Modern concepts of information based in computation are centrally reliant on the idea of the system as a holistic and encompassing structure that might be complex, but never includes true indeterminacy. The unconscious of the Freudian subject on the other hand is centrally marked by an indeterminacy that is not transferable to the digital sphere. How to conceptualize these competing ontologies and their effect on the subject? The current zeitgeist more often than not implies a universal computability, especially with the genesis of modern AI. However, by taking the logical basis of computability into account a different picture appears. To demarcate where psychoanalysis and continental philosophy’s concept of the subject leave the realm of the computable, the foundational logics of Heidegger and Lacan are utilized.