Awareness of ignorance

2.1 A neo-Fregean account

Although the distinction between meaning (sense, connotation) and reference (denotation) was present in the writings of some authors before the twentieth century (most notably, John Stuart Mill), Gottlob Frege first elaborated a semantic theory based on it. Frege held that the sense (Sinn) of a linguistic expression is a “mode of presentation” of the entity that is its referent (Bedeutung); he then argued that by grasping the sense of an expression, we are able mentally to represent its referent. Senses, on Frege’s account, belong to an objective third realm and, therefore, are not mental entities; grasping a sense, on the other hand, is to be in a certain mental state, one that represents that sense. This Frege called Vorstellung (usually translated as idea), which he thought was too psychologistic to deserve any further philosophical attention. To represent an object requires one to first represent a sense through an idea, and that sense (in effect) represents that object. This is how we are able to think about, represent, and refer to an object.^[8] Although Frege never considered the question, how unknown objects can be mentally represented by an agent through such a process, his theory definitely allows for it:

The sense of a proper name is grasped by everybody who is sufficiently familiar with the language or totality of designations to which it belongs; but this serves to illuminate only a single aspect of the referent, supposing it to exist. Comprehensive knowledge of the referent would require us to be able to say immediately whether every given sense belongs to it. To such knowledge we never attain. (Frege 1892, 210–211)

Given an object that we can think about and a sense that we grasp, we may not always know whether that sense belongs to it. This could happen when we have considerable, but not comprehensive knowledge of both the object in question and the referent determined by the sense that we are considering, but we do not know whether this particular sense is true of the object. Our ignorance could then be captured by an identity statement. Babylonians, for instance, had considerable knowledge of the heavenly body they called “Hesperus,” but they did not know that the sense they attached to the name “Phosphorus” was true of it – despite the fact that they had considerable knowledge of Phosphorus as well. But it should also follow from what Frege says here that grasping a sense does not always require an agent to have considerable knowledge of its referent. We can easily grasp the sense of the term “the closest planet to Earth on which there is liquid water,” and when we are asked whether this sense belongs to (or is true of) Mars, we may admit we do not know this. In fact, no one may know this. Unlike the Hesperus/Phosphorus case, this time, we could admit that we do not know of any object as being the referent of this expression. Here, our ignorance is not only about whether an identity statement is true or false, but we are also ignorant of the referent of an expression. Grasping a sense does not, as such, put us in close epistemic contact with its referent. That Frege allows for this is further indicated by another example he gives:

It may perhaps be granted that every grammatically well-formed expression representing a proper name always has a sense. But this is not to say that to the sense there also corresponds a reference. The words ‘the celestial body most distant from the Earth’ have a sense, but it is very doubtful if they also have a reference. (Frege 1892, 211)

If one knows the description has no referent, no ignorance is involved, but if it is “doubtful” whether that is the case, then one does not know whether the description does have a referent. Clearer examples can be given; we can easily grasp the sense of the description “the closest planet to Earth on which there is intelligent life” and presumably none of us knows whether it has a referent. There can also be a description that we may know to refer to an object, without having any further knowledge of that object. One may, for instance, know that “the closest planet to Earth that has exactly 6 moons” must have a referent, when all that they know is that such a planet exists and whatever can be deduced from the description and the relevant background knowledge. There can also be cases in which we know that a description has a referent of which we have some knowledge, but we do not know which object that is. Even if you have some knowledge of all the planets in our solar system, you may not know which one is “the planet that has the most amount of iridium on it”; you may know that you have substantial knowledge of the object in question, but not under the given mode of presentation. The thrust of the matter is that under the Fregean theory, grasping the sense of a term does not always require one to have knowledge of its referent. This is all the more apparent when the term in question is a full declarative sentence; grasping the sense of a sentence allows us to entertain a thought (Gedanke), but that does not require us to know what its referent is, which according to Frege is one of the two peculiar objects that he called “the True” and “the False.”

A Fregean account of awareness of ignorance requires us to extend Frege’s semantic distinction between the sense and the referent of an expression to get the epistemic distinction between an agent’s knowledge of the sense of an expression and the agent’s knowledge of the referent of that expression.^[9] For an agent to become aware of their ignorance, there must be a sense that the agent grasps through which they mentally represent the object that is determined by that sense. This could happen in any one of three cases: either the agent does not know whether there is such an object; the agent knows that there is such an object but has no knowledge of that object except for what can be trivially deduced from the information content of that sense; or the agent knows that they have some knowledge of that object but not under the mode of presentation of the sense in question. For all three cases, we may distinguish between two aspects of mentally representing an unknown; there is first the content of the representation of the unknown object, which I shall call “the content of ignorance,” and the unknown that is represented by that content, which I shall call “the object of ignorance.” Even if one does not endorse the Fregean distinction between sense and reference, this more general distinction is still genuine.

