Definitions
CONNOTATION AND DENOTATION
Connotation and Denotation
So far we’ve looked at two theories of meaning–
the Idea Theory and Verificationism. In both
theories there are two aspects to meaning,
which we might call connotation and
denotation.
Connotation
Connotation corresponds more closely with the
ordinary English sense of the word ‘meaning’:
on the Idea Theory, for instance, the ‘meaning’
or connotation of a word is an idea. The word
‘dog’ has as its meaning the idea of a dog.
Denotation
But there’s another sense in which the word
‘dog’ means dogs (those furry smelly barking
things): it applies to dogs and it’s true of dogs
(and false of everything else).
Denotation involves the relation between words
and the world– what words apply to/ are true
of.
Relation between the Two
The two aspects of meaning are not unrelated.
The Idea Theory’s theory of connotation (words
connote ideas) explains why words have the
denotations they do (they denote what the
ideas resemble). So ‘dog’ is true of dogs because
‘dog’ connotes the idea of a dog, and dogs
resemble the idea of a dog.
Verificationism
Verificationism has a similar structure: words
mean (connote) sets of possible experiences,
and are true of the things those experiences
verify. ‘There is a dog’ is true when there is a
dog, because it connotes the experiences {I hear
barking, I see a furry thing, the furry thing
smells}, and when I have those experiences,
there is a dog.
Structure of a Theory of Meaning
Here’s the structure of the theories we’ve
considered so far:
• Words are arbitrarily and conventionally
associated with connotations.
• Connotations plus a certain relation
(resemblance, verification) determine
denotations.
A particular theory says what the connotations
are, and what the certain relation is.
DEFINITIONS
“The Definition Theory”
According to “the Definition Theory” the
connotation of a word is a definition, and the
denotation of the word is what the definition is
true of.
Circularity
I say “the Definition Theory” in quote-marks
because no one actually holds the theory in any
sort of general form (with one exception we’ll
consider later).
The principal problem with a generalized
definition theory is that it’s circular.
Generalized Definition Theory
By “a generalized definition theory” I mean a
theory according to which every expression has
a definition as its meaning, including all the
expressions that show up in the definition. So if
‘bachelor’ := unmarried man
Then ‘unmarried’ and ‘man’ will also have
definitions as their meanings.
Circularity
Here’s the sense in which a generalized
definition theory is circular:
Let’s say x defines y
If, and only if
x is in the definition of y or x is in the definition
of a word that defines y
Then for any finite set of words, all of which
have definitions, some word w defines w.
Problem with Circularity
The problem with circularity is that it trivializes
the claims of the Definition Theory. If I want to
know what a word is true of by learning its
definition, I have to know what the words that
define it are true of. But for some word w, w
defines w. So in order to learn what w is true of,
I have to already know what w is true of. It
doesn’t help to remove w, because it follows by
the same logic that the language with w
removed is also circular.
Dictionaries and Circularity
This is why you can’t learn a foreign language–
say Kalaallisut– merely from a dictionary where
Kalaallisut terms are defined by other Kalaallisut
terms. When you look up a word all you get are
a bunch of words you don’t know. When you
look up those words, the same thing happens.
And it never ends, because eventually the
definitions start sending you in circles.
The Attraction of Definitions
There’s something that’s very attractive about
the Definition Theory, even if it can’t be
generalized. If you ask somebody, “What does
‘defenestrate’ mean?” what they give you is a
definition. You can find the meanings of words
in dictionaries– that is, you can find definitions
there. Giving, finding out, and knowing
meanings seems to involve definitions.
Particular Definition Theories
The way to go then is to adopt a particular
definition theory. On such an account, not every
word has a definition for its meaning, only some
particular subclass of all the words. The
undefined words are the primitive vocabulary.
Everything else is defined in terms of the
primitive vocabulary, or defined in terms of
things that are defined in terms of the primitive
vocabulary, or… etc.
Hybrid Theory of Meaning
Adopting a particular definition theory requires
that you also adopt a separate theory of
meaning to explain what the primitive
vocabulary means. For example, in the Carnap
reading ‘x is an arthropod’ had a definition for a
meaning. It was defined by logical operations on
protocol sentences. Protocol sentences had no
definitions: their meaning was their verification
conditions.
