Cognitive processes are often modelled in computational terms. Can this still be done if only minimal assumptions are made about any sort of representation of reality? Is there a purely knowledge-based theory of computation that explains the key phenomena which are deemed to be computational in both living and artificial systems as understood today? We argue that this can be done by means of techniques inspired by the modelling of dynamical systems. In this setting, computations are defined as curves in suitable metaspaces and knowledge is generated by virtue of the operation of the underlying mechanism, whatever it is. Desirable properties such as compositionality will be shown to fit naturally. The framework also enables one to formally characterize the computational behaviour of both knowledge generation and knowledge recognition. The approach may be used in identifying when processes or systems can be viewed as being computational in general. Several further questions pertaining to the philosophy of computing are considered.