2.2 A neo-Russellian account

The preceding neo-Fregean account may seem to be incompatible with Russell’s semantic theory, which appears to reject the distinction between the meaning of an expression and its referent. If so, would it then follow that Russell’s theory cannot account for how we can mentally represent unknowns and become aware of our ignorance? Definitely not. In fact, Russell not only had all the resources to give such an account, but he also could have made a finer distinction between a strong and a weaker sense of awareness of ignorance, by appealing to his distinction between “knowledge by acquaintance” and “knowledge by description”:

I shall say that an object is ‘known by description’ when we know that it is ‘the so-and-so’, i. e. when we know that there is one object, and no more, having a certain property. … We know that the candidate who gets the most votes will be elected, … but we do not know which of the candidates he is, i. e. we do not know any proposition of the form ‘A is the candidate who will get most votes’ where A is one of the candidates by name. We shall say that we have ‘merely descriptive knowledge’ of the so-and-so when, although we know that the so-and-so exists … yet we do not know any proposition ‘a is the so-and-so’, where a is something with which we are acquainted. (Russell 1912, 113)

Here, the agent has both knowledge and ignorance of the very same person, but no contradiction emerges from this because the available knowledge is knowledge by description, although the knowledge that is absent is knowledge by acquaintance. This is how one may, without falling into a contradiction, become aware of their lack of acquaintance of an entity. These would then be cases of awareness of ignorance in some strong sense. Russell of course held (at that time) that all our knowledge of particulars external to our minds is knowledge by description and never knowledge by acquaintance. Although such an account may have the merit of showing us the limits of our knowledge, it certainly cannot give us a full account of ignorance, since under normal conditions when we are aware of our ignorance concerning an external particular object, we do believe that we can achieve some epistemic progress in overcoming our ignorance even if it never yields complete acquaintance of that object.

Knowledge by description is a broad category for Russell, in that it holds of our knowledge of things by perception:

My knowledge of the table as a physical object … is not direct knowledge. Such as it is, it is obtained through acquaintance with the sense-data that make up the appearance of the table … . My knowledge of the table is of the kind which we shall call ‘knowledge by description’. The table is ‘the physical object which causes such-and-such sense-data’. (Russell 1912, 47)

These two examples Russell talks about, one concerning the candidate who gets the most number of votes and the other concerning the table, are supposed to be both cases of knowledge by description, but quite obviously there is a sharp difference between them. In the first example, one could legitimately ask the question “who is the candidate who will get the most number of votes?,” but no analogous question seems to suggest itself in the second case.^[10] By asking such a question, one implies their ignorance of the person in question, which could be either a lack of knowledge by acquaintance or a lack of knowledge by description of the person in question. If the former is the case, then the question is unanswerable, so why ask? And the latter apparently cannot be the case, given that one already knows the person in question by description, so again, why ask? But we can ask such questions, and we frequently do. And when we do so, we normally imply our ignorance in a weaker sense. Had Russell been interested in the topic he could have posited a third category that he could have called “ignorance by description.” Your knowledge of a table in front of you could then be a case of knowledge by description, but in the case of the candidate who will get the most number of votes, you could be said to possess ignorance by description. Although acquaintance is an absolute term that does not admit of degrees, Russell did acknowledge, in a short passage, that one’s epistemic connection to a particular can come in degrees:

It will be seen that there are various stages in the removal from acquaintance with particulars: there is Bismarck to people who knew him, Bismarck to those who only know of him through history, the man with the iron mask, the longest-lived of men. These are progressively further removed from acquaintance with particulars …’. (Russell 1910, 116)

In each case, we have a denoting phrase in which the agent knows that there is one and only one particular that satisfies it, and the epistemic connection of the agent to that entity gets weaker and weaker. No matter how much we are removed from acquaintance though, these are all supposed to be cases of knowledge by description. The only kind of ignorance Russell appears to acknowledge is our lack of acquaintance with these particulars. There is, however, a good sense in which someone “who knew Bismarck” is not ignorant of Bismarck, but someone who merely knows that there is one and only one entity who is the longest-lived of men, may not know who this person is. It would be quite awkward for a friend of Bismarck who knows him well to ask the question “who is Bismarck?,” but it would be very natural for someone who does not know who the longest-lived of men is to ask “who is the longest-lived of men?” When we ask such a question our goal is not to acquire complete acquaintance with the person in question; that would make the question unanswerable. Just like when one says, “I know who Bismarck is,” we do not take him to be acquainted with Bismarck; when one says “I do not know who is the longest-lived of men,” we do not normally take him to imply his lack of acquaintance. In the first case, one may have a very rich mental file of Bismarck, but in the second case, one may possess merely a definite description and whatever follows from it. Obviously, there is a significant epistemic difference between these cases, so much so that we may take the first to be an example of knowledge by description, whereas the second case may be said to be an instance of ignorance by description.

