Knowing, believing and thinking clearly about word meanings

An essential part of good mental hygiene is having a clear understanding of the role language plays in leading us astray when reasoning about complex questions. The deceptively simple question 'What is knowledge?' attracts more than its fair share of linguistic confusions so today's Mind Patch™ will use it as a pretext to expose some common misunderstandings that people have about word meanings. And while the main point of this essay is to correct these misunderstandings, it will provide what I think is a fairly definitive answer to the knowledge question, and hopefully awaken the non-specialist reader to the scale of the rabbit hole that is language, and perhaps thereby cultivate in them a level of interest befitting these phenomena.

Philosophers may struggle to understand precisely what it means to know something, but the everyday intuitions of very small children are sophisticated enough to allow them to get away with using this word without anything remotely bad happening.

The perils of knowing too much.

To be fair, philosophers are also perfectly capable of using the word know appropriately at parties, but it's one thing to have an intuitive understanding of a word's meaning and quite another to arrive at an explicit account of what we mean by it.

Philosophers of knowledge generally agree that to know something is to believe something that is true but tend to make an exception when the belief in question arises by dumb luck. It doesn't seem quite right to say that a person knows something when the basis of their belief is a faulty or deceptive argument that only stumbles upon the correct conclusion by chance, or a rumor that turns out to be true only by coincidence. Since Socrates, there has been a tradition of dealing with these cases by arguing that knowledge isn't just true belief, but justified true belief. Modern theories of knowledge have picked some holes in the justification condition but they still typically insist that there has to be some kind of legitimate connection between something being true and it being believed.

A thought experiment featuring a somewhat justified true belief
that it doesn't feel quite right to call knowledge.

Throughout the long history of this debate, the way philosophers have tested definitions of knowledge has remained essentially unchanged: They look for clever examples that reveal where a proposed definition conflicts with their intuitions about how the word can be used. But there is a fatal flaw with this approach, which brings me to my first lesson for thinking clearly about word meanings.

LESSON 1: Truth vs. acceptability

Consider the following pair of sentences:

1. Jill has two sons and a daughter.
2. *Jill has two sons and a female.

The first sentence sounds fine, but the second sentence, although very similar to the first, doesn't seem quite right. (In case you're wondering, the convention in linguistics is to mark such problematic sentences with an asterisk.) The interesting thing to note about this is that the set of all daughters and the set of all females happen to be identical. That is, all daughters are females and all females are daughters. Despite this, it's clear that these words cannot be used interchangeably. In a discussion about Jill's family structure, we need to use the word daughter rather than female, not because Jill's daughter isn't a female but because the word female doesn't reference the relevant relationship. In the same way, the word knowledge might be the wrong word to use in certain communicative contexts without necessarily being an inaccurate description of whatever it's meant to refer to. The upshot is that we can't reject the possibility that a given belief is an instance of knowledge purely on the basis that it doesn't feel right to call it that in one particular sentence. We need to consider instead whether there could be any sentence at all in which a particular belief can be appropriately called knowledge. We'll look at this in more detail shortly, but we need to cover a few more lessons first. Lesson two concerns a much more famous issue within the philosophy of language.

LESSON 2: Family resemblances

Ludwig Wittgenstein famously argued in his Philosophical Investigations that the many and varied things we call games only share a family resemblance with one another (having a strong overlap in the features they possess) without there being any particular features that every single game has in common. He observed for instance that there are both games of skill and games of luck, that there are games involving competition between players, and games, like solitaire, that are played alone, and while many games involve an element of winning or losing, there are again exceptions like ring-a-ring-a-roses. Based on these observations, Wittgenstein concluded that there simply couldn't be any single characteristic that is shared by such a diverse set of activities, and that the convention of calling them all games is only our way of saying that they form a family of related activities.

He preferred the metaphor of family resemblances to describe categories like this, but this could be misleading insofar as it suggests that it's only the number of shared characteristics that determine whether something is or isn't a member of a category. Categories also have structure, and they have this structure because of the way they are built up over time. Existing words are constantly being put to novel uses by metaphorical extension in ways that are often useful enough to eventually become conventionalized senses of a word. Each time this happens, a category grows a new limb related to the one it grew out of so that after several iterations of this process, a category will assume a tree-like structure where neighboring limbs are very similar, and very distant ones, less so.

