Why the Standard View of Ignorance Prevails

Abstract

Rik Peels has forcefully argued that, contrary to what is widely held, ignorance is not equivalent to the lack or absence of knowledge. In doing so, he has argued against the Standard View of Ignorance according to which they are equivalent, and argued for what he calls “the New View” according to which ignorance is equivalent (merely) to the lack or absence of true belief. In this paper, I defend the Standard View against Peels’s latest case for the New View.

Introduction

What is ignorance? The most straightforward and widely held answer is that it is the lack or absence of knowledge, an answer that has considerable lexicographical support. The OED, for instance, defines ‘ignorance’ as follows: 1.a. “The fact or condition of being ignorant; want of knowledge (general or special).”¹ This view is also widely held by linguists such as Stephen Levinson who notes that “not ignorant logically implies knows (because ignorance and knowledge are contradictories)” (2000, p. 208).² Dubbed the “Standard View of Ignorance” in this journal in Le Morvan (2012, 2011), it seems so intuitive that it has received little critical attention by epistemologists.

Despite its intuitiveness, Rik Peels has forcefully challenged it in three noteworthy recent articles in this journal: “What is Ignorance?” (Philosophia (2010) 38: 57–67), “Ignorance is Lack of True Belief: A Rejoinder to Le Morvan” (Philosophia (2011) 39(2): 344–355), and “The New View on Ignorance Undefeated” (Philosophia (2012) 40: 741–750). He argues for an alternative, the “New View,” according to which ignorance is (merely) the lack of true belief. His second article is a rejoinder to my defense of the Standard View in “On Ignorance: A Reply to Peels” (Philosophia (2011) 39(2): 335–344). His third is a rejoinder to my defense of it in “A Vindication of the Standard View of Ignorance” (Philosophia (2012) 40(2): 379–393).

Peels deserves a lot of credit for putting the undeservedly neglected question of the nature of ignorance on the epistemological agenda. His valiant efforts notwithstanding, my aim in this paper is to defend the Standard View against his new and important challenge. In doing so, a number of noteworthy lessons will emerge concerning the nature of ignorance.

The paper is organized as follows. I will begin by reviewing the distinction between propositional and factive ignorance, a distinction at the heart of the debate between the Standard and New Views. After reviewing this distinction, I will discuss it in relation to three key issues: (i) whether Peels commits a contradiction, (ii) a putative conversational implicature of “is ignorant that p”; and (iii) ignorance of falsehoods. I will next discuss Peels’s Linguistic and Excuse Arguments for the New View and argue that they fail. I will then consider two arguments against the New View and for the Standard View that I will call the “Argument from Gullibility” and the “Argument from Sloppiness” respectively, arguing that they withstand Peels’s criticisms. I will conclude by drawing together important lessons of this discussion.³

The Distinction Between Propositional and Factice Ignorance

In defending the Standard View in Le Morvan (2012, 2011) I argued that Peels conflated factive and propositional ignorance in making his case for the New View and against the Standard View. Let’s review this distinction. Propositions have truth conditions, and we can distinguish between these propositions and their truth-conditions on the one hand, and the satisfaction of those truth-conditions on the other. Consider the following three propositions:

• p ₁ – 21 is evenly divisible by 7.

• p ₂ – 22 is evenly divisible by 7.

• p ₃ – Every odd number greater than 7 can be expressed as the sum of three odd primes.

Clearly, p ₁ is true while p₂ is false. As for p ₃ (“the Three Primes Problem”), it is presumably either true or false, but we don’t know its actual truth-value given the current state of number theory. Each of these three propositions has truth-conditions, and our considering each entails that we are not ignorant of them. This is so even if, as in p ₂ , these truth-conditions are not satisfied, or, as in p ₃ , we are not (at least yet) in a position to ascertain whether they are satisfied. Worth noting is that a proposition’s truth-conditions should not be confused with its truth: a false proposition has truth-conditions even though it is not true because they are not satisfied. Propositional ignorance is ignorance of propositions themselves and their concomitant truth-conditions while factive ignorance is ignorance that these truth-conditions are satisfied. It’s possible to be both propositionally and factively ignorant at the same time. My two-year son, for instance, is propositionally ignorant of p ₁ and factively ignorant that p ₁ even though it is true. One can be factively ignorant, however, without being propositionally ignorant. I, for instance, am factively ignorant that p ₃ but not propositionally ignorant of p ₃ .