Although Russell denied the distinction between sense and reference, his Theory of Denotation, as layed down in Russell (1905), is itself sufficient to give an account of awareness of ignorance. First, grasping a proposition (constituted by the objects with which one is acquainted, which are denoted by the logical parts of a sentence denoting that proposition) does not require one to know whether it is true or false, which is an instance of what I shall call “propositional ignorance.” Second, when we consider a definite description, its denotation appears at two distinct levels; within a sentence, it dissolves into quantifiers, sense-data, and properties; but it also denotes an object in the outer world, regarding which we may be ignorant, either in the strong or the weaker sense; this is an instance of what I shall call “non-propositional ignorance.”

2.3 A unified account

The process by which we represent an unknown and become aware of our ignorance can then be put as follows:

We mentally represent entities that we have experienced and thus are known to us to some degree;

we then merge two or more of these representations together by utilizing some syntactic rules to produce a complex representation whose object we have not experienced which is partially or completely unknown to us;

by an act of epistemic self-reflection we come to realize that this complex representation determines an object that is unknown to us.

It follows then that awareness of ignorance is:

an intensional state in that it has conceptual content,

an intentional state since it is always directed to, or is about the object of ignorance which is determined by the intensional content,^[11]

a meta-representational state, since it requires the agent to represent a representation as determining an unknown object.^[12]

There are now some finer points that may be more controversial. One is the problem of existence. When I claim that mentally representing an unknown is an intentional state, I mean it in a weak sense of intentionality, which does not entail the existence of such an object. When Le Verrier was aware of his ignorance concerning the planet perturbing Mercury, his ignorance was directed toward what he thought to be an unknown planet, which he dubbed as “Vulcan,” only to find out that there is no such planet.^[13] Here, the basic existential presupposition of ignorance turns out to be false. Even if one rejects the idea that mental representation is involved in such a case, it is still an obvious example of awareness of ignorance and it is also a clear counter-example to the view (that is prima facia plausible) that in order to be aware of your ignorance of something you must have partial knowledge of it.

Another controversy is the problem of causality. Causal theories of mental representation claim that there must be a causal relationship between a mental representation and its object. To mentally represent, say, the moon, we need to have some causal connection to it. In such cases the object itself is partially responsible, in causal terms, for our mental representation of it. Such a view is also true of many cases of mental representations involved in awareness of ignorance. When you hear a knock on the door, and you do not have a clue who it might be, that would, under normal circumstances, immediately cause you to construct in your mind a representation of the person knocking on the door. Dinosaurs became extinct some 65 million years ago, leaving behind traces that allowed us to represent to ourselves the cause of their extinction, which is still unknown. The casual thesis can account for such cases where the object of ignorance is causally responsible for us having a mental representation of it. This, however, is not always the case. Scientists were eager to know if there is liquid water on other planets within our solar system, which led them to construct a description such as “the closest planet to Earth which naturally contains liquid water” by which they were able to represent an unknown planet. There was some evidence that this could have been Mars, but it was not conclusive. Assuming that Mars is in fact that planet closest to us on which there is liquid water presently, the question we should ask is this: was the evidence of there being water on Mars causally responsible for scientists having this mental representation? If the observation of the indirect evidence of liquid water on Mars motivated them to construct this description, then there is a causal connection; but it could have been just the other way around; they may have constructed the description first, and then start seeking what its referent could be, if there is one, which is presumably historically more accurate. Sometimes we experience the indirect causal impacts of an entity that motivate us to construct such a description, and yet at other times, we use our imagination and creativity to construct a description and we realize that its referent is unknown to us. In the latter cases, the object in question does not appear to be causally responsible in any way for us to construct the description by which we are able to represent an unknown entity. All in all, we may say that when an agent is aware of their ignorance, the unknown object may be represented in two different ways; in one case, the unknown object is causally responsible for the representation, in the other case, it is not.

This unified account suggests that awareness of ignorance also has an ethical dimension, in an Aristotelian sense. Merely constructing a content whose referent is unknown, by itself, is not sufficient for an agent to become aware of their ignorance. One may entertain a representation without realizing that they are ignorant of its object, if they are simply uninterested in the topic, or they may think that they know, when in fact that they do not, or they may simply not have the meta-cognitive ability to come to realize their ignorance. This requires them not only to possess the capacity for meta-representation, but may also require certain traits that may be considered as epistemic virtues, such as conceptual creativity, inquisitiveness, open-mindedness, epistemic humility, curiosity, etc. This issue ought to be addressed in the emerging field of virtue epistemology.