Important Point
This means that understanding a word cannot in
general be the same thing as knowing its
definition. Only understanding non-primitive
vocabulary involves knowing definitions, since
the primitive vocabulary does not have any
definitions.
Explanatory Virtues of Definitions
If you found out that all people with large ears
were rich and that only people with large ears
were rich, that would be interesting, and would
call out for investigation.
However, it’s not interesting that all and only
bachelors are unmarried men, and we don’t
need an investigation to determine that they are
or why they are.
Explanatory Virtues of Definitions
Definitions can explain this difference. Anyone
who knows what ‘bachelor’ means knows the
definition of ‘bachelor’ (because this is the
meaning) and hence knows that bachelors are
unmarried men. This is why it’s not interesting,
and why you don’t need to survey the bachelors
to find out if they’re unmarried. You know in
advance of a survey, by knowing what bachelor
means, that is, its definition.
Definitions and Informal Validity
Definitions can also help us explain informal
validity. A formally valid argument is one where
the conclusion follows from the premises, no
matter what the non-logical expressions mean:
Mimi is orange & Mimi is a cat.
Therefore, Mimi is orange.
Definitions and Informal Validity
Definitions can also help us explain informal
validity. A formally valid argument is one where
the conclusion follows from the premises, no
matter what the non-logical expressions mean:
x is F & x is G.
Therefore, x is F.
Definitions and Informal Validity
But you seemingly can’t explain some
(intuitively valid) inferences in the same way. We
can call these ‘informally valid’ inferences:
Fred is a bachelor
Therefore, Fred is unmarried
Definitions and Informal Validity
But you seemingly can’t explain some
(intuitively valid) inferences in the same way. We
can call these ‘informally valid’ inferences:
x is H
Therefore, x is F
Some inferences like this are not valid.
Definitions and Informal Validity
However, if “Fred is a bachelor” really means
“Fred is unmarried & Fred is a man,” then
informal validity simply becomes formal validity:
Fred is unmarried & Fred is a man.
Therefore, Fred is unmarried.
Definitions and Informal Validity
However, if “Fred is a bachelor” really means
“Fred is unmarried & Fred is a man,” then
informal validity simply becomes formal validity:
x is F & x is G.
Therefore, x is F.
All inferences of this form are valid.
Definitions and Understanding
Even though we require a separate theory of
understanding for the primitive vocabulary, it
might be thought that definitions help explain
what it is to understand at least some
expressions. To understand the definable (nonprimitive) expressions in a sentence is to
retrieve their definitions from memory. That
doesn’t solve the general problem of
understanding, but it’s a good first step.
Definitions and Concept Acquisition
Fodor (1975) argues that you cannot learn basic
concepts, they have to be innate. Suppose COW
is a basic concept. To learn that ‘cow’ means
COW involves (i) hypothesizing that ‘cow’ means
COW (ii) testing that hypothesis against the
linguistic evidence and (iii) having the
hypothesis confirmed by the evidence. This
means that to learn what ‘cow’ means, you must
be able to hypothesize (think) it means COW,
and so you must already possess COW.
Virtues of Definitions
• Definitions explain how we know facts like all
bachelors are unmarried, and why they’re true.
• Definitions explain informal validity by reducing it
to formal validity.
• Definitions provide a model of non-primitive
word understanding.
• Definitions explain how it is we can acquire new
concepts: we construct them out of old ones.
Definitions and Concept Acquisition
Well, it’s likely we have some innate concepts,
like CAUSE, and UP, and MAMA, and HUNGER.
But surely the concepts CARBURETOR, and
SUSHI, and NEPTUNE, and QUARK are acquired
sometime after birth. If Fodor’s argument is
right, they must be complex concepts. The
reason we can learn, say, CARBURETOR, is that
it’s defined out of other concepts, which were
either innate or defined out of other concepts…
Lexicalism
As natural as the Definition Theory seems, many
philosophers have argued that there are fewer
definitions than we might think, and maybe
almost none at all. They hypothesis that most
words don’t have definitions in terms of other
words is called Lexicalism (because it says that
the primitive terms = the lexical items, i.e. the
words).
AGAINST DEFINITIONS
The Problem of Examples
Philosophers are fond of ‘bachelors are
unmarried men.’ Why? Because it’s really hard
to find examples of definitions that work– where
the defining part means the same thing as the
defined part. ‘Bachelor’ isn’t even obvious (is
the pope a bachelor? Are 14 year-olds?). Kinship
terms and animal terms are about the only good
bets.