Having reviewed the distinction between propositional and factive ignorance, let’s now consider Peels’s remarks on it in his latest article. He now concedes that it makes sense even though he had previously characterized it as “highly unnatural” (2011, p. 350).⁴ He says that all he meant by this charge is that in ordinary language, ‘S is ignorant that p’ means that S is ignorant that p is true. We agree on this point, a point that was never in contention. But Peels also now claims that it still seems right to him that we do not need the concept of propositional ignorance, and this is because we can understand all cases of ignorance in terms of factive ignorance. As he puts it:

Ignorance of the truth-conditions TC of some proposition p is ignorance that TC are the truth-conditions of p and that is an instance of factive ignorance. Thus, propositional ignorance is merely a subspecies of factive ignorance. As long as Le Morvan has not told us anything else about propositional ignorance than that it entails ignorance of the truth-conditions of a proposition, we have no reason to think that propositional ignorance is distinct from factive ignorance—for all we know, propositional ignorance is a particular kind of factive ignorance. All the work that needs to be done can be done by using the concept of factive ignorance, where ignorance is to be spelled out as it is spelled out by the New View: ignorance is absence of true belief (2012, p. 743).

Notice that Peels equates (i) ignorance of the truth-conditions TC of a proposition p with (ii) ignorance that TC are p’s truth-conditions. Such an equation, however, is mistaken. Consider for example the following propositions:

• p ₄ – For any x, x is a raven → x is black.

• p ₅ – For any x, (~x is a raven v x is black) v x is a swan.

Notice that p ₄ and p ₅ are logically equivalent and hence have the same truth-conditions TC. Suppose that S is not ignorant of p ₄ and its truth-conditions TC, but does not realize that p ₄ and p ₅ are logically equivalent. It’s thus possible for S in this way to be ignorant that TC are p ₅ ’s truth-conditions without being ignorant of TC which, as it turns out, are the truth-conditions of p ₅ . ⁵ In other words, (ii) does not entail (i). Hence, (i) and (ii) are not equivalent.

Even if we grant moreover that (i) entails (ii), it does not follow that (i) is a subspecies of the species instantiated by (ii). For instance, (a) being mute entails (b) being unable to sing opera, and (b) is a subspecies of the species of being unable to sing. It doesn’t follow from this, however, that being mute is a subspecies of being unable to sing. In general, just because x entails y, it does not follow that x is a subspecies of the species instantiated by y.⁶

Since (ii) does not entail (i), and even if (i) entails (ii) it does not follow that (i) is a subspecies of the species instantiated by (ii), Peels’s reasoning in no way shows that we can understand all cases of ignorance in terms of factive ignorance and that we therefore do not need the concept of propositional ignorance.⁷

Let’s now turn to three important matters concerning the need for the concept of propositional ignorance: (1) Peels’s putative contradiction, (ii) a conversational implication of “is ignorant that p”, and (iii) ignorance of falsehoods.

• (i) Peels’s Putative Contradiction

Consider Peels’s claim that “someone who falsely believes that p is not ignorant of p and by that I mean of p’s truth” (2011, p. 350). In Le Morvan (2012) I argued that this claim yields a contradiction when held with the New View that Peels purports to defend. How does this contradiction arise? To begin with, I reasoned that if someone S falsely believes that p (that is, believes that p and p is false), then it follows that S does not believe that p when p is true. I proved this as follows where “S does not believe that p when p is true” is understood as logically equivalent to “p → ~(S believes that p)”:

• 1. (S believes that p) & ~p. (assumption)

• 2. ~p. (1, simplification)

• 3. ~p v ~(S believes that p). (2, addition)

• 4. p → ~(S believes that p). (3, logical equivalence)

In light of this proof, it cannot be logically disputed that, if someone S falsely believes that p (that is, believes that p and p is false), then S does not believe that p when p is true, on the natural understanding that “S does not believe that p when p is true” is logically equivalent to “p → ~(S believes that p).”

On my reading of the New View in Le Morvan (2012) someone who does not believe that p when p is true is ignorant that p (is true) because not believing that p when p is true suffices for being ignorant that p (is true). Given the proof above, it follows that someone who falsely believes that p is ignorant that p (is true). I thus concluded that Peels’s claim “that someone who falsely believes that p is not ignorant of p and by that I mean of p’s truth” (2011, p. 350) contradicts the very New View he endeavored to defend if what he means by ‘is not ignorant of p and by that I mean of p’s truth’ is ‘is not ignorant that p (is true)’.⁸ This is because, in this case, Peels holds that S is not ignorant that p (is true) while the New View he is endeavoring to defend entails that S is ignorant that p (is true)—hence the contradiction. As I noted, Peels could avoid this contradiction by invoking the distinction between propositional ignorance and factive ignorance and by holding that someone who falsely believes that p is not propositionally ignorant of p even if factively ignorant that p, but doing so would undermine his claim that the concept of propositional ignorance is not needed and we only need the concept of factive ignorance.

Peels responds that this argument fails for several reasons, but gives only the reason he takes to be the most important. Here it is in his words:

The conclusion, proposition (4), says that if p is or were true, S would not believe that p—and, hence, would be ignorant that p. It does not say that S is ignorant that p, because the conclusion does not say that p is true. When I said that S is ignorant that p if and only if S fails to believe that p is true, I meant that S is ignorant that p if and only if <S fails to believe that p & p is true>, not that S is ignorant that p if and only if <if p were true, then S would fail to believe that p>. Saying that S is not ignorant that p when p is false is perfectly compatible with saying that S would be ignorant that p if p were true. Thus, we do not need the distinction between propositional and factive ignorance to avoid the consequence that someone who falsely believes that p is ignorant that p (2012, pp. 743–744).