4.1 Non-propositional ignorance

Awareness of ignorance that does not have propositional content is abundant. One may be ignorant as to who is the shortest spy, why the sky is blue on Earth, when the next lunar eclipse will take place, where the sun will set on the shore, how a mobile phone works, which parliament has the highest number of females, what is the essence of virtue, and so on. In each and every such case, we can always formulate a linguistic expression, usually in the form of a definite description, whose meaning gives the content of ignorance and whose referent gives its object. What allows us to acquire awareness of our ignorance concerning a specific object is that we can grasp the content of a definite description, but have very little, or even no knowledge of its referent. That is why the object of non-propositional ignorance is never a truth value; it could be a person (motivating a who-question), a cause or a reason (motivating a why-question), a place or a location (motivating a where-question), a time, date, or duration (motivating a when-question), a way, method, or procedure (motivating a how-question), or any other kind of entity that we can refer to (motivating a what-question).^[19]

Those who wish to hold that all our mental states have propositional content may object to this. This can be perhaps be done by utilizing a sophisticated version of Millian semantics. Such a theory first claims that there are singular propositions, where an object rather than its representation is a part of the proposition; second, it holds that a singular proposition may have different guises such that an agent may know the proposition under one guise, but not know it under another. We may then claim that every wh-question can be answered by a singular proposition such that that very proposition is grasped by someone (under a certain guise) who is in fact ignorant of the answer (which is a different guise of the very same proposition). If a case can be made for this, then it may appear to follow that the content of ignorance can always be given by a proposition. Such a position can perhaps be extracted from the startling argument due to Stanley and Williamson (2001) which attempts to reduce know-how to know-that. They argue that for Hannah to come to know how to ride a bike, is for her to come to know a very special singular proposition in the form “w is a way to ride a bike” under a special guise that they call a “practical mode of presentation.” It then follows that to know how to do something is simply to know a proposition; and that not knowing how to do something is not to know the proposition in question. Obviously, such a view can then be extended to cover other cases of wh-ignorance. Would it then follow that all cases of awareness of ignorance have propositional content? If Hannah does not know how to ride a bike, she may be taken to be ignorant of a skill; with some reflection, she may then become aware of her ignorance. Can the content of her ignorance be captured by the singular proposition in the form “w is a way to ride a bike”? If so, then she must be in a position to entertain the proposition in her mind. But if w is a special kind of practical mode of presentation such that grasping it would entail that Hannah knows how to ride a bike, then it cannot be the content of her ignorance when she is aware that she does not know how to ride a bike. If, on the other hand, we assume that Hannah can grasp this proposition under a different guise, it still cannot be the content of her ignorance, in the typical way, because she would already know that the proposition is true. All in all, awareness of ignorance concerning a skill is not awareness of ignorance concerning whether a proposition is true or false. This is the case even if know-how can be reduced to know-that.

Going back to Holmes, when he becomes aware of his ignorance as to who murdered Smith, there may be a singular proposition that answers the question, “Who murdered Smith?,” which may be said to give the content of his ignorance. If Bill is in fact the murderer, the singular proposition in question would then be Bill is the murderer of Smith. Now, intuitively, we may say that Holmes is not in a position to grasp this proposition if he has no prior connection to Bill. But under the Millian view, we are considering if Holmes has sufficient evidence that there is one and only one murderer, then he may be in a position to grasp the singular proposition Bill is the murderer under one guise. Suppose that Holmes, apart from being a great detective, has pursued a side career in the philosophy of language, has read Frege’s Puzzle, Salmon (1986), and was completely persuaded by Salmon’s account of Millianisim. As a result of this, we may imagine him having developed the habit of naming the unknown murderer for every homicide case he is assigned to. Suppose in this case he names the murderer of Smith “Murdy.” He now could claim that he is in a position to grasp the singular proposition Murdy is the murderer of Smith. Now, of course, if he grasps it, he also knows that it is true, as long as he knows that Smith was murdered single-handedly. He could even say: I know the true answer to the question, “Who is the murderer of Smith?”; it is Murdy. It is quite an odd feature of Millianism that we would not have a standard way of expressing our ignorance in such cases. As a Millian, Holmes ought to admit that he does not know, in some sense, who the murderer is. He could claim: “What I am ignorant of, is not whether Murdy is the murderer, I already know that; rather I wish to know this proposition in some more privileged way by grasping it under another guise which would entail that I know who Murdy is.” But then, Holmes could also claim that he knows who Murdy is; he is the murderer of Smith, and once again, he would have to say that he knows who Murdy is under one guise, but not under another. We have had such actual cases in which murderers were named before they were caught. Consider the famous Unabomber case. After several explosives were mailed to certain university and airline offices, the police, being convinced that they all were coming from a single source, coined the name “Unabomber” (shorthand for the “university and airline bomber”) to denote an unknown criminal. They were aware of their ignorance as to who was responsible for mailing these bombs. They asked: who mailed these bombs? But in act, they did have an answer, which they knew to be true; it was the Unabomber who mailed the bombs … who else? Under the Millian view, this proposition is identical to the proposition that Kaczynski mailed the bombs, which implies that the police in fact did grasp this proposition even before they caught the criminal. Does all this imply that the content of their ignorance was propositional? Perhaps so, but then their ignorance cannot be captured by a whether-question. That is because the police in fact knew that the Unabomber mailed the bombs, even before they caught the criminal, and if they knew this, they also knew all along that Kaczynski mailed the bombs. Similarly, if Holmes is in a position to grasp the singular proposition that Bill is the murderer, under a certain guise, he is not ignorant of whether it is true, given that he would know that it is true, even before he finds out who the murderer is. As we shall see in the next section, one may know a proposition to be true yet not know the fact that makes it true; this is one such case. So, even if Holmes’ ignorance could be said to have propositional content, it is not an instance of its typical form that motivates a whether-question. In any case, if we have some respect for the way in which we use language, there must be some intuitive sense in which Holmes simply does not know who the murderer is, and if so, the content of his ignorance is simply not a proposition. Today, we know that the Unabomber is in fact Theodore Kaczynski; the common sense view is that we did not know this earlier (contra to Millianism); anyone interested in him can find out a lot about his life, his character traits, his political views, why he carried out these attacks, etc. This rich file appears to be sufficient for us to claim that we now know who the Unabomber is. Someone who has never heard of him before reading these lines may still find a bit of mystery here. They may even ask, “who is Theodore Kaczynski?” They may take an interest in the issue and search for his name online to find out more about him. This would indicate that they are aware of their ignorance concerning who Theodore Kaczynski is. The more we come to know about a person, the richer our mental file of that person becomes; how rich it must become so that we no longer consider ourselves as being ignorant of that person depends on many factors: what epistemic standards we set for ourselves, how much interest we have in the topic, what the stakes are within the context we are in. If you set the standards too high, as we occasionally do in philosophy, you may even find yourself asking yourself the question, “Who am I?”^[20] That is why ignorance is not an all-or-nothing affair; it comes in degrees. It is rarely the case that ignorance can be fully eliminated, no matter how rich your mental file is about a person or an object, there will always be more for you to learn. The only exception to this is when the object of our ignorance is an entity of which we can have complete knowledge, which is rarely or perhaps never the case. Awareness of ignorance, therefore, is not something we should always expect to be fully eliminated.^[21] This account makes ignorance a gradable notion that is context-sensitive and interest-relative. Perhaps that is what led philosophers to concentrate on ignorance that has propositional content and neglect non-propositional ignorance. This is based on the assumption that propositional knowledge is not a gradable notion, that is, it does not come in degrees; and even if knowledge attributions are context-sensitive, this is not as worrisome as the context-sensitivity of know-wh attributions. This, I believe, rests on a mistake: because propositional ignorance is not always about truth, an agent who knows that a proposition is true can still remain ignorant about other aspects of that proposition.

