1. food and drink
2. desserts and baking

TheMeaninglessnessofOrdinary
ThoughtandLanguage
Bryan Frances
Draft of a chapter in a book manuscript
It is not surprising to hear someone proclaim that questions of meaning can be profound. Some of us
puzzle over the meaning of human existence. Those of us of religious persuasion typically fret over the
meaning of spiritual experience or human misery. Occasionally someone will declare that human
existence has no meaning at all. This may strike you as an odd thesis, depending on your cultural
upbringing, but at least it’s one that we can get our heads around if we put some work into it: we can
eventually see why someone would hold that thesis.
What we don’t do, however, is question whether our words, sentences, and thoughts have any meaning.
Surely it is the most obvious thing in the world that ‘The tree in the backyard is next to the shed’ differs
in meaning from ‘The rose bush in the backyard is next to the patio’. And that of course entails that
some things, such as sentences, have meaning. The meaning in question isn’t anything profound, for
sure. It’s just ordinary, everyday linguistic meaning. Furthermore, it’s clear that our thoughts have
meaning as well: at one time you’re thinking of dinner and another time you’re thinking of Mecca; those
are thoughts with different meanings. But just as in the other chapters of this book, we can discover the
oddest mysteries hidden in the most ordinary things, such as our perfectly commonplace words and
thoughts.
In chapter 3, on mysteries concerning ordinary material things, there were several junctures in which
the phenomenon of vagueness was crucial. Philosophers and others who are interested in the nature of
thought and language have been puzzling over vagueness for millennia. Their research provides the
impetus for Vagueness Nihilism, the view that virtually none of our ordinary words, sentences, concepts,
or even thoughts has meaning. Naturally, this entails that virtually nothing I write here has any meaning.
And the thoughts running through your head? Meaningless as well. Have a nice day.
Introduction to Vagueness
The word ‘vague’ has several meanings in everyday life; we need to focus on the one that may lead to
the annihilation of almost all meaning. I will not be able to give a rigorous explanation of the relevant
kind of meaning of ‘vague’, and even if I aimed for rigor I would run up against the bounds of
controversy, but I can supply a relatively uncontroversial explanation adequate for our purposes.
We start with a mildly helpful characterization of what vagueness is: a word is vague = it isn’t precise.
The word ‘rich’ is vague because it’s not perfectly precise; vagueness is the opposite of precision. And
now of course we need to know what precision is. Opinions differ, but there are two things most
philosophers point to when explaining what precision, and hence vagueness, is.
One thing many people are tempted to say is that vague words are what philosophers call tolerant: ‘rich’
is tolerant in the sense that you can’t have someone who is rich, take just one penny away from her, and
thereby instantaneously make her not rich. The word ‘rich’ is “tolerant” of small changes in the sense
that whether or not the word applies to something isn’t going to be affected by miniscule differences.
Another way to say this: there is no perfectly sharp boundary between the rich folks and the non-rich
folks. Instead, there is a gradual transition from the rich to the non-rich: if you have rich person, you
take away one penny, the term ‘rich’ will still apply, as it’s tolerant of miniscule changes like the loss of a
penny. Same for ‘pumpkin’: you can’t take away a single electron from a pumpkin and thereby
instantaneously make it no longer a pumpkin; the term ‘pumpkin’ is tolerant.
The second thing people tend to point out when explaining vagueness is the phenomenon of borderline
cases. Roughly put, a word (or concept) is said to have borderline cases when we can imagine a situation
in which we know all the relevant facts about the situation and the word’s meaning but those facts don’t
determine an answer to the question ‘Does the word apply to the situation?’ For instance, the phrase
‘tall for an undergraduate Fordham student in 2012’ is vague because we can imagine knowing all the
heights of the undergraduates and yet not be able to decide on whether the phrase applies to Fordham
undergraduate Roberta. Her height is above the average, but not so much as to clearly count as tall. We
would say that it’s a “judgment call” when it comes to the question ‘Is Roberta tall for an undergraduate
Fordham student in 2012?’ The word ‘pumpkin’ has borderline cases as well because we can imagine a
situation in which there is a sort-of pumpkinish thingie before us, we know tons of facts about both it
and pumpkins in general, and yet there doesn’t seem to be any way to figure out whether the word
‘pumpkin’ applies to the pumpkinish thingie. For instance, imagine a pumpkin that gets a little smashed
up and then slowly rots away. When we look at the smashed-rotted thingie and are forced to answer
the question ‘Well, is it a pumpkin or not?’ we want to say something like ‘Look, it’s a judgment call. It
used to be a pumpkin. But now it’s not definitely a pumpkin and it’s not definitely not a pumpkin; it’s in
between the categories ‘pumpkin’ and ‘non-pumpkin’.’ Color terms are probably the most
straightforward borderline words: there are lots of color shades that don’t quite seem red but don’t
quite seem non-red either: they are in between the categories, on the border of them.
Hence, vagueness is the opposite of precision and is associated with both tolerance and borderline
cases; that’s our three-fold handle on vagueness. Even so, it is easy to confuse vagueness with any of
several closely related notions. In order to understand the rest of the chapter we should separate it
from the following similar notions.

Whether or not something counts as “tall” depends on what is called the contrast class. For
instance, Carla is tall for a 10th grader but not tall for a girl on her high school basketball team.
So she is tall relative to one contrast class—10th graders—but not tall relative to a different
contrast class—people on the girls high school basketball team. Until the contrast class is
specified, implicitly or explicitly, you can’t determine what ‘Carla is tall’ is really saying; it is
semantically incomplete until the class is somehow indicated. Some people would say that this
shows that ‘Carla is tall’ is “vague”, but all they really mean by ‘vague’ here is that the sentence
is incomplete and its truth-value is relative to the contrast class.

Whether ‘is tasty’ is true of Bryan’s chocolate chip cookies depends on the person making the
evaluation: one person might find my cookies not tasty (the bastards!) while another person
might find them tasty (the enlightened). So, ‘is tasty’ applies to a certain cookie of mine
according to the taste buds of Genius Georgia but it doesn’t apply to that cookie according to
the taste buds of Bastard Bob. A word is subjective when this is true of it: whether the word
literally applies to a situation depends on certain factors involving the person judging whether
the word applies to the situation.

A word is ambiguous when it has at least two literal dictionary meanings. For instance, ‘bat’ can
mean the baseball bats or the flying mammal bats.

A word is polysemous when it has at least two very closely related literal meanings. For instance,
‘wood’ can indicate a substance found in trees or it can indicate a forest of trees. (In the Winnie
the Pooh stories the forest in which they live is called ‘The Hundred Acre Wood’.) These two
meanings are very closely related. Similarly, ‘bank’ can indicate a financial corporation or it can
indicate the building in which the corporation is housed (assuming the corporation has just one
building). Thus, ‘bank’ is both polysemous and ambiguous (as it can stand for a river bank as well
as a financial institution).
Each of the above sample words, ‘tall’, ‘tasty’, ‘bat’, ‘wood’, and ‘bank’ are vague: each is tolerant,
imprecise, and can have borderline cases. But we don’t want to confuse the vagueness of ‘bat’ with its
ambiguity; these are distinct characteristics that the word ‘bat’ has.