What are we to make of this response? Let’s begin by going back to Peels’s characterization of the New View as holding that ignorance is the absence or lack of true belief. The natural way of understanding the absence of something x is to take it as the complement of the presence of x. Take speckled hens, for instance. The natural way of understanding the absence of speckled hens is take it as the complement of the presence of speckled hens. Speckled hens are present if and only if (i) there are hens and (ii) they are speckled. Speckled hens are absent if and only if (i) is not the case or (ii) is not the case (or both are not the case).

Similarly, the natural way of understanding the New View’s central thesis that ignorance is the absence of true belief is to take it as holding that ignorance’s complement is (the presence of) true belief. Notice that S has a true belief that p if and only if (i) S believes that p and (ii) p is true. Therefore S fails to have that true belief that p if either (i) or (ii) is not the case (or both are not the case); that is, it is not that case that S believes that p or it is not the case that p (or both). On this natural understanding of the New View then, someone’s ignorance that p amounts to

• (a) S is ignorant that p ↔ [~(S believes that p) v ~p].

  This is turn is logically equivalent to:

• (a)′ S is ignorant that p ↔ [p →~(S believes that p)].

Peels does not dispute that the New View, when read as (a) or (a)′, is contradicted by his claim “that someone who falsely believes that p is not ignorant of p and by that I mean of p’s truth.” He responds (p. 743) that he did not intend the New View to be understood in terms of (a) or (a)′, but rather as:

• (b) S is ignorant that p ↔ [~(S believes that p) & p].

His position thus clarified and made explicit, he is quite right that, when the New View is read as (b), the contradiction in question does not arise. Consider, however, what the New View understood as (b) requires us accept. Even though Peels repeatedly tells us that ignorance is the absence of true belief, the New View (as he understands it) does not entail that the complement of ignorance that p is (the presence of) true belief that p. This is because on (b) the complement of ignorance that p is instead that either S believes that p or it is not the case that p.

But isn’t it quite strange to hold that (the presence of) true belief is not the complement of the absence of true belief? Consider this analogy. Suppose someone claimed that the complement of the absence of speckled hens is to be understood not as <there are hens and they are speckled>, but rather as <there are hens or they are not speckled>. The absence of speckled hens on such a view is <there are no hens and they are speckled> instead of the much more plausible <there are no hens or they are not speckled>. This is a very strange way of understanding the absence of speckled hens, so strange that it verges on an informal reductio. The New View, when read as (a) or (a)′, does not have a similar kind of strange consequence, but Peels has repudiated this natural reading in favor of (b) which does. So while Peels avoids Le Morvan’s charge of contradiction by reading the New View in terms of (b), his doing so comes at quite a high intuitive cost.⁹

In any case, whether read as (a) or as (b), the New View also entails the very implausible consequence that, if p is true, simply believing that p suffices for not being ignorant that p. To see just how implausible this is, take the following scenario (one among many that can be generated). Suppose that, in 1695, S tripped, bumped his head, and suffered some neurological damage. As a result of this damage, S came to believe Fermat’s Last Theorem, namely that no three positive integers x, y, and z can satisfy the equation x ⁿ + y ⁿ = z ⁿ for any integer value of n greater than 2. The New View read as (a) or (b) entails the highly implausible consequence that, simply in virtue of believing it, S was not ignorant that Fermat’s Last Theorem is true. Why is this so implausible? Because until it was proven in 1995, Fermat’s Last Theorem was one of the most difficult unsolved mathematical problems and its proof required important developments in algebraic number theory among other things. It strains credulity to think that S in 1695 was not ignorant that it is true simply in virtue of believing it. To be sure, in believing it, S was not propositionally ignorant of Fermat’s Last Theorem, for such propositional ignorance would have precluded believing it. The New View read as (a) or (b), however, entails the much stronger and implausible consequence that S was not factively ignorant in 1695 that Fermat’s Last Theorem is true. Notice, by contrast, that the Standard View of Ignorance has no such highly implausible consequence; it can explain why S was ignorant of Fermat’s Last Theorem in 1695 in terms of S’s not knowing that it is true. I take this to be an important advantage of the Standard View over the New View.¹⁰

In sum, the New View can be read as (a) or (b). While (a) seems to be the more natural reading and affords a more plausible account of the complement of ignorance, Peels repudiates it in favor of (b). While doing so allows Peels to avoid the contradiction that Le Morvan (2012) showed arises with (a), it gives a very strange account of the complement of ignorance. Moreover, on either (a) or (b), the New View has the implausible consequence that, for any proposition p, so long as p is true, S’s merely believing that p suffices for S’s not being factively ignorant that p, even in situations where neither S nor anyone else is in a position to ascertain whether p is true.

