Functional Distributional Semantics (FDS) models the meaning of words by truth-conditional functions. This provides a natural representation for hypernymy but no guarantee that it can be learnt when FDS models are trained on a corpus. In this paper, we probe into FDS models and study the representations learnt, drawing connections between quantifications, the Distributional Inclusion Hypothesis (DIH), and the variational-autoencoding objective of FDS model training. Using synthetic data sets, we reveal that FDS models learn hypernymy on a restricted class of corpus that strictly follows the DIH. We further introduce a training objective that both enables hypernymy learning under the reverse of the DIH and improves hypernymy detection from real corpora.