Very few, if any, words are not vague. The term ‘positive integer’ doesn’t seem to be vague but perfectly
precise: there is a perfectly sharp boundary between the integers that are positive and the ones that
aren’t positive. In the sequence of integers ‘-3, -2, -1, 0, 1, 2, 3’ we can locate the exact cutoff: it’s when
we go from 0 to 1. If we take the entire number line, with all real numbers on it (so, all the fractions and
irrational numbers in addition to all the integers), there is still a sharp cutoff in the sense that counting
down from the positive integers there is a single last positive integer, the number 1, and everything after
that is not a positive integer (the wrinkle being that there is no such thing as the number immediately
less than 1; that’s a result of the property denseness applied to the real numbers: between any two real
numbers there is another real number).
Introduction to Sharpism
Now we are almost ready to present the paradoxical argument against meaningful thought and
language. We will start with a story about pumpkins.
But before we do that we have to do something else: we need to get familiar with the idea of taking a
specific claim and doing something called ‘evaluating it with respect to a series of situations’.
Consider the claim ‘There are at least twenty chairs in room 101’. We can evaluate this claim with
respect to how things were on Monday, on Tuesday, on Wednesday, etc. On Monday it might be true,
as there were 36 chairs in room 101 on Monday. And it might be false when evaluated with respect to
Tuesday and Wednesday because on those days the room contained just ten chairs. What we’re doing
here is taking a single claim, ‘There are at least twenty chairs in room 101’, and evaluating it—figuring
out whether it is true—with respect to a bunch of situations. The argument of this chapter does the
same kind of thing, with the exception that the situations are imaginary and not sequential. Now for the
pumpkin story.
A few days before Halloween you are walking on Farmer Fred’s farm, on your way to his pumpkin patch.
Your niece wants to pick out a pumpkin to take home and carve. You say to her, in an obviously apt and
relevant circumstance, ‘There is a pumpkin by the tree’. You weren’t able to see any pumpkins there, as
the view was blocked by a shed, but you remember from last year that there were pumpkins near that
huge tree you see towering behind the shed.
Suppose you uttered that sentence to your niece at noon. Given that there are such things as
pumpkins—which may seem obvious, but don’t forget the considerations of the previous chapter—you
spoke truly: just as you said, there was a living pumpkin by the very tree you indicated at noon. Call the
situation you were in at that time S1; so ‘There is a pumpkin by the tree’ is true when evaluated with
respect to S1. S1 is the whole situation you were in at noon on that day: it’s a snapshot of what the world
was like at a certain instant in time.
Now I want you to imagine if things had been ever so slightly different: imagine that the top of the
pumpkin had had one fewer electron in it. Call that alternative imaginary situation, with the single
microscopic difference from S1, S2. Our question is this: was there a pumpkin by the tree in S2?
Obviously, it’s very reasonable to think that the answer is ‘yes, of course’. The only difference between
S1 and S2 is the absence of a single microscopic particle. So, given that there was a pumpkin in S1, there
was one in S2.
This is the phenomenon of taking a claim and “evaluating it with respect to” multiple situations. Just like
how we could take ‘There are at least twenty chairs in room 101’ and evaluate it with respect to many
different situations, we can do the same with ‘There is a pumpkin by the tree’.
Now imagine situation S3, which is exactly like S1 except that the top of the pumpkin has two fewer
microscopic particles in it. Our new question is this: was there a pumpkin by the tree in S3? And of
course, just as before with S2, it’s very reasonable to think that the answer is ‘yes’: there was a pumpkin
by the tree in S3, as the pumpkin is different by a mere two electrons off its top.
Repeat the process over and over: each time consider a pumpkin with one fewer particle in it, starting
from the top and working down. For each imaginary S situation consider the question ‘Is there a
pumpkin by the tree in the new situation?’ Another way of doing the very same thing: for each S
consider the pumpkin claim ‘There is a pumpkin by the tree’ and ask yourself whether it’s true. We are
evaluating the pumpkin claim with respect to many zillions of situations, the Ss.
One could do this literally a trillion times and the first and the trillionth situations, S1 and Strillion, would
still look identical to the naked eye: a difference of a trillion particles from the top of a pumpkin would
be literally undetectable without instruments, as particles like electrons are so small and so numerous in
a pumpkin (e.g., I estimate that there are at least 1030 particles in a pumpkin, which is a million times a
trillion times a trillion).
If we add up a gazillion of these microscopic differences, all that will be left is … nothing. The tree will
still be there, and there will be grass around it, but there will be no pumpkin material whatsoever. So
Sgazillion isn’t a situation with a pumpkin by the tree because there is absolutely nothing remotely
pumpkinish in that scenario. The pumpkin claim evaluated with respect to that situation, Sgazillion, is false.
So at what point in the sequence of situations, the Ss, did there stop being a pumpkin by the tree? We
started with a nice, healthy pumpkin and then considered a sequence of situations, each nearly identical
to the one before in the sequence. Eventually, we had a situation with no pumpkin by the tree. So when
did ‘There is a pumpkin by the tree’ go from just true to something else?
The sharpist says this: I don’t know when the pumpkin claim goes from just true to something else, but I
do hold that there’s got to be two consecutive rows in which that’s exactly what happens.
However, when faced with the question ‘When did the pumpkin claim go from just true to something
else?’ nearly everyone will insist that there is something wrong with the question. The question is
demanding a particular cutoff: for some number n, at situation Sn there was a pumpkin by the tree (so
the pumpkin claim was true when evaluated with respect to Sn), we then considered situation Sn+1,
which differed from the previous section by one microscopic particle, and in that situation Sn+1 the
pumpkin claim wasn’t just true. But of course, we are inclined to say, there is no such sharp cutoff!
Instead, we insist, the pumpkin goes away in a gradual manner, not all of a sudden. Imagine seeing a
sequence of photographs of the pumpkinish thing, starting with S1 and proceeding through S2, S3, and
the rest in rapid succession. It would look like a pumpkin being very slowly destroyed from the top
down, particle by particle. There would be no one point where you could say with any confidence ‘Right
there! That’s the very point when the pumpkin no longer exists. An instant before it existed, but with
that one particle gone it no longer exists’.
Yes, that is the entirely reasonable thing to say. No doubt about it. However, a compelling line of
reasoning seems to prove that it’s wrong. And no one knows what’s wrong with the reasoning, if there’s
anything wrong with it at all.
Mystery 8: Why Sharpism Seems Inevitable Yet Crazy
We have a single claim, the pumpkin claim, evaluated at each of many very similar situations S1, S2, S3,
etc. The first situation involves a perfectly ordinary, full-grown, and healthy living pumpkin by the tree.
Each subsequent situation differs from the previous situation by a miniscule difference. We end up with
the following puzzling table:
Situation
S1
S2
S3
…
Sn
…
Sgazillion – 2
Sgazillion – 1
Sgazillion
Status of the
Pumpkin Claim
True
True
True
…
?
…
False
False
False
What goes in the big open space in the second column—those zillions of rows? As soon as we have
something other than ‘true’, proceeding from the top downwards, then we have our (first if not only)
cutoff (cutoff = change in status of the pumpkin claim). Even if some entries will be blanks, meaning that
the pumpkin claim is neither true nor false, the first of those blanks (counting down from the top) will
mark a cutoff. The pumpkin claim is true with respect to one situation and then has some other status—
I don’t care what—with respect to the very next situation. I’m not assuming that there is a cutoff, I’m
arguing for it. The heart of the argument for a sharp cutoff is painfully simple:
(a) In the first few trillion rows the correct entry is ‘true’.
