The Logic of Nonsense: Can There be Logical Significance without Meaning?
Dawn Chow
February 18, 2009
It is clear from various of Wittgenstein’s comments that he adopts some version of
Frege’s context principle – that is, the principle that words have meaning only in the context of a
proposition. There are compelling reasons for holding at least some version of the context
principle, but it leads to a well-known puzzle: if individual words have no meaning whatsoever,
then it seems rather odd that we can combine them together in new ways to form sentences that
do mean something.
I do not intend to delve into the minutiae of the current debate regarding the contextuality
and compositionality of language and how, if at all, they can be reconciled. Instead, I want to
address one particular, very natural assumption about what the context principle must mean for
Wittgenstein. This assumption leads the claim that words have meaning only in the context of a
proposition to sound much more extreme and thus problematic than it ought to.
For both Frege and Wittgenstein, the argument for the claim that words have meaning
only in the context of a proposition rests heavily on the distinction between the psychological
and the logical in language. The idea is that isolated words tend to seem meaningful to us, but
when we examine that appearance, we see that we are mistaking our psychological associations
with the word, our intentions when saying the word, and so on, for actual meaning, which is a
logical rather than psychological matter. If one is convinced by this argument, it might be fairly
natural to conclude that isolated words have no logical significance whatsoever. Logical
significance, as opposed to merely psychological significance, is what constitutes meaning, so if
words outside meaningful propositions were to have logical significance, that would seem to
1
suggest that they have meaning as well. Thus one might think that what the Wittgensteinian
view requires is that words occurring in isolation or in nonsense sentences have only
psychological signification and nothing else.
I will instead argue that, so long as we adopt Wittgenstein’s more nuanced understanding
of both the context principle and the psychological-distinction, we can accept both of these
principles without having to adopt the conclusion that words out of context have no logical
significance whatsoever. A view of words as having a certain degree of logical signification of
their own, even when taken out of a meaningful context, allows for a more convincing picture of
what goes on when we understand or fail to understand what others say.
I
Before embarking on the above project, we first need to get a little clearer both on what is
meant by the context principle, and on what is meant by the distinction between the
psychological and the logical with regards to language. Let’s start with the latter topic: what is
the psychological-logical distinction for Wittgenstein?
Wittgenstein’s distinction between the logical and psychological in language is of course
derived from Frege’s. Merely psychological aspects of language for Frege include “mental
images or acts of an individual mind”1 and those aspects of language “meant to act on the
feelings and mood of the hearer, or to arouse his imagination.”2 Thus the connotations of words
are merely psychological for Frege.
The way that ‘but’ differs from ‘and’ is that we use it to intimate that what follows it
contrasts with what was to be expected from what preceded it. Such conversational
suggestions make no difference to the thought.
1
2
Foundations of Arithmetic, p. 90 in The Frege Reader.
“Thought’, p. 330 in The Frege Reader.
2
Regarding such “conversational suggestions,” Frege argues, “they do not touch the thought, they
do not touch what is true or false.” 3 Thus what is relevant to the thought in what is said – that is,
to the logical in what is said – are those factors which affect the sentence’s truth conditions, what
states of affairs it rules in or rules out. If I believe the sentence “He went to the party and he
didn’t have a good time” is true, then I certainly think “He went to the party but he didn’t have a
good time” is true as well, and vice versa. So the difference is merely psychological.
Similarly, Frege argues that the difference between using the word “horse” or “steed” is
merely psychological: these words differ in their connotations, in the images and emotions they
call up, but not in their sense. The idea here is not just that these words denote the same object,
for that is true of phrases like “Morning Star” and “Evening Star” which refer to the same thing
but clearly have different senses. The idea must be that “horse” and “steed” have not just the
same object but also the same sense. This would mean that not only can we replace any
extensional use of one for the other salva veritate, but we can replace even intensional uses of
one for the other salva veritate. If “Mary thinks there is a horse in the stable,” is true, then
“Mary thinks there is a steed in the stable” is true as well.4 If Mary would express her own belief
using “horse” rather than “steed,” that is for psychological rather than logical reasons. Perhaps
the one word just occurs to her first, or feels more fitting, or she wants to give her listener one
sort of mental image rather than another – but none of those have to do with whether it is true or
false that she thinks there is a steed in the stable.
3
Ibid., p. 331.
One might well object that there are at least some intensional contexts in which “horse” and “steed” are not
substitutable. Take, for example, the sentence, “Mary felt upon seeing it that this was no mere horse, but a steed.”
That is, sometimes the connotation of a word is not merely a passive tag-along to the description of the person’s
thought (as it seems to be in “Mary thinks there was a steed in the stable”), but is precisely what is doing the work of
picking out what it is the person thinks. One response to this objection might be to agree that in that context, the
word “steed” has a different meaning than usual, in which it does not have the same sense as “horse” but instead
means something like “a magnificent exemplar of a horse.” I’m not sure that’s entirely satisfactory, however.
4
3
Wittgenstein certainly agrees with Frege that the mental images we associate with words
or the intentions we have in speaking are psychological rather than logical matters. Much of the
Investigations consists in Wittgenstein describing things like feelings, mental images, intentions,
and other mental states, and showing that no such psychological facts could possibly constitute
what it is to mean something, or understand something, or follow a rule. Thus Wittgenstein is
just as concerned with Frege to distinguish between the psychological and the logical, and to
keep us from mistaking the one for the other.
