  We draw attention to one specific issue raised by Ioannidis (2005), that of
very many hypotheses being tested in a given field of investigation. To better
isolate the problem that arises in this (massive) multiple testing scenario, we
consider a utopian setting where the hypotheses are tested with no additional
bias. We show that, as the number of hypotheses being tested becomes much
larger than the discoveries to be made, it becomes impossible to reliably
identify true discoveries. This phenomenon, well-known to statisticians working
in the field of multiple testing, puts in jeopardy any naive pursuit in (pure)
discovery science.
