[OPE] Algorithms and dialectics

Date: Mon Apr 07 2008 - 18:32:07 EDT

```In Stanley Kubrick's film 2001: A Space Odyssey based on the book by Arthur C. Clarke, the HAL 9000 computer is named after "Heuristic ALgorithm". This is an algorithm that replaces the optimal solution with an improvement in run time. We can, however, also design algorithms with query routines aiming to find an optimum-fit solution in a data set, perhaps using probabilistic procedures. Techniques of this kind are sometimes used for data interpolation, data estimation or predictive purposes.

In an administrative job I have, I use fairly simple algorithms (as well as Boolean operations). However, there are several issues with algorithmic procedures I think.

Firstly, the data set must be appropriately formatted in some way so that it can be searched, that is to say it must be constructed/demarcated in some way, and it is often difficult to construct/demarcate it without errors or various types or inconsistencies, or without presuming the validity of particular categorical distinctions.

Secondly, the solutions are only as good as the query procedures, and the optimal result is optimal only relative to the intended result of the procedure.

Thirdly, if the data set is infinite, then we have no way of telling whether the solutions found really are optimal, and the query routine is in principle endless, unless we halt it after a certain number of operations.

Finally, all that the query procedures can achieve, is to find candidate solutions optimal from the point of view of the predetermined algorithmic procedure. So, in a sense, we induct those premises or data which fit best with the chain of inferences (logical steps) that necessarily lead to a predetermined conclusion. A more crude analogy would be that we select facts which lead to the conclusion. This is precisely the problem of bureaucratism: nothing new is discovered other than what fits with a predetermined conclusion, a conclusion which can be asserted from the start because the bureaucrat has power and commands reasoning to follow a certain path.

But, to my knowledge, all this is not really the purpose of dialectical reasoning at all. The purpose of dialectical reasoning is instead to define, place and connect the different elements of a totality in a logically coherent way so that its essence is revealed, its appearance-forms, its dynamics, its limits and its developmental possibilities - as the dialectical story unfolds, the initial premises are developed (in terms of new contradictions and how these are mediated or overcome) and they are validated in a self-revelatory way, so that at the end everything important about the totality has been explained in a meaningful way.

Nevertheless the dialectical story is not simply "true by definition" (tautological) since it continually inducts (or retroducts) new premises which, although non-arbitrary, are not simply deducible from the preceding narrative and which do not follow a completely formal-logical sequence of inferences. It examines facts which appear to contradict the story, and how those contradictions can be resolved.  It is not whether the end state (the conclusion) is reached that is important per se, but rather whether, between the beginning and the end, the real structure of the subject has been revealed in all salient respects, so that all facets of the story are mutually supporting.

The dialectical story, in other words, aspires to state the fullest meaning of the subject, or at least its essential meaning. But I think this differs from just an algorithmic procedure. The purpose of the algorithm is obviously not to generate the meaning of the algorithm, or to form concepts adequate to a reality being studied. Instead we refer to certain meanings, to construct the algorithm, and then import data which match the criteria of the algorithm.

In general, as I have said before on OPE-L, I think dialectical reasoning is a form of non-arbitrary reasoning (reasonable inference) which