But where precisely the line between the psychological and the logical is drawn is
different for Wittgenstein than for Frege. For instance, Wittgenstein would surely not agree with
Frege that the connotations of words are ordinarily purely psychological rather than logical. At
least in his later work, Wittgenstein is concerned with all the different uses of language, not
merely in the use of language to state propositions describing states of affairs and deduce other
propositions from them. And his use of the term “logic” broadens accordingly to mean
something like his (similarly idiosyncratic) use of the term “grammar.” He equates
“misunderstand[ing] the logic of our expressions” with “giv[ing] an incorrect account of the use
of our words.”5 Thus when Wittgenstein refers to the “logic” of a bit of language, he is not
referring solely to those aspects of it relevant to its truth conditions, but instead he is referring to
all of the aspects of it relevant to its function, its use, in the language. In this sense, there is a
logical aspect as well as a psychological aspect to the difference between using “but” and “and,”
or “horse” and “steed,” in the same sentence, for in both cases the words have different uses,
play different roles in our linguistic practices.
Philosophical Investigations, §345: “‘If it is possible for someone to make a false move in some game, then it
might be possible for everybody to make nothing but false moves in every game.’—Thus we are under a temptation
to misunderstand the logic of our expressions here, to give an incorrect account of the use of our words.”
5
4
Another way Wittgenstein’s account of the logical-psychological distinction must differ
from Frege’s is that Wittgenstein rejects Frege’s assumption that there must be a metaphysical
basis for the distinction. For Frege, if thoughts are to have logical rather than merely
psychological signification, they must necessarily be eternal, unchangeable, and independent of
any thinker. Cora Diamond describes this as the “mythology” of the psychological-logical
distinction. 6 Wittgenstein maintains some version of the psychological-logical distinction, but
he rejects the accompanying mythology.
So what does the psychological-logical distinction consist in once we broaden our notion
of the logic of language and free the distinction from metaphysical mythologies? Diamond
describes the psychological-logical distinction as that between “what empirical psychology
might show us of people’s minds and what belongs to the mind,”7 that between merely
descriptive ways and normative ways of describing the mental and linguistic. For a sentence to
mean something, for instance, is not a feeling or mental state, nor is it the sociological fact that
others respond in a certain way to my words. Those are all things we could ascertain
empirically. But meaning contains an ineliminable normative element: if I claim that a certain
proposition means x, then part of what that I am claiming is that everyone ought to understand it
as meaning x – whether they in fact do or not.
The example of rule-following will help to illuminate the nature of the logical with regard
to language. Suppose that a given community holds as valid the rule, “Do not eat anything
which suckles its young.” The rule has no exception for unintentional violations: that is, the rule
means just what it says, and the formulation given is not a shorthand for “Do not knowingly eat
anything which suckles its young.” But the people of this society kill whales for food, believing
6
7
Diamond, Cora. “Philosophy and the Mind,” p. 4.
Ibid., p. 5.
5
them to be fish. No one in that society believes that a person is violating their rule by eating
whale meat, but such an act is nonetheless a violation of the rule. Whether an act was in accord
with a given rule is not subject to change: it would be nonsensical to say that while today it is the
case that I broke rule x today, next week it will not be the case that I broke rule x today. If it is
discovered that whales suckle their young, the people of this imaginary society will either stop
eating whales in recognition that doing so was against their rule and they had not known it, or
they will change their rule. It is not open for them to claim that their present rule is exactly the
same as their past rule, but that the same act is against that rule now and was not against it then.
There are various psychological, or more broadly, empirical, kinds of description we can
use for an act claimed to be in accord with a rule. We can describe how that act fits with
previously established patterns of behavior which the actor and others describe as adhering to the
rule, or we can evaluate whether the rule-giving community considers the behavior to be in
accordance with it. We can describe certain feelings associated with the act – whether it feels
constrained, as if it were done in accord with a rule, or is accompanied by the actor’s belief that
he or she is acting in accord with a rule. But, as we can see in the above example, all those
things could be the case for a given act without that act’s actually being in accord with the rule.
Whether or not the act is actually in accord with the rule is a logical matter. To say that these
imaginary people have broken the rule by eating whale meat is to make a claim that cannot be
reduced to any merely empirical description of what has happened. It is to claim that they have
done something which, given their rule, they ought not have done.
If rules did not function this way, if they did not have this objectivity which sometimes
allows us to break them without anyone realizing it, they would not be able to play the role of
rules for us at all. Thus the objectivity of a rule, that which makes following it something
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different from thinking one is following it, is a feature of a certain form of life. We create rules
for ourselves which have this characteristic of normativity, of timelessness and objectivity, so
that we can order our lives in a certain way. We then feel inclined to describe the objectivity of
these rules by saying they are independent of us, and indeed in some sense they are, but not in
any way that requires a metaphysical explanation of how this is possible.
I would not want to argue that the normativity of language use is entirely reducible to
rules – the “norms” involved in language are often too loose to be helpfully described as “rules.”
But language is, like rule-following, a fundamentally normative affair, and for related reasons.
The point of Wittgenstein’s private language argument is that language use (like rule following)
must be constrained to be useful, to be genuine language use at all. If I say, “My neighbor’s cat
is orange” but, upon my next visit to my neighbor, find it to be grey, it is not true that by
“orange” I meant the color we ordinarily call “grey.” I was wrong. If I could not be wrong in
saying my neighbor’s cat is orange, then my words would be useless; there would be no point in
speaking about the color of my neighbor’s cat if whatever word I chose to describe the cat’s
color would be defined as whatever color the cat happened to be. Thus making a claim, like
following a rule, is a logical matter with an ineliminable normative element. Part of what it is for
me to have asserted that “My neighbor’s cat is orange” is that it is possible for me to be right or
wrong in saying so.
