  In the area of the foundations of quantum mechanics a true industry appears
to have developed in the last decades, with the aim of proving as many results
as possible concerning what there cannot be in the quantum realm. In principle,
the significance of proving no-go results should consist in clarifying the
fundamental structure of the theory, by pointing out a class of basic
constraints that the theory itself is supposed to satisfy. In the present paper
I will discuss some more recent no-go claims and I will argue against the deep
significance of these results, with a two-fold strategy. First, I will consider
three results concerning respectively local realism, quantum covariance and
predictive power in quantum mechanics, and I will try to show how controversial
the main conditions of the negative theorem turn out to be, something that
strongly undermines the general relevance of these theorems. Second, I will try
to discuss what I take to be a common feature of these theoretical enterprises,
namely that of aiming at establishing negative results for quantum mechanics in
absence of a deeper understanding of the overall ontological content and
structure of the theory. I will argue that the only way toward such an
understanding may be to cast in advance the problems in a clear and
well-defined interpretational framework, which in my view means primarily to
specify the ontology that quantum theory is supposed to be about, and after to
wonder whether problems that seemed worth pursuing still are so in the
framework.
