This 1962 documentary Logic by Machine (Computer and the Mind of Man) gets off to a slow start but it’s worth a watch:
From the same timeframe, 1963, there are some collected papers from a conference, where the organiser clearly had great difficulty getting comfortable with the idea of non-numerical computing, the very subject of the conference:
Advances in Programming and Non-Numerical Computation
In the first part, an introduction gives a succinct historical account of the development of programming since the invention of the digital computer, and the other four chapters discuss the theory and the developing practice of methods of communicating with the computer, particularly for non-numerical purposes. The second provides a summary of possible non-numerical work, and more detail on three particular applications, in theorem-proving, game-playing, and learning, and information retrieval.
It is hoped that this book provides a suitable introduction for a final year student seeking interesting research possibilities not too closely connected with his undergraduate work. It should also give to the intelligent layman, who is prepared to do some non-trivial reading, ideas about just what a machine can do, how it does it, and some of the methods, and the problems, of making further advances.