Similarly, if I tell you that my neighbor’s cat is orange, but meant to say “grey” and was
picturing a grey cat while I was saying the words, I have not by virtue of my intentions and
associated mental images told you that my neighbor’s cat is grey. I told you that the neighbor’s
cat is orange; I said something false. The word “orange” in my assertion cannot mean “grey”
merely because I was thinking of the color grey rather than the color orange when I said it,
7
because to mean something is a logical matter and not a fact about my mental states.8 If my
statement “My neighbor has an orange cat” is actually an assertion at all, then part of what that
entails is that there are cases when I ought not say it – as, for instance, when what I intend to
communicate is that my neighbor has a grey cat.
This general point applies not just to language used to state facts but to language used for
other purposes also. There are right and wrong (or at least better and worse, meaningful and
nonsensical, appropriate and inappropriate) ways of asking questions, telling jokes, making
promises, expressing feelings, and so on. Thus any correct account of the logic of our language
will necessarily be a normative one, one that can account for the possibility of speaking wrongly
in any given situation. It is this normative dimension of language that is logical in
Wittgenstein’s sense.
II
Having sketched a general picture of the logical-psychological distinction as it functions
in Wittgenstein’s thought, I will turn now to the context principle.
The principle that “The meaning of a word must be asked for in the context of a
proposition, not in isolation” is the second of the three “fundamental principles” with which
Frege begins the Foundations of Arithmetic. If one does not observe this principle, Frege argues,
“then one is almost forced to take as the meaning of words mental images or acts of an individual
mind,” thereby violating the psychological-logical distinction. 9
Wittgenstein does takes care to note that sometimes we (legitimately) use the word “meaning” in a merely
psychological way: “In certain of their applications the words ‘understand’, ‘mean’ refer to a psychological reaction
while hearing, reading, uttering etc. a sentence. In that case understanding is the phenomenon that occurs when I
hear a sentence in a familiar language and not when I hear a sentence in a strange language.” Thus when I say that
to mean something is a logical matter, I of course don’t mean there is nothing one could mean by “to mean
something” that could be cashed out purely in psychological terms. But those are not the senses of “meaning” we
are using here.
9
Foundations of Arithmetic, p. 90 in The Frege Reader.
8
8
The reasoning here seems to run something like this. As a speaker of English I associate
the word “cat” with the idea of domestic felines. For this reason, I am likely to think that the
word “cat” by itself has a meaning: it refers to cats. But in the context of a sentence, the word
“cat” may play any variety of logical roles. It may refer to a cat, but it may also be a verb, the
name of a person, an abbreviation, or part of a set of words indicating an only indirectly related
concept such as “cat fight” or “game of cat and mouse.” Thus the word “cat” does not have the
same meaning independent of the proposition it occurs in; its meaning is dependent on its
context. If the word occurs alone, without any such context, then we cannot determine it as
meaning any one of those things as opposed to the others, and so alone, it just doesn’t yet have a
meaning. The fact that I associate the word “cat” most strongly with its usage as a common
noun referring to cats, rather than any of the other uses the word has, is a merely psychological
fact and not a fact about what the word by itself means. Just because seeing the word alone
makes me think of a cat cannot make it so that the word by itself actually means a cat rather than
any of the other things it could mean.
Cora Diamond, in “What Nonsense Might Be,” applies this same general line of
argument to words which occur, not in total isolation, but in the context of nonsensical
sentences. Take the sentence, “Caesar is a prime number.” Someone who holds to what
Diamond calls the “natural view” of nonsense will say that the words in this sentence all have
meanings, but that they fit together in a nonsensical way. “Caesar” refers to a person, whereas
“is a prime number” is something that can be said only of numbers. But, as Diamond points out,
in a sentence like this which makes no sense, we have no reason to take “Caesar” to refer to a
person rather than having some other meaning:
It is perfectly true that if I say “Caesar is a prime number” my state of mind, my
intentions, and so on, may be exactly the same as when I use the word “Caesar” to refer
9
to some or other person. But suppose we follow Frege and distinguish sharply between
the psychological and the logical. We can then see that from the fact that my state of
mind or intentions are the same, it does not follow that the word “Caesar” as it occurs in
the context “----is a prime number” has the logical role of standing for a person, the role
it does have if for example I ask you when it was that Caesar crossed the Rubicon.10
If we accept something like Frege’s context principle, then the actual meaning of the term
“Caesar” can only be fixed in a meaningful context. And the sentence “Caesar is a prime
number” is not a meaningful context because it makes no sense. There is nothing in that
sentence which could enable us to fix the meaning of “Caesar” as referring to a person, rather
than having the meaning it has in “I am eating a Caesar salad,” or the meaning it might have as a
password, or so on. It simply does not have any particular meaning at all.
Not only does this seem like a natural extension of the context principle, but Wittgenstein
seems explicitly to describe nonsensical sentences this way. Diamond highlights the following
quotation:
Though it is nonsense to say “I feel his pain,” this is different from…saying a string of
nonsense words. Every word in this sentence is English, and we shall be inclined to say
that the sentence has a meaning….The task will be to show that there is in fact no
difference between these two cases of nonsense, though there is a psychological
distinction in that we are inclined to say the one and be puzzled by it and not the other.11
Wittgenstein here says that there is a distinction between a string of nonsense words and a string
of perfectly good English words which form a meaningless sentence, but that this distinction is a
merely psychological one. But in the more important sense, in what I think is clearly the logical
sense, there is “in fact no difference” between those two kinds of sentences. What must that
mean? Well, one obvious logical feature of a string of nonsense words is that none of the words
composing it mean anything. If a string of perfectly good English words which form a nonsense
sentence is no different, logically, from a string of nonsense words, then that seems to require
10
11
“What Nonsense Might Be,” 99.