• (ii) A Putative Conversational Implicature of “is ignorant that p”

On the Standard View, if S falsely believes that p, then S is ignorant that p. This is because p’s being true is a necessary condition for S’s knowing that p, and since on the Standard View ignorance that p is the complement of knowledge that p, it follows that S is ignorant that p. Thus, if Sam falsely believes that he was robbed by a Canadian, then Sam is ignorant that he was robbed by a Canadian.¹¹ Peels (2012, p. 744) responds that to him “this sounds just confused.” As he puts it:

If someone says “Sam was ignorant that he was robbed by a Canadian”, then that conversationally implies that Sam was in fact robbed by a Canadian. Of course, if Sam falsely believes that he was robbed by a Canadian, then Sam is ignorant as to whether or not he was robbed by a Canadian. But we would describe that by saying “Sam is ignorant that he was not robbed by a Canadian” or “Sam is ignorant as to whether or not he was robbed by a Canadian” or “Sam falsely believes that he was robbed by a Canadian”, but not by saying “Sam is ignorant that he was robbed by a Canadian” (2012, p. 744).

Peels here makes an interesting point about the conversational implicature of ‘is ignorant that p.’ Conversational implicature is, however, not a matter of semantics (what expressions mean) but rather a matter of pragmatics (what is done with words or sentences that goes beyond the literal meaning of the expressions involved). Peels and I may be at an intuitional impasse here in that to me, unlike to him, it does not sound confused at all to say that S is ignorant that p even though p is false.¹² By my lights, if someone says for instance “Sam was ignorant that he was robbed by a Canadian,” this leaves open whether Sam was indeed robbed by a Canadian and can be used in a manner compatible with the possibility that he was not.

But let’s suppose, for the sake of argument, that Peels is right about this putative conversational implicature. Does it follow from this that the New View is right and the Standard View is wrong? No. Consider a parallel point about the expression ‘not knowing that p.’ I trust that Peels would wisely not deny the widely held semantic tenet that p’s being false suffices for not knowing that p. Let’s call this tenet “ST.” Now suppose someone claimed that to her the expression ‘Sam does not know that he was robbed by a Canadian’ has the conversational implicature that Sam was robbed by a Canadian and that it sounds confused to assert this expression if he was not robbed by a Canadian. Would this show that we should reject ST?

No. Given the semantics/pragmatics distinction, we could perfectly well respond that this putative conversational implicature concerns the pragmatics of ‘not knowing that p’ but not its semantics. Accordingly, even if this putative conversational implicature were the case, it would not follow that we must reject ST. Similarly, even if Peels were right about the putative conversational implicature of ‘is ignorant that p’ that he noted, we can similarly respond that it concerns the pragmatics of the expression and not its semantics. Therefore, even if Peels were right in this way, it would not follow that we have to reject the Standard View’s tenet that p’s being false suffices for S’s being ignorant that p.¹³

Moreover, suppose that both ‘is ignorant that p’ and ‘does not know that p’ have the conversational implicature of suggesting that p is true. Now consider by contrast the expression ‘does not truly believe that p’ that Peels takes to be equivalent to ‘is ignorant that p’; ‘does not truly believe that p’ either has or does not have this conversational implicature. If it does, then Peels’s calling into question the Standard View because of this conversational implicature should, by parity of reasoning, call into question the New View as well. If it does not, then ‘is ignorant that p’ and ‘does not truly believe that p’ have different conversational implicatures, and while this does not by itself entail that they are not semantically equivalent, this pragmatic difference may raise some doubt about this equivalence. Either way, Peels’s case against the Standard View and for the New View is far from compelling.

• (iii) Ignorance of Falsehoods

As I pointed out in Le Morvan (2012) distinguishing between propositional and factive ignorance allows us to make sense of how one can be ignorant of falsehoods. I gave a thought experiment in which Ulrike Schmidt lived in the former East Germany where the Stasi maintained a lengthy file of her activities and proclivities, a file that happened to contain many falsehoods. To me, it makes eminent sense to suppose that she was ignorant of those falsehoods: she was propositionally ignorant of those falsehoods, and this ignorance was dispelled when she gained access to her files. Le Morvan argued that examples like this undercut Peels’s thesis that we can only be ignorant of truths, and hence not of falsehoods.

Peels (2012) still insists that it seems mistaken to him that one can be ignorant of falsehoods. He answers:

Surely, Schmidt was ignorant that the file contains those falsehoods. But notice that it is a truth that the file contains such falsehoods. What about the falsehoods themselves? Let one of them be the proposition that Schmidt had contacts with the American government. As a matter of fact, Schmidt had no such contacts and she knows that she had no such contacts. Now, is Schmidt ignorant of this falsehood? That is, is she ignorant that she had contacts with the American government? Of course, not. She is fully aware and knows that she has no contacts with the American government. We should not confuse that ignorance with ignorance of the fact that the file contains such a false claim about her. Hence, we have not been given a convincing reason to reject my thesis that one can only be ignorant of truth (2012, p. 744).