(b) The ‘true’ entries that start off from the top of the second column don’t go in every row of that
column (as it’s clear that near the bottom the entries are ‘false’).
(c) So, there is some row when the top block of entries that read just ‘true’ stops in the sense that
the entry in the next row isn’t just ‘true’. It could be something obvious like ‘false’. Or, maybe
it’s ‘neither true nor false’. Or, maybe it’s ‘meaningless’. Or, maybe it’s something fancy like ‘not
true, not false, and not meaningless but X’, for some exceedingly sophisticated and urbane X. In
any case, that row marks a cutoff—that is, the pumpkin claim is just true with respect to the
situation from one row, but the claim has some other status with respect to the situation in the
next row—regardless of what appears in the next row (if anything at all).
On the assumption that vague sentences such as ‘There is a pumpkin by the tree’ are ever true and
there are any pumpkins in the universe, premise (a) certainly appears obviously and definitely true:
surely S1, S2, S3, S4, and trillions more of the subsequent situations each contained perfectly good
healthy pumpkins (again, the sum total of a few trillion of these changes wouldn’t even be visible to the
naked eye and wouldn’t affect the functioning of the living pumpkin in any biological way), and ‘There is
a pumpkin by the tree’, understood to have its perfectly ordinary meaning expressed in perfectly
ordinary circumstances, was nothing other than just plain true with respect to those trillion or so
situations. Thus, the first trillion or so rows in the second column of the table seem to get ‘true’ (or, if
you like, ‘true & not false’) put in them. That’s premise (a).
There’s simply no question that premise (b) is true, on literally any philosophical theory at all: no one is
going to say that in situation Sgazillion there is a pumpkin by the tree. Recall that at that point the pumpkin
material has been completely removed.
In order to see why (c) seems to follow from (a) and (b), in the sense that if (a) and (b) are true then (c)
has to be true as well, consider a different table in which the entries in the second column start out one
way (so the analogy to premise (a) is true) but don’t go on that way through the whole table (so the
analogy to premise (b) is true too):
Situation
S1
S2
S3
…
Sn
…
Sgazillion – 2
Sgazillion – 1
Sgazillion
Numerical Status
of Pumpkin Claim
1
1
1
…
??
…
56
56
56
You don’t know what the numbers mean and you don’t know what limitations there are on the numbers
that can appear in the right column (e.g., whether there can be fractions like 7/8 in addition to whole
numbers like 1 and 56). However, even when saddled with this ignorance a quick glance at the table is
all you need to feel perfectly confident in concluding that the sequence of ‘1’s that starts the top of the
right column has to end at some point, and thus there will be a pair of consecutive rows X and X + 1 such
that row X is the last one of the initial sequence of ‘1’s and in the next row X + 1 there is something
other than the simple ‘1’. That’s a sharp cutoff in numerical value. You have no idea whether at the first
cutoff the numbers go from ‘1’ to ‘56’ or ‘1’ to ‘2’ or ‘1’ to ‘-34.45’ or ‘1’ to ‘1.0000000000001’ or
whatever. But you do know, immediately and with very little thought, that there simply must be a last
row, counting down from the top, that has a simple ‘1’ in it and the next row will have something else
(or a blank).
Well, that’s all premise (c) is saying: if the correct entries at the top of the column are ‘true’s, and the
‘true’s don’t go throughout the whole column—that’s premises (a) and (b)—then there simply must be a
sharp cutoff: adjacent rows in which some row Sn has just ‘true’ in it and the next row Sn + 1 has
something else in it. That’s just logic.
It makes no difference for the existence of cutoffs (which is the thesis of sharpism) as to what goes in
the bottom row Sn + 1 (if anything). Perhaps the entries in the second column of our table don’t go from
‘true’ to ‘false’. That is, maybe the claim made by your use of ‘There is a pumpkin by the tree’, when
applied to situations Sn and Sn+1 goes from true to indeterminate—or maybe to indeterminately
indeterminate (or indeterminately indeterminately indeterminately … indeterminate). Or maybe to just
plain meaningless. Or maybe to both true and false (so it keeps being true but just adds falsity for some
strange reason). Or maybe it goes from ‘true & not X’, for some status X (let your creativity blossom
here in wondering what X might be), to ‘true & X’. Or maybe its status with respect to Sn+1 changes with
the wind, or my hair color, or some more likely factor (we’ll look at issues relating to context later in the
chapter). Or maybe it has no status whatsoever with respect to Sn+1 (not even meaningless). Or, what
might not be any different, there might be no fact of the matter as to the status with respect to Sn+1
(whatever that idea comes to). Or perhaps it becomes incoherent to even apply the pumpkin claim to
Sn+1. Finally, maybe the truth about the pumpkin claim with respect to Sn+1 is best captured by a Zen
master’s reaction to ‘What is the sound of one hand clapping?’
One can think of some clever things to say regarding the status of the pumpkin claim when evaluated
with respect to some rows; I’ve tried to give a hint of some of them immediately above. But one of the
great strengths of the argument for sharpism is just this: it doesn’t matter which of these many options
one takes. Be as clever or as simple-minded as you like with your theory regarding the status of the
pumpkin claim, it still seems inevitable that its status is ridiculously dependent on the minuscule
difference of a single electron. The point is that ‘There’s a pumpkin by the tree’, understood in the
perfectly normal way, is true, meaningful, and not false when evaluated with respect to the first trillion
or so situations, but at some point in the series of situations it stops having that exact status. That’s all
the sharpist is saying.
It’s important to understand the thought experiment. For one thing, we are not changing the pumpkin
over time: we are not imagining that the pumpkin in S1 loses a particle once a nanosecond, for instance,
until it’s entirely gone. S2 doesn’t come temporally after S1; the pumpkin isn’t rotting before our eyes.
Instead, we are imagining a great many different situations each of which contains the whole episode of
your visit to Farmer Fred’s pumpkin patch. In each situation you pull up in your car with your niece, get
out, and start walking on Farmer Fred’s farm. And then your niece says ‘Where are the pumpkins?’ and
you reply with the pumpkin sentence ‘There is a pumpkin by the tree’. In S1 she goes over to the tree
and sees a nice full pumpkin; in Sgazillion she goes over to the tree exactly as in S1 and sees no pumpkin at
all (and then complains to you that you were wrong). In certain intermediate situations she goes over to
the tree and sees half a pumpkin (and then complains that the pumpkin isn’t good enough for
Halloween).
Thus, each situation is virtually identical in many relevant ways. For instance, in your mouth, ‘There is a
pumpkin by the tree’ has the very same meaning in each possibility. The entire history of English is
exactly the same, you are exactly the same, your linguistic, physical, and psychological history is exactly
the same, your physical environment is almost exactly the same (just one particle difference each
time!), and your interaction with your niece is exactly the same (until she goes around the shed to see
the area by the tree).
I hear the following complaint: the table given earlier can’t be completed! So, the thought goes, the
problem never arises. Or maybe the complaint is this: it’s indeterminate whether the table can be
completed! Or maybe it’s indeterminate whether it’s indeterminate whether it can be completed, or….
