Compositionality is composability without emergence

Compositionality is composability without emergence.

I claim the opposite of compositionality is emergent effects. The common definition of emergence is a system being ‘more than the sum of its parts’, and so it is easy to see that such a system cannot be understood only in terms of its parts, i.e. it is not compositional. Moreover I claim that non-compositionality is a barrier to scientific understanding, because it breaks the reductionist methodology of always dividing a system into smaller components and translating explanations into lower levels.

Hedges, 2017, On Compositionality

Compositionality is a powerful property because it allows us to decompose a problem into approachable pieces, analyze those pieces saparately, and arrive at the answer to the whole. Compositionality allows us to scale our mathematical reasoning.

Type theory is the field of mathematics that studies compositionality.

I’m interested in composition specifically because it can provoke emergence. Emergence requires a mechanism of composition.