Notes
[Notebook Turkey, DB 55]
[Sunday 12 January 2003 - Saturday 18 January 2003]
[page 146]
Sunday 12 January 2003
Ruben Hersh, Tymoczko page 20: 'It is not the case that a doubtful proof would become certain by being formalized. On the contrary the doubtfulness of the proof would then be replaced by the doubtfulness of the coding and programming'.
[page 147]
Insight (Hersh 20) "Nevertheless it turns out that it is understanding that verifies correctness of formal computation, not the other way round."
This is probably half true. There is nothing like formalism that works to give confidence in a process.
Monday 13 January 2003
Tuesday 14 January 2003
Wednesday 15 January 2003
Facing work on the engine transplant again [in my old vehicle]. This sort of work raises all sorts of deeper issues of environment and technology. Used oil can be repulsive, perhaps not in the same league as a dead cow, but part of a similar cycle. This is where the concept of cycle enters, and we have gradually refined it to the level of mathematical abstraction.
Mathematics abstracts from body, that is realization, but it is able to talk about embodied reality because the logical confinement that gives us the proof structure in mathematics is also operating in embodied reality, so that mathematics has been called 'unreasonably effective'. Here we take the view that the ground for this effectiveness is the constraint of consistency which we use as a bound in mathematics as well as everywhere else. At the lowest physical level, any inconsistency that we might potentially observe is masked by uncertainty. Like all other parts of reality (?), mathematics can reflect on itself, but as Gödel showed, each reflection implies transfinite growth. Insofar as the cardinal of a set of logical symbols in ℵ0, the cardinal of the set of Gödel numbers of all possible expressions made with these symbols is ℵ1. Are the Gödel numbers dense in the space ℵ1, ie is every element of ℵ1 the Gödel number of some expression. Yes? No? Yes - position dependent systems of representing numbers with strings ℵ0 long of ℵ0 different symbols can represent ℵ1 different numbers, so we can
[page 148]
say that each of the ℵ1 different numbers represents an expression which is a unique string.
Thursday 16 January 2003
Friday 17 January 2003
On the Theology Company white and green papers. Defining our positions and policies.
Denzinger is in effect a compendium of Roman Catholic Church white papers - or are these laws? Denzinger.
discussion (green), policy (white), decision (law) execution (government)
Most documents of Vatican II are 'white papers' Abbott.
The Theology Company can begin by matching them and maybe adding or deleting some issues. Vatican II developed 16 texts.
1. Lumen Gentium - Dogmatic Constitution on the Church, ie the Church's self-definition - same for The Theology Company: 'what are we?'
Is The Theology Company a religion? Yes and no.
