The writing process of the paper on the Church-Turing thesis, random processes and platonism has come to an end. The paper is forthcoming in Philosophia Mathematica . A more or less final version of the paper is available here . (wrt to earlier versions, I added a bunch of remarks and answers to possible counterarguments, explained what Church randomness is and why Church-random sequences are not Turing-computable and elaborated on the intuitive source of the conceptual conflation involved). Many thanks to Leon Horsten , Liesbeth De Mol , Robert Thomas , Jeffrey Ketland , Gualtiero Piccinini , Stanisław Dercz and two anonymous referees for discussion and comments.