A comparative analysis for resemblance
Cécile Meier
Goethe-Universität, Frankfurt
1
Introduction
This paper contains a new semantic analysis for the verbal expression resemble. It is
argued that resemble is best conceived as a degree predicate, very much in analogy to
(transparent) gradable adjectives like close to (see Mador-Haim & Winter 2007). This
move can explain why resemble happily combines with the traditional positive, comparative and superlative operators, degree intensifiers and the like, and it meets the philosophical tradition that resemblance is a 4-place comparative relation (Lewis 1986; Williamson
1988). Nevertheless, resemble is an intentional idiom (i.e., not transparent): it is well
known that
• this predicate shows an ambiguity with respect to the specificity of its object: This
horse resembles a unicorn (a particular mythical object or just any unicorn),
• it does not allow for substitution of the object by extensionally equivalent expressions, and
• it does not allow for an existential generalization with respect to the object.
These (and related) phenomena are explained by combining Zimmermann’s (1993) property analysis for intentional predicates and the theory of non-existent objects by Parsons
(1980) with the insights of von Stechow (new positive operator) and Heim (relational
meaning for gradable predicates) for a comparative semantics (see, e.g., von Stechow
2006).
2
The Problem
So-called intensional predicates with a comparative meaning component differ from predicates like seek in that a propositional analysis is not possible for them. (i) We do not
observe ambiguities with adverbial modification, as exemplified in (1). And (ii) binding
effects contradict a propositional analysis. In (2) only the reflexive pronoun is licit. A
propositional analysis would predict that an anaphoric pronoun should also be available.
(1) Mary resembles tomorrow a queen. (Kartunnen, Ross, McCawly).
a. ‘Mary resembles something that will be a queen tomorrow.’
b. ‘Tomorrow, Mary will resemble something that is a queen.’
(2) Maryi doesn’t resemble herselfi /*heri anymore. (Ross)
The impossibility of a propositional analysis for predicates like resemble and the restriction on quantifiers (i.e., only indefinites, definite descriptions and proper names may
get the unspecific reading) motivated the property analysis for intentional predicates.
Zimmermann (1993) proposed the rule in (3) for resemble on the basis of prototypical
properties.
(3) resemble(@)(x, P ) = 1 iff there is a (possibly complex) property P ∗ such that:
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(i) P ∗ (@)(x) = 1 and
(ii) For all y, j: if y is a prototypical representative of objects that have P , then
P ∗ (j)(y) = 1.
This rule explains the unspecific readings, and it explains why genuine quantifiers cannot
occur in the object position of this predicate unless they get a specific reading, compare
(4) (and see Moltmann 1997: 18 for discussion).
(4) This horse resembles every unicorn.
However, firstly, this rule cannot capture the subject opacity of constructions with resemble, as observed in (5).
(5) A unicorn resembles a horse.
Second, the notion of prototypicality in the definition is problematic: It is odd to say that
a Ferrari resembles a tomato, although both objects prototypically share the color red.
Zimmermann’s proposal cannot predict the oddity. Moreover, thirdly, and most importantly, it is not clear how comparative expressions interact with the notion of ‘resemble’
in terms of prototypical properties.1
3
Comparative Similarity
I will mainly concentrate on the last phenomenon: comparative expressions of resemblance. Consider the sentence in (6).
(6) Mary resembles her mother more than Mary’s brother resembles his father.
This sentence expresses a comparison between similarities/differences of pairs of individuals with respect to the looks, the character, the height, hair color or the like (some
salient property). The dimension of comparison or the kind of features that are compared
is left unexpressed in this sentence, however. Comparative similarity judgments may be
underspecified with respect to the dimension of comparison. The respects of similarity
could easily be made explicit in terms of a with respect to-phrase, as in (7).
(7)
a. Mary resembles her mother more
with respect to their height.
b. Mary resembles her mother more
with respect to their looks.
c. Mary resembles her mother more
with respect to their hair color.
d. Mary resembles her mother more
with respect to their character.
than Mary’s brother resembles his father
than Mary’s brother resembles his father
than Mary’s brother resembles his father
than Mary’s brother resembles his father
We may vary the respects of similarity, but the common semantic core of the construction
remains invariant.