4.2 Propositional ignorance

There are various things regarding which one may be said to be ignorant in connection with any specific proposition. First, one may be ignorant of a proposition, period, if one has never entertained that proposition; this could happen if one has the conceptual apparatus to grasp the proposition in question, but has never done so, or instead, it may be that the person is not able to grasp the proposition due to limitations of their idiolect. Ignorance of a proposition in this sense is not something of which the subject who is ignorant is aware. Such ignorance attributions will always have to be in the third-person, as, for instance, when we say that Socrates was ignorant of the proposition that the Higgs boson is an elementary particle. Setting aside this kind of ignorance, let us concentrate on cases in which an agent in fact grasps a proposition.

For an agent S and a proposition p that S grasps, there are three different ignorance attributions we can make:

S is ignorant whether p (call this “whether-ignorance”),

S is ignorant that p (call this “that-ignorance”),

S is ignorant of the fact that makes p true (call this “fact-ignorance).

Suppose Sue does not know whether the Higgs boson is an elementary particle, but unlike Socrates, she grasps the proposition in question. She can then become aware of her ignorance by a bit of self-reflection and then state her ignorance by uttering: “I am ignorant as to whether the Higgs boson is an elementary particle.” Here, what she is ignorant of is whether the proposition in question is true or false, and the object of her ignorance then can be captured by a definite description: the truth value of the proposition that the Higgs boson is an elementary particle. The object of ignorance in such a case is a truth value, and the content of ignorance contains a proposition. This holds for any instance of whether-ignorance. As simple as it sounds, it gives rise to various philosophical questions: What is a truth-value? Is it a peculiar object that is the referent of a sentence, as Frege suggested? Or is it merely a property of a proposition? If so, what kind of property is it? Is it a genuine property concerning whether the proposition corresponds to reality? How then can a mathematical proposition or a normative one be true? Are there different realms for which we have different kinds of truth? Or is truth a deflationary property? These are some of the controversial questions that have been raised about the notion of truth, which have given rise to an enormous philosophical literature. The question as to what is the unknown that we represent when we express our awareness of ignorance concerning whether a proposition is true or false does not have any straightforward answer to everyone’s liking. For each and every distinct theory of truth, we could get a different object of awareness of ignorance. If we take the oldest, the most popular and perhaps the most intuitive theory of truth, namely the correspondence theory, which, on its most popular version, a proposition is true just in case it corresponds to a fact, and false otherwise, it would follow that being ignorant of whether a proposition is true, is not knowing whether that proposition does or does not correspond to a fact. In what follows I will assume that this theory is correct at least for some simple truths, but I will not presuppose that facts are entities completely independent of our conceptual schemes.