Peels is right that Schmidt was ignorant that the file contains those falsehoods. But let’s consider more closely the false proposition that she had contacts with the American government. Let’s call this proposition ‘q’. Peels in his reasoning above equates (i) being ignorant of (proposition) ~q with (ii) being ignorant that ~ q. He then claims that (ii) is surely not the case because Schmidt knew that she had no contacts with the American government, and so concludes that (i) is not the case either.

His equation of (i) and (ii), however, elides the distinction between propositional and factive ignorance. Given this distinction, it simply does not follow that, because Schmidt was not ignorant that she had contacts with the American government, she therefore was not ignorant of the false proposition that she was, a falsehood that had secretly been contained in the Stasi file. We should not confuse factive and propositional ignorance.

Consider an analogous example to further illustrate the inadequacy of Peels’s response. Suppose that Miguel knows that he is an American citizen. Suppose also that Mike has spread the rumor that Miguel is an illegal alien, a rumor that Miguel has not yet heard. Isn’t Miguel ignorant of this rumor? Peels’s line of reasoning very implausibly entails that Miguel is not. Why? Because, on this line of reasoning, Miguel knows that he is an American citizen, therefore knows that he is not an illegal alien, therefore is not ignorant that he is an illegal alien, therefore is not ignorant of the rumor that he is an illegal alien. (Notice the shift from not being ignorant that to not being ignorant of.) On this line of reasoning, Miguel’s not being ignorant that he is an illegal alien entails that he is not ignorant of the rumor that he is an illegal alien, and reasoning in this way elides the distinction between propositional and factive ignorance. Yes, Peels can say that Miguel is ignorant that Mike has spread this rumor. But why should we suppose that it follows from this that Miguel is not ignorant of the rumor itself? In fact, his ignorance of the rumor explains Miguel’s ignorance that Mike has spread it.

In short, nothing in Peels’s response succeeds in dispelling the implausibility of his denying that we can be ignorant of falsehoods. The distinction between propositional and factive ignorance shows how it makes perfect sense to suppose that we can be ignorant of such falsehoods.

Peels’s Linguistic Argument for the New View

In arguing for the New View, Peels (2011) appealed to what he takes to be some linguistic intuitions. He asked us to consider two kinds of cases. The first are A-type cases of justified true belief such as Gettier cases that are close to knowledge but not knowledge. He gave the example of his believing truly that it is 3 PM on the basis of his seeing a (formerly well-functioning clock) that happens to indicate it is 3 PM even though it has stopped working. He claimed that it’s implausible to say that in this case he is ignorant that it is 3 PM. The second are B-type cases of mere true belief. He gave the example of someone Jim who lives in Miami and who, believing he will be the next president of the US, also believes that r (that the next president of the US lives in Miami). As it turns out, the next president of the US (a female congressman) lives in Miami, so r is true. According to Peels, while Jim may be ignorant of many other propositions, “it seems that Jim is not ignorant of r” (2011, p. 352).¹⁴

On the basis of these intuitions, Peels (2011, p. 364) offered the following argument:

• P1′: In A-type scenarios, S truly believes that p, but just falls short of

• knowing that p. [def.]

• P2′: In A-type scenarios, S is not ignorant of p. [ass.]

• P3: In B-type scenarios, S merely truly believes that p. [def.]

• P4: In B-type scenarios, S is not ignorant of p. [ass.]

• P5: If in both A-type and B-type scenarios, S is not ignorant of p, then it is

• plausible to assume that in all in-between cases – cases in which S truly

• believes that p without merely truly believing that p and without just

• falling short of knowing that p – S also fails to be ignorant of p. [ass.]

• P6: In all cases in which S truly believes that p without knowing that p, S is

• not ignorant as to whether p. [from P2′, P4, and P5]

• P7: If S believes or suspends judgment on a false proposition p or if S fails

• to believe a true proposition p, then S is ignorant as to whether p. [ass.]

• C′: Ignorance is lack of true belief. [from P6 and P7]

In Le Morvan (2012) I countered (among other things) that the argument obviously begs the question against the Standard View by taking A-type and B-type scenarios to not be cases of factive ignorance. Peels in effect assumed the New View in taking them to not be cases of ignorance. It thus gives us no independent reason for accepting the New View and for rejecting the Standard View. Distinguishing factive from propositional ignorance, adherents of the Standard View can insist that while S‘s believing that p entails that S is not ignorant of the proposition p, it does not entail that S is not ignorant that p is true. Not being ignorant of a proposition that happens to be true is not equivalent to not being ignorant that it is true. I suggested that Peels’s intuition that A-type and B-type cases are not cases of ignorance stems from a failure to properly distinguish factive from propositional ignorance. Looking again at Peels’s argument, one could add that in using the expression “as to whether p” as equivalent to “that p”, Peels slid between “not being ignorant of p” and “not being ignorant as to whether p”, a slide that elides the distinction between propositional and factive ignorance.

