Knowledge as de re true belief?

Abstract

In “Facts: Particulars of Information Units?” (Linguistics and Philosophy 2002), Kratzer proposed a causal analysis of knowledge in which knowledge is defined as a form of de re belief of facts. In support of Kratzer’s view, I show that a certain articulation of the de re/de dicto distinction can be used to integrally account for the original pair of Gettier cases. In contrast to Kratzer, however, I think such an account does not fundamentally require a distinction between facts and true propositions. I then discuss whether this account might be generalized and whether it can give us a reductive analysis of knowledge as de re true belief. Like Kratzer, I think it will not, in particular the distinction appears inadequate to account for Ginet-Goldman cases of causally connected but unreliable belief. Nevertheless, I argue that the de re belief analysis allows us to account for a distinction Starmans and Friedman recently introduced between apparent evidence and authentic evidence in their empirical study of Gettier cases, in a way that questions their claim that a causal disconnect is not operative in the contrasts they found.

1 Facts versus true propositions

The view has been proposed by several authors that one way of capturing the difference between knowledge and justified true belief might be in terms of the kind of objects they select for (see Russell 1918; Vendler 1972; Kratzer 2002 among others). The idea is that knowledge selects for facts, whereas belief selects for propositions. On that view, a fact is more than a true proposition, and to know a fact is more than to merely believe a true proposition. But what does it mean to know a fact, as opposed to believing a true proposition? Kratzer (2002) considers a version of Goldman’s (1967) causal account of knowledge, in which knowledge is defined in terms of de re belief about some fact:

Kratzer gives an application of this analysis to Russell’s (1912) pre-Gettier scenario, in which a man has a true belief, but which falls short of constituting knowledge:

“If a man believes that the late Prime Minister’s name began with a B, he believes what is true, since the late Prime Minister’s last name was Sir Henry Campbell Bannerman. But if he believes that Mr. Balfour was the late Prime Minister, he will still believe that the late Prime Minister’s last name began with a B, yet this belief though true, would not be thought to constitute knowledge.” (Russell 1912, pp. 131–132)

On Kratzer’s analysis, the belief that the late Prime Minister’s name begins with a B is true qua propositional belief, but the corresponding fact is the fact that Bannerman’s name starts with a B. The man simply fails to have the propositional belief he has as a de re belief about that fact.

That analysis is suggestive, but it raises the question: what is it to have a de re belief of some fact? Kratzer in her paper offers to capture facts in a framework of situation semantics. In this short paper, I propose a critical examination of the idea that knowledge could be treated as de re belief of some kind, but in a more conservative framework than Kratzer’s, and in particular without committing myself to an ontological distinction between facts and true propositions. Like Kratzer, I believe that the de dicto/de re distinction is relevant for the analysis of Russell’s puzzle, and of Gettier’s puzzles, but I think the distinction can be captured entirely in terms of binding and scope mechanisms.

Below I first present an analysis of both puzzles in epistemic logic, and then ask whether we might identify knowledge with de re true belief. In agreement with Kratzer, we will see that Goldman’s fake barn cases do not seem amenable to an analysis in terms of de re true belief alone, and moreover that close kins to Gettier’s original cases also appear not to fall under that account. On the other hand, I will argue that the de re analysis casts light on a distinction recently proposed by Starmans and Friedman (2012) between what they call apparent versus authentic evidence in their empirical study of laymen’s judgments about Gettier scenarios. The goal of this paper is modest: my ambition is not to present a new analysis of knowledge, but mostly to contribute to the current debates on the typology of Gettier cases, by determining which aspects may and which may not be treated in terms of the de re versus de dicto distinction, and first by examining how best to articulate that distinction.

2 Russell’s puzzle and de re belief

Let a denote Bannerman, and b denote Balfour. Let S stand for the complex predicate: “having a name starting with a B”, and let P stand for the complex predicate: “being a late Prime Minister”. Let us assume that both names a and b are part of our man’s mental repertoire, like the corresponding predicates. To make things realistic with regard to Russell’s scenario, we may assume that our man (let us call him Ralph) believes the propositions expressed by the four following sentences:

That is, Ralph believes: “Balfour is a late Prime Minister”, “Balfour has a name starting with a B”, but also “Bannerman has a name starting with a B”, and “at most one person is late Prime Minister”. We also suppose Ralph’s beliefs to be closed under logical consequence.

