Disclaimer: don't read this unless you are already interested in Carl Hewitt's direct logic.
Carl Hewitt's Direct Logic is a strange thing, if it is a thing at all. However, part of the mystery stems only from communication problems. It is hard to understand because it violates the following standard assumptions without sufficient mention or discussion --- though (some of) the violations might have a point in software engineering. However, it's still not clear whether (a) these problems can all be solved satisfactorily (b) .
- A conventional logic has a syntax in the usual sense, so that the set of judgements is countable. Direct Logic's judgements can refer to an uncountable set of actors. Therefore, Direct Logic's judgements cannot be encoded through Gödel's natural numbers.
- Conventionally, proof checking is decidable. It's unclear to me how Direct Logic's proof checking can be decidable; but maybe it only looks at a finite part of each actor. But if proof-checking is decidable, why can't you turn an ex