Truth-conditional semantics has been successful in explaining how the
meaning of a sentence can be decomposed into the meanings of its
parts, and how this allows people to understand new sentences. In this
talk, I will show how a truth-conditional model can be learnt in
practice on large-scale datasets of various kinds (textual, visual,
ontological), and how this is empirically useful, compared to
non-truth-conditional models. I will then take stock of the bigger
picture, and argue it is (unfortunately) computationally intractable
to reduce all kinds of language understanding to truth conditions. To
enable a more complete account, I will sketch a new approach to
probabilistic modelling, which maintains tractability by relaxing the
strict demands of Bayesian inference. This has the potential to
explain how patterns of language use arise as a result of
computationally constrained minds interacting with a computationally
demanding world.