But no: none of that matters. First, I (the sharpist) never said we could complete it. Second, I never even
said that we either could or could not complete it. Third, I never said there was a unique correct answer
for each row (more on that point below). Finally, on virtually anyone’s view the first trillion or so slots in
the second column can be completed: they all have nothing other than ‘true’ in them, assuming
pumpkins and trees exist at all and sentences with vague terms can ever be true. Now you tell me:
starting from the top, what is the last row we can correctly complete with just ‘true’? The one hundred
trillionth row? Then that’s our cutoff, and I couldn’t care less what you want to say about the row after
that one, no matter how philosophically sophisticated it is.
You might want to say, at some point in the table, ‘We might as well stop at this point, although we
could have stopped earlier’. But in the trillionth row for instance you could not have stopped putting in
‘true’; that would have been just as much of a mistake as if you had stopped after the first row or the
thousandth row. Maybe you think for some but not all rows we have a “genuine choice” as to putting in
‘true’. Fine: when do we start to have such a “choice”, since we obviously don’t have such a “choice” in
the first trillion rows? As soon as you say ‘Okay, now we have a choice with the next row: we can put
‘true’ in it or we can put something else in it’ we have our sharp cutoff.
So, I’m not assuming that each question of the form ‘What is the status of the pumpkin claim when
evaluated with respect to Sx?’ has an answer. One might accuse me of implicitly assuming that truth
statuses cannot switch back and forth. For instance, the entries for four consecutive rows, counting
down from the top, can’t be T, T, F, and T. I do suspect that such an assumption is right, but the
argument for sharpism doesn’t rely on it. Even if there are such strange switches in truth statuses, we
have sharp cutoffs.
You might think that I’m illicitly assuming that for any pair of consecutive rows the question ‘Do they
have the same status?’ has a correct answer. Sadly, no! Virtually everyone will agree that ‘true’ goes in
the first row, and they’ll agree that ‘Do the first and second rows have the same status?’ has an answer:
‘Yes, they have the same status’. And most everyone will agree that ‘Do the second and third rows have
the same status?’ has an answer: ‘Yes, they have the same status’. And most everyone will agree that
‘Do the third and fourth rows have the same status?’ has an answer: ‘Yes, they have the same status’. It
doesn’t take a genius to see where this is going. There may be many possible “correct” answers to the
question ‘Do the mth and (m + 1)th rows have the same status?’, depending on what number m is. So the
possible answers aren’t merely ‘Yes’ and ‘No’. But as soon as we have an answer not identical with ‘Yes,
they have the same status’, we have our cutoff. So, even if one is like many philosophers in holding that
‘Do the mth and (m + 1)th rows have the same status?’ sometimes has an answer but sometimes doesn’t,
depending on what number m is, this move won’t help us avoid sharp cutoffs.
When a very intelligent person is first exposed to this problem of vagueness—in the guise of the table
above—usually they will have little hesitation in telling you about a million different ideas about various
important philosophical notions such as reference, indeterminacy, the notion of definitiveness, context
dependence, language use, the nature of truth, and meaning. This is the relatively easy part. My advice:
ask them (or yourself) how anything they just said applies to the individual entries in the right column of
the pumpkin table given above. Is the top one true? Yes or no? What about the second one? Yes or no?
The third? The last? Demand responses of them of these individual questions, even if the responses
come as ‘Well, that one is neither true nor false’ or ‘This one is true in some contexts of evaluation and
false in others’ or ‘This one has no status at all’ or ‘This one neither has nor lacks a status’ or even ‘There
is no answer to that one! You can’t say anything about it!’ The sharpist, who says that there has to be a
sharp cutoff in the table, says that it just doesn’t matter what fancy answers are offered: you can be as
clever as you like with your high-minded ideas about what goes in the table and all she will do in
response is point out that the column starts out with ‘true’ in it (the top rows), it doesn’t have ‘true’ in
all the rows, and, thus, there simply must be a first row, counting from the top, in which there is
something other than just plain ‘true’ in the column. That’s just inexorable logic; and that’s a sharp
cutoff because the pumpkin claim goes from true to something else with nothing more than the
movement of a quark or electron. Until we get to the serious business of taking a stand on the status of
the individual rows, and then seeing the consequences of those stands, discussion of vagueness is
almost completely wasted. A person won’t start productive work on the problem until she attempts to
figure out what might show up in the second column of the table given above. Only then will she
discover the true difficulty.
I suspect that the main mistake at least some of us—including some very smart people—are inclined to
make when thinking about this problem is that while we display plenty of ingenuity in thinking of
interesting things to say about borderline cases—the cases in which it seems completely impossible to
say whether or not ‘pumpkin’ applies—we forget that a very simple answer is correct for the first and
last entries, the clearly non-borderline cases. Eventually, the simple ‘true’ answer for the first few trillion
rows has to cease, and it doesn’t matter, to the existence of sharp cutoffs, what we say about the
borderline cases (or, assuming there are such things, the borderline borderline cases, or the borderline
borderline borderline cases, etc.). Note that the argument for sharpism never even mentions borderline
cases!
In my experience, when presented with the above argument for sharpism people tend to have one of
the following reactions.

The argument is flawed because of some term that is context-dependent. What counts as a
pumpkin varies with context. Or something like that.

The problem has to do with incompleteness of meaning. When the person said ‘There is a
pumpkin by the tree’ what did she have in mind? Was she talking about full pumpkins? Until we
know exactly what she said we can’t fill out the table. In ordinary life we don’t need to know the
exact details of someone’s assertion or thought, but in order to fill out the table we are hardly in
the realms of ordinary life: now we need to ask what it was she really had in mind.

The problem lies in the notion of truth. Sentences and thoughts aren’t just true and false. In
reality, they are true to various degrees. By insisting that the first few trillion rows have ‘true’ in
them the sharpist is making a mistake.
In a thorough book on this mystery, we would investigate these responses in detail. For our more
limited purposes, I’ll make just a few brief remarks on them.
You would be right to think that ‘There is a pumpkin by the tree’ is highly context-dependent. For
instance, it’s natural to think that what counts as a pumpkin is context-dependent. If I’m looking for
Halloween pumpkins in a pumpkin patch, then the answer to my use of ‘How many pumpkins are over
there?’ might be ‘four’; but if I’m interested in how many of the pumpkin seeds we planted earlier in the
patch have now generated pumpkins, then the answer to my use of ‘How many pumpkins are over
there?’ might be ‘fourteen’ even though I’m in the very same pumpkin patch. After all, not just any
pumpkin has what it takes to be a Halloween pumpkin.
More to the point, a use of ‘There is a pumpkin by the tree’ has no truth-value—it’s not true or false or
anything else—if we strip away contextual factors (including speaker’s intentions) because in that case it
fails to have any meaning. It would be like the sentence ‘John has a bat in his attic’, where we don’t
specify whether we are talking about baseball bats or flying mammalian bats (and we didn’t specify who
John was either, or the time in question, or which attic). Unless you somehow specify all those things
you don’t have a complete meaning. And if you don’t have a complete meaning, then the sentence is
neither true nor false. Hence, both the “context matters” and “incomplete meaning” responses have
some real merit to them.