Assume for the ease of exposition that we compare the family members in (6) with
respect to their height as in (7a). Height has the advantage of being measurable extensively. The comparison process for individuals with respect to their height is well
1
Note that Maienborn (2006: 5f) analyzes resemble in terms of exemplification of so called Kimian
states that are abstract entities and resemble degrees. But this proposal offers no solution to the intensionality problem, and it is not possible to integrate it into the semantics of degree.
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understood.2 Under these assumptions, the sentence in (6) may be paraphrased as in (8).
It must be contextually salient that we are comparing heights.
(8) ‘The difference between Mary’s height and her mother’s height is smaller than the
difference between Mary’s brother’s height and their father’s height.’
Note that the paraphrase has the schema in (9).
(9) For any measurement function µ and any individuals a, b, c, d:
Diff(µ(a), µ(b)) < Diff(µ(c), µ(d)).
We might visualize the paraphrase as in (10), assuming that b abbreviates Mary, a
abbeviates Mary’s mother, c Mary’s brother, and d Mary’s father.
z
}|
{ Diff(µ(a),µ(b))
(10) a
b
c
d
|
{z
} Diff(µ(c),µ(d))
Not only the dimension of comparison may be left unexpressed linguistically. Consider the
elliptical constructions in (11) and (12). In (11) the second element of the compared pairs
is implicitly kept invariant, in (12) the first element of the compared pairs is implicitly
kept invariant.
(11) Mary resembles her mother more than Mary’s brother resembles her mother.
Diff(height(a), height(b)) < Diff(height(c), height(b))
(12) Mary resembles her mother more than Mary resembles her father.
Diff(height(a), height(b)) < Diff(height(a), height(d))
The dimension for the two pairs of individuals can be identical as in the previous
examples. But different dimensions of do not necessarily lead to incommensurability.
Consider (13).
(13) Mary resembles her mother more with respect to their height than with respect to
their character.
Diff(height(a), height(b)) < Diff(char(a), char(b))
Sentence (14) can be viewed as a variant of the comparative construction that reminds
us of the positive constructions with respect to adjectival comparison. It means that the
difference in properties between a pair of individuals is smaller than some contextually
supplied standard of comparison c.
(14) Mary resembles her mother.
Diff(height(a), height(b)) < c
4
The Semantics
In order to derive the paraphrases, I rely on the comparative semantics in the tradition
of von Stechow and Heim. The ontology for the semantics includes scales, degrees as
points on a scale and segments consisting of stretches on that scale. Segments on a scale
2
I refer the reader to Tversky (1977) and Hahn et al. (2003) for other strategies of measuring similiarty.
Tversky proposed to weigh common and distinctive features of individuals against each other. Hahn et
al. proposed to compare sets of putative transformations from one individual to another.
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come in three different varieties: so-called positive extents (initial segments), negative
extents (final segments) and differentials (intermediate segments).
A measure function assigns an ordinary degree to any individual in the domain. The
empirical order between the individuals must be preserved by the order of the values of
this function and there may be measuring units used with the scale. We may consider a
scenario as in (15), where height is a measure function that assigns every individual its
(maximal, actual) height.
(15)
a.
b.
c.
d.
height(Mary) = 1.70m
height(Mary’s brother) = 1.75m
height(Mary’s mother) = 1.67m
height(Mary’s father) = 1.80m
In a first step, I propose the following semantics for resemble. This version has to be
refined in order to capture the unspecified readings observed with indefinites in object
position of resemble (see below). The relation expressed is a four-place relation that takes
a measure function (the denotation of the with respect to-phrase), two individuals and a
degree as arguments, and gives a truth value. Note that the comparisons between the
differences pattern with negative polar adjectives in general. The differences compared
are negative extents: resemble collects a set of degrees that are greater than the difference
between the compared items.
(16) [[resemble]] = λµλyλxλd[Diff[µ(x), µ(y)] < d]
The measure function µ contributes two degrees that can be viewed as an intermediate
segment on a scale. “Diff” is an abbreviation for the function that measures the distance
between the two limits of that segment. It may be defined as in (17).
(17) Diff(D) = max(D) − min(D)
Maximality for degrees is defined as usual. Minimality is defined analogously.
(18) If D is a set of degrees and ≥ is a suitable ordering relation, then
max(D) = ιd[d ∈ D & ∀d′ ∈ D[d ≥ d]].