In any case, Wittgenstein's key insight was that entities don't all have to share a set of properties to belong to the same category, which means we should consider the possibility that the things we call knowledge might not all have a single set of properties in common either, like being justified, true and believed. Instead, it may be that the collection of things we call knowledge are merely grouped under this term because they share a particular kind of family resemblance.

LESSON 3: Defining vs. non-defining features

Even if all instances of knowledge have a core set of features in common, there would be no reason to expect all of these features to be relevant to the meaning of the word. We can illustrate this again with the words female and daughter. If there is a set of features shared by all females, exactly the same set of features must necessarily be shared by all daughters, so thinking about this set will not help us account for the difference in meaning. To understand how these two words succeed in meaning different things, we have to make a distinction between the features that the members of a category possess, which are the same for females and daughters, and the subset of these features that function as defining features, which are different for the words female and daughter.

The distinction between defining and non-defining qualities can be obscured in a question like What is knowledge? which could either be about the definition of the word knowledge as encoded in the minds of speakers, or about the nature of whatever this word refers to. Compare this with the question What is a star? This could be about the nature of stars (what they're made of, what makes them shine, and so on), but even if we knew nothing about these things, we'd still be able to tell whether a given object was or wasn't a member of the category star. We could use the word without anything remotely bad happening, as did everyone who lived before astrophysicists finally figured out that stars are objects like the Sun at much greater distances, or that they shine because of nuclear fusion. These properties were only discovered as recently as the twentieth century. Prior to that, people were able to use the word star without knowing any of this because only some of the qualities we now associate with stars are what we might want to call defining qualities. This is also one of the reasons why H₂O is an inadequate definition of water. English speakers were unquestionably using the word water before there was any scientific understanding of the molecular structure this formula describes, so the formula simply cannot have had anything whatsoever to do with what the word meant, at least prior to such discoveries. Like our unenlightened ancestors, small children can speak meaningfully about stars and water well before they've had an opportunity to learn more than a tiny fraction of the vast number of things that are true of them, certainly before they've learned about nuclear fusion in stars or what hydrogen and oxygen might have to do with water. Some people get away with using these words successfully at parties without ever learning about such details so we shouldn't expect these things to be particularly relevant when it comes to understanding how the meanings of these words are encoded in the minds of native speakers.

A star is in fact indistinguishable from an idealized spherical sheep that is
extremely massive and hot, and which radiates vast amounts of energy
by converting lighter elements into heavier ones deep inside its belly.

LESSON 4: The two ways of saying what something is

It can be unclear whether a what-is question is asking about the meaning of a word or about the nature of the thing it refers to, but these questions need to be approached in entirely different ways. When inquiring into the nature of a thing, it doesn't make the slightest bit of difference what you call it. You don't have to call it anything if you don't want to. Certainly if there is a conventional label for the thing you're examining, you can make life easier by using it when describing your findings, but you could equally single out the object of your inquiry using a multi-word description of it, or by pointing at it. It doesn't really matter. Words won't get in your way.

Figuring out the meaning of a word is an entirely different process. Linguists do this by collecting examples of how words are actually used in the wild, which means analyzing how native speakers use them in writing and conversation, and by probing their intuitions to clarify which conventions they're using. They don't need to examine physical examples of whatever the words might refer to in the real world, take measurements, or anything like that. The irrelevance of the real world is particularly obvious in the case of words for things that don't exist, fictional things like unicorns and teleportation. These words succeed in having perfectly intelligible meanings despite the non-existence of the phenomena they label. The word spaceship had a meaning too before humankind had ever made a functioning example of one. And the word star would also be perfectly intelligible even if there were no such things as stars or in the unlikely event that our understanding of the nature of stars turns out to be completely wrong and those shimmering objects in the night sky are icy rather than fiery, or made of wool.

This description could have been used to define the word spaceship had it been
the intended function of the technology rather than an incidental one.

Philosophers of knowledge appear to be interested in both kinds of what-is question, but to the extent that they are interested in the precise conditions that capture our intuitions about when the word knowledge can be used, they're inquiring into the meaning of the word rather than the nature of what it refers to, and this inquiry can safely ignore whether there is any such thing as knowledge, and whether it's possible to acquire it. It may turn out that knowledge has the same status as unicorns, or that knowledge in the strictest sense is ultimately beyond the grasp of mortals, but neither of these things should prevent us from determining what the word means.

