‘Halt! What goes there?’ looks at some results about what formal reasoning can and can’t do, and some of the philosophical implications of these facts. It considers the workings of computers and explains computations—or algorithms. It asks if there is an algorithm we can apply to a program and inputs to determine whether or not a computation with that program and those inputs terminates, discussing Georg Cantor’s Halting Theorem along with diagonalization. The answer is no and this is what Alan Turing proved. The Church–Turing Thesis, which claims that one can write a computer program for every algorithm, is also considered.