Superlatives and Comparatives Carl Pollard Department of - - PowerPoint PPT Presentation

Superlatives and Comparatives

Carl Pollard

Department of Linguistics Ohio State University

May 16, 2012

Carl Pollard Superlatives and Comparatives

External Superlatives

• a. The meanest dog [in the neighborhood, namely Butch] bit

Felix.

• b. Kim climbed the tallest mountain [on Earth, namely

Everest].

Carl Pollard Superlatives and Comparatives

Internal, or Focus-Sensitive, or Associate Superlatives

• a. The meanest dog bit Felix.

Paraphrase: The (meanest) dog that bit Felix was meaner than the (meanest) dog that bit any other entity (in the relevant comparison set).

• b. Kim climbed the tallest mountain.

Paraphrase: The (tallest) mountain that Kim climbed was taller than the (tallest) mountain that any other entity (in the relevant comparison set) climbed. Note: Boldface indicates a focal (H*) accent. In certain contexts, the superlative phrase might also bear a contrastive-topic (L+H*) accent.

Carl Pollard Superlatives and Comparatives

An Ambiguous Associate Superlative Sentence

• a. Kim owes Sandy the most.
• b. First reading: The amount Kim owes Sandy exceeds the

amount anyone else owes Sandy.

• c. Second reading: The amount Kim owes Sandy exceeds the

amount Kim owes anyone else. Note: we can force the first (second) reading by placing the focal accent on Kim (Sandy).

Carl Pollard Superlatives and Comparatives

A Triply Ambiguous Associate Superlative Sentence

• a. Kim thinks Sandy makes the most.
• b. First reading: Kim thinks: Sandy makes more than anyone

else makes.

• c. Second reading: Kim thinks Sandy makes more than s/he

(Kim) thinks anyone else makes.

• d. Third reading: Kim thinks Sandy makes more than anyone

else thinks Sandy makes. Note: We can force the third reading by placing the focal accent

• n Kim, but the sentence is ambiguous between the first two

readings when the focal accent is on Sandy.

Carl Pollard Superlatives and Comparatives

Pretheoretical Explanation

The superlative and the associate have adjacent scope (‘parasitic scope’ or ‘tucking in’). If Kim is focused, then they have to scope at the root clause (because operators can raise but not lower). If Sandy is focused, then there is ambiguity as to whether they scope in the root clause or the complement clause.

Carl Pollard Superlatives and Comparatives

Toward an Analysis of Superlatives

• a. Fido cost the most.
• b. We take this to mean that Fido is the unique maximizer of

the function that maps (relevant) entities to their prices.

• c. Something’s price is the maximum amount that it costs.
• d. So our target semantics for this sentence is

(um Fido λx.(max λd.(cost d x))) where the function um is subject to the meaning postulate

• e. ⊢ um = λx.λf .∀y((y = x) → (f x) > (f y)):

e → (e → d) → t (here d is the type of (monetary) degrees)

• f. (d) simplifies to:

∀y((y = Fido) → ((max λd.(cost d Fido)) > (max λd.(cost d y)))) But how do we get (d)?

Carl Pollard Superlatives and Comparatives

Three Kinds of Comparatives

• a. Jo owes more than five dollars to Bo. (simple comparative)
• b. Jo owes more than Yo spent d on Fido to Bo. (comparative

(sub)deletion)

• c. Jo owes more to Bo than Kim. (remnant comparative, aka

phrasal comparative)

• d. Jo owes more to Bo than to Kim. (remnant comparative)

Note: In the simple and subdeletion examples, the than-phrase can be extraposed; while in remnant comparatives, the than phrase must extrapose to the right of both the comparative morpheme and (possibly focally accented) phrase with which it is compared (the associate).

Carl Pollard Superlatives and Comparatives

Preliminary Observations

• a. All comparatives contain a comparative morpheme, and

a phrase introduced by either than or as.

• b. In simple comparatives, the complement of than is a

degree phrase (Deg).

• c. In subdeletion comparatives, the than-complement is a

sentence that appears to have a Deg missing (in traditional terminology, subdeleted), indicated by d.

• d. Each remnant comparative has two phrases, optionally

bearing focal pitch accents, which, intuitively, denote the two things being compared. One of them, called the remnant, is the than/as complement; and the other is called the associate.

• e. Semantically, each sentence expresses a comparison

between two degrees belonging to the same scale (e.g. the scale whose members are monetary values, such as the one denoted by five dollars).

Carl Pollard Superlatives and Comparatives

Informal Meaning Analysis

• a. The (maximum) amount that Jo owes to Bo exceeds five

dollars.

• b. The (maximum) amount that Jo owes to Bo exceeds the

(maximum) amount that Yo spent on Fido.

• c. The (maximum) amount that Jo owes to Bo exceeds the

(maximum) amount that Kim owes to Bo.

• d. The (maximum) amount that Jo owes to Bo exceeds the

(maximum) amount that Jo owes to Kim.

Carl Pollard Superlatives and Comparatives

Slightly More Formal Meaning Analysis

• a. Jo owes more than five dollars to Bo. (simple comparative)

(lub λd.(owe bo d jo)) > $5

• b. Jo owes more than Yo spent d on Fido to Bo. (comparative

subdeletion) (lub λd.(owe bo d jo)) > (lub λd.(spend fido d yo))

• c. Jo owes more to Bo than Kim. (remnant comparative)

(lub λd.(owe bo d jo)) > (lub λd.(owe bo d kim))

• d. Jo owes more to Bo than to Kim. (remnant comparative)

(lub λd.(owe bo d jo)) > (lub λd.(owe kim d jo))

Carl Pollard Superlatives and Comparatives

Fine Points

For simplicity we stick to extensional analysis, using basic types e, t, and d (degrees). We would need (hyper-)intensional types, e.g. degree concepts, for non-rigid degree expressions like Fido’s price. For simplicity we pretend the only scale is degrees of monetary value, axiomatized as a linear order (hence an upper semilattice). In a more complete analysis of associate superlatives and remnant comparatives, we must take into consideration the presupposition that the context provides a salient (property whose extension is the) comparison set (of which the denotation of the associate is a member).

Carl Pollard Superlatives and Comparatives

Some Even Finer Points

In a richer fragment, we would need different types for degrees in different scales, e.g. linear extents, areas, volumes, masses, velocities, etc. We axiomatize each degree type to be an upper semilattice, so that every finite nonempty set of degrees has a lub. Technically, we use least upper bounds (lub] rather than the usually assumed maximums. Concomitantly, we require that all nonempty sets of degrees (not just finite ones) have a lub. For a linear scale such as monetary values. this requires adjoining a top element that represents having infinite monetary value. Without these assumptions, analyses of subdeletion tend to fail for unexpected, nonlinguistic, reasons.

Carl Pollard Superlatives and Comparatives