To deal with definite descriptions, given a predicate Px I will use $P'x$ as an abbreviation for the complex predicate $Px \wedge \forall y (Py \supset x=y)$. Thus, $P'x$ means that x is the only object satisfying P.¹ One way of representing “Ralph believes that the late Prime Minister is Balfour” is by the following de dicto ascription, in which the belief operator scopes above the existential operator:

Similarly, one can represent “Ralph believes that Balfour’s name starts with a B”:

From those two ascriptions, it follows by closure that “Ralph believes that the late Prime Minister’s name starts with a B”, which we can represent as:

The expression “the late Prime Minister” is read purely de dicto here, however. Given , we also have:

Although Ralph mistakenly ascribes the property of being the late Prime Minister to Balfour, I shall assume that the names “Balfour” and “Bannerman” rigidly denote the same distinct individuals in the actual world and in Ralph’s belief worlds (for Ralph does not mistake them for being the same individual, we may suppose he even met both in the past, and keeps distinct representations for each of them). From (6) and from the rigidity assumption, it follows that $\exists x(x=a \wedge B_{r}Sx)$. From the assumption that $P'a$ is true in the actual world, it follows from this that:

That is: “of the actual late Prime Minister [who turns out to be Bannerman], Ralph believes that his name starts with a B”.² What fails to hold, however, is the following:

That is: “of the late Prime Minister, Ralph believes that he is the late Prime Minister and that his name starts with a B”. We can be even more explicit, and see the following to fail:

That is: “of the late Prime Minister, whose name starts with a B, Ralph believes he is the late Prime Minister and that his name starts with a B”. It is easy to construct an epistemic model of Ralph’s situation in which all of the previous assumptions are true relative to the actual world, but where (8) and (9) come out as false.

The comparison between (5) and (9) is instructive: basically, the de dicto content of (5) is true in the actual world, but Ralph fails to refer it to the right entity. So Ralph has a correct de dicto belief, but an incorrect de re belief. Putting them side by side, what we see is a contrast between:

(10)-a says that Ralph believes a true proposition, whereas (10)-b says that Ralph believes a proposition which is true of some actual objects. Under adequate assumptions, (10)-b entails (10)-a, but not conversely. Prima facie, this looks like a promising way of capturing the difference between an accidentally true belief, referred to the wrong objects in Ralph’s belief worlds, and a true belief holding as a fact in virtue of being anchored to the right objects. This difference is obtained without postulating a primitive difference between facts and true propositions, but merely in terms of scope mechanisms.

3 Gettier’s puzzles

Two puzzles appear in Gettier’s celebrated paper. The first case (Case I) has a structure very similar to Russell’s case, since it also involves a definite description. Smith has “strong evidence that Jones is the man who will get the job, and Jones has ten coins in his pocket” (Gettier 1963). Let us represent what Smith believes by the following sentences:

As it turns out, Smith is the man who will get the job, but also “unknown to Smith, he himself has ten coins in his pocket” (Gettier 1963). Hence the following two sentences hold in the actual world:

The following de dicto ascription can be made truly about Smith:

However, the following de re ascription is false given the scenario:

Parallel to the previous analysis, we can distinguish between the true proposition Smith believes, and the failure of Smith to refer the components of that true proposition to the right objects as follows:

Hence Gettier’s first puzzle too can be captured in terms of scope mechanisms. What about Gettier’s second case? In the second case (Case II), Smith has some reason to believe that Jones owns a Ford, and he furthermore infers about his other friend Brown, “of whose whereabouts he is totally ignorant”, that “either Jones owns a Ford, or Brown is in Barcelona”. As it turns out, Brown is indeed in Barcelona, but Jones does not own a Ford. So Smith’s beliefs can be represented by the following sentences:

Prima facie, Gettier’s second case does not appear to rest on a de re/de dicto ambiguity. On the other hand, there is a strong analogy between the occurrence of a disjunction under the scope of the belief operator in (19)-b and the occurrence of an existential quantifier in our previous examples, since an existential quantifier is nothing but a generalized disjunction. One way in which we can build a tight parallel with the previous cases is first to observe that the following contrast holds in the scenario. Although the following sentence is true:

the following version, in which disjunction takes scope over belief, is false:

Indeed, the first disjunct is false, since Smith falsely believes Jones to own a Ford; and the second disjunct is false too, since Smith does not have the belief that Brown is in Barcelona. The distinction between those two sentences is exactly congruent with a scope distinction. To make a tighter parallel with our previous representations, one option is to handle disjunction as an existential quantifier ranging over sentences, and to use a truth operator.³ The previous two examples are then matched by the following de dicto versus de re counterparts:

(22)-a says that one of the two sentences “Jones owns a Ford”, “Brown is in Barcelona” is true, and Smith believes that one of those two sentences is true (this holds in the scenario, since Smith believes “John owns a Ford” to be true). (22)-b too says that one of those two sentences is true, and that Smith believes of that sentence that it is indeed one of those two sentences and that it is true. (22)-b, however, is false, unlike (22)-a, for Ab is the only actually true sentence, and of that sentence Smith has not formed the belief that it is true.

4 Problems

Both for Russell’s problem case, and for Gettier’s two cases, we thus have a uniform mechanism which appears to do justice to the intuition of a difference between a merely true belief, and a belief true in virtue of corresponding to a fact. This mechanism, which only involves binding and scope relations, allows us to capture Kratzer’s proposed analysis without having to distinguish facts and true propositions. Since the intuition that Russell and Gettier intended to convey is that there is a fundamental difference between justified true belief and knowledge, the question is whether we might equate knowledge with true belief de re.

If true belief de re is taken to mean a true belief whose truth rests on the right connection to some element in the actual world which makes the belief true, then an argument in favor of this analysis is that we have at least factored in an important externalist component, the one that is arguably missing from so many analyses in which the notion of justified belief is referred only to internal reasons for belief. In all the de re logical forms we have proposed, for which the belief ascriptions turned out false, what fails is an adequate connection with the actual truth-maker of the proposition believed.

There are three main difficulties for the present account, however. The first is that the account of disjunctive knowledge in Gettier’s Case II will in many cases be too strong. For instance, Brown may see someone in the distance and be in a position to know that it is either Tweedledee or that it is Tweedledum, yet without knowing which.⁴ In such a case, Brown believes neither the proposition that it is Tweedledee nor the proposition that it is Tweedledum, yet by assumption he does know the disjunction. The same problem occurs with existential indefinites more generally: Brown may know that someone left without knowing of anyone in particular that that person left. The analysis of knowledge in terms of de re belief thus seems to force cases of de dicto knowledge to be de re. Some maneuvers could be used in response. For example in the analysis of Gettier’s case II, if we include the disjunction itself among the set in (22)-b, we could still maintain a wide scope analysis of belief in cases in which knowledge does hold. Uegaki and Marty (2013) propose such a semantic analysis of knowledge for disjunctions that does incorporate the disjunction itself among the alternatives triggered by a disjunction.⁵ That generalization may be enough to handle the problem, but even so it may not be enough to address further difficulties of a different nature.

The second problem is indeed that we can find cases very similar to Gettier’s original two cases, but for which failure of a de re connection is not clear.⁶ Quine (1987, in his entry on “Knowledge”) gives the example of two people who go on a cruise on November 7, 1918, having just read from a paper the false news that the war was over. They land at their destination four days later, with the belief, now turned true, that the war is over. Should we say that their belief that the war is over on November 11 is not a belief of the war that it is over? Admittedly, they misrepresent how long the war lasted, but it seems they linked their false belief on November 7 to most of the same military events and episodes that eventually ended on November 11. A similar difficulty arises in Russell’s stopped clock example (Russell 1948: pp. 170–171). Suppose that the clock has been stopped for a day, and I happen to watch it at exactly 12:15 pm, when it indicates 12:15 pm. Intuitively, I do not know that it is 12:15 pm in that situation (at least, not on the basis of that evidence). However, my belief that it is 12:15 pm on the basis of watching the clock could still be described as a belief of the actual time that it is equal to 12:15 pm. The intuition here is that if the time had been different, I would inadequately believe of the time that it is 12:15 pm, but this is not a failure of an appropriate de re connection. Or suppose that I form the belief that 7 is a prime number, because I believe that all odd numbers greater than 1 are prime. Suppose moreover that I form this belief by thinking attentively and explicitly of the number 7, and of the property of being a prime number. Intuitively, this is a case in which my belief is de re of the number 7. The problem, instead, seems to be that my justification for the belief is faulty. Kratzer might retort that my belief that 7 is prime is not de re about the fact that 7 is prime, but really about a non-fact (namely the proposition that all odd numbers greater than 1 are prime). Likewise, we might argue that although it is a belief of the number 7, it is not really a belief of the property “prime”, because the latter is misrepresented. But this would seem too strong. It does seem possible to have de re knowledge of properties and individuals which we do not represent integrally or perfectly. What allows us to successfully apply the de re analysis in Gettier’s original cases may therefore turn on accidental features of those cases (the particular disjunctive structure of the belief in case II, the clearly wrong reference of the description viewed from the believer’s perspective in case I), rather than on essential features.