Consider now Io, who, unlike Sue, knows that the Higgs boson is an elementary particle. If Io knows that Sue does not know that the Higgs boson is an elementary particle, then he may correctly say “Sue is ignorant that the Higgs boson is an elementary particle.” This is a case of that-ignorance. (It is a rare construction in the English language, so much so that it may sound ungrammatical to some ears.) The distinction between whether-ignorance and that-ignorance may initially appear uninteresting. This is because one may think that whether-ignorance can be reduced to that-ignorance, i. e., a subject’s ignorance whether p, may be taken to be the subject’s being ignorant that p, and being ignorant that non-p. This may not be correct, if attribution of that-ignorance is factive, that is if an assertion in the form S is ignorant that p, entails p. If it does, then it would follow, first, that whether-ignorance cannot be reduced to that-ignorance, and second, that that-ignorance attributions cannot be made in the first person. Rik Peels appears to commit himself to the view that that-ignorance is factive: “First, we would not say that someone who believes a false proposition p and, thereby, lacks knowledge of p, is ignorant of p. One can only be ignorant of truth, so it seems” (Peels 2010, p. 4).^[22] Now what would appear to support this position is that a statement such as “people in the old days were ignorant that the earth is round” seems fine, although “people in the old days were ignorant that the earth is flat” appears to be very awkward. The reason why the latter statement sounds awkward may be because it simply expresses a falsity. If so, then it appears that in order for us to attribute that-ignorance to others, we would have to know that the proposition is true. This may appear to be problematic. Consider Peter Unger (1975) who has argued for “universal ignorance,” the view that no one ever knows anything to be so. If what he says is correct, then it follows that Unger himself does not know anything. But, if that-ignorance is factive, would it then follow that Unger is contradicting himself by asserting the doctrine of universal ignorance? It would seem so if we tried to paraphrase this doctrine in term of that-ignorance. Unger cannot single out a proposition, such as the proposition that the Earth is round, and then assert that everyone is ignorant that the earth is round, for in order for him to assert it, he would have to know that it is true, which contradicts his statement. The best he could then do is quantify over true propositions and claim that for every such proposition p, everyone is ignorant that p, although he cannot instantiate it to any particular proposition. There may be problems here concerning whether one is justified in asserting a universal claim, while not being able to assert an instance of it. In any case, this is where whether-ignorance comes to the rescue, since it is not a factive notion. There may be no contradiction for Unger to assert that for every proposition p, everyone is ignorant whether p (although under the knowledge-account of assertion he would be violating a linguistic norm.) This time he can give many instances as examples. That-ignorance does appear to have a use in which it is factive; whether this is the case for all of its uses I shall leave open. If it is, then it may also follow that that-ignorance can never be used in the first-person: A statement in the form “I am ignorant that p,” would be another Moore-type of case, in which I imply, not only that I do not know that p, but also that p is true. First-person attributions of that-ignorance would then be unassertable; although not because they would express falsities, but rather because they would violate certain norms of assertion. If that-ignorance is factive, then it also follows that we cannot attribute that-ignorance to an agent when the proposition in question is in fact false. This is the case both for first- and third-person attributions. I cannot say “I am ignorant that the Earth is flat,” nor can we say that Sue is ignorant that the Higgs boson is not an elementary particle (assuming that the Higgs boson is an elementary particle). When Sue is ignorant whether the Higgs boson is an elementary particle, it would then follow that Sue herself cannot attribute that-ignorance to herself; that is, she cannot assert the sentence “I am ignorant that the Higgs boson is an elementary particle,” although it is true. The best she can say is “I am either ignorant that the Higgs boson is an elementary particle, or I am ignorant that it is not, but I do not know which.” That-ignorance constructions would then be useful for us to attribute ignorance to others, but not to ourselves. This would be one way in which we may become aware of the ignorance of others which bears on what cognitive scientists call a “theory of mind.” As Peels notes, such ignorance attributions also show that the standard view which identifies ignorance with lack of knowledge cannot be universally correct.^[23] These are some of the interesting philosophical issues concerning propositional ignorance. There is, however, a question, which I believe deserves much more attention than any of the foregoing ones and is by far more significant philosophically. Is a subject’s ignorance regarding a proposition completely eliminated when the subject comes to know whether the proposition is true? I will argue that not every instance of awareness of ignorance that has propositional content is about truth, i. e., a subject’s ignorance concerning a proposition may not be fully eliminated even when they come to know that it is true. To see this, consider now the distinction between whether-ignorance and fact-ignorance.

When one is ignorant about whether a proposition is true or false and then finds out that the proposition is true, we would normally say that their ignorance has now been eliminated. This does eliminate their whether-ignorance, but I wish to argue it does not always eliminate another type of ignorance with respect to the very same proposition. In order to show this, I shall presuppose a minimal amount of realism with respect to the notion of truth, and the ontology of facts as truth-makers. For a simple singular proposition in the subject/predicate form, I will presuppose that such a proposition is true if and only if there is a particular fact that makes it true. I will set aside the well-known problems concerning whether such an account can be generalized to all truths.

