contemporary defender of the view, the view has roots as far back as Austin (1946) and Fred Dretske’s relevant alternatives epistemology (1970). In his 1946, Austin asserts that we can come to know a bird is a goldfinch by providing enough reason to rule out the alternatives that are ‘within reason, and for present intents and purposes,’ (84) without ruling out all the alternatives. Using the goldfinch example, Austin argues that we can know the bird is a goldfinch by describing its behavior and markings without being able to rule out that the bird is stuffed. Later, Dretske claims that a subject only knows a proposition relative to a set of alternatives, which he calls ‘contrasts.’ Dretske also states that when the set of contrasts changes, the subject no longer knows what the subject originally knew. For Dretske’s view, see Dretske (2000, 1970, 1981) and see Blaauw (2008), 229, for a brief summary of the challenges to Dretske’s view and the difference between Dretske’s view and contemporary Knowledge Contrastivism.

3. See Schaffer 2012, 414. Earlier, Schaffer makes the more modest claim that his view is more natural given the data (Schaffer 2007b, 392, 2005, 244). On the other hand, Schaffer himself is clear about the virtues of a binary view of the knowledge relation, calling the binary view ‘intuitively plausible and theoretically elegant’ (Schaffer 2007b, 386). It seems, then, that with respect to naturalness or elegance, the binary view is initially preferable to Knowledge Contrastivism, but since Schaffer believes the binary view is incompatible with the data, Knowledge Contrastivism is more natural.

4. The new problem is created by using Jonathan Schaffer’s reply to Kallestrup’s proposed solution to the Problem of Convergent Knowledge. Kallestrup responds to the Problem of Convergent Knowledge in Kallestrup (2009); Schaffer responds in Schaffer (2009).

5. I have rephrased Schaffer’s formulations of the questions and the resulting answers from his formulations in his 2005, 241, and 2007b, 348, which were not contrastive but were rather disjunctions.

6. See Schaffer 2007b.

7. Schaffer claims that this fourth point is confirmed experimentally (2007b), 390, and footnote 11, and in Schaffer and Knobe (2012).

8. Kallestrup (2009) and Jonathan Kvanvig (2013) propose this view.

9. See Schaffer 2009 for this reply, though the reply is not explicitly formulated into the new problem.

10. It is worth adding that any solution to the Problem of Nearly Convergent Knowledge must entail that if one instance of knowledge is ternary, all instances of knowledge are ternary. Baumann (2008) argues against the view that if there is one instance of knowledge that is three-place, then every instance of knowledge is three-place, and Schaffer (2012, 413–4) replies persuasively. A similar Schaffer-style response could be given to Buenting (2010), who argues that in some, but not all, cases, a ternary knowledge relation reduces to a binary one.

11. The correct target proposition must be among the alternatives. Using the multiple-choice question analogy, multiple-choice questions that indicate the structure of the question being asked need to have the correct answer among its options. (The term ‘target proposition’ was introduced by Morton and Karjalainen (2008), 273, and refers to the main object of the attitude, which here is the correct answer to the multiple-choice question and the consequent of the conditional I propose is the answer to contrastive questions.)

12. In his 2008, van Woudenberg proposes this binary view as a way of responding to other arguments for Contrastivism, and in that issue, his position is represented by Blaauw (2008) as the view that all known propositions are conditionals whose antecedents contain the disjoined alternatives (‘[T]he knowledge relation has the following form: “s knows that if {p v q}, then p”’) (Blaauw 2008, 232). The solution here motivates the proposal in van Woudenberg (2008), employs the proposal as a response to a different and new argument for Knowledge Contrastivism, and, as will be explicated later, revises the 2008 proposal so that the known proposition is sometimes, but not always, a conditional.

13. Grice (1989), 26.

14. An anonymous referee also raised the following objection: one can know the conditional that I propose is the answer to a contrastive question (if p or q then p) without having the relevant contrastive knowledge (p rather than q). This happens when the subject (1) knows that if p or q, then p, (2) has no opinion whether p or q, (3) has no opinion whether p, and (4) has no opinion whether q. When the subject meets conditions 1–4, on most genuine uses of the contrastive phrase, the subject does not know that p rather than q. For example, for G. E. Moore to know that he has hands rather than wings, Moore needs to think that he has hands.

