Definitions CONNOTATION AND DENOTATION Connotation and Denotation So

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 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 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 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 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 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 1 a. The ship sank. 1 b. The pirates sank the ship. 2 a. The water boiled. 2 b. The chef boiled the water. 3 a. The glass broke. 3 b. The child broke the glass. 4 a. The door opened. 4 b. 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 5 a. The pirates caused the boat to sink, and I’m surprised they did. 5 b. The pirates caused the boat to sink, and I’m surprised it did. 6 a. The pirates sank the boat, and I’m surprised they did. 6 b. The pirates sank the boat, and I’m surprised it did.

‘Kill’ vs. ‘Cause to Die’ 7 a. John caused Mary to die, and I’m surprised he did. 7 b. John caused Mary to die, and I’m surprised she did. 8 a. John killed Mary, and I’m surprised he did. #8 b. 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” 9 a. Floyd caused the glass to melt on Sunday by heating it on Saturday. #9 b. 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 10 a. John caused Bill to die by swallowing his tongue. [Ambiguous] 10 b. 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 10 b 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, 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?