Kinship Terms
•
•
•
•
•
•
•
Sister:= female sibling
Brother:= male sibling
Mother:= female parent
Father:= male parent
Grandmother:= female parent of parent
Uncle:= sibling of parent
Cousin:= child of sibling of parent
Animal Terms
We often have words for male-X, female-X,
young-X, group-of-X, and meat-of-X:
• Boar := male pig
• Sow := female pig
• Piglet := young pig
• Drift := group of pigs
• Pork := meat of pigs
Historically Unsuccessful
That’s not very much to build an entire theory
off of. Proponents of definitions have tried to
find lots of other examples, but historically the
project hasn’t been very successful. One
example involves causative verbs: sink, boil,
break, open, etc.
Causative/ Anti-causative
1a. The ship sank.
1b. The pirates sank the ship.
2a. The water boiled.
2b. The chef boiled the water.
3a. The glass broke.
3b. The child broke the glass.
4a. The door opened.
4b. The actor opened the door.
The Causative Analysis
The idea here is that the causative “sink” is
defined by the anti-causative “sink” + “cause”:
“The pirates sank the ship” := The pirates caused
the ship to sink.
Furthermore, maybe even some words that
don’t alternate are similar: “kill” = “cause to
die.”
Problems with the Analysis
In a classic paper called “Three Reasons for Not
Deriving ‘Kill’ from ‘Cause to Die,’” (1970) Fodor
presents three reasons for rejecting this
analysis.
First, Fodor argues that ‘die’ should not be
handled in the same way as ‘sink.’
Distribution of Causitives
5a. The pirates caused the boat to sink, and I’m
surprised they did.
5b. The pirates caused the boat to sink, and I’m
surprised it did.
6a. The pirates sank the boat, and I’m surprised
they did.
6b. The pirates sank the boat, and I’m surprised
it did.
‘Kill’ vs. ‘Cause to Die’
7a. John caused Mary to die, and I’m surprised
he did.
7b. John caused Mary to die, and I’m surprised
she did.
8a. John killed Mary, and I’m surprised he did.
#8b. John killed Mary, and I’m surprised she did.
More Problems
So ‘kill’ doesn’t pattern like ‘cause to die.’ Still, it
looks like causative ‘sink’ does pattern with
‘cause to sink’, so can we keep that part of the
analysis? Fodor argues ‘no’ again.
“You Melt It When It Melts”
9a. Floyd caused the glass to melt on Sunday by
heating it on Saturday.
#9b. Floyd melted the glass on Sunday by
heating it on Saturday.
“one can cause an event by doing something at
a time which is distinct from the time of the
event. But if you melt something, then you melt
it when it melts.” (p. 433)
Fodor’s Final Argument
10a. John caused Bill to die by swallowing his
tongue. [Ambiguous]
10b. John killed Bill by swallowing his tongue.
[Only the silly reading]
Causation Not Direct Enough
The point isn’t that there is only one clause to
modify in the 10b example. Suppose I’m driving
down the street and a clown runs in front of me,
waving his arms. Being distracted, I drive into a
tree:
TRUE: The clown caused my car to crash.
FALSE: The clown crashed my car.
The Problem of Examples
There aren’t many good candidates for (good)
definitions. Most dictionary “definitions” are no
such thing.
A Semantic Limerick
“There existed an adult male person who had
lived a relatively short time, belonging or
pertaining to St. John’s, who desired to commit
sodomy with the large web-footed swimmingbirds of the genus Cygnus or subfamily Cygninae
of the family Anatidae, characterized by a long
and gracefully curved neck and a majestic
motion when swimming.
A Semantic Limerick
“So he moved into the presence of the person
employed to carry burdens, who declared: “Hold
or possess as something at your disposal my
female child! The large web-footed swimming
birds of the genus Cygnus or subfamily Cygninae
of the family Anatidae, characterized by a long
and gracefully curved neck and a majestic
motion when swimming, are set apart, specially
retained for the Head, Fellows and Tutors of the
College.”
The Joke
There once was a lad from St. John’s
Who wanted to bugger some swans
So he went to the porter
Who said, “Take my daughter,
The swans are reserved for the Dons!”