It is obvious how to combine these semantics with the comparative and positive
operator introduced in adjectival semantics. The comparative operator more/-er is a
relation between sets of degrees.
(19) [[more/-er]] = λD∗ λD[{d: D(d)} ⊇ {d: D∗ (d)}]
Consider our sentence in (6) repeated in (20a) again. (20a) is represented by the
logical form in (20b) à la Bresnan (1973). The than-clause is assumed to be attached to
the degree operator, and than provides the binder of the degree variable.
(20)
a. Mary resembles her mother (in height) more than Mary’s brother resembles
his father (in height).
b. more/-er(λd[Mary’s brother[ d [resembles his father (in height)]]],
λd[Mary[ d [resembles her mother (in height)]]])
The truth conditions are stated in (21). Given the assumptions in (15), (21a) is
equivalent to (21c).
(21)
a. {d: Diff(height(Mary), height(Mary’s mother)) < d} ⊇
{d: Diff(height(Mary’s brother), height(Mary’s father)) < d}
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b. {d: Diff(1.70m, 1.67m) < d} ⊇ {d: Diff(1.75m, 1.80m) < d}
c. {d: 0.03m < d} ⊇ {d: 0.05m < d}
The sentence is true if the difference in height between Mary and her mother is smaller
than the difference in height between Mary’s brother and her father.
The positive operator posits a relation between a set of degrees and a truth value.
It presupposes that the relevant scale is partitioned into a neutral zone, a positive zone
and a negative zone. N is a function that assigns an interval scale S a neutral zone. In
our case this is the zone where we are indifferent whether two individuals resemble each
other or not with respect to some measurement. The operator is defined as in (22).
(22) [[posS,N ]] = λD[∀d[d ∈ N (S) → d ∈ D]], where N is the neutral zone on the scale
S.
The positive operator is a universal quantifier over degrees.
(23)
a. Mary resembles her mother (in height).
b. posS,N (λd[Mary[ d [resembles her mother (in height)]]])
The truth conditions are stated in (24). Given the assumptions in (15), (24a) is equivalent
to (24b).
(24)
a. ∀d[d ∈ N (S) → d ∈ {d: Diff(height(Mary), height(Mary’s mother)) < d}]
b. ∀d[d ∈ N (S) → d ∈ {d: 0.03m < d}]
It is true if the difference between Mary’s height and her mother’s hight does not exceed
any of the values in the neutral zone. Which degrees there are in the neutral zone must
be determined contextually.
The value for µ may be contextually supplied, as well, in case no with resepect tophrase is part of the sentence. What counts as a salient measure function may depend on
the context of utterance but also on psychological parameters of stereotypical perception.
This assumption accounts for the unacceptability of the sentence in (25).
(25) This Ferrari resembles a tomato.
Salient respects of resemblance are the form or function of an object but obviously not
the color as it seems. As soon as we add the phrase with respect to color to the sentence
in (25), the unacceptability disappears.
So far we only considered constructions with definites in the object position of resemble. For constructions with indefinites, I assume that my ontology provides a measure
function that maximalizes the measures of the individuals that fall under the indefinite
(see Heim-Mador and Winter’s location function). µ∪ may be defined on the basis of µ
as in (26).3
(26) For any property P : µ∪ = max{µ(x) : P (x)}.
Let us call this measure function unified measure function in accordance with MadorHaim & Winter (2007), although this operation is just some form of maximality operator
well known in comparative semantics.
Following Zimmermann, I propose that resemble combines with an argument of the
predicate type. Its definition must be revised accordingly, as in (27).
3
Note that other operations instead of maximalization that have the average measure of the all the
individuals as a value, e.g., or the expected value or some vale for closeness to a prototype are also
imaginable. This point needs further investigation. The problems wee encounter are akin to problems in
defining the standard of comparison in genuine comparatives.
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(27) [[resemble]] = λµλP λxλd[Diff(µ(x), µ∪ (P )) < d]
Consider an application of this definition for a sentence as in (28a). The LF of this
sentence is analogous to the sentence with a definite description in the object poition.
(28)
a. Mary resembles a top model (in height).
b. posS,N (λd[Mary[ d [resembles a top model (in height)]]])
The truth conditions are stated in (29).