The third difficulty, already emphasized by Kratzer in her paper, is that an analysis of knowledge based exclusively on the notion of true de re belief does not appear to be general enough. Besides the original Gettier cases (and those like the example just mentioned), there are also Ginet-Goldman cases. In Goldman’s 1976 scenario (based on a case proposed by Ginet), Henry is traveling across the land and points to a particular building of which he thinks that it is a barn. It turns out the building is a real barn, but that “unknown to Henry, the district he has just entered is full of papier-mâché facsimiles of barns. These facsimiles look from the road exactly like barns, but are really just façades” (Goldman 1976). The intuition in this case is that Henry is simply lucky: Henry has formed a true belief, and that belief has the right connection to its truth-maker, but it fails a reliability condition. Because of that, Kratzer’s analysis of knowledge is as follows (Kratzer 2002: p. 664):

“S knows p if and only if

• (i) There is a fact f that exemplifies p,

• (ii) S believes p de re of f, and

• (iii) S can rule out relevant possible alternatives of f that do not exemplify p.”

An observation Kratzer makes is that knowledge ascriptions violating conditions (i) and (ii) are “clearly false”, whereas knowledge ascriptions violating condition (iii) are “vulnerable and context-dependent”. This observation implies that knowledge ascriptions involve at least two dimensions of evaluation, a dimension of causal connection to the right truth-maker, and a dimension of counterfactual sensitivity to the truth-maker (basically: if the circumstances had been different, the belief would have varied accordingly).

What Kratzer suggests, moreover, is that a failure along the dimension of causal connection is in a sense more dramatic than a failure along the dimension of counterfactual sensitivity. Whether this is so or not is a difficult question, about which recent experimental studies on laymen’s judgments bring conflicting evidence, and about which experts disagree. For example, Starmans and Friedman (2013: p. 663) write the following about the Ginet-Goldman cases:

“So although such ‘fake barn’ cases are often referred to as Gettier cases, they do not feature the disconnect characteristic of most other Gettier cases. And in fact, philosophers themselves are quite divided on whether to attribute knowledge in these cases (e.g., Lycan 2006; Sosa 2007; Turri 2012).”

Their view of the typology of Gettier cases is in support of Kratzer’s intuition in this case. Nagel et al. (2013a), on the other hand, acknowledge that Ginet-Goldman cases are a new species of Gettier cases, but they also disagree that the distinction is of fundamental importance to the analysis of Gettier cases in the broad sense (Nagel et al. 2013b).

My own inclination here is to agree with Kratzer and Starmans and Friedman that Gettier cases in the narrow sense (original Gettier cases) and Ginet-Goldman cases really manipulate distinct dimensions of evaluation. On the other hand, we cannot seek much support from Starmans and Friedman’s study in favor of Kratzer’s judgment, for what they conclude from their findings is that denials of knowledge in Gettier scenarios are not as sensitive to the causal disconnect between a belief and what makes it true as to the kind of evidence that the belief is formed on. Let us consider their distinction, and see where it leaves us.