Consider a proposition expressed by a sentence s in the form “a is F,” where a is a singular term that refers to an object and F refers to a property. For an agent S, who grasps the proposition expressed by sentence s, we may raise three distinct questions concerning the agent’s epistemic situation with regard to that sentence and its parts.

Does S know whether “a is F” expresses a truth?

What is S’s epistemic connection to the referent of a?

What is S’s epistemic connection to the referent of F?

These three questions are different; an answer to one does not provide an answer to the other two. This does not imply that the three questions are completely independent; that is, an answer to one of the questions may at least suffice to narrow the range of possible answers to the other two. First, consider the case when the answer to the first question is negative. This is the situation when S grasps proposition p through sentence s (“a is F”), and S does not know whether p. Does this tell us anything about the answers to the other two questions? It may be said that given that S grasps the proposition through sentence s, then S must have some epistemic connection to the referents of a and F. Putting aside the predicate term F for a moment, let us consider the subject term a of the sentence. S grasps the term a; in other words, S knows the meaning of the term a. Does that give us any information concerning S’s knowledge of the referent of a? One may be tempted to think that given that S grasps the proposition, S must have some close epistemic connection to the referent of the subject term of the sentence, but we have seen earlier that this is not always the case. Suppose Sue grasps the proposition expressed by “the Earth naturally contains iridium,” but she does not know whether it is true. Her epistemic connection to its subject term is quite close; she knows a lot about the planet on which she lives. Now consider the sentence “the 98th prime number is larger than 500.” Sue easily grasps this sentence too but suppose again she does not know whether it expresses a truth. That would be the case, for instance, if Sue does not know what the 98th prime number is. What is her epistemic connection to its referent? How much knowledge does she have concerning the 98th prime number? Well, if she knows that prime numbers are infinite and well-ordered, then she can claim to know that she knows that the term “the 98th prime number” has a referent. She then has existential knowledge. She can also use her background knowledge of prime numbers to make some deductions and say for instance “I know that 98th prime number is not divisible by any number other than itself and 1.” She can trivially produce many such propositions all of which she would know to be true. No matter how many such propositions she produces as such, that would not change the fact she does not know what the 98th prime number is, until she calculates it, or looks it up. Consider now the sentence “the closest planet to Earth on which there is intelligent life has an atmosphere.” Once again, suppose that Sue grasps what the sentence says but does not know the proposition expressed by it. The reason why she does not know it may not be because she does not know whether a planet sustaining intelligent life must have an atmosphere. We may even assume that every planet that sustains intelligent life must have an atmosphere, and that Sue knows this. The reason why Sue does not know this proposition is because she does not even know whether there is such a planet, that is, she does not even know whether the subject term of her sentence does have a referent. Although Sue grasps the meaning of the subject term of the sentence “the closest planet to Earth on which there is intelligent life” she knows nothing about its referent. All in all, when an agent does not know a proposition they grasp through a sentence, we could have cases in which the agent (a) has a very close epistemic connection to the referent of the subject term of the sentence, (b) has a very remote epistemic connection to the referent of the subject term of the sentence, or (c) knows nothing about the referent of the subject term of the sentence. This shows that answering the first question negatively says little about what the answer to the second question is.