Taken from a 1935 lecture; cited by Diamond in “What Nonsense Might Be,” p. 106.
10
that those English words don’t mean anything either when they occur in a meaningless sentence.
And as already argued, this claim makes perfect sense in light of the context principle. The
words of the nonsense sentence cannot have their meanings fixed by the role they play in a
proposition, because if the sentence they are found in is meaningless, there are no meaningful
roles to play in it. So the only way these words could have meanings at all was if they carried
those meanings with them independently of context, which is precisely what the context
principle denies.
All of the above insights seem to fit within a general, Fregean and Wittgensteinian
understanding of the context principle. But it is important to note that Wittgenstein’s version of
the context principle is a bit more nuanced than Frege’s, at least in its explicit formulation. Most
especially, Wittgenstein will differ from Frege in what exactly constitutes a “proposition” for the
purposes of the claim that words have meaning only in propositions. Moore cites a comment of
Wittgenstein’s on this issue:
On the statement, ‘Words, except in propositions, have no meaning,’ he said that this ‘is
true or false, as you understand it’…in what he called ‘language games’, single words
‘have meanings by themselves’, and…they may have meaning by themselves even in our
ordinary language ‘if we have provided one’.12
Elsewhere he says,
Here we might say – though this easily leads to all kinds of philosophical superstition –
that a sign ‘R’ or ‘B’, etc., may be sometimes a word and sometimes a proposition. But
whether it ‘is a word or a proposition’ depends on the situation in which it is uttered or
written.13
Frege’s restricts his discussion of the context principle to words occurring or failing to occur in
more complex sentences.14 What Wittgenstein makes clear is that, if what we are interested in is
Moore, G. E. “Wittgenstein’s Lectures in 1930-33,” p. 261.
PI 49.
14
Nonetheless, I do think Frege’s system also has room for the idea that single words can, in ordinary language,
function as full propositions. But while Wittgenstein both states this feature of our language explicitly and finds it
12
13
11
find out whether a word is playing a meaningful role or not, whether it occurs inside a larger
sentence is not the main question. A single word may function as a proposition, as a fully
meaningful linguistic unit, in many contexts. Take, for example, the word “No” as an answer to
a question or a statement of refusal, or the word “Fire” shouted inside an occupied building.
Instead, the real context that matters for Wittgenstein’s version of the context principle is
not the context of a sentence but the entire context in which the word occurs. The word “Fire”
does not need to occur in the context of a larger sentence to have meaning, but it does have to
occur in some context into which it fits meaningfully. The context of being shouted by a person
in an occupied building is one such context where the word “Fire” has meaning.
I will continue to describe the context principle as the principle that “Words have no
meaning outside a proposition.” However, the reader should understand that a word which
occurs in a context in which it is playing a meaningful role, and which is thus functioning as a
proposition, does not count as occurring “outside a proposition” in the sense we are interested in.
In any case what matters is that the word or phrase occurs in a context where it is being used to
actually say something, something meaningful.
III
As we have seen, the context principle is largely justified by the psychological-logical
distinction. Words outside the context of a meaningful proposition are not playing logical roles
in the way they do when they are functioning in the context of a proposition. Thus we will not
be able to specify any meaning for them at all, unless we mistake merely psychological
associations with those words for actual meaning. It is thus natural to conclude that words
occurring in isolation or in nonsense sentences have no logical significance whatsoever, but only
noteworthy, Frege would merely see a single-word proposition like “Fire!” as something like an abbreviation of a
complex statement like “There is a fire here.”
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psychological significance. It might seem that if they had any logical significance, that would
mean they had some degree of meaning. Furthermore, as already noted, a word occurring
outside the context of a meaningful proposition has no logical role to play. And if it is not
playing a logical role, that would seem to mean that there is nothing logical to it at all. The only
logical statement we can make about such a word is that it is meaningless.
Diamond seems to endorse something like this line of thought in her article on nonsense:
Frege’s idea…is that if we want to focus on the work done by the (as it were) working
parts of a sentence, those in virtue of which the whole sentence means what it does,
then…what we want is not to be seen at all if we look not at the working parts in action in
the sentence but at the mere isolated word. If you look at the words alone, nothing that
can pertain to them in isolation will be relevant to what the words do as working parts of
a sentence.
The claim here is that nothing about an isolated word is so much as relevant to what it does when
it is in a meaningful sentence. Since what it does in a meaningful sentence is to play a logical
role, then if nothing that pertains to an isolated word is relevant to that logical role, that seems
fairly clearly to imply that nothing that pertains to an isolated word is logically significant. If we
have agreed with Diamond about the truth of the context principle, this is an intuitively appealing
way of cashing it out. But it leads to a strange sort of puzzle. If isolated words have nothing
logical to them at all, how is it that we can combine them together in right and wrong ways at
all? One might respond that isolated words have psychological significance – we associate
mental images with them, are naturally inclined to say them in these cases and not those, and so
on. And so one might think we can build up actual propositions by means of these merely
psychological associations. But the whole point of the logical-psychological distinction is that
the logical is a normative domain and the psychological is not, so it is hard to see why, if words
have only psychological significance, we cannot combine them any way we like without ever
being wrong in doing so.
