SCALAR (NON-)IDENTITY AND SIMILARITY
The semantic properties of certain uses of different and the same (1) have recently attracted
considerable interest (see e.g. Beck 2000, Barker 2004, and references cited therein). An assumption
common to much of this work is that these adjectives respectively express non-identity and identity of
individuals. Under this view, basic predicative uses of different and the same like those in (2) would
denote the relations in (3). The standard view immediately accounts for the fact that different and the
same are logical complementaries (4). However, it suffers from at least two problems. First, the relations
of individual identity and non-identity cannot hold to varying degrees, but both different and the same
may occur with degree modifiers (5) (Huddleston & Pullum 2002; see also Laca & Tasmowski 2003 on
French différent). It is simply not clear how the denotations in (3) will accommodate such modification.
Second, this view does not predict that either adjective should enter into any logical relations with the
adjective (a)like, when in fact both do. Beginning with different and like, sentences of the form a and b
are more different than c and d and c and d are more alike than a and b are logically equivalent (6a). In
this, different and like pattern with antonymous gradable adjectives, which also participate in such
equivalences (6b). Turning to like and the same, their behavior in if not and or at least appositives (see
Carlson 1981) indicates that a relation of logical subordination holds between them, with the same
stronger than like (7). These facts show that the meanings of different, the same, and like ought to be
related in some principled way, but the view presented in (3) does not leave room for such relatedness.
To account for these facts, I propose that different and the same instead be taken as respectively
expressing non-similarity and maximal similarity, with like simply expressing similarity. The notion
"similarity" is formalized in terms of properties: a property counts as a similarity between two
individuals if it is shared by both, while a non-similarity is a property that distinguishes between two
individuals. Then, sentences of the form a is like b and a is different from b assert the existence of either
a similarity or a non-similarity between a and b, while sentences of the form a is the same as b assert that
every property counts as a similarity between a and b, i.e., that maximal similarity obtains (8) (see
Nunberg 1984 for a related view of the same). In previous work, I have argued that such an analysis
accounts for a variety of facts concerning the form and interpretation of "comparative" uses of different,
the same, and like (9); here, the relevance of shared or distinguishing properties to simple non-
comparative uses can be seen from grammatical restrictions on in that S clauses (McCawley 1970), which
must identify either a similarity or a non-similarity when occurring with like and different (10).
Like the one in (3), this proposal also captures the complementarity of different and the same (cf.
(4)); given the logical equivalence of ¬ and ¬, a sentence containing different expresses the negation
of the corresponding sentence with the same (compare (8a) to (8c)). However, this proposal also provides
for an understanding of their logical relations with like. The subordination of like to the same (cf. (7))
follows immediately, given that is logically weaker than (compare (8b) to (8c)). The relation
between different and like (cf. (6a)) is not so straightforward, as it requires an account of the degree
modification of different and like seen in (5a) and (6a). (NB: the modification possibilities for the same
(cf. (5b)) follow from its status as a universal quantifier.) Here, I assume that rather than simply asserting
the existence of a (non-)similarity, different and like instead relate pairs of individuals to degrees
representing the extent of (non-)similarity between them. The scale associated with like is thus ordered
by the relation in (11a), while the one associated with different is ordered by the relation in (11b). The
relations in (11a) and (11b) are inverses, which is sufficient to account for the logical equivalence in (6a);
indeed, the logical equivalence in (6b) is standardly accounted for with the assumption that the scales
associated with antonymous gradable adjectives are also inversely ordered.
An additional benefit of this proposal is that it provides some insight into why sentences like those in
(12) are not invariably false, as the proposal in (3) predicts. Such sentences can be true when the domain
of properties that count as (non-)similarities is restricted, either contextually or by adjuncts such as in all
relevant respects, to consist of only relevant properties. For example, (12b) will be true when all relevant
properties constitute similarities between my old car and my new one. Finally, note that when the domain
of properties is unrestricted, a is the same as b will entail that a and b are identical (the entailment from a
is different from b to the non-identity of a and b follows regardless of the presence of such restrictions).
EXAMPLES
(1) a. Jack and Diane live in different cities.
b. The same waiter served everyone.
(2) a. My new car is different from my previous one.
b. Water is the same as H20.
(3) a. different = xe.ye.x y
b. the-same = xe.ye.x = y
(4) Contentment isn't the same as happiness.
Contentment is different from happiness.
(5) a. My new car is {a bit, quite, very, really} different from my previous one.
b. Frozen fish is {almost, nearly, just about, not quite, roughly} the same as fresh fish.
(6) a. English and American Sign Language are more different than French and Spanish.
French and Spanish are more alike than English and American Sign Language.
b. Jack is taller than Diane. Diane is shorter than Jack.
(7) a. Your new car should look a lot like, if not the same as, your previous one.
(compare to Most, if not {all, *some}, of us enjoy our beer served warm.)
b. Your new car should look the same as, or at least a lot like, your previous one.
(compare to Most, or at least {*all, some}, of us enjoy our beer served warm.)
(8) a. My new car is different from my previous one is true in w iff P>[¬(Pw(n) Pw(o))]
b. My new car is like my previous one is true in w iff P>[(Pw(n) Pw(o))]
c. My new car is the same as my previous one is true in w iff P>[(Pw(n) Pw(o))]
(9) a. Paris looks a lot different than it used to (look).
b. Paris looks nearly the same as it used to (look).
c. Paris looks a lot like it used to (look).
(10) a. Jack is like Diane in that they both have red hair.
he has red hair *(too).
b. Jack is different from Diane in that he has red hair, while hers is brown.
*(only) he has red hair.
(11) For any individuals a, b, c, e and world w:
a. d.likew(d)(a)(b) > d.likew(d)(c)(e) iff
|{P D>: Pw(a) Pw(b)}| > |{P D>: Pw(c) Pw(e)}|
b. d.differentw(d)(a)(b) > d.differentw(d)(c)(e) iff
|{P D>: ¬(Pw(a) Pw(b))}| > |{P D>: ¬(Pw(c) Pw(e))}|
(12) a. People are really no different from computers: we take input (our perception), react, process
input, and retain memory.
b. In all relevant respects, my new car is the same as my old one.
REFERENCES
Barker, C. 2004. Parasitic scope. ms. (available at www.semanticsarchive.net)
Beck, S. 2000. The semantics of different: Comparison operator and relational adjective. Linguistics and
Philosophy 23: 101-139.
Carlson, G. N. 1981. Distribution of free-choice any. In R. Hendrick et. al. (eds.), Papers from the
Seventeenth Regional Meeting of the Chicago Linguistic Society, 8-23.
Huddleston, R. and G. Pullum. 2002. The Cambridge Grammar of the English Language.
Laca, B. & L. Tasmowski. 2003. From non-identity to plurality: French différent as an adjective and as a
determiner. In J. Quer et. al. (eds.), Romance Languages and Linguistic Theory 2001: Selected
Papers from `Going Romance' Amsterdam, 6-8 December 2001, 155-176.
McCawley, J. 1970. Similar in that S. Linguistic Inquiry 1: 556-559.
Nunberg, G. 1984. Individuation in context. In M. Cobler et. al. (eds.), Proceedings of the Third West
Coast Conference on Formal Linguistics, 203-217.