Imagine a machine, equipped with sensors, receiving a stream of sensory information. It must, somehow, make sense of this stream of sensory data. But what, exactly, does this involve? We have an intuitive understanding of what is involved in “making sense” of sensory data – but can we specify precisely what is involved? Can this intuitive notion be formalized? In this thesis, we make three contributions. First, we provide a precise formalization of what it means to “make sense” of a sensory sequence. According to our definition, making sense means constructing a symbolic causal theory that explains the sensory sequence and satisfies a set of unity conditions that were inspired by Kant’s discussion in the first half of the Critique of Pure Reason. According to our interpretation, making sense of sensory input is a type of program synthesis, but it is unsupervised program synthesis. Our second contribution is a computer implementation, the Apperception Engine, that was designed to satisfy our requirements for making sense of a sensory sequence. Our system is able to produce interpretable human-readable causal theories from very small amounts of data, because of the strong inductive bias provided by the Kantian unity constraints. A causal theory produced by our system is able to predict future sensor readings, as well as retrodict earlier readings, and impute missing sensory readings. In fact, it is able to do all three tasks simultaneously. The engine is implemented in Answer Set Programming (ASP) and induces theories expressed in an extension of Datalog that includes causal rules and constraints. We test the engine in a diverse variety of domains, including cellular automata, rhythms and simple nursery tunes, multi-modal binding problems, occlusion tasks, and sequence induction IQ tests. In each domain, we test our engine’s ability to predict future sensor values, retrodict earlier sensor values, and impute missing sensory data. The Apperception Engine performs well in all these domains, significantly out-performing neural net baselines. These results are significant because neural nets typically struggle to solve the binding problem (where information from different modalities must somehow be combined together into different aspects of one unified object) and fail to solve occlusion tasks (in which objects are sometimes visible and sometimes obscured from view). We note in particular that in the sequence induction IQ tasks, our system achieves human-level performance. This is notable because the Apperception Engine was not designed to solve these IQ tasks; it is not a bespoke hand-engineered solution to this particular domain. – Rather, it is a general purpose system that attempts to make sense of any sensory sequence, that just happens to be able to solve these IQ tasks “out of the box”. Our third contribution is a major extension of the engine to handle noisy and ambiguous data. While the initial implementation assumes the sensory input has already been preprocessed into ground atoms of first-order logic, our extension makes sense of raw unprocessed input – a sequence of pixel images from a video camera, for example. The resulting system is a neuro-symbolic framework for distilling interpretable theories out of streams of raw, unprocessed sensory experience.