In reply, I do think there are cases in which a subject genuinely knows the answer to a contrastive question while meeting conditions 1–4 above. I address one of these cases in the body – a subject may be asked, ‘Is that a goldfinch rather than a wave of blue anger?’ Using the multiple-choice setup, I argue that the subject knows the answer by presuming that the only relevant options are those presented in the question (without having an opinion about whether all the relevant options are included) and then eliminating the obviously false one. In that case, the subject knows the answer to the contrastive question while meeting conditions 1–4 above, precisely because, by going through the multiple-choice elimination process, the subject knows that if it’s a goldfinch or a wave of blue anger, it’s a goldfinch.

Nevertheless, on most uses of the contrastive phrase, a subject does not know p rather than q when the subject meets conditions 1–4 above. One explanation for this fact is that it is rare that subjects meet conditions 1–4 above. In most cases in which we say that a subject knows p rather than q, the subject plainly knows p or believes that the alternatives presented to them are relevant alternatives. If a subject plainly knows p, the subject can know p rather than q easily – if S knows p, then S knows that if p or q, then p. Further, if the subject believes that the alternatives presented to the subject (or those taken for granted in a given context) are relevant alternatives, the subject can easily make an inference to come to believe the proposition in the consequent. So, the fact that most of the uses of the contrastive phrase presume that 1–4 are not met can be explained, and the account I’ve proposed can explain even the use of the contrastive phrase when 1–4 are met.

Another reply one could make, but which I do not endorse: one could hold that knowledge does not require the kind of belief that is accessible to the subject upon their reflection (or perhaps knowledge does not require belief at all), in which case one could believe the use of the contrastive knowledge phrase to carry a false implicature; because it is a common mistake to think that knowledge requires belief, it is also a common mistake to assume that knowing p rather than q requires believing p, q, or their disjunction.

15. I have assumed that the reasonability of one’s belief can be defeated on further evidence and that another’s testimony provides evidence. Without these assumptions, even a proponent of binarity might hold a view that fails to meet the desiderata in this section or, alternatively, hold that the outcomes in this section are not, in fact, desiderata. I set aside these considerations in this section, since it is a prevalent belief that the reasonability of one’s belief can be defeated on further evidence and that another’s testimony provides evidence, as evidenced by debates in the literature on disagreement and skepticism.

16. This implication is a result of a Contrastivist desideratum, ‘epistemic modesty,’ in which those with a smaller contrast class in the third place of the knowledge relation cannot thereby come to know the contradictory of those with a larger contrast class. What closure principles Contrastivism is entitled to and whether they yield epistemic modesty is a point of contention. Kvanvig (2007, 2008) and Hughes (2013) argue that they do; Kelp (2011) argues that they do not.

17. The fact that the expert’s challenge fails to move the rationality of the novice’s belief is due to the falsity of an inference rule, Expand-q, which is required for the expert’s challenge to affect the novice’s rationality. According to the rule, when a proposition q₁ contains disjuncts that are a proper subset of the set of disjuncts contained in q₂, Kspq₁ → Kspq₂. Contrapositively, ~Kspq₂ → ~Kspq₁. Since the expert does not know that the bird is a goldfinch rather than a set of alternative birds that is larger (q₂) than the set of birds against which the novice knows that the bird is a goldfinch (q₁), the expert’s failure to know that the bird is a goldfinch would result in the novice’s failure to know only if the experts’ failure to know (~Kspq₂) entailed the novice’s failure to know (~Kspq₁). As shown above, it does not because Expand-q is false. See Schaffer (2005, 262–3).

18. Schaffer (2005) is explicit about the failure of Skepticism and Mooreanism as described in the above paragraph. According to Schaffer, Skepticism or Mooreanism would be effective only if the following were true: ‘(C3’) If Moore doesn’t know that he’s handed rather than envatted, then he doesn’t know that he has hands rather than stumps.’ He then reiterates that ‘C3’ is false – just because ‘Hands or vat-images of hands?’ falls beyond Moore’s discriminatory range does not imply that ‘Hands or stumps?’ does too.’ (264).

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Chris Tweedt

Dr. Chris Tweedt holds a Lecturer position at Christopher Newport University. His primary areas of research are epistemology, business ethics, and philosophy of religion.