Informal Validity Again
Before I suggested that definitions might help
reduce informal validity to formal validity. So if
“John is a bachelor” just means “John is
unmarried and John is a man” then the
seemingly informal inference from “John is a
bachelor” to “John is unmarried” is actually
formally valid (conjunction elimination).
“bachelor” → “unmarried” works because
bachelor = unmarried + X.
Informal Validity Again
However, Fodor et al. suggest that this can’t
work in general. Consider the inference:
This is red, therefore this is colored.
Notoriously, red ≠ colored + X, for any X. So this
isn’t an inference of the form: colored + X →
colored.
Definitions and Understanding Again
Another virtue of definitions is that they’re
supposed to provide a model for how we
understand the non-primitive vocabulary: by
retrieving its definition from memory. Fodor et
al. argue on empirical grounds that it’s simply
implausible that definitions are retrieved from
memory when sentences involving supposedly
“defined” terms are understood.
Empirical Research
Here’s the sort of anti-definition research Fodor
et al. adduce. It’s a robust finding in psychology
that inferences involving negatives take longer
to perform than inferences involving only
positives. If I give you two squares, one of which
is red and the other of which is green, you’ll be
quicker at pointing to the correct one when
asked “Which is red?” than you would be if
asked “Which is not green?”
Empirical Research
Therefore, we expect that if bachelor is
processed as NOT-married man, it should show
the same inferential lag as complex symbols
with overt negations. Fodor, Fodor, and Garrett
(1977) “The psychological unreality of semantic
representations” found just that. It should be
noted that Fodor et al. (1980) describe this
evidence as “rather tentative.”
Empirical Research
I am not claiming that we have particularly good
evidence against the involvement of definitions
in language processing. I am not a psychologist
and I haven’t kept up on the research on
definitions since 1980. What’s valuable in Fodor
et al.’s argument is that it makes clear that
certain questions (like this one) in the
philosophy of language are amenable to
empirical treatment and are thus in some ways
outside the scope of philosophical practice.
Understanding: Final Point
We know from the vicious circularity argument
that some terms we understand (the primitive
vocabulary) must be undefined. By hypothesis
we understand these terms, so we know that
understanding without definitions is possible.
Thus in a sense definitions are superfluous in an
account of understanding. If furthermore there’s
empirical evidence that they actually don’t play
a psychological role, that’s pretty damning.
Concept Acquisition
Definitions also provided an explanation of how
we can acquire new concepts on the hypothesis
formation and confirmation model of learning.
On this model, learning happens by proposing a
hypothesis, testing it, and accepting it if it’s
confirmed or rejecting it otherwise. The
problem is that if you don’t already have the
concept, e.g., BACHELOR, you can’t propose the
hypothesis ‘bachelor’ means BACHELOR, and
hence can’t ever learn what ‘bachelor’ means.
Definitions and Concept Acquisition
However, if you already understand UNMARRIED
and MAN, then you can propose the hypothesis
‘bachelor’ means UNMARRIED MAN and if
‘bachelor’ really does mean that (because that’s
the definition of ‘bachelor’) then presumably
you can learn it. Definitions to the rescue!
The Lexicalist Response
Fodor at least has a strange response. Yes, that’s
one way to go, he would say. But, alternatively,
it’s also possible to accept the consequence that
no simple English expression is learnable, and
that all the concepts that correspond to them
(like BACHELOR and CARBURETOR) are innate–
we’re born with these concepts! Most
philosophers think Fodor is a little bit crazy for
endorsing the second option.
More Plausible Routes?
Oved (2009) suggests that we can use
descriptions that are not definitions to latch
onto certain properties that we otherwise can’t
represent. Once latched onto, we can introduce
new concepts that have the content in question.
So for example, you might use “Granny’s favorite
color” to think about redness, and then
introduce a new concept RED to represent
redness– even though ‘red’ can’t be defined as
“Granny’s favorite color” (not co-intensional).
Where We Stand
• Definitions can’t explain how all words get
their meaning. Since another explanation is
needed, they’re slightly superfluous.
• Definitions can’t explain all informal validity.
Since another explanation is needed, they’re
slightly superfluous.
• Definitions can’t explain all word
understanding. Since another explanation is
needed, they’re slightly superfluous
Where We Stand
• Furthermore, there are only a handful of really
plausible examples of possible definitions.
