Learning to infer object representations, and in particular part-whole hierarchies, has been the focus of extensive research in computer vision, in pursuit of improving data efficiency, systematic generalisation, and robustness. Models which are \emph{designed} to infer part-whole hierarchies, often referred to as capsule networks, are typically trained end-to-end on supervised tasks such as object classification, in which case it is difficult to evaluate whether such a model \emph{actually} learns to infer part-whole hierarchies, as claimed. To address this difficulty, we present a SYNthetic DAtaset for CApsule Testing and Evaluation, abbreviated as SynDaCaTE, and establish its utility by (1) demonstrating the precise bottleneck in a prominent existing capsule model, and (2) demonstrating that permutation-equivariant self-attention is highly effective for parts-to-wholes inference, which motivates future directions for designing effective inductive biases for computer vision.