paradigms
The discussion hangs around three paradigms for mathematical software, numeric, symbolic and logical.
The first two are already mature, the third is speculative.
Each of these paradigms more or less subsumes the previous one, in terms of its capabilities, with a couple of exceptional aspects which we will mention, both connected with rigour.


logical power
When it comes to the logical paradigm, I want to distinguish two levels of capability.
I associate these with the terms engineering logic and intelligent logic.
The second is what you get if you manage (in this restricted logical domain) to crack the machine intelligence problem.
I consider how to do engineering logic in a way which is sympathetic to, but independent of, intelligent logic.