(29) ∀d[d ∈ N (S) → d ∈ {d: Diff(height(Mary), height∪ (a top model)) < d}]
In a semantic model where all the top models range between 1.75m and 1.85m in height,
Mary resembles them in height if her height is close to that of the tallest top model (by
maximalization). Maybe other values for the cup-operator like the central tendency of
top model heights are more suitable in such cases: see footnote 3. In our little scenario,
however, the sentence is false, since Mary’s height is only 1.70m.
This definition of resemble is compatible with proper names and definites in the
object position. I assume a lifting operation for these types of argments. Quantifers are
only interpretable by some sort of quantifying-in operation (or quantifier raising).
Let me note before passing on that differ from is (at least on one reading, see Beck
2000) just the positive polar variant of resemble. This construction may be defined as in
(30).
(30) [[differ from]] = λµλP λxλd[Diff(µ(x), µ∪ (P )) ≤ d]
Consider the minimal pair in (31) for a comparison of resemble and differ.
(31)
a. His car resembles a truck.
b. His car is different from a truck.
Treating differ from and resemble as some kind of antonyms captures the intuition that
we consider the psychological distance between the car and the most typical truck as small
in the case of resemble, as in (31a), but as big in case of differ, as in (31b).
5
Further Applications
The restriction on quantifiers in the object position of resemble is readily derived since
resemble only takes predicates as internal arguments. In this respect I am following plainly
the solution of Zimmermann (1993).
The specificity ambiguity amounts to an ambiguity in scope of the indefinite with
respect to the comparative/positive operators. Consider, for example, the sentence in
(32). (32a) and (32c) are the logical forms for the unspecific and the specific reading,
respectively.
(32) Tom’s horse resembles a unicorn.
a. posS,N (λd[Tom’s horse[ d [resembles a unicorn]]])
b. ∀d[d ∈ N (S) → d ∈ {Diff(µ(Tom’s horse), µ∪ (a unicorn)) < d}]
c. a unicorn λx[posS,N (λd[Tom’s horse[ d [resembles x]]])]
d. ∃x[unicorn(x) &
∀d[d ∈ N (S) → d ∈ {Diff(µ(Tom’s horse), µ∪ (λy[y = x])) < d}]]
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(32b) states the truth conditions for the unspecific reading, and (32d) the truth conditions
for the specific reading. (32d) may undergo existential closure, or it may be interpreted
within a DRT-like framework. However, it should be noted that neither reading is intensional. This view is only tenable if we assume that resemble is an extranuclear predicate
in the sense of Parsons (like worship). Unicorns are existing though actually non-existent,
mythical objects. And resemble may be true of such objects. At this point I have to refer
the reader to Parsons (1980) for the details.
The lack of existential generalisation and the lack of substitutivity may also be
accounted for in terms of extranuclearicity. The substitution of the expression a unicorn
with a centaur is not licit because the expressions refer to different sets of non-existent
individuals.
(33)
a. Tom’s horse resembles a unicorn.
b. Tom’s horse resembles a centaur.
A generalization to the existence of unicorns or centaurs is not possible, because they do
not exist in the actual world.
Subject opacity may be accounted for in terms of genericity, see Carlson & Pelletier
(1995). The genericity operator construes a tripartite structure. The restriction contains
the indefinite, while the scope of the operator contains the property of resembling a horse,
as in (34a).
(34) A unicorn resembles a horse.
a. gen(unicorn λx[posS,N (λd[x [ d [resembles a horse]]])])
b. genx(unicorn(x), ∀d[d ∈ N (S) → d ∈ {d: Diff(µ(x), µ∪ (a horse)) < d}])
Note that this correctly predicts that there is no restriction on genuine quantifiers for the
subject position and indefinites do not get a universal interpretation.
6
Conclusion
I am following Zimmermann (1993) in postulating the property analysis for predicates like
resemble. Morever, I hope to have shown that a comparative semantics is mandatory for
resemble. The analysis is apt to explain the specificity ambiguity for these constructions
without regressing to a propositional analysis for the construction. An intensional analysis
is not necessary, and a propositional analysis is not necessary either. Resemble is a degree
predicate, and resembles worship more than seek. Non-existent objects are needed in
order to analyse the case of worship. That is, the ontology does not get enriched by
comparative constructions. Worship does not show the specificity ambiguity, since it is
no comparative construction. I conclude that the specificity ambiguity may have two
reasons: either the predicate is intensional or it is comparative.
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