Recently I picked it back up. I pinpointed where my frustration started, page 10. I didn't get it, and was lost from there on. Berlinski starts his story about the origins of the idea of the algorithm, with Leibniz and his work in logic. According to Berlinski, very little had happened in formal logic since Aristotle and his syllogisms. With the syllogism, Aristotle codified inference.
- All men are mortal
- Socrates is a man
- Therefore, (I can infer that) Socrates is mortal
- ∀ x (Man(x) → Mortal(x))
- ∴ Mortal(Socrates)
That, of course, is what Berlinski's example in the book shows, only I couldn' t follow it. The reason it is important is that it means inference can be achieved with a mechanical procedure of substitution.