Review

Summary

Together these 7 entities form the basis for all research, scientific study, knowledge, and related phenomena.

In this case, L7-Wonder enables and infuses the whole Inquiry framework with curiosity and a readiness to be surprised. This provides for openness, subtlety and new possibilities. Together with L6-Judgement, it enables the effective use of L5-Relations, L4-Measurement, L3-Comparisons, L2-Concepts & L1-Data in research of all sorts.

Popper's criteria for an analytic model was: "does it proceed from some simple, new and powerful unifying idea about some connection or relation between hitherto unconnected things?" (p.241 in Conjectures & Refutations, 1974).

The simple and powerful unifying idea here is human purpose brought into focus as we move from the reception of impressions (L1) to the effecting of actions based on understanding relations (L5).

Mathematical Association

L	Elements	Function	Use of Numbers	Use of ' = '	Use of ' 0 '
7	Wonder	To activate the need to know.	n/a	n/a	n/a
6	Judgement	To maximize conviction.	To assign a probability	n/a	n/a
5	Relation	To enable understanding that supports action.	To formulate	is a function of e.g. y = f(x)	Metaphorical e.g. not relevant, not useful.
4	Measurement	To provide general application.	To calculate	is absolutely equal to	Arithmetical zero No quantity Lowest possible value
3	Comparison	To apportion value.	To order (or rank)	is equivalent to	Equi-valent Equilibrium Neutral point
2	Concept	To reduce confusion.	To label	is identical to	Not used Non-existence
1	Data	To make evident what is hidden or unnoticed.	To count	is an example of	Absence Empty set

Dichotomizing the Hierarchy

While all divisions are possible, two divisions stand out

The lower 5 levels specify (represent) all fundamental forms of representational activity that constitute inquiry.

Between L5 and L6

The lower 5 levels are forms of actual representation of the world. L5 completes the system by connecting examples of any level including its own (but not higher levels). This lower division describes all possible practical and concrete operations of inquiry in the real world.

The upper division with 2 levels, judgement-L6 and wonder-L7 can be viewed as about stimulating, directing and checking representational activity. They provide a potential for effective representation, and serve as controllers of representation. Here is where choices are made about bigger issues like: what should be represented? what current knowledge can be accepted? how is uncertainty to be reduced?

Between L4 and L5

This is generates the standard content v context internal duality which will be explored further in the Tree framework. The lower 4 levels are required to represent the world, the upper three levels are the context, concerned to ensure that representation is meaningful, useful and liable to be correct. Note that scaling is only an issue in regard to content, the lower 4 levels.

Exoteric and Esoteric Inquiry

Although our focus is on rigorous inquiry and scientific studies, it is evident that inquiry occurs beyond academe.

Science is itself an esoteric activity: for those dedicated few (even if in modern times they seem to have become many). However, inquiry and knowledge is exoteric and a concern for all.

The esoteric aspects relate to:

• greater concern for certainty in relation to every step
• engagement with the deep mystery and unknowability of objects of study
• commitment to research methods to bolster or optimize judgement.

---

An important perspective on the drive for certainty is revealed by an examination of the oscillating duality which deals with the locus of control and the tension between subjectivity and objectivity in any inquiry.

Originally posted: 23-Aug-2015.