Exclusive Company: Only and the Dynamics of Vertical Inference ...

io Only and the Dynamics of Vertical Inference
As recognized by Barwise & Cooper (1981: 193), quantifiers with the same
monotonicity orientation combine with and, excluding but, as seen in (21),
(21) a man and three women few violins and no cellos
some students and every professor no men and very few women
most men and any FC women no dogs and hardly any NP i cats
while monotonicity-discordant quantifiers most combine with but:
(20) John {# and/but] no woman
few women {# and/but) many men
most of the dogs {# and/but) few of the cats
(vs. most of the dogs [and/#but] a few of the cats
Crucially, only phrases pattern as downward monotonic quantifiers:
(23) many men {# and/but) only 3 women
no men {and/#but} only 3 women
4 CONVERSION AND EXISTENTIAL IMPORT
But in fact only phrases must be downward monotonic, given the converse
relation between only and all, recognized since the medievals:
(24) a. Tantum animal est homo convertitur in istam: omnis homo est animal, per
istam regulam: Exclusiva affirmativa convertitur in universalem P
(John of Holland, in Bos 1985: 27)
b. only (A, B) (only As are Bs) « all Bs are As ~ B c A
The interdefinability of exclusives and universals appears in a variety of traditional
sources, e.g. Peter of Spain's Tactatus Exponibilium (Mullally 1945: 106-7),
and is exploited, defended, or assumed—often in the form of the subset relation
in (24b))—by a bevy of moderns, including Lobner (1987), Chierchia &
McConnell-Ginet (1990: 427), de Mey (1991), Johnson-Laird & Byrne (1991:
128), Higginbotham (1994: 459-63), and von Fintel (1994, 1995), enough of a
quorum to challenge the assertion that 'these days, those who adopt this analysis
are few and far between' (von Fintel 1994: 13 5).
Given this convertibility, to say that only Democrats supported Clinton is to
say that all Clinton-supporters were Democrats. But, as has been recognized for
a couple of millennia (cf. Horn 1989: Section 1.1.3 for summary and Moravcsik
1991 for a new look), there is an existential inference, generally assumed to hold
in the pragmatics, that is characteristically associated with the assertion of a
universal. 14 Thus we can infer that (for all the speaker knows) there were indeed
Clinton-supporters; otherwise the ^//-statement would be too uninformative
to assert. 15
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