Now let us consider cases when the answer to the first question is positive, that is, when our agent grasps proposition p through sentence s, and S knows that p. What could that tell us about S’s epistemic connection to the referents of the parts of the sentence s? Let us first start with a case in which the subject has close epistemic connections. Sue grasps and knows the proposition expressed by the sentence “the Earth contains liquid water.” Like any normal adult, Sue has very rich mental files both of the Earth and of water and the containing relation. She knows a lot about the referent of both the subject term of the sentence and its predicate. Now consider the sentence “the Higgs boson is an elementary particle.” Suppose Sue has read this in some reliable physics journal that she trusts. If it is true that the Higgs boson is an elementary particle, then Sue knows this. Her knowledge is an instance of knowledge by testimony. How much does Sue know about the referents of the parts of this sentence? Unlike the previous cases, it may be said that this time Sue must have some partial knowledge of the referents of the parts of this sentence, given that she knows the proposition it expresses. Concerning the Higgs boson, for instance, Sue must at least know that it exists, and perhaps a bit more than that. After all, it would sound very awkward for Sue to say “I know that the Higgs boson is an elementary particle, but I do not know whether the Higgs boson exists”; and it may also sound awkward for her to say “I know that the Higgs boson is an elementary particle, but I know nothing about the Higgs boson.” The reason why such assertions sound awkward may be because they always express falsities, and the reason that they express falsities is because a knowledge attribution in the form “S knows that a is F,” entails a proposition in the form “S knows that a exists, and has at least some partial knowledge of a.” If so, in order for Sue to come to know that the Higgs boson is an elementary particle, she must not only know that the Higgs boson exists, but she must also have some partial knowledge of it. How much must she know? What is the minimum amount of knowledge that she must possess about the Higgs boson for her to know the proposition in question? This is not an easy question to answer, and it is not even clear that the question has a definite answer. How much world knowledge one must have in order to have word knowledge is one of the most challenging questions in the philosophy of language. For Sue to grasp the term “the Higgs boson,” she must have a mental file of it which contains some information; not all of such information has to be accurate, but some of it must be accurate in order for the file to be a file of the Higgs boson. Now we may wish to distinguish this accurate information into two parts; the part required for the mental file to be a file of its referent, and the remaining part which is added later. The former is what we may call a “file-opener.” This is what is required for an agent to fix the referent of the term in question and is also what is required for the agent to grasp the meaning of that term. When we ask Sue what she knows about the Higgs boson, the answer she gives will be retrieved from her mental file of the Higgs boson. Not everything she says in answer to our question must be from the file-opener part. For instance, she may say that the Higgs boson is what gives mass to some particles. This may be from the file-opener part, for she may have opened up her file by learning that this property was what was used by Higgs and others to fix the reference of the term. Upon learning that a gap in the Standard Model was the lack of an explanation concerning why some particles have mass, Sue knows that the term was coined as a term to denote a kind of particle that would enable physicists to fill this gap. If so, Sue initially may have opened up her file by the reference fixing description “the particle which gives mass to other particles.” She may have later learned that the Higgs boson is the particle associated with the Higgs field. This may be information she acquired that is not part of the file-opener, assuming that she did not initially need it to grasp the term. Some may say that if one has never heard of the Higgs field, then one is not in a position to grasp the term “Higgs boson.” If so, we may wish to add this to the file-opener part of Sue’s mental file. There may be no precise criteria that determine when an agent acquires a new concept or comes to know the meaning of a term in their idiolect. What is important for my purpose here is not whether there are such precise criteria. It may very well be that the transition from a state of ignorance concerning the meaning of a term to a state of having acquired the knowledge of the meaning of the term has no sharp boundaries, allowing for intermediate states that are indeterminate. If this is correct, and I believe it is, there comes a point when we pass some threshold such that we acquire the knowledge of the meaning of a term sufficient for us to use it to express our beliefs, our knowledge, and our ignorance. The point is that once we pass this threshold, our knowledge of the referent of that term may still allow us to express our ignorance of it. When Sue passes the threshold concerning her knowledge of the meaning of the term “Higgs boson,” her knowledge of this entity may still not be much. She may still have a very high degree of ignorance about the Higgs boson. Although she knows that the Higgs boson is an elementary particle, she may still be curious about the Higgs boson and wish to inquire into it so as to learn more about it. Consider now the referent of the predicate part of our original sentence. Sue grasps the concept of an elementary particle. Suppose that when we ask her, “Is an elementary particle an indivisible entity that constitutes physical reality?” Sue hedges, and admits that she does not know the answer. Upon some self-reflection, Sue then may come to realize that there is plenty more for her to learn not just about the Higgs boson, but also about an elementary particle. Now consider the sentence as a whole: “the Higgs boson is an elementary particle.” If true, it is made true by a fact, namely the fact of the Higgs boson’s being an elementary particle. If Sue can express her ignorance concerning the parts of the sentence, then she can express her ignorance concerning this fact. Although she knows that the proposition is true, she is still ignorant (to some degree) of the fact that makes it true. By coming to know that a proposition is true, we eliminate our whether-ignorance, but that does not always put us in close epistemic contact with the fact that makes that proposition true. If Sue is an open-minded self-reflective epistemic agent, she may say “I know that the Higgs boson is an elementary particle, but I am quite ignorant of the fact that makes it true.” Knowing that the proposition is true is merely knowing that such a fact exists. At times, one may perhaps even come to know with complete certainty that a proposition is true, yet not know the fact that makes it true. You may know with complete certainty that the 98th prime number is not divisible by 3, but that does not imply that you know what makes it true, if you do not know what is the 98th prime number. Holmes may come to know that the murderer of Smith is insane, without knowing the fact that makes it true, if he does not know who the murderer is. If you are ignorant as to what is the color of the sky on Venus on a sunny day, and I tell you that it is Solange Knowles’s favorite color, you could then come to know the proposition that the color of the sky on Venus on a sunny day is Solange Knowles’s favorite color, if you take my word for it, although you would not know the fact that makes that proposition true if you do not know what Solange Knowles’s favorite color is.^[24] Then when you learn what color that is, that may still not imply that you have no ignorance left concerning this fact. Just like our ignorance concerning who someone is, what something is, why and when and where and how something happened, etc., our ignorance concerning a fact that makes a proposition true is also a state that comes in degrees and can rarely (perhaps never) be fully eliminated, since we rarely (perhaps never) have full acquaintance with a fact.

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