13
It is certainly true there are not the same sort of norms regarding isolated words that there
are regarding propositions. There are right and wrong ways to understand a proposition, but
because words outside the context of propositions don’t mean anything in particular, there can be
no right or wrong ways to understand them. Nonetheless, I think there is another sense in which
individual words of a language do have a normative and therefore logical aspect. Words alone
may not have meanings, but they have different possibilities of meaning, and any given word has
certain roles it can and certain roles it cannot play in a proposition. In what follows below, I will
argue that individual words have, not no logical significance whatsoever, but a highly
indeterminate logical significance. What I mean by that will become clear through a series of
examples.
IV
We have already noted that for Wittgenstein, single words can function as meaningful
propositions in certain contexts. On the other hand, often a fully-formed, complex proposition
has no meaning for us if taken out of context:
‘After he had said this, he left her as he did the day before.’—Do I understand this
sentence? Do I understand it just as I should if I heard it in the course of a narrative? If it
were set down in isolation I should say, I don’t know what it’s about. But all the same I
should know how this sentence might perhaps be used; I could myself invent a context
for it.15
Not only is the sentence Wittgenstein cites clearly meant to have significance as part of a much
larger and more interesting narrative we do not have, but it explicitly appeals for its meaning to
contextual elements which have not been given. The sentence tells us that the time during which
the action occurs is “After he had said this,” but we do not know what he said or when, and it
tells us that the way he leaves is “as he did the day before,” but we do not know how he left the
day before. It is as if the sentence has holes in it, and we feel inclined to try to invent a context
15
Wittgenstein, Ludwig. Philosophical Investigations, §525.
14
to fill the holes. By contrast, a sentence like “Whales are mammals” communicates a meaning
without needing any further context, aside from the fact that it is intended to be read by a speaker
of English.
I want to argue that there is a very real sense in which a sentence like “After he had said
this, he left her as he did the day before” is not merely vague but meaningless. That might seem
to be going a bit far, and certainly Wittgenstein himself does not explicitly use that word for it.
But the logical status of that sentence, when taken out of context, is the same as the logical status
of other pieces of language that Wittgenstein does explicitly call meaningless.
Wittgenstein states elsewhere, “there is no half a proposition. That is, what is true of a
word holds true for half a proposition: it only has a sense in the context of the proposition.”16
Not only is the word “cat” meaningless out of context but, “…gave him a cat” is meaningless as
well, given that it occurs outside a context in which it serves as a complete proposition. These
seems quite a sensible extension of the context principle: just as something does not fail to be a
proposition merely in virtue of being only one word long (as we see in the case of “Fire!”),
something does not succeed in being a proposition merely in virtue of being several words long.
But of course, if the half-proposition “…gave him a cat” occurs in answer to the question
“What did his mother do that the boy is so happy about?”, it is no longer be a half-proposition
but a complete and meaningful statement. Just as “Fire!” functions as a proposition in the right
context, “Gave him a cat” can also function as a meaningful proposition in the context of a
conversation in which someone has just asked a certain sort of question.
Thus whether “gave him a cat” is meaningful depends entirely on the context in which it
occurs. The sentence “After he had said this, he left her as he did the day before” seems to work
16
Wittgenstein, Ludwig. Big Typescript, p. 2e.
15
the very same way. Both of them contain obvious gaps in meaning which we can at best try to
fill by inventing a context for them. Standing alone, neither seems to say anything in particular.
It may seem odd to claim of a sentence like “After he had said this, he left her as he did
the day before” that it is not a proposition, simply because it is grammatically (in the nonWittgensteinian sense) full formed, with both a subject and a predicate. But this seems like a
case where we are misled by psychological associations and expectations into thinking we are
seeing something logical. Just as it is hard for us to see that there is no logical difference
between a nonsensical statement like “I feel his pain” or “Caesar is a prime number” and pure
gibberish like “Gibbledy gobbledy goo,” it is also hard to see that “After he had said this, he left
her as he did the day before” tells us no more than “…gave him a cat” does. Something’s having
the pattern of grammatically complete sentence leads us to have certain expectations regarding it,
to feel that in it we are being given a piece of information. But that does not mean it actually has
a meaning.
Thus not only individual words but also fragments taken out of larger sentences, whole
sentences, and presumably even series of sentences may fail to have an independent sense and
thus fail to be genuine propositions. A linguistic utterance qualifies as a proposition when it
performs some complete linguistic function: it gives some specific command, asks some
question, describes some state of affairs, expresses some sentiment, etc. It does not leave us
guessing about possible meanings, but instead simply communicates a meaning. Because it has a
meaning, it can be understood rightly or wrongly, while sub-propositional utterances cannot.
V
Of course, we cannot divide all bits of language into two tidy piles, one consisting in all
the propositions and the other consisting in all the non-propositions. For some utterances we will
16
not be sure whether to say they have a sense on their own or not. “After he had said this, he left
her as he did the day before” seems pretty clearly to tell us nothing at all when given on its own,
but what about a sentence like “Mary went to buy milk”? Taken alone, I do not know who Mary
is or why she is buying milk or when or why I ought to care that she is, and all these are things
we might think of as important to understand regarding such a sentence. But the sentence also
does not seem as obviously incomplete as Wittgenstein’s example does.
Whether something qualifies as a proposition or not depends on whether we would say
that we understand the utterance rather than merely guessing about what meanings the utterance
could possible have. Wittgenstein says this regarding his vague example sentence: “If it were set
down in isolation I should say, I don’t know what it’s about. But all the same I should know
how this sentence might perhaps be used; I could myself invent a context for it.” We can invent
a context for fragments of propositions, even for individual words, but the fact that we have to
invent a context to make them meaningful, shows that they have failed to actually communicate
any particular meaning to us. But there are grey areas; there are some utterances about which we
are not sure whether to say we straightforwardly understand them or are merely guessing about
meanings.