5 Apparent evidence and authentic evidence

Starmans and Friedman (2012) conducted a series of experimental studies which appear to challenge the idea that ordinary ascriptions of knowledge are sensitive to the causal disconnect that features in the original Gettier scenarios. They found that nonacademic participants do ascribe knowledge to a significant extent in a certain class of Gettier-like scenarios where philosophical intuitions would suggest that the agent merely has a justified true belief. More precisely, they found no significant difference between levels of knowledge ascription in such Gettier conditions and in various control cases. Nevertheless, they found that amongst those Gettier scenarios, ascriptions of knowledge were sensitive to whether an agent’s belief was formed on the basis of what they call “apparent evidence” versus “authentic evidence”. The distinction between apparent and authentic evidence is explained as follows (Starmans and Friedman 2013: p. 663):

“Authentic evidence is informative about how the world actually is when the belief is formed, and basing a belief on authentic evidence necessarily makes the belief true when it is formed. Apparent evidence only appears to be informative about how the world actually is, and basing a belief on apparent evidence does not guarantee that the belief is true when it is formed.”

The apparent/authentic distinction is reminiscent of the distinction between fallible versus infallible evidence, but the point of the distinction is in fact different. Apparent evidence for Starmans and Friedman is evidence that is not just fallible, but wrong: the content of the corresponding belief is false, though it may support a true proposition by accident. Authentic evidence on the other hand gives a belief that is guaranteed to be true at the moment it is formed. It is infallible in that sense, but not in a way that would secure knowledge at a later time, since it is compatible with a “knowledge loss” characteric of Gettier cases (see Nagel et al. 2013a, b, and Machery et al. 2015 for a discussion of Starmans and Friedman’s data).

An example of a Gettier case based on apparent evidence which Starmans and Friedman used in their study is one in which a character named Corey believes that he has a quarter coin from 1936 in his piggy bank. His belief is in fact formed on the basis of the wrong perception of a 1938 coin whose date is hard to read. As it turns out, Corey does have an actual quarter coin from 1936 in his piggy bank, but is not aware of it. The corresponding Gettier case involving authentic evidence is one in which Corey believes he has a coin from 1936 in his piggy bank because he inserted a 1936 coin himself. Unbeknownst to him, there is another quarter from 1936 in his piggy bank. Corey takes a 10 min nap during which his friend Scott who needs a quarter picks the one Corey has just inserted, leaving the other untouched. In each scenario, the question for which Starmans and Friedman probed participants’ judgments was whether, “at the end of the story”, Corey “really knows” or “only believes” that there is a coin from 1936 in his piggy bank.

For this pair of scenarios and another such pair, what Starmans and Friedman found was a striking contrast, with an average of 67 % of participants attributing knowledge in the Authentic Evidence conditions, versus only 30 % in the Apparent Evidence conditions.⁷ The question for us is: can we capture this difference in terms of the de re/de dicto distinction used previously, or is there again a genuinely distinct dimension of evaluation at stake? Consider the following sentence:

Let us consider our two paraphrases, the de dicto paraphrase, and the de re paraphrase (with “Cx” for “x is a coin from 1936”, and “Px” for “x is in Corey’s piggy bank”):

The de dicto ascription (24)-a is true in the two scenarios, the Apparent Evidence as well as the Authentic Evidence scenario. What about (24)-b? Whether in the Apparent Evidence case or in the Authentic Evidence case, the only actual coin from 1936 that is left in the piggy bank at the end of the story is not one about which Corey has any de re belief. So in both cases, (24)-b is false at the end of the story. However, consider the same belief ascription relative to the beginning of the story. At the beginning of the story, (24)-b is this time true in the Authentic evidence case: for Corey has a correct de re belief about the coin from 1936 he inserted. But (24)-b is false in the Apparent evidence case.

This observation raises two questions. One is whether participants sufficiently paid attention to the adverbial “at the end of the story” (which does not feature in the target sentence, but right before it). Another, assuming that participants did pay attention to the temporal adverbial as they should have, is how much, toward evaluating the sentence “Corey really knows that there is a coin from 1936 in his piggy bank”, the temporal reference of the embedded clause needs to be constrained by the expression “at the end of the story”. What could be happening is that participants refer the knowledge state to the correct de re belief Corey had at the beginning of the story, but then judge it to be reliable enough relative to normal circumstances to count it as knowledge at the end of the story, given the rather exceptional circumstances of the Authentic evidence scenario. If that were the case, it might give support to the idea that knowledge is ascribed in the way suggested by Kratzer: first by checking that the causal condition is satisfied, and then by accepting the belief in question to be reliable enough in general, in spite of the abnormal circumstances described.

