What happens between understanding the logical structure of something and the usage of techniques for measuring reality? In Hume’s theory of causation, he deployed an implicit ontology of event regularity together with a constructivist (he wouldn’t have used the term, but that’s what it was), communication-oriented logic of understanding and theory-building about causes. Critical Realists and others argue that this can’t be right because many of the theories which are constructed (e.g. gravity, relativity, etc) predict regularities where none have been investigated, implying that there must be something ‘real’ that is discovered in a theory rather than simply something constructed through the communications of scientists. But maybe there is a question about how logic and measurement relate to one another? After all, Hume’s idea of scientists’ conversation carries an implicit logic of communication which has successively been shown to be more and more complex in its relations to reality (Kuhn’s paradigms, Popper’s falsification, etc, etc).
What appears to emerge from the work of those philosophers of science who have explored the discourse of science is a kind of ‘ordering’ of that discourse – the way that paradigms shift and interact, the way that institutional structures and other social forces come into play, the way that technologies change the picture. In effect, what seems to occur is the negotiation of a lot of ‘status functions’ as Searle would call them – “x says ‘this is the way the world is’ producing evidence z to support it; x is backed up by institution a and academic community u; x is opposed by counter-examples from scientist y in institution b and academic community v” … and so on. The logic of the ordering of a discourse relates in some way to the measurements that might actually be made of the phenomena in question.
Absence is the most fundamental feature in the ordering of anything: whatever position we take, it will always include (as a background) the possibility of “no position”; positivists might wish to deny absence as an element of their thought, but the denial of absence is itself an absence and ultimately this weakens the status of any positivist argument. Positions are subsets of other positions; positions vary in the network of status functions that operate around them. The logical structure of a theoretical position relates to the deontic powers it deploys and to those deontic powers which bear upon it. It may be that this logical structure is similar to the logical structure of number as we find in Badiou’s mathematical theory and Conway’s concept of “surreal” numbers. To argue this is to start to expose the “logic” of Hume’s scientific discourse.
What then of measurement? It seems to me that the most important thing we must grasp in our measurement is what is “not there”; this is much more significant that what “is there”. Of course, most measurement concentrates on the ‘present’, so there is a question about how we might measure the absent. Really it is about measuring the ground rather than the figure, or at least inferring the ground from the figure. I could be wrong about this, but I think that Shannon’s information theory is important in allowing us to think about the ‘message’ (the present) but also the ‘redundancy’ (the absent).
My reinterpretation of Hume suggests that science proceeds through the coming together of logic and measurement (isn’t Euclidian geometry like this?) Indeed, looked at this way, ‘regularity’ (which plays such an important role for Hume) is reinterpreted as ‘redundancy’. So what we see is a mapping of measured redundancies (which are absences) with the logical structures of status functions declared by scientists.
Am I stretching things too far to suggest that this holds out a possibility of educational empiricism? Our educational theories have a logical ordering determined by the networks of status functions that they declare. Institutional structures and patterns of usage also have a logical structure. These seem mappable to me as networks of commitments and obligations. But in addition to this logical structure, there is an empirical structure of measurable redundancies. Can we bring them together? Can we move forwards if we do? Maybe we should have a go…