But no rude contextual stripping is going on in the argument for sharpism. The sharpist told us to take
the claim made by the perfectly ordinary use of the pumpkin sentence in the situation you were in with
your niece. The sharpist didn’t say ‘Take the sentence without specifying the speaker’s intentions, the
time of day, etc.’ And she didn’t put any implausible constraints on what determines the meaning
expressed by your use of ‘There is a pumpkin by the tree’. Perhaps all sorts of complicated factors
(speaker’s intentions, conversational history, etc.) conspire to determine the (complete) meaning of the
claim. We let them do their work in fixing the meaning and then take the contextually informed claim
that results and assess that complete claim with respect to S1, S2, etc. The claim being evaluated doesn’t
change and it isn’t contextually bereft; what changes is the situation it’s evaluated with respect to.
I’ve left unspecified the vocabulary to be used in filling out the statuses in the second column. And I
assumed that we will choose, correctly, ‘true & not false’ for the first few trillion situations. One might
protest that we need to use more discriminating vocabulary, including phrases like ‘true to degree 0.7’
or ‘perfectly true’ or ‘just a notch less true than in the previous row’. This is the basic idea behind the
last of the three responses described a couple pages back. Or maybe the truth about truth is wildly
revisionary and terms like ‘true’ and ‘false’ are exceedingly crude and must be replaced entirely; so we
don’t even get to use ‘true to degree 0.7’. This amounts to what is called an error theory regarding truth
and falsehood since it’s saying that the notions of truth and falsity are erroneous in that they don’t
apply to anything. I will examine some of the details of these intriguing possibilities below.
However, revising ideas about truth alone won’t solve the problem. We have been focusing on a
declarative sentence, ‘There is a pumpkin by the tree’. But we can run the sharpist argument on ‘Please
bring me a glass of cold water’ or ‘Close the door!’ to show that there are sharp cutoffs corresponding to
requests and demands. If you request X and demand Y, and then you get both X and Y, then we say that
your request and your demand have been satisfied. Requests and demands don’t have truth-values but
they do have satisfaction-values. Consider a situation in which you ask someone ‘Please bring me a glass
of cold water’. In the first situation he brings you a full glass of water at temperature 40 degrees
Fahrenheit. Your request is fulfilled or satisfied. In the second situation the water is 40.00001 degrees.
Your request is fulfilled. In the third situation the water is 40.00002 degrees. Your request is fulfilled. In
the last situation, the water is 99 degrees; your request is not fulfilled. The sharpist will argue that there
has to be some last situation in which your request was fulfilled—even though the very next situation is
virtually identical to the previous one. You can see how the argument will go, being exactly analogous to
(a)-(c) given earlier. Avoiding sharpism will not be accomplished by saying something radical about truth
unless the point also holds for satisfaction in general (the satisfaction of requests, demands, etc.).
In most of the remainder of this chapter I’ll be searching for possible mistakes in the sharpist reasoning.
In this chapter I’m not concerned with the number of satisfaction cutoffs or how many different truthvalues there are, although those are important issues in logic and philosophy. Clearly, the simplest
scenario would be one cutoff between the true and the false. Someone who thinks that the pumpkin
claim (which of course was a perfectly good claim if any utterance of any vague sentence can be used to
make a claim) must be either true or false with respect to any situation will admit just the one cutoff:
the claim goes from true-and-not-false to false-and-not-true. Those philosophers are called
epistemicists. But the argument for cutoffs given above doesn’t rest on that assumption. The argument
doesn’t proceed in anything like ‘Such and such logical principle is our best bet; it requires cutoffs; so,
our best bet is that there are cutoffs’. If there are excellent reasons for thinking that truth comes in
degrees, reasons that have nothing to do with vagueness or sharpism, then perhaps many rows won’t
have either ‘true & not false’ or ‘false & not true’ in them; that’s a separate issue. But as I’ll show in
below even with degrees of truth we’re stuck with sharp cutoffs (lots of them).
People object to sharpism for a variety of reasons. Paramount among recent philosophers are epistemic
concerns—issues having to do with knowledge, evidence, and belief: if there are sharp cutoffs, we need
an explanation of why we can’t know where they are.
However, I think the main difficulty with sharpism, the one that really curls my remaining hairs, has
nothing to do with epistemology. The problem isn’t our lack of knowledge of the cutoffs; it’s the lack of
any plausible story of the production of sharp cutoffs. In order for the pumpkin claim to be just true in Sn
and not just true in Sn + 1 it would require an incredibly precise meaning: a meaning that somehow was
sensitive to the microscopic difference between those two situations. But now consider this: how could
your utterance to your niece of ‘There is a pumpkin by the tree’ get such a precise meaning?
Nobody really knows how, exactly, words and sentences get meanings. Clearly, it has a lot to do with us:
we give our words meanings. This is true for some words, such as names: I get a puppy and name her
‘Xixi’. How a word like ‘the’ or ‘collection’ or ‘seven’ or ‘lack’ gets their meanings is more complicated,
for sure. Linguists, cognitive scientists, psychologists, and philosophers of language investigate the
question of how words and sentences get their meanings.
If sharpism is true, then some collection of facts determines that your use of ‘There is a pumpkin by the
tree’ expressed a meaning that is just plain true in Sn but not just plain true in Sn + 1. But is that really
possible: could your sentence acquire such a keen meaning? Keep in mind how ridiculously precise the
cutoff can be. The worry here isn’t that the natural facts available for determining cutoffs aren’t precise
enough, whatever exactly it means for a fact to be precise or vague (this brings up the issue of
vagueness in the world, as opposed to vagueness in language or thought; we looked at that issue in the
chapter on existence). Presumably, there are exceedingly precise (if not perfectly precise) facts about
linguistic use (how we actually use our words) and linguistic dispositions (how we are disposed to use
words in new situations). The problem is seeing how any of those facts, precise or not, could fix precise
cutoffs. We just can’t see how a normal claim could acquire such an incredibly discriminating meaning.
Even if we gathered exceedingly detailed data on language use, linguistic dispositions, and the nature of
the physical environment, how on earth would all that detail even matter to the fixation of cutoffs?
Consider a world exactly like ours except that your friend Jones had slightly different dispositions
regarding ‘pumpkin’, or maybe slightly different uses of ‘pumpkin’; would that minuscule change alter
the cutoff for your use of ‘There is a pumpkin by the tree’? Who can say? In my opinion, these questions
about the determination of meaning are the fundamental ones for vagueness—at least they are the
fundamental questions to pose after we see that the argument for sharp cutoffs is incredibly good
(we’re in the process of seeing that).
I can think of a picture that may help make the miracles seem a bit less miraculous. When one throws a
dart at a dartboard, and hits the dartboard, there is a certain exact location where the dart hit. (Perhaps
not completely exact, depending on how these vagueness problems are to be resolved, but pretty close
anyway.) One did not intend to hit that very spot (whether or not the spot is a vague object), and a mere
mortal could never have foreseen that one would hit that very spot. But one hit that precise spot
anyway. Well, perhaps the “meaning determining” facts for ‘There is a pumpkin by the tree’ act like the
dart thrower: they conspire to hit a very precise boundary. There was no intention to hit that very spot:
neither you nor anyone else intended to hit the Sn/Sn + 1 cutoff. Neither was there any way to foresee
that the meaning would have one status with respect to Sn + 1 but a different one for Sn. But the facts
made it true anyway. So sharpism is true after all.