What is Peels’s response? It amounts to insisting that “a confusion between propositional ignorance and factive ignorance is not the origin of the adherent to the New View’s intuition that in A-type cases and B-type cases S is not ignorant that p,” that adherents of the New View have the additional linguistic intuition that such cases are not ones of factive ignorance, and that we should take adherents of the New View on their word that their “linguistic intuitions in A-type and B-type scenarios are really intuitions about factive rather than propositional ignorance” (2012, p. 745).

I can only ask readers to look at Peels’s discussion of A-type and B-type scenarios, and to judge for themselves whether he conflated therein propositional and factive ignorance. In any case, it remains that he begs the question in deriving P6 from P2`, P4 and P5. This is because Peels assumes what he needs to prove in assuming that from S’s non-ignorance of p, it follows that S is not ignorant as to whether p. In arguing against the Standard View, Peels cannot simply assume or take for granted that S’s non-ignorance as to whether p, which is presumably equivalent to (or at least entails) S’s non-ignorance that p, follows from S’s non-ignorance of p. The argument thus gives us gives no independent reason for accepting the New View over the Standard View.

Peels’s Excuse Argument for the New View

The Excuse Argument in Peels (2011) boils down to the following line of reasoning. Peels contended that it is widely held that ignorance, as long as it is blameless, provides at least a partial excuse, and the New View can make sense of this while the Standard View cannot. Consider proposition p that an old barn in front of S is a historical monument. According to Peels, if S, the director of a demolition company, is blameless in (a) disbelieving that p or (b) in not believing that p or (c) in suspending judgment that p, then S has a full excuse in cases (a) or (b) and at least a least a partial excuse in case (c). Since on the New View, all instances of ignorance are instances of disbelieving, not believing, or suspending judgment, the New View can make sense of how blameless ignorance provides at least a partial excuse. However, on the Standard View, there is another kind of ignorance, namely, true belief that falls short of knowledge. Whether S merely truly believes that p or knows that p, in either case this makes no difference to S’s degree of blameworthiness if S destroys the old barn. But since mere true belief is, on the Standard View, an instance of (factive) ignorance, Peels concluded that it entails that not all cases of blameless ignorance provide at least a partial excuse. And this, Peels charged, is incompatible with the widely accepted view “that ignorance, as long as it is blameless, provides at least a partial excuse” (2011, p. 354)

In response, I pointed out in Le Morvan (2012) that we have to consider for what blameless ignorance provides at least a partial excuse. For an action, presumably, but not just any action: S’s being blamelessly ignorant that an old barn in front of S is a historical monument does not, we would all agree, provide S an excuse for (say) assassinating President Obama. However blameless it may be, the ignorance in this case is exculpatorily irrelevant to this action. Thus, it’s important to specify that what is widely accepted is not the idea that ignorance, as long as it is blameless, provides at least a partial excuse tout court; we need to also specify the crucial clause that this excuse is only for an action to which the ignorance is exculpatorily relevant in the sense of providing an excuse for it. Blameless ignorance confers blamelessness to an action only if such ignorance is exculpatorily relevant to this action.

I argued that this clarification allows us to see what is wrong with Peels’s charge against the Standard View. S’s mere true belief that p, which qualifies as factive ignorance on the Standard View, is exculpatorily irrelevant (that is, not relevant, does not provide an excuse) to S’s action of demolishing the old barn. Accordingly, this factive ignorance, however blameless, provides no excuse for S’s demolishing the barn and so S is blameworthy for doing so. As I pointed out, Peels’s Excuse Argument in no way shows that the Standard View is incompatible with the widely held view properly clarified, namely that ignorance, as long as it is blameless, provides at least a partial excuse only for an action to which the ignorance is exculpatorily relevant. What Peels has done is given an example where ignorance however blameless (that is, on the Standard View the mere true belief that the old barn is a historical monument) is clearly exculpatorily irrelevant to an action (i.e., of demolishing the barn).

In response, Peels (2012) agrees that not every instance of ignorance is exculpatorily relevant to an action. But he contends that it does not follow from this that S’s true belief that p is exculpatorily irrelevant to S’s demolishing the old barn. As he puts it (where S is “Matthew”):

In fact it seems that it is exculpatorily relevant, for ignorance of proposition p is what could possibly excuse Matthew for destroying the old barn. If Matthew blamelessly disbelieves that true proposition p, then that ignorance excuses him for destroying the old barn. If he blamelessly suspends judgement on the true proposition p, then that ignorance partially excuses him for destroying the old barn. If he is blamelessly deeply ignorant that p is true—if he neither believes that p nor disbelieves that p nor suspends judgement on p, say, because he cannot even grasp p—he is clearly fully excused for destroying the old barn. But if he truly believes that p, then he is clearly blameworthy for destroying the old barn—unless further excuses, such as compulsion, hold. True belief that p is exculpatorily relevant, then, in that it renders Matthew blameworthy unless further excuses hold. On the Standard View, however, if Matthew merely truly believes that p, then he is ignorant that p. And it is widely accepted that ignorance provides at least a partial excuse. But his true belief clearly does not excuse him at all. Hence, the Standard View should be rejected (2012, p. 746).