LESSON 5: Blurry words

Discovering the meaning of a word isn't guaranteed to be a particularly satisfying experience if what we're seeking is precision because a definition can only be as precise as the meaning it's attempting to capture, and some meanings are inherently vague. It's a bit like that scene in Deconstructing Harry where a film crew is having trouble focusing on an actor until they realize that the problem isn't with their lenses but with the actor himself who is just having a blurry day.

The out of focus scene from Deconstructing Harry (1997) by Woody Allen

There are a few ways that the meaning of the word knowledge could be inherently vague. One way is if there is a gradual transition from beliefs that aren't knowledge to beliefs that are, much as day fades into night. If describing a moment around dawn or dusk, we might hesitate to use either of these words because using it under these circumstances might mislead a listener into thinking we're speaking about a more prototypical case. We might hesitate about using the word knowledge on the fringes of its category too for the same reasons.

We don't generally specify the meaning of words any more than we have to either, which means that questions that probe beyond the necessities of daily life will typically reveal a certain amount of vagueness about just about everything. Our distant ancestors were running around using the word life without any need for a definition that was precise enough to determine whether viruses fitted the bill. Why would they? They didn't know viruses existed. The question What is life? has occupied (or distracted) some great minds, but it's only difficult to answer because it contains a word whose meaning is inherently soft around the edges. Words are our servants, not our masters so we could simply choose to define life in a more precise way if we wanted to. According to taste, we could define it in such a way that it included viruses, or in a way that excluded them. It would be completely up to us. Whatever decision we made wouldn't affect the nature of viruses, or make them more or less morally significant. It would only affect what we called them.

Likewise, we could simply choose to define the word knowledge as true belief to get around the messy business of justification entirely, but if we want to actually understand how language works in the mind, then we have to probe the intuitions of native speakers about meanings that emerge naturally within a linguistic community.

In principle, a successful account of what the word knowledge means to native English speakers in the wild might include some mention of inherent vagueness. It would certainly explain the awkwardness we feel about using the word in some of the highly contrived circumstances that are described in the thought experiments philosophers use to explore the issue. As it happens, I don't think this is the key to the problem, but it's a possibility that ought to be considered, not just in this instance but whenever we're attempting to capture a precise definition.

LESSON 6: Round squares

Another reason we might not be able to tell if a belief qualifies as knowledge would be if the concept of knowledge actually turns out to be incoherent. There are arguably many terms in common use that are muddled in ways that require very subtle reasoning to disentangle. Perhaps knowledge is one of them. Perhaps knowledge isn't the sort of thing that could exist, even in principle. The difficulty of defining knowledge is certainly an enduring problem, but questions don't always have to be about deep, impenetrable mysteries to be difficult to answer. Some can achieve that honor simply by failing to make sense. Perhaps philosophers of knowledge have merely snagged themselves on a particularly subtle form of nonsense.

One kind of nonsense is the self-contradictory kind that round squares belong to, and there is no law that prevents us from assigning a self-contradictory definition to a word. If we had nothing better to do, we could for example, define the word nonut to mean something that is simultaneously both a donut and not a donut. This is probably useless as an idea (except perhaps as a description of every policeman's favorite quantum superposition), but we have no trouble formulating the concept and assigning a label to it.

Another way to produce nonsense is to presuppose something that is untrue. To get a sense of the trouble that false presuppositions can cause, consider the states that a door can be in. We tend to think that if a door isn't open, it must be closed. We might have doubts about precisely where the boundary lies between these two states, but they're opposites, so we could easily be seduced into thinking that when a door isn't in one state, it must be in the other. But if you saw an unattached door lying on a rubbish heap, would you say it was open or would you say it was closed? Would such a door really be in one or the other of these two states? It's unlikely anyone seeing it there would spontaneously use either adjective to describe it, nor would they be in any danger of thinking it was teetering on the boundary between being open and closed, but philosophers who were sure that doors must be in one or the other of these two states might nevertheless end up discussing the door on the rubbish heap in increasingly unhinged ways.

In practice, we only ever talk about a door being open or closed when it's mounted over some kind of gap that the door is intended to block. We presuppose that the door we are talking about is mounted when we use words like open and closed, and it wouldn't make sense to use them otherwise. To do so would be the linguistic equivalent of dividing by zero.

Assigning truth values to sentences that contain false presuppositions is asking for trouble.

