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Compositionality. Compositionality. “ The meaning of the whole depends on (and only on) the meanings of the parts and the way they are combined.”. Arguments from compositionality. What’s at Stake?.
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Compositionality “The meaning of the whole depends on (and only on) the meanings of the parts and the way they are combined.”
What’s at Stake? Before we consider arguments for or against compositionality, let’s look at what’s at stake. At various points, compositionality has been used to argue against all of the theories of meaning we have considered in class.
Vs. the Idea Theory According to the idea theory, the meaning of a word is an idea, where ideas are construed as something like “little colored pictures in the mind.” Let’s consider an example: what’s your idea of a pet?
What’s at Stake? Before we consider arguments for or against compositionality, let’s look at what’s at stake. At various points, compositionality has been used to argue against all of the theories of meaning we have considered in class.
Vs. the Idea Theory According to the idea theory, the meaning of a word is an idea, where ideas are construed as something like “little colored pictures in the mind.” Let’s consider an example: what’s your idea of a pet?
Vs. the Idea Theory That clearly doesn’t work. Notice that we cannot say that in the context of “____ fish” “pet” means something other than . This would make the meaning of “pet” non-local (depend on surrounding context) and that’s not allowed on any compositional theory. Conclusion: the idea theory violates the principle of compositionality.
Vs. Verificationism Let’s suppose that the meaning of a sentence is the set of experiences that it probably causes you to have. So a cow will probably cause you to hear cow-sounds, so cow-sounds are part of the meaning of “cow.” In other words the probability of cow-sounds is increased by the presence of cows.
Cows are Safe Let’s suppose that the vast majority of cows are safe. So the meaning of “cow” does not include the experience of bodily harm, because encountering a cow lowers, rather than raises, the chances that you’ll experience bodily harm.
Brown Things are Safe Let’s also suppose that brown things are in general safe. So again, “brown” doesn’t have the experience of bodily harm as part of its meaning either. You’re less likely to experience this around brown things than around other-colored things.
Brown Cows are Dangerous However, suppose that the small number of dangerous cows and the small number of dangerous brown things are allbrown cows. Thus the meaning of “brown cow” contains the experience of bodily harm. That experience confirms the presence of brown cows.
Brown Cows are Dangerous But how is this possible? Neither the set of experiences that is the meaning of “brown” nor the set of experiences that is the meaning of “cow” contains the experience of bodily harm.
Brown Cows are Dangerous The meaning of “brown cow” thus seems to depend on something other than the meanings of its parts, “brown” and “cow”: verificationism violates the principle of compositionality.
The Causal-Historical Theory Let’s call that baby ‘Feynman’ Feynman Feynman Feynman Feynman
The Causal-Historical Theory Let’s call that baby ‘Feynman’ Feynman Feynman Feynman Feynman Historical Chain of Transmission
The Causal-Historical Theory Feynman Feynman Feynman Feynman Denotation
No Connotations The causal-historical theory, unlike the other theories we’ve considered so far, does not use a connotation (idea, experience, definition) to determine the denotation. Denotations are determined by non-mental facts.
Direct Reference Theory The resulting view is known as direct reference theory. This is just the claim that names and natural kind terms “directly” refer to their denotations, and that connotations aren’t involved in mediating the process.
Direct Reference Theory The meaning of a name, for example, is the person named. There is nothing more to meaning than reference/ denotation.
Semantic Closure TRUE: Lois Lane believes Superman can fly. FALSE: Lois Lane believe Clark Kent can fly.
Vs. Direct Reference But notice that the two sentences differ only in that parts with the same meaning (reference) have been swapped: ‘Superman’ and ‘Kent.’ So it seems like if compositionality is true, then the direct reference theory is false.
Vs. the Use Theory Does knowing how word W1 is used and how W2 is used suffice for knowing how [W1 W2] is used? This seems unlikely.
Imagine teaching a Martian how the word ‘black’ is used. We might show it color samples or something.
Similarly we might teach the Martian how ‘people’ is used, by giving examples.
Fundamental Acceptance Property Recall that for Horwich, the fundamental acceptance property underlying all uses of ‘black’ is to apply ‘black’ to surfaces that are clearly black. Suppose we taught a Martian this. And suppose we taught a Martian how to apply ‘human’ or ‘person’ (distinguishing us from other apes). Could the Martian work out how to use ‘black person’? I think not.
Interests in Exaggeration We (humans) have a vested interest in exaggerating differences in skin tone in order to effect a certain constructed social order.
Interests in Exaggeration Unless you know about this proclivity to exaggerate, (which doesn’t affect normal color ascriptions), then you can’t predict ascriptions of the form ‘COLOR + person.’
Interests in Exaggeration Using ‘black’ (or ‘red’ or ‘yellow’) for a color and using ‘person’ for a certain sort of animal doesn’t determine how to use the ‘COLOR + person’ form.
Vs. The Use Theory The point is that complex expressions can acquire uses that aren’t determined by the uses of their parts. Consider the English insult “Mama’s boy.”
Vs. The Use Theory If you’re a child, and a male, it’s not insulting to be called a ‘boy.’ Nor is ‘Mama’ an insult. But put them together, and that’s insulting, even if you are a Mama’s boy. Just learning the use of the parts won’t tell a second-language learner of English that the whole is insulting.
Argument from Understanding The principal argument in favor of compositionality is simply the argument from our ability to understand a potential infinitude of novel utterances to the purported best explanation of this fact, compositionality.
Premise 1: Productivity English is productive: There are infinitely many grammatical, meaningful sentences of English possessing an infinite number of distinct meanings.
Premise 2: Finitude Human beings have finite minds. In particular, they can only store or remember a finite amount of information. • If the mind = the brain, the brain is finite. • There is a finite amount of time that children have to learn language.
Premise 3: The Only Game in Town It is impossible for beings with finite minds to learn/ understand productive languages unless those languages have compositional semantics.
Conclusion Since some humans do in fact learn/ understand English, it must have a compositional semantics.
Systematicity There is another argument for compositionality. It starts with the observation that English is systematic. Suppose that E1, E2, E3, and E4 are all English expressions.
When This Is True: • E1 can combine with E2 to form a grammatical sentence [E1 E2]. • E3 can combine with E4 to form a grammatical sentence [E3 E4]. • E1 is of the same grammatical category as E3 • E2 is of the same grammatical category as E4
When This Is True: Example: ‘Dogs’ can combine with ‘chase cars’ to form the sentence ‘Dogs chase cars.’ ‘Cats’ can combine with ‘eat mice’ to form the sentence ‘Cats eat mice.’ ‘Dogs’ is of the same grammatical category as ‘cats.’ (Plural Noun Phrases) ‘Chase cars’ is of the same grammatical category as ‘eat mice.’ (Verb Phrases)
Claim 1 Anyone who can understand [E1 E2] and [E3 E4] can also understand [E1 E4] and [E3 E2], when the latter are well-formed. Example: Anyone who can understand ‘dogs chase cars’ and ‘cats eat mice’ can also understand ‘dogs eat mice’ and ‘cats chase cars.’