Unfortunately for Peels, his response fails. First of all, on both the New View and on the Standard View, not believing that p (if p is true) is a sufficient condition for being factively ignorant that p. His points therefore about Matthew blamelessly disbelieving that p, and blamelessly suspending judgment that p, and blamelessly being unable to grasp that p are not in dispute. Now, consider the case where Matthew’s true belief that p fall shorts of knowledge that p. Yes, this mere true belief qualifies as ignorance on the Standard View. And, yes, if Matthew truly believes that p in this way, then he is clearly blameworthy for destroying the old barn (unless other excuses hold). But how does it follow from this, as Peels suggests, that Matthew’s true belief that p is exculpatorily relevant to his destroying the barn? If ‘exculpatorily relevant’ is used in Le Morvan (2012)’s sense of providing an excuse for an action, Peels in effect is saying that Matthew’s true belief that p provides him an excuse and so makes him blameless or not blameworthy for demolishing the old barn.¹⁵ But it’s exactly the opposite that follows! Matthew demolished the old barn despite truly believing that it is a historical monument. His true belief (amounting to ignorance on the Standard View) is excupatorily irrelevant (that is, not relevant, does not provide excuse) to his action of demolishing the old barn. The Standard View is perfectly compatible with the widely held view that all cases of blameless ignorance provide at least a partial excuse for an action to which it exculpatorily relevant. But just because all cases of blameless ignorance provide at least a partial excuse for an action to which it is exculpatorily relevant, it doesn’t follow that all cases of ignorance are blameless and provide such an excuse for an action, or that all cases of blameless ignorance are exculpatorily relevant to an action. The Standard View is compatible with the possibility that some instances of ignorance are not blameless and do not provide even a partial excuse to an action, and is also compatible with the possibility that some instances of blameless ignorance are not exculpatorily relevant to an action, but all this is fully consistent with the idea “that ignorance, as long as it is blameless, provides at least a partial excuse” so long as we are careful to specify the required clause: only for an action to which the ignorance is exculpatorily relevant. Peels has traduced (unintentionally I trust) the Standard View in rejecting it. His Excuse Argument is the opposite of sound.¹⁶

Two Arguments against the New View (and for the Standard View)

We have seen above how Peels’s attempt to refute my defense of the Standard View fails. Let’s now consider two arguments against the New View, arguments inspired by two objections against the New View that Peels (2012), having heard them presented to him, endeavored to refute. The first argument I shall recast as the “Argument from Gullibility” and the second as the “Argument from Sloppiness.” Both arguments are motivated by intuitions that support the Standard View, and so Peels aims to defend the New View against them.

The Argument from Gullibility

According to the New View, ignorance is merely the absence or lack of true belief. It presumably follows on this view that one can decrease one’s total ignorance by being gullible—that is, by believing propositions regardless of whether one is justified in doing so. This is because gullibility can lead one to believe many true propositions, thereby decreasing one’s total ignorance as this is understood on the New View.¹⁷ Such a consequence, however, is highly implausible. The Standard View does not entail such a consequence, for it holds instead that one can only decrease one’s total ignorance by increasing one’s knowledge and not by increasing the amount of one’s mere true beliefs. Therefore, we have good reason to prefer the Standard View over the New View.¹⁸

The Argument from Sloppiness

Consider Adam, who is sloppy in his reasoning, and Bert who is intellectually conscientious in his reasoning. Adam is likely to believe more propositions than Bert, and hence more true propositions. Insofar as Adam believes more true propositions by sloppy reasoning than Bert does by intellectually conscientious reasoning, it follows on the New View that Adam decreases his total ignorance more than Bert.¹⁹ Such a consequence is also highly implausible. By contrast, the Standard View does not entail this consequence, for it holds that ignorance is the absence of knowledge, and one’s total knowledge is presumably not increased by sloppy reasoning. Therefore, we have further good reason to prefer the Standard View to the New View.²⁰

Peels (2012) responds by adducing the following considerations that I shall distinguish as (A), (B), (C), and (D).

• (A) He notes that the New View is an account of ignorance of particular propositions, not of ignorance as a “general trait or property of a person” (p. 748). He therefore characterizes these objections as irrelevant to the New View.

  Peels however is wrong to characterize them as irrelevant. Here is why. The Arguments from Gullibility and Sloppiness concern how, if the New View is true, the scope or extent of one’s total ignorance can be reduced by simply believing propositions which happen to be true. One’s total ignorance is presumably a function of the particular propositions of which one is ignorant. This is the case on the Standard View; if it is not on the New View, we have further reason to prefer the former over the latter.