I want to argue then that we should think of there being a sort of spectrum of
determinacy of meaning. We attribute the status of meaningfulness only to utterances which are
fairly far along on this spectrum, by and large determinate in meaning. The word “cat” taken
alone is extremely indeterminate: as noted in my original argument for the context principle, it
could easily occur as a noun, a verb, part of an adjectival phrase in “cat fight,” and so on. On its
own, it is clearly meaningless. A phrase like “…gave him a cat” is still meaningless, but because
it is more complex, it is more constrained in the number of roles it could play. It thus gives us
17
more to go on if we were to try to invent a likely context, and it has a bit more in common with
utterances that would qualify as meaningful. “After he said this, he left her as he did the day
before” is perhaps a tiny bit farther along the spectrum, and “Mary went to buy milk” seems far
enough along that we want to classify it as independently meaningful. But that sentence is still
more evident in its need for further context than a sentence like “Whales are mammals.”17
But I should clarify that I do not mean by “determinacy of meaning” the ideal posited by
Frege and the early Wittgenstein on which concepts have or ought to have determinate
extensions, such that every object is either in the extension of a concept or is not. Indeterminacy
in this sense, what we might call ‘internal’ indeterminacy, occurs when the precise extension of
the class of things falling under a given concept is unclear. The sentence “I have a blue pen” is
indeterminate in this sense because there are some colors about which one is not sure whether to
say they are blue rather than purple or green. As Wittgenstein points out in his later work,
however, a concept with blurred edges is still a concept.18 A concept which was entirely
indeterminate, which applied no more in one situation than any other, would of course be
meaningless, but the ordinary blurriness of the concepts we use does not make our propositions
any less meaningful. The indeterminacy of the concept “blue” is merely an aspect of that
concept; part of what it is to grasp the concept is to recognize its ambiguity with regard to certain
hues.
Of course, even “Whales are mammals” abstracted from any further context might not mean what we would
ordinarily take it to mean. In some contexts it could serve instead as a password or as an adjective in the phrase
“Whales are mammals propositions,” serving as an informal term referring to the class of trivial categorical
statements. No matter how broad the context one knows for a proposition, it is always possible to posit a yet
broader context which shows the meaning of the proposition to be different from the meaning one took it to have.
Wittgenstein points out in the Investigations that it is always theoretically possible to misunderstand any
proposition, but this does not imply that our propositions are meaningless. Attempts to ground meaning in such a
way that there is a point at which any misunderstanding is impossible are rooted in confusion; that is not the way
language works. Thus just because we can raise hypothetical alternate meanings, this ought not lead us to think
there is no significant logical difference between “Whales are mammals” and “…gave him a cat” such that one can
be described as meaningful and the other not. What we can and should say is that the less context we have for an
utterance, the less determinate its meaning and the more likely we are to be mistaken.
18
Wittgenstein, Ludwig. Philosophical Investigations, §71.
17
18
The kind of indeterminacy I am concerned about, the kind which is connected with the
meaningfulness of an utterance, involves not unclarity about what things fall under a given
concept but about which of multiple different conceptual roles is being played by a word. The
statement “I have a blue pen” could theoretically mean not that I have a small blue instrument
used for writing with ink, but that I have a fenced-in area meant for keeping livestock, the fences
of which have been painted blue. If, because of some unusual context, it is unclear which of
these two interpretations of the statement is the correct one, then the indeterminacy of this
sentence’s meaning is a matter of ‘external’ rather than ‘internal’ indeterminacy. The trouble is
not the blurriness of any individual concept, but rather that I am unsure which of two completely
different concepts is meant. If I do not know whether the speaker means to be claiming to have
one kind of pen or the other, I do not really know what is being said.19
Of course, the distinction between confusion about whether something falls under a
concept and confusion about which of two different concepts is being referred to is one that itself
can be ambiguous. In some cases (as in the above example of “pen”), it is clear that a single
word refers to two completely unrelated and distinct concepts; but in other cases the relation
between concepts is closer and it is not clear whether we want to say that the word refers to
separate, related concepts or merely one complex concept with blurry edges. In saying that the
pen is blue, for instance, it is slightly unclear whether I mean to be saying that it has blue ink or
that the outside of the pen is blue. These are two related notions of what it means for an object to
be blue, but they are much more closely related to one another than the concept of a fenced area
19
Sentences like this for which there are some finite number of interpretations, however, we will probably not want
to describe as so indeterminate as to be meaningless – this would, I think, be a grey area. The fact that I know the
sentence means one of those two things constitutes enough determinacy for me to say that the sentence has
communicated at least some meaning to me: namely, that the speaker has some material possession, which is either
a fenced-in area or a writing utensil. It is when the utterance has a non-finite list of possible meanings, as in
“…gave him a cat,” that it no longer makes sense to claim to have gained any meaning from it whatsoever.
19
is to the concept of an instrument used for writing. If this is the only ambiguity I perceive in the
sentence, I am not likely to conclude that I do not know what has been said, or to feel that I am
“guessing” about what is meant.
Thus the larger the number of live candidates for an utterance’s meaning and the less
closely related to one another these candidates are, the less determinate its meaning. An
individual word out of context is highly indeterminate because it can be used in innumerable
different ways that have nothing to do with one another, so about them we say they are
meaningless. But there is some much smaller degree of indeterminacy of this sort in most of our
propositions and a small degree of indeterminacy does not prevent us from claiming to
understand a proposition.