LESSON 7: The invariance of presuppositions under negation

Presuppositions are also interesting when it comes to negation. Negating a sentence will flip the truth value of whatever it directly asserts but not what the sentence presupposes, so while The door is open and its negation The door is not open both assert different things about the position of the door with respect to the gap the door is mounted on, the negated version doesn't flip the values of various truth claims that the positive sentence presupposes. For instance, under a natural interpretation, we would not take the sentence The door is not open to imply that the door does not exist, that the gap does not exist, or that it isn't mounted on the gap. All of these presuppositions remain intact under negation.

Armed with this insight, we can begin to see something important about the meaning of the word knowledge given that one of the three pillars of the justified true belief account behaves very much like the presupposed claims in the door example. Interestingly, the odd one out here isn't the justification condition, which has traditionally attracted the most controversy, but the truth condition.

Let's look at some examples. In the context of an ordinary non-philosophical conversation at a party, the proposition Dick Laurent is dead would normally be presupposed as background knowledge both when embedded as the subordinate clause in sentence (3), and within its negation (4).

3. Fred knows that Dick Laurent is dead.
4. Fred doesn't know that Dick Laurent is dead.

We would typically understand the negated version (4) to mean that while it is true that Dick Laurent is dead, Fred happens to be unaware of the fact. The part of the meaning that is negated is just Fred's awareness of the fact that Dick Laurent is dead.

This makes the truth condition of the traditional account of knowledge quite unlike the belief condition. While sentence (4) doesn't negate the truth of the subordinate clause, it does negate that Fred believes it. Belief, unlike truth, is therefore part of what the statement asserts rather than what it presupposes.

That's the core of Lesson 7, but for completeness, I would like to indulge in a slight digression about certain uses of the word know. The following details are not central to my argument so you can safely skip ahead to Lesson 8 if the finer details aren't important for you at this point in your life.

Digression:

Note that if we want to avoid any presuppositions about whether Dick Laurent is alive or dead, we can speak of knowing if or knowing whether instead of knowing that as in sentence (5). Everything I'm arguing about presupposition pertains to the knowing that form.

5. Fred doesn't know if/whether Dick Laurent is dead.

The speaker who utters sentence (3) is responsible for presupposing the embedded proposition, and they might for example feel free to do so because it was already established without controversy earlier in the conversation. In any case, a listener who is just joining the conversation could infer that the speaker believes the embedded proposition (that Dick Laurent is dead) in addition to what the speaker is directly asserting in the main clause (that Fred knows it). Likewise, a listener would also be able to infer that the speaker believes the embedded proposition (that Dick Laurent is dead) when they utter the negated sentence.

So far so good, but there is a complication when speaking of knowing that in the first person. If Fred himself uttered the first person version of sentence (3) shown in sentence (6), he would be the person doing both the presupposing and the knowing simultaneously. This is fine, but if we interpreted the negation of this sentence (7) along the same lines as we interpreted the negation of the third person version (4), it would lead to a contradiction since it would involve claiming not to know something that one is explicitly presupposing.

6. I know that Dick Laurent is dead.
7. I don't know that Dick Laurent is dead.

Note that this is actually only a problem when negating a first person claim to knowledge in the present tense. If Fred spoke about not knowing something in the past tense as in (8), it would not lead to a contradiction because his past self could easily have a different state of knowledge to his present self.

8. I didn't know that Dick Laurent was dead.

Interestingly, people do sometimes use sentences like (7), just not generally with an interpretation along the lines we're considering here. A brief search for I don't know that in an English language corpus reveals plenty of examples of I don't know that being used to mean something akin to I doubt that as in I don't know that I will ever be able to convince you, which closely resembles the I don't know whether sense. So instead of letting the I don't know that form go to waste as an unusable permutation, at least some speakers have assigned it a slightly different function.

There is another potential use of what I'm calling the unusable permutation that might be called upon when a listener does not accept the truth of an embedded presupposition that a speaker injects into a conversation. There is an example of a conversation like this in the film Lost Highway. Conveniently, this conversation occurs between two non-philosophers at a party. Also conveniently, one of these non-philosophers happens to be called Fred and, speaking in the first person and in the present tense, Fred happens to say that he doesn't know that Dick Laurent is dead.


The party scene from Lost Highway (1997) by David Lynch (Given the nature of David Lynch, I probably shouldn't make any strong claims about this being a typical linguistic exchange).
(The relevant dialogue begins at the 4m19s mark)