Then, using the universal quantifier
, '[for all][epsilon]>0'
We've been concerned here with children's knowledge of the linguistic principles regulating the interaction between the universal quantifier
and negation in sentences like (19) and (20) below:
The use of universal quantifiers
to comprehend and express the for all and every phrases is more natural and intuitive than negating existential quantifiers.
MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]  We therefore will assume that the universal quantifier
in [Phi] is strict.
When Lukasiewicz reinterprets Aristotle's inferential necessity as a universal quantifier
, he adds: "this, of course, is all known to students of modern formal logic, but some fifty years ago, it was certainly not known to philosophers.
Carlson observes that (11a), an example with a book, and (11b), an example with some books, are ambiguous in at least two ways; a book/some books can take either a wide scope or a narrow scope over the universal quantifier
Second, there was a strong effect of the type of universal quantifier
used on the subject.
Gentzen's contribution is important even if his main concern was not that of giving a semantic explanation, because he makes a clear and explicit use of the notion of 'proof from premises' to define both negation and the conditional, and introduces a definition of the universal quantifier
somehow connected to it: the definition in terms of 'proofs with free variables', which has later been adopted by other authors, such as Per Martin-Lof or Goram Sundholm.
In other words, despite the experimenter's use of any, children refrained from using any in upward entailing contexts, such as the nuclear scope of the universal quantifier
Zubizarreta proposes that the binding configuration in (82), (83), and (84) is established at AS, where the universal quantifier
is represented as a topic.
As additional evidence, note that a universal quantifier
in the position of to no relatives in (1b) can distribute over a direct object on its left:
With a number of pragmatic and syntactic tests like focusing, wh binding, and the interaction between negation and the universal quantifier
dou, we show that a threefold distinction is necessary.