• (B) Even though he thinks the two objections are irrelevant, Peels also thinks there are reasons to hold that they are not as convincing as they may initially seem, reasons that he admits are rather sketchy (p. 749). He asks us to imagine a scenario in which someone disbelieves all false propositions and believes all true ones, but does so in an unreliable manner such that his believing does not qualify as knowledge. Peels avers that we would not describe this person as ignorant of something: “What would she possibly be ignorant of? There is no truth that she fails to believe and no falsehood that she fails to disbelieve” (p. 748). ²¹ He adds: “If this is true, however, then it seems plausible that by acquiring more true beliefs, one becomes less ignorant: every true belief that one acquires is one little step in the direction of believing all truths and, thereby, ridding oneself of all ignorance” (p. 748).

  Peels’s response fails. Why would we not describe this person as ignorant of something? We would not because she is presumably not propositionally ignorant of anything. But it simply doesn’t follow that there is no proposition p such she is not factively ignorant that p unless one elides the distinction between propositional and factive ignorance. It similarly does not follow that every (mere) true belief one acquires—regardless of how unreliably or accidentally or irrationally this came about—is by itself one more step in ridding oneself of all factive ignorance.

• (C) As for the intuitive plausibility of the first objection, Peels claims it can be explained by distinguishing between the scope and degree of ignorance. By voluntarily believing a large number of propositions and hence certain true beliefs, one reduces the scope of one’s ignorance: “there are less (sic) propositions that one is ignorant of (even though there may remain an infinite number of propositions that one is ignorant of)” (p. 748).²² Doing so, however, means that one also acquires certain false beliefs. “Hence, even though one may become ignorant of less (sic) propositions one’s degree of ignorance may not thereby become lower. It may even increase, if it is true that one is more ignorant if, say, one disbelieves a true propositions (sic) than if one suspends belief on a true proposition” (p. 748).

  This response of Peels’s to the Argument from Gullibility fails. While it’s not clear what he means by degree of ignorance, let’s suppose he is right and turn to his point about the scope of ignorance. Does (a) merely believing a large number of propositions some of which are true suffice for (b) decreasing the scope of one’s factive ignorance? Yes, on the New View, (a) is a sufficient condition for (b). But to assume as does Peels that (a) suffices for (b) is to assume what is precisely at issue, and gives us no independent reason for rejecting the Argument from Gullibility.

• (D) As for the intuitive plausibility of the Argument from Sloppiness, Peels notes that, “if Bert is intellectually more conscientious than Adam, then (i) he is probably less ignorant than Adam on certain propositions and (ii) he is less likely to acquire false beliefs on certain issues than Adam” (p. 748). With respect to (i), Peels holds that Bert unlike Adam “presumably knows that he is conscientious, he knows how to investigate something carefully, he knows that certain things ought to be carefully studied before one believes them, and so forth” (pp. 748–749). Peels thinks that part of the intuition that Bert is less ignorant than Adam can therefore “be explained by the fact that there are probably certain propositions that Bert knows or truly believes and that Adam does not know or truly believe” (p. 749). With respect to (ii), Peels claims that “if Bert is less likely to acquire false beliefs on certain issues, then his degree of ignorance may be lower, even though he might be ignorant of a higher number of propositions, as I pointed out above” (p. 749).²³

Peels’s response to the Argument from Sloppiness also fails. It may very well be that Bert is less likely to acquire false beliefs than Adam. It may very well be that Bert knows “that he is conscientious, he knows how to investigate something carefully, he knows that certain things ought to be carefully studied before one believes them, and so forth.” Let’s even suppose it’s true that “Bert is less likely to acquire false beliefs on certain issues” and “his degree of ignorance may be lower, even though he might be ignorant of a higher number of propositions.” But even if all this is true about Bert, it does not explain away the intuition behind the Argument from Sloppiness. This intuition is that it’s highly implausible to think Adam’s (or anyone who is intellectually sloppy) total (factive) ignorance can decrease from merely acquiring true beliefs no matter how intellectually sloppily this came about. The intuition concerns Adam, and Peels’s points about Bert do not explain it away. The Argument from Sloppiness stands.

Conclusion

His valiant efforts notwithstanding, Peels fails in his attempt to refute the Standard View of Ignorance. We have seen moreover that there are good reasons to believe it and to reject the New View. The verdict of the Standard/New View debate should be that the Standard View prevails.

Defending the Standard View against Peels’s challenge has helped to bring to light a number of important lessons concerning the nature of ignorance. These include the following:

• (1) Propositional ignorance should be distinguished from factive ignorance.

• (2) It’s possible to be both propositionally ignorant of p and factively ignorant that p.

• (3) It’s possible to be factively ignorant that p without being propositionally ignorant of p.

• (4) Propositional ignorance is not reducible to (a kind of) factive ignorance.

• (5) We can be propositionally ignorant of falsehoods and not just of truths.

• (6) The complement of ignorance that p is knowledge that p, and not mere true belief that p.