I have been equating “being meaningful” with having a certain degree of determinacy of
meaning. It might seem that these are two different things, but at least in practice they amount to
the same. We have a natural tendency to try to make something meaningful out of any bit of
language we encounter. But because incomplete utterances get their meaning only from whole
propositions of which they are a part, the only way to work out their meaning when they occur
outside the context of a proposition is to work out what whole proposition they could be a part
of. When what we have is in fact merely a half-proposition, a fragment of a complete
proposition, we will be able to come up with multiple different propositions the utterance could
be a part of and thus multiple different meanings it could have. This shows us that its meaning is
indeterminate. But this is merely another way of saying that do not know what it means, that it is
meaningless to us.
But suppose we come across something that looks like a fragment of a complete
sentence, but find that we can work out what single proposition it must be a part of with a fair
20
degree of certainty. This could happen if I heard someone say “Gave him a cat,” and it took me
a bit to realize that this was said in response to a question, and thus the full proposition this
sentence would fit into would be the sentence, “What the mother did that the boy is so happy
about was that she gave him a cat.” In this case, because I can work out the full proposition that
“gave him a cat” fits into, I can fix a single meaning for this fragment sentence. But then,
logically speaking, it turns out that what I had was not actually a fragment of a proposition at all
but a complete proposition – just one I initially failed to recognize as such. Given that nonlogical factors like whether the utterance is a single word or a sentence with a subject and
predicate are irrelevant to the logical status of the utterance as a proposition or not, what
determines whether something is a proposition is simply whether it is possible to fix a
determinate meaning for it.20
But in positing a spectrum of determinateness of meaning and connecting it up with
meaningfulness, I do not mean to be suggesting that we view meaningfulness as occurring on a
similar spectrum. There is some grey area in attributions of meaningfulness, some utterances
about which we are not sure whether to say they qualify as propositions or not. But in general
we can draw a qualitative distinction between utterances which are and utterances which are not
independently meaningful, not merely a quantitative distinction between degrees of
meaningfulness. If the meaning of some utterance is characterized by a certain degree of
indeterminacy, it is reasonable to say that it is flatly meaningless on its own. An utterance is
meaningful only if it falls above a (somewhat blurry) point on the spectrum of determinacy of
Well, that’s a bit too quick. Something could be a perfectly fine proposition which I just happen to be incapable
of fixing a determinate meaning to. But to get into the difference between a proposition’s actually meaning a certain
thing and its seeming to me to mean a certain thing would be to add an extra, altogether unnecessary layer of
complexity to the discussion.
20
21
meaning, that point being that at which we are not guessing at possible meanings for an utterance
but instead understanding it as meaning some specific thing.
VI
I have argued that we should understand sub-propositional bits of language as
meaningless because they are indeterminate in their meaning, but as nonetheless possessing
varying degrees of indeterminacy (and thus varying degrees of determinacy). If this is really the
way to think about meaningfulness and determinacy, then it seems that we must understand subpropositional utterances as having logical signification of some kind, however weak. To be
indeterminate (beyond a certain degree) with regard to meaning is to be meaningless, but it
nonetheless seems important to point out that the kind of signification which parts of
propositions have when taken out of context is continuous with the kind of signification they
have in context. What’s more, this way of thinking about words seems to fit well with some of
the ways Wittgenstein speaks about the context principle.
Wittgenstein states: “A word only has meaning in the context of a proposition: that is
like saying only in use is a rod a lever. Only the application makes it into a lever.”21 A rod
serves as a lever only if it is functioning as such in a given machine; in some other machine the
same rod could serve a variety of other structural purposes (perhaps a long skinny wheel, or
wedged under a door to keep it from opening). In the same way, the English word “cat” can
serve a variety of different purposes depending on the proposition in which it occurs. But a rod
cannot play just any role whatsoever in a machine. If an otherwise complete machine has a
space for a three-inch cogwheel which it needs in order to run, a one-inch rod cannot be placed
in that space and yield a working machine. Similarly, the word “cat” can play many roles in
language, but it cannot play just any role at all. It cannot in this precise situation go in the
21
Wittgenstein, Ludwig. Philosophical Remarks, §14.
22
following sentence like this, for instance: “The rose cat red.” The word “is”, however, could go
in that sentence and yield something meaningful.
Of course, it might make sense to say “The rose cat red” in some other context, if we
were playing some sort of game with words perhaps. The uses to which the word “cat” can be
put is not finite. Any list I give of the roles a word might have could be expanded indefinitely
once I account for the fact that a word can be given any use at all, so long one is using it in a
context in which it has in fact been given that use. But that the word “cat” could play that kind
of role only in that kind of context and not in others constitutes a logical constraint on the use of
the word “cat.” It is true that any given word can have any given meaning in some situation, but
it is also true that in any given situation every word has ways in which it cannot be used. If it
could be used any way at all it would be useless.
That “The rose cat red” is nonsense is a logical, not a psychological, fact. But that that
sentence is meaningless while “The rose is red” is not constitutes a logical fact about the word
“cat”: that it cannot be used in that way in that context to produce something meaningful.
Granted, this is a purely negative fact, and a very thin and uninteresting one at that. I cannot
specify what the word “cat” does mean outside a meaningful context, nor can I even give an
exhaustive list of the things it cannot mean. All I can do is point out specific individual ways of
employing the word that will not result in something meaningful, and specific individual ways of
employing it that would. But however thin they might be, these constitute logical facts about
individual words.
