Definitions

1. Definitions

2. Connotation and denotation

3. 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.

4. 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.

5. 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.

6. 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.

7. 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.

8. 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.

9. definitions

10. “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.

11. 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.

12. 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.

13. 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.

14. 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.

15. 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.

16. 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.

17. 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.

18. 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.

19. 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.

20. 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.

21. 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.

22. 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.

23. 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.

24. 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

25. 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.

26. 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.

27. 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.

28. 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 (non-primitive) 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.

29. 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.

30. 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.

31. 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…

32. 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).

33. Against definitions

34. 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.

35. 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

36. 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

37. 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.

38. 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.

39. 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.”

40. 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.’

41. 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.

42. ‘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.

43. 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.

44. “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)

45. 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]

46. 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.

47. The Problem of Examples There aren’t many good candidates for (good) definitions. Most dictionary “definitions” are no such thing.

48. 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 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.

49. 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.”

50. 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!”