The digital transfer of the mind to a computer system (i.e., mind uploading) requires representing the mind as a finite sequence of bits (1s and 0s). The classic “stored-program computer” paradigm, in turn, implies the equivalence between program and data, so that the sequence of bits themselves can be interpreted as a program, which will be algorithmically executed in the receiving device. Now, according to a previous proof, on which this paper is based, a computational or algorithmic machine, however complex, cannot be free (in the sense of ‘self-determined’). Consequently, a finite sequence of bits cannot adequately represent a free mind and, therefore, a free mind cannot be digitally transferred, quod erat demonstrandum. The impossibility of making this transfer, as demonstrated here, should be a concern especially for those who wish to achieve it. Since we intend this to be a rigorous demonstration, we must give precise definitions and conditions of validity. The most important part of the paper is devoted to explaining the meaning and reasonableness of these definitions and conditions (for example that being truly free means being self-determined). Special attention is paid, also, to the philosophical implications of the demonstration. Finally, this thesis is distinguished from other closely related issues (such as other possible technological difficulties to “discretize” the mind; or, whether it is possible to transfer the mind from one material support to another one in a non-digital way).