One might object to this claim based on a point I have already made, that a word can in
principle be given any use whatsoever, so there is no role a word cannot at least theoretically
play. Thus it might seem that words out of context are not just highly indeterminate but entirely
23
indeterminate, not on the spectrum of determinacy of meaning at all, and then it seems there
would not be any logical facts about them. But if this point led us to think that words do not
have logical signification, it would have to lead us to think that propositions do not have logical
signification either. It is in principle possible that all the words in the sentence “Whales are
mammals” have been given meanings other than their normal ones, such that it actually signifies
that trees have leaves. That there are theoretically possible situations in which the sentence
means that trees have leaves instead of meaning that whales are mammals should not prevent me
from attributing the sentence “Whales are mammals” its usual logical significance.
The same rule which applies to propositions applies to rules for the use of words: if they
are given to us without any context which would lead us to believe they are doing something
very different from what they ordinarily do, we are justified in understanding them to be doing
what would ordinarily do. We are justified in assuming some sort of minimal standard context if
there is no specific reason not to – that is, we are justified in excluding from consideration any
possible meaning of an utterance which, as a condition of its being a possible meaning, relies on
an appeal to the fact that words can in principle be given any meaning whatever. Just as I am
justified in thinking that if I overhear someone say “Whales are mammals” that it means what I
would ordinarily take that proposition to mean, I am also justified in thinking that if I can make
out only the word “cat” in a sentence someone else says, the sentence they just said was not “The
rose cat red.” If these sorts of assumptions were not justified (even though they occasionally
turn out false), we would never be able to make use of language at all.
One might object that while this principle is sound for propositions, it ought not be
extended to sub-propositional utterances, because doing so will lead us back to the sort of
position the context principle rejects, on which words have meaning on their own. Could one
24
not, given my principle of assuming a minimally standard context, say that a word like “cat”
really can be taken to mean a small furry mammal, even when it occurs on its own, because after
all that is its “standard” use? The answer is no. To know what “cat” means requires a context
far greater than the minimal one I have said we are justified in assuming. The other meanings I
can adduce for the word “cat” – its use as a verb, as a part of larger phrases with only indirectly
related meanings such as “cat fight” or “game of cat and mouse,” have much more in favor of
them as interpretations than merely the fact that a word can in principle be given any meaning
whatever. The word “cat” actually has those uses in the English language. Similarly, a
figurative use for a word, even if it is not already a meaning the word has in the language, has
more in favor of it than the bare principle that a word can in principle be given any meaning
whatever. Thus, assuming a minimally standard context will still leave us with innumerable
possible roles for the word “cat,” or for any word, to be used. So a principle of assuming a
minimally standard context will not allow us to attribute meaning to individual words taken out
of context.
To reiterate my point here: We are justified in thinking of words as having some degree
of determinacy even when taken on their own, for the fact that the word “cat” cannot be used as
the word “is” constitutes some small degree of logical determinacy. Just as a rod is not a lever
except in the context of a machine, a word does not have any determinate meaning or function
except in the context of a proposition. But a rod still has a specific shape which limits its
potential uses, and while it can be melted down and molded into a new shape, for it to take on
this new shape one has to melt it down and mold it, and that too is a feature of the structure of the
rod. Similarly, no word can be used in any way whatsoever, and though we can give them new
meanings, they can only have those new meanings in a specific context in which they have been
25
assigned them. Thus instead of saying of individual words that they have no logical signification
but only psychological signification, we ought instead to say that their logical signification is
indeterminate.
I will address one final objection one might make against my argument that individual
words should be understood as having logical signification. To return to the point at which we
started, recall the quotation cited by Diamond in which Wittgenstein says that there is no logical
distinction between a nonsensical sentence like “I feel his pain” and a sentence composed of
gibberish words. But on my view, words which are part of some language do have some degree
of logical signification even in isolation, because there are roles they can play. By contrast,
gibberish words do not – or if we want to say that even gibberish words have certain roles they
can play in our linguistic practices, to the extent this is true their logical signification is at any
rate of a different and even weaker kind than that of English words taken out of context. It might
seem that in arguing that words have some logical signification, no matter how minimal and
indeterminate, out of the context of any proposition, I must reject the claim that a sentence
composed of such words really has the same logical status as a sentence composed of gibberish
words.
As I have just argued, in order to maintain the claim that words have logical signification
independent of propositions, or even that propositions can be understood as having the logical
signification we ordinarily take them to have, we must presume some minimal standard context
unless there is reason to do otherwise. The word “cat” cannot function as a copula except in
some specific context, as in a game with words, in which it has arbitrarily been given that role.
That it can have that role only in a context in which it has been assigned that meaning it never
otherwise has is what allows us to still claim a small degree of determinacy for the word on its
26
own. But with regard to a sentence like “Caesar is a prime number,” we are no longer justified
in assuming any sort of minimal standard context, because when we assume such a minimally
standard context the proposition is nonsensical. We must then step back and say, “If this
sentence means anything, it could mean anything at all.” Once we see this, we are in the same
position we are in with regard to a sentence like “Gibbledy gobbledy goo.” In either case, the
only way the sentence could have a meaning is if it occurs in some context in which the words of
the sentence have been assigned some arbitrary meanings which we do not presently have access
to.
Thus the case of genuinely nonsensical propositions is different from the case of
proposition fragments. Both are meaningless, because they communicate nothing to us. But
while proposition fragments present to us various possibilities of meaning, nonsense sentences
do not even do that. No possible meaning one could suggest for a sentence is any more plausible
than any other, and thus a nonsense sentence is absolutely indeterminate. It is this that makes all
nonsense sentences logically the same. Sentences involving category errors do not differ
logically from strings of gibberish, even in the minimal way in which a word and a more
complex and less indeterminate fragment of a proposition are logically different despite both
being meaningless.
27