Whether or not any of these explanations is the case, it remains an interesting observation that we can at least capture the distinction between apparent evidence and authentic evidence proper in terms of the distinction between de re and de dicto belief. If only for that reason, I think this mitigates Starmans and Friedman’s claim that “while people sometimes do deny knowledge in Gettier scenarios, it is not because of the disconnect [between the fact justifying the belief and the fact making the belief true]” (2013: p. 663).

Because the de re/de dicto mechanism is meant to represent different levels of causal connection, I would actually argue that more of the causal dimension of knowledge ascriptions remains relevant to an analysis of knowledge than the previous counterexamples suggest. This point deserves emphasis, both in the context of the current debates about the universality of Gettier intuitions (see Machery et al. 2015), and concerning the question of the defining properties of knowledge. What remains particularly surprising about Starmans and Friedman’s findings is indeed that such a large proportion of participants grant knowledge to the agent in cases of authentic evidence at the end of the story. However, we can explain it if participants mostly base their judgments on the consideration that i) the proposition believed at the beginning of the story is believed on the basis of an appropriate de re connection ii) although that proposition is no longer made true by the same objects at the end of the story, the difference is practically irrelevant (meaning that truth-makers at the end are in a sense functionally identical to the ones at the beginning).

Indeed, in Starmans and Friedman’s Gettier cases involving authentic evidence, the causal disconnect is in most cases harmless: for example, a burglar replaces a watch with a type-identical watch, in a way that is supposed to respect the former beliefs of the agent about the disposition of objects in the room. Although the final belief that there is a watch on the table is no longer about the same watch, the causal disruption between the initial state and the end state makes almost no difference, neither to the reliability of the belief formation process, nor to the agent’s future transactions with the world. Such cases significantly differ from even Gettier’s type I cases in both regards (the man who will get the job is not the same as the one believed in any relevant sense of “same”). In cases of apparent evidence, the causal connection between the facts justifying the belief and the facts making it true is immediately more remote, and it is harder to find that connection appropriate, as the data confirm. This observation matters, for it means that pragmatic considerations inevitably impact the way in which ordinary knowledge ascriptions are made.

6 Conclusions

The first and promising conclusion we reached, in support of Kratzer’s own methodology, is that an analysis of knowledge in terms of true de re belief accounts surprisingly well for the original Gettier scenarios: it accounts not just for the first of Gettier’s cases, but also for the second. Furthermore, unlike Kratzer we did not have to distinguish facts and true propositions to account for the original Gettier cases in terms of de re belief. It was enough to use mechanisms of binding and scope. This is not to say that thinking of facts as distinct from true propositions is necessarily misguided, but merely to say that we do not have to worry about the definition or construction of facts in order to account for the original Gettier cases in terms of that distinction.

Our second main conclusion immediately tempers the optimism of the first: what we saw is that, irrespective of how it is implemented, a de re-belief analysis gives us at best partial truth conditions for knowledge. In agreement with Kratzer’s own scepticism, we saw that we must prise apart Gettier cases in the narrow sense from Ginet-Goldman cases: both manipulate different dimensions of evaluation. Even setting aside Ginet-Goldman cases, we found cases very much like Gettier’s original cases, for which failure of a de re connection is not clear.

Despite that, I have argued that the de re/de dicto distinction may be used to cast light on Starmans and Friedman’s distinction between authentic versus apparent evidence in their study of Gettier cases, in a way that sets the judgments they found on a continuum with the de re analysis of the original Gettier cases. Specific attention to cases of apparent evidence matters, because when we compare Starmans and Friedman’s findings with those of other studies (in particular Nagel et al. 2013a, b, but see also Machery et al. 2015), their results challenge the philosophical intuition that knowledge ought to be denied in all Gettier-like scenarios. I think that what the apparent versus authentic distinction confirms is rather that the gist of the original Gettier cases lies in the dimension of causal connection between belief and its objects.