In my opinion, the main problem here is that we just can’t see how the obvious meaning-determining
facts—about linguistic use, linguistic dispositions, natural kinds in the environment, et cetera—could
conspire to hit any spot at all. Perhaps they can release the dart, so to speak, but they don’t have
enough energy to get the dart over to the board, resulting in precise cutoff. In my opinion, the
fundamental challenge to the sharpist is to explain how sharp cutoffs come about. More specifically, the
challenge is to explain how your use of the sentence hit the Sn + 1/Sn cutoff in particular. In some sense,
the basic argument for sharpism looks something like an argument that your use of the pumpkin
sentence had to hit some cutoff; what we need now is an explanation of how it hit the particular cutoff
it really hit. The sharpist has a good argument that cutoffs simply must exist; but she needs a story of
how they are generated.
I suppose that it’s no surprise how a sentence such as ‘The pumpkin by the tree has lost an electron
compared to how it was at time t’ could be false when evaluated with respect to one situation A and
then true when evaluated with respect to temporally subsequent situation B even though the only
difference between A and B is the miniscule movement of an electron. The sentence has linguistic parts
that make the electron-sensitive cutoff make sense; we can see where the sensitive cutoff comes from.
(Another example: ‘There are ten electrons in existence’.) This is an important lesson:
Those who object to sharpism need not be against all sharp cutoffs for vague sentences.
The initial problem with sharpism is that we don’t see anything in the sentence ‘There is a pumpkin by
the tree’ that could make it just plain true when evaluated with respect to one situation X and then false
(or any status other than just plain true) when evaluated with respect to situation Y even though the
only difference between X and Y is the miniscule movement of an electron. So, is there something in the
context of utterance, say, that gives it such a discriminating meaning? We’ve never seen anything in
linguistics or psychology or anywhere else that does the job as far as I know. Is there some exceedingly
sharp line out there in nature dividing the pumpkins from the non-pumpkins that the pumpkin claim is
attracted to, thereby giving it its sensitive cutoff? I know of no reason to think so; to think so is to
believe in miracles; and remember ‘pumpkin-like’ and all the other examples one could think of that
don’t seem to have corresponding sharp joints out in nature (even if you think that nature provides a
perfectly sharp line for ‘pumpkin’ it’s hard to see how it, with or without the help of facts about
linguistic usage, could provide such a line for ‘pumpkin-like’, ‘greenish’, etc.). We are left with nothing to
generate the sharp cutoff. That’s the central problem with sharpism, at least by my lights.
One could profitably think of the problem with sharpism as having to do with truthmakers, where a
truthmaker is the thing in the world that makes a sentence true (e.g., a red ball is the thing in the world
that makes ‘The ball is red’ true). The main problem with sharpism is finding a truthmaker for, or at least
an illuminating story that reveals the facts behind, the truth ‘The meaning that so-and-so expressed with
her utterance of ‘There is a pumpkin by the tree’ has one status when evaluated with respect to Sn + 1 but
has another status with respect to Sn’. More precisely: we need an explanation of the truth ‘The claim
that so-and-so expressed with her utterance of ‘There is a pumpkin by the tree’ has the status ‘true &
not false’ when evaluated with respect to S1 through Sn but a different status with respect to Sn + 1’.
At this point one might accuse me of not being fair to the sharpist. I seem to have been saying that we
shouldn’t accept cutoffs until we get a picture of how they come about. But, someone might say, no one
has told us how meaning facts are generated, vague or precise. One millennium, many ages ago, there
were no meaning facts (as there were no animals with linguistic or other fairly advanced cognitive
abilities); in the next millennium or so there were such facts; what made it the case that meaning facts
came into existence? Given that no one can provide the explanation of vague meaning facts, it seems a
bit unfair of me to object to sharp cutoffs because we can’t provide explanations of precise meaning
facts.
But the philosopher who hasn’t accepted sharpism need not say that we shouldn’t accept sharp cutoffs
until we get a picture of how they come about. She need not object to sharp cutoffs at all in claiming
that sharpism is crazy. Even if one is certain that there are sharp cutoffs, one should still be volcanically
upset that we can’t even come close to even imagining how they come about!
My puzzlement over how cutoffs are generated is not the result of any assumption that no semantic
facts are hidden from us. On the contrary, I suppose that there are all sorts of semantic truths that are
tremendously difficult to uncover (why should semantics be different from anything else?). There may
even be semantic truths that we simply cannot know, even as a matter of metaphysical necessity.
Recent philosophers of mind toy with the idea that there are truths about the physical basis to our
conscious experiences that are impossible to know for beings with our cognitive capacities (kind of like
how monkeys are unable to understand advanced calculus). But many people know, or at least
confidently believe, that conscious experiences do arise from entirely non-mental materials and
processes. A long time ago there were no conscious experiences; then a few millennia later there were
such experiences; the experiences somehow arose out of the non-experiences. Let’s suppose I know
that this happens; I just don’t know, and perhaps cannot know, how it happens. (God, if he exists, is such
a tease: making me just smart enough to think of questions I cannot answer even though I find them
fascinating.) The vagueness case is somewhat different: I’m not as sure that my ordinary utterances
have exceedingly discriminating meanings as I am that I have sensory experiences that arose out of nonexperiences. Even if the production of experience from non-experience might strike me as comparably
miraculous to the acquisition of sharp cutoffs, I’m not as sure that the latter really ever happens.
And does any of this “Maybe we just can’t understand this stuff” matter? Suppose the two miracles
(generation of sharp cutoffs and generation of experiences from non-experiences) are on a par of
miraculousness. Even so, I’m not going to stop trying to understand the generation of experience from
non-experience; neither am I going to stop trying to understand the generation of cutoffs. Accepting
sharpism might be the grand step needed to solve the sorites paradox (more on that issue in the final
section below), but then we encounter the paradox of the generation of sharp cutoffs (and of course we
still need to decide how many cutoffs there are, what they are like, etc.). Progress indeed, but less than
what we wanted. If one accepts sharpism, then one’s next research project on the topic of vagueness
surely is to figure out how on earth sharp cutoffs are generated; anything else is detail. In my opinion, if
you’re a sharpist, then your philosophical energy should be focused like a laser beam on meaning
determination (i.e., on the question of how our language acquires sharp meanings).
In addition, and this is crucial when deciding whether we should accept sharpism even without the story
of how cutoffs are generated, the sharpist can’t just assume that utterances are true in some situations
and false in others. If she convinces me that sharpism would have to true if my utterances were like
that, then I might conclude that since nothing could ever fix the cutoffs, my utterances of vague
sentences aren’t like that. This is a radical response, but so is sharpism. Once you’re convinced of
sharpism, you have got to get very busy working on the problem of figuring out what determines
insanely precise meanings; otherwise lots of people are going to become skeptics about the statuses of
vague terms and sentences.
And that’s why some philosophers toy with the idea that vague sentences do not have complete
meanings. The argument goes as follows.
1. If ordinary vague sentences have ordinary meanings, in the sense that they are sometimes but
not always true (as was the case with the pumpkin sentence: it was true in some situations but
false in others), then sharpism would have to be true.
2. If sharpism were true, then there would have to be some way that sentences acquire
miraculously precise meanings.
3. But that’s just impossible.
4. Therefore, ordinary vague sentences do not have ordinary meanings in the sense that they are
sometimes but not always true.
The sharpist accepts (1) & (2) but balks at (3); the vagueness nihilist accepts (1)-(3) and thus (4). She is
forced to say that although sentences certainly bring up all sorts of concepts in our minds—it certainly
feels as though you’ve got some definite ideas in your consciousness—neither sentences nor the
thoughts expressed with those vague sentences have ordinary meanings, where ordinary meanings are
the things that are true in some situations and false in others (as we explained earlier). When you think
you have had a complete, coherent thought—one that is true but expressed with a vague sentence—
you are mistaken. Virtually none of our thoughts or sentences have true meanings. When you think to
yourself ‘George Washington was the first president of the USA’, although some meanings went through
your mind, what did not happen is this: a complete, truth-evaluable meaning went through your mind.
Instead, the thought running through your head is compatible with an enormous number of perfectly
precise meanings, and nothing about you or your language or your linguistic context picks any one of
them out as the one you really had in mind. So the vagueness nihilist is a nihilist about ordinary, vague
meanings: there aren’t any.
What we have done in this chapter is look at a series of situations, the Ss, that when combined
appropriately generate what seems to be a knockdown proof of sharpism—and yet, there are excellent
reasons to think sharpism just can’t possibly be true. That’s the paradox. It’s usually called the sorites
paradox, and the series of Ss is called a sorites series.
My favorite story about vagueness concerns Professor Timothy Williamson, of Oxford University. He is
widely recognized to be the foremost authority in the world on the topic of vagueness. He is scary
smart. He once wrote a book on vagueness. His goal starting out the project was to refute sharpism
once and for all. Instead, he discovered that the argument for sharpism is so good that sharpism is very
probably true. So he flipped his view to its exact opposite, based on his reading of the evidence, pro and
con, regarding sharpism. He followed the argument where it leads, even though it went against his
prejudices. That’s a noble quality to have.
In chapter 1 I made some promises, ones that are usefully characterized as focusing on several
commonsensical thoughts. In chapter 2 we found good reason to doubt the thought ‘Bananas are
yellow, at least in part’. Chapter 3 contained arguments that put pressure on the more fundamental
thought ‘There are bananas’. In this chapter 4, we encountered evidence that suggests that thoughts
employing vague concepts lack complete meanings. But the thoughts that survived the onslaught of
chapters 2 and 3, expressed with sentences such as ‘There are particles arranged pumpkin-wise’, involve
vague notions such as ‘pumpkin-wise’. As you can imagine, what we did with ‘There is a pumpkin by the
tree’ can be done with ‘There are particles arranged pumpkin-wise’. Thus, the argument of this chapter
suggests that the latter thought lacks a complete meaning, and as a consequence fails to be true. The
campaign against commonsensical truth just keeps growing, chapter by chapter.
Let’s suppose for a moment that sharpism is true. One might hope that the connection between the
utterance you made to your daughter at Farmer Fred’s place and the sharp cutoff is some brute fact,
some truth that cannot be explained at all. After all, there probably are some truths that just can’t be
explained; couldn’t this be one of them? If so, then maybe sharpism could be true but not so
mysterious.
But it’s hard to find any good reason to believe that cutoff facts are brute—other than the admittedly
quite good reason that there seem to be such cutoffs (since the argument for them is so powerful) and
we can’t imagine any remotely plausible explanations of them! The connection between your noise and
the sharp cutoff is a complex, highly contingent, linguistic fact that should admit of explanation. There
just has to be an explanation of why ‘The cutoff that so-and-so expressed in S1 with their utterance of
‘There is a pumpkin by the tree’ is met when evaluated with respect to Sn – 1 but not with respect to Sn’ is
true.
Here’s why there must be an explanation. Presumably, although your linguistic noise L hit the Sn – 1/Sn
cutoff (when going from just plain true to something else), it could have hit the Sn/Sn + 1 cutoff, or some
other cutoff, instead. Thus, the connection between L and the Sn – 1/Sn cutoff is contingent (i.e., it could
have been located somewhere else). And surely it isn’t just logically possible that the connection be
between L and the Sn/Sn + 1 cutoff; it is physically possible as well. No laws of nature, for instance, would
have to be different in order for L to hit the Sn/Sn + 1 cutoff instead of the Sn – 1/Sn cutoff. (You might think
that necessary truths, like the truth that 2 + 2 = 4, do not admit of explanations; but we are considering
contingent—not necessary—truths.) Furthermore, the fact we’re trying to explain, the connection
between L and the Sn – 1/Sn cutoff, isn’t anything like the contingent fact that electrons and protons are
oppositely charged (pretending, just for the sake of having an example, that the latter is contingent and
somehow fundamental). Instead, the cutoff connection [linguistic noise L]  [cutoff Sn – 1/Sn] is positively
screaming for an explanation. The highly contingent fact that L bears the relation “is satisfied by” to Sn – 1
but not to Sn is a clearly contingent, empirical, complex fact that is in no way primitive; it should be
capable of some kind of explanation that helps us “see” how it could happen. For me, this is the central
constraint on any theory that admits sharp cutoffs: it has to supply the explanations.
And even if the connection between L and the Sn – 1/Sn cutoff is necessary, I still need an explanation.
If I’m wrong about all that and there is no explanation of how my noise got that sharp cutoff, then there
had better be a very interesting “second-order” explanation of that lack of “first-order” explanation.
That is, there has to be an informative explanation of why there is no explanation of the cutoffs.
In the rest of this chapter I’ll look at two ways someone might try to evade Vagueness Nihilism.
Degrees of Truth
Up until now I’ve assumed that when filling out the table one should use terms like ‘true’, ‘false’, and
‘indeterminate’. You might think that we shouldn’t really use unbelievably crude and quaint terms like
‘true’, ‘false’, and ‘indeterminate’. Such terms are for philistines. And when we move to the right alethic
vocabulary, the mystery will crumble. In this section I’ll look at several ideas along this line.
A natural idea here (there are others that are significantly different) is that the pumpkin claim doesn’t
go from ‘true & not false’ to ‘false & not true’ or ‘indeterminate’ or anything else like that. Instead, it
goes from 100% true to just under 100% true. This transition isn’t puzzling at all. The pumpkin is very
gradually becoming less of a pumpkin, and, quite appropriately, the truth status of the pumpkin claim
decreases very gradually as well in response to the physical change.
Assume for the moment that the pumpkin claim is perfectly true, fully true, and 100% true (or however
one wants to put it), with respect to at least the first trillion situations, S1 through Strillion. (As noted
earlier, a trillion atoms or atomic particles is nothing for a living pumpkin, even a small one.) Since it’s
not 100% (or fully or perfectly) true for all the situations, at some point it goes to something less than
100% true; perhaps it goes to 99.999% true. The cutoffs haven’t gone away! The pumpkin claim has a
meaning that is 100% met in S1 through Strillion – 1 but is only 99.999% met in Strillion. It hardly matters to
the existence of cutoffs.
Perhaps the cutoffs aren’t supposed to go away but are supposed to be tamed, so the answer to ‘Aren’t
cutoffs implausible?’, is negative. But it remains true that the pumpkin claim is 100% true in the first
trillion – 1 situations but just 99.999% true with respect to Strillion. How on earth could that happen? How
could your use of ‘There is a pumpkin by the tree’ acquire a meaning so that it’s 100% true in all the
situations corresponding to the first trillion – 1 electron movements but only 99.999% true in the
situation that results in the very next nanometer movement of an electron? The cutoff is still completely
mysterious.