• Thus, if we accept that some primitive terms
are learned, then definitions can’t explain all
concept acquisition. Since another
explanation is needed, they’re slightly
superfluous.
• This is beginning to suggest that definitions
are superfluous.
Definitions and the A Priori
However, there is one other virtue of definitions
we’ve thus far neglected. Definitions explain
how we know without investigation that all
bachelors are unmarried men. In order to know
what “bachelor” means, you have to know its
definition. It is defined as “unmarried man,”
therefore anyone who knows what “bachelor”
means knows that bachelors are unmarried
men. This requires no investigation into the
marital status of bachelors.
However, many philosophers have become
disenchanted with the idea that there are things
that are true “in virtue of meaning” (analytic
truths). This is partly due to the Quine paper we
talked about last time, “Two Dogmas of
Empiricism.” Remember that Quine’s central
point was that confirmation is theory-relative.
The Web of Belief
Quine’s picture is that our beliefs form a “web”
where change in the degree of belief in any
statement affects the degrees of belief in all of the
others, simultaneously. Some statements are more
toward the “periphery” of the web (observation
statements), and they are more likely to change
with changing experience. But sometimes
“recalcitrant” experience causes us not to revise the
periphery, but the more central, deeply theoretical
(and even logical) statements.
Nothing is Safe
On this model, no belief is immune from
revision. If experience seemingly disconfirms
even logical truths, and it does it persistently
enough (“recalcitrant experience”) then
eventually you’ll have to accept the experience
and reject the logical truths. That’s the model.
Quine vs. Definitions
If you accept the model, then definitions are too
strong of an explanation for how we know that
all and only bachelors are unmarried. Because if
that’s a simple matter of definition, then no
experience should lead us to reject the claim
that bachelors are unmarried. But our model is
that any claim can be rejected when faced with
recalcitrant experience.
One Dogma
(In fact, that was the first “dogma of
empiricism”: that there were analytic truths–
things that were true in virtue of what they
meant.)
THE ABSURDITY OF FIT
The Absurdity of Fit
In one sense, all the views we’ve considered in
class so far are views on which meaning is a type
of “fit.” On the idea theory, meanings
(connotations) are ideas. Ideas have a certain
pre-existing structure: just as in a painting the
different parts are related to one another, and
colored in various ways, and so forth.
Idea Theory and Fit
In order to find out what an idea represents, we
go out and find the things that best fit the idea,
that most closely match its pre-existing
structure, that best resemble it. Whatever best
fits the pre-existing structure is what the idea
represents.
Verificationism and Fit
While verificationism doesn’t have the same
“little colored pictures” view of ideas or the
resemblance theory of representation, it too
involves a type of fit. In advance, words are
associated with specific experiences that are
stipulated to verify them. Why does a certain
experience verify “That is red”? Because we said
so, that’s why. We say in advance what
experiences verify which sentences, then we go
look and see what experiences we have.
Definitions and Fit
Similarly, a definitions view is a type of fit as
well. We say in advance what the definitions of
words are. You don’t discover that bachelors are
unmarried, you sit down and make it true by
fiat.
The Absurdity of Fit
But there’s something terribly wrong with the
idea that meanings are specified in advance of
our encounters with the world. That before any
experience of the world, we sit down and draw
up a structural description, or a set of
experiences, or a verbal description and say
“whatever I find that’s like this, I will call ‘a
dog’!”
The Paradox of Inquiry
The worry here is that on any of these models,
you can’t be radically wrong. If ‘gold’ is true of
what most closely resembles your idea of gold,
then most of your beliefs about gold must be
true. And the same goes for most of your beliefs
about anything. If representation is what fits
best with what you’ve drawn up in advance, in
advance of inquiry, you can be pretty sure you
already know what’s true and what isn’t.
The Paradox of Inquiry
In fact, this problem is as old as Plato, and it’s
called “the paradox of inquiry.” The paradox is:
suppose you want to know, say, the nature of
lightning. If you know what lightning is in
advance, then you don’t need to investigate,
because that’s what you wanted to know. But if
you don’t know, how do you know when you
discover it, that lightning is X? You find X, but
you don’t know that it’s lightning, because you
don’t know what lightning is!
Next Time
Next time we’ll look at the other aspect of the
paradox of inquiry. Let’s suppose we don’t
specify meanings in advance. How do we get
along in a world where we don’t (necessarily)
know what we mean?