(P8-03) Locality of knowledge and methods – in what space?

Elsewhere we claimed that A.’s academic practices have spanned a broad gamut of approaches, illustrating the practical uses of (1) being (as a law student) a legal positivist, of (2) being (as a computer programmer and information scientist) a logical positivist, of (3) being (as a law PhD student) a critical theorist, of (4) being (as an occasional ICT-project adviser) an inclusive pragmatist, of (5) being (as interested in complexity theory) a post-structuralist and of (6) being (acknowledging that we need stories to suggest some logic in this weird collection) a narrativist.

Now a serious questions is this: in what space can we locate these positions, or pinpoint them as distinct loci? In what spaces can legal positivists live apart from, yet together with, logical positivists (and each of the others)? Can we patch these loci into some sort of useful lattice, field or landscape?

When I read Philip Anderson’s More Is Different, something of a 2-dimensional space that could be used for locating the objects of the diverse disciplinary ‘species’ (philosophy, humanities, sciences, social sciences) presented itself. One of its axes (the t-axis) would support the notion of time and the other axis (the c-axis) would support the notion of composition.

Let us imagine such a Cartesian space and pick a single moment in time (a single spot on the t-axis). Let us subsequently imagine that we have some intuitive measure of research-object composition, for instance that the cosmos is a composite of elementary particles and thus higher up the measure of composition than elementary particles. Lets further imagine that someone has put in colored dots (red, blue, green, yellow – per disciplinary species respectively) for all philosophy-, humanity-, science- and social-science research subjects currently pursued in the academic world. One would expect to find green dots almost exclusively at the bottom (particle physics) and at the top of the c-spectrum (cosmology). One would expect to find many green dots more in the middle of the c-spectrum (medicine, biology e.g) yet there the green dots will cluster together with blue and yellow dots as the social sciences and humanities come in. One would further expect that the green dots would avoid a specific band in the c-spectrum where “ought to” issues live that the sciences cannot see and where blue, yellow and red dots compete for attention.

There is yet another axis to introduce: the t-axis, which stands for time. We have well-established measures for time ready at hand: lets choose years. When we imagine the c-axis to span from cosmological subjects to quarks, and when we imagine the t-axis to span from 0 to 14 billion years (where ‘now’ rests at year 13.7 billion) we can get some feeling for how the dynamics of the different sciences have evolved when we imagine that relevant objects that emerge in time do start out as grey and gain their colors as they become interesting to the scientific disciplines.

In this manner, we can gain some feeling for the idea that knowledge and methods are local. Yet, the Cartesian t-c space has problems. In many disciplines, dynamics are interesting in terms of actions, reactions, transformations, generations rather than years. We will need the possibility to create subsets of time-spans, somehow, and work with them. Moreover, in many disciplines the contingencies and complexities of composition are extremely important, and seem to defy the possibility of a useful composition measure.

Our hunch is that we will be able to overcome these problems, when we accept the c-axis to represent the levels in a powerset lattice (the powerset of a given set, ordered by inclusion), and when we allow research objects to be defined by contingent networks between nodes in the powerset.

We will not further this line of thought as a mathematical subject. We will use it intuitively and forget about its math, as we are sure that such math is way above our heads.

References

Anderson, P.W. 1972. More is different. Science, 177 (4047), 393–396.

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