You might think that maybe pumpkinhood has some deep joint in nature that provides the reason why
the claim went from 100% true to 99.999% true. I find this utterly implausible, but just consider altering
the case somewhat: ‘There is something pumpkin-like by the tree’ or ‘There is something like a pumpkin
by the tree’.
Furthermore, what does it even mean for something like ‘There is a pumpkin by the tree’ to be 99.999%
true? I guess I can see (almost anyway) how someone might think that ‘All the marbles are in bucket’ is
99.999% true when there are 100,000 marbles total and all but one are in the bucket. But how would
that work for ‘There is a pumpkin by the tree’? Good luck justifying some made-up answer to that
question.
Nothing changes if we adopt some non-numerical notion of ‘true to some extent’. The pumpkin claim
starts out “fully” true for the first trillion or so situations and eventually isn’t “fully true”. So, at some
point it goes from “fully true” to something else, perhaps to “just an eensy weensy bit less than fully
true”. We still have a mysterious cutoff, once again between Strillion – 1 and Strillion. In truth, this option is
just like the one discussed earlier that complained that the evaluations don’t go from ‘true & not false’
to ‘false & not true’.
However, we can alter the degrees-of-truth idea to avoid some of these unpleasant objections and
significantly increase the odds of finding the fatal flaw in the argument for sharpism. Let’s suppose that
when we start to take away even the first electron (from the point at which the pumpkin is at its largest,
say; more on that in a moment) the pumpkin claim goes from fully true to some tiny fraction less than
fully true. So there is a miniscule decrease in status with every subsequent situation. There are sharp
cutoffs everywhere, thereby diminishing the significance of any one of them.
I see three main problems with this proposal. But first I should make clear that I’m not arguing against
the truth of the degrees-of-truth idea. Here I will argue only against the proposal’s ability to block the
argument for sharpism, or explain how cutoffs are generated.
Problem 1. The proposal thus far has failed to even address the argument for cutoffs! Instead all we
have is a recommendation that we change the subject and look away: don’t talk about truth and
falsehood anymore; talk about degrees or amounts of truth instead. But you can’t make a problem go
away by ignoring it. It’s still true that the pumpkin claim starts out true and not false for billions of
situations but doesn’t stay that way; so how are we to explain how it was true and not false in Strillion – 1
but some other status in Strillion? One possible answer for the degrees-of-truth advocate: in order to be
‘true & not false’ it has to be at least 72.3689% true, and in the physical transition from Strillion – 1 to Strillion
it finally went below 72.3689% true. Then we have another mysterious linguistic miracle: our use of
‘true’ is such that it hits the 72.3689% mark. How on earth did facts about linguistic use, linguistic
dispositions, and the physical world determine that 72.3689% is the magic number for the ordinary
meaning of ‘true’? You might think that 50% is more natural, but for what it’s worth I don’t see any
justification forthcoming.
This shows the futility in objecting that this whole exercise has been silly because there is no way to fill
out the table since I have yet to explain what the rules are for filling it out. Is the rule this: an entry in
the second column of the table is “correct” only when it’s 100% or perfectly true? Or is the rule this: an
entry is “correct” only if it’s more than 50% true? Or is the rule something else? Until we know the rule,
one might think that we can’t fill out the table.
Well, you tell me what the rule is; pick one yourself. Let’s say it’s ‘An entry is correct only if it’s 100%
true’. Then the entries start out ‘true & not false’ and eventually have to switch to something else. The
same holds if the rule is ‘An entry is correct only if it’s more than 50% true’. The cutoff in question
changes, but there are still mysterious cutoffs.
There is a way to alter the proposal to get around that objection. One could say that ‘true’ and ‘false’
pick out no alethic statuses whatsoever. Neither ‘true’ nor ‘false’ goes in any of the rows. All claims of
the form ‘Claim C is vague and true’ aren’t true. Truth and falsity are primitive notions that must be left
behind in any serious theory of language, thought, and logic. (This amounts to an error theory for truth
and falsity, since it says that these notions are erroneous in the sense that they fail to apply to
anything.) The main idea here is that although truth and falsity fail to apply to vague sentences and
thoughts, such sentences and thoughts do have alethic statuses. Think of the alethic statuses as being
the real numbers from 0 to 1. Then the alethic status of the pumpkin claim starts out at 1 and gradually
goes down to 0. But the remaining two of our trio of problems reveal the difficulties with this idea, even
if one is willing to buy the error theory for ‘true’ and ‘false’.
Problem 2. How could the status of your linguistic noise ‘There is a pumpkin by the tree’ come to be so
incredibly sensitive to microscopic changes inside the pumpkin? We still have linguistic miracles. And
don’t forget ‘There is something pumpkin-like by the tree’, if you’re tempted to think that there are
exceedingly sharp facts about pumpkin-hood “out there in nature”.
Problem 3. When in the pumpkin’s development does it reach alethic status 1? Is it when it’s maximally
big? Why? Or does it never hit 1? Moreover, and this is a different point, which nanometer electron
movements count as increasing the status and which result in decreases? Good luck defending any
answers. Philosophers who think about vagueness do themselves a disservice in focusing on terms such
as ‘tall’ and ‘middle aged’, for which there is a nice numerical measure (height for tallness and age for
middle agedness) going along with the predicate. And the reason you can’t defend any answers to the
above questions about pumpkins is that it’s so implausible that our vague sentences have meanings that
would ground such answers.
Compositional Nihilism Again
We already encountered this view in chapter 3. As we saw, this view is a lot less crazy than it seems. I
won’t investigate it here. I will note, however, that although it does away with the pumpkin argument
(because ‘There is a pumpkin by the tree’ is never true) as well as many other vagueness arguments, it
does not seem to get rid of sharp cutoffs entirely, which would mean it doesn’t block the argument to
sharpism. There are three reasons for this.
First, even if the pumpkin claim is never true, it sure seems as though it’s sometimes “appropriate” to
assert (e.g., in S1) and other times not “appropriate” to assert (in Sgazillion). That’s enough to generate the
mystery: the claim is appropriate when evaluated with respect to one situation and has some other
status (inappropriate, indeterminately appropriate, etc.) when evaluated with respect to the next
situation. Or, if you think ‘appropriate’ won’t work, then just substitute some other term (e.g., ‘perfectly
happy’, ‘successful’, ‘pragmatically useful’, etc.) and make it precise in any way that allows the pumpkin
claim to start off satisfying the term while eventually failing to satisfy the term.
Second, suppose we are considering a bunch of possibilities. In P1 there is just one electron; in P2 there
are exactly two electrons; in P3 there are exactly three electrons. And so on. The compositional nihilist
will agree that all of this can be true, as she admits the existence of electrons even though she rejects
the existence of flowers and coffee cups. Now suppose I say, with regard to Pgoogol, ‘There are many
electrons’. What I said, with respect to Pgoogol, is true. When we take what I said and evaluate it with
respect to P1 or P2 or P3, what I said, the electrons claim, is false. So, for what n is the electrons claim
true and not false with respect to Pn + 1 but not just true and not false with respect to Pn? How did my
utterance of ‘There are many electrons’ pick out the Pn + 1/Pn boundary? Our cutoff miracles haven’t
gone away, even if there are no composite objects (objects with parts) in any possible worlds.
Third, ‘There are some particles arranged pumpkin-wise’ seems to start out true, even if there are no
composite objects, and end up false. Even the compositional nihilist admits it. But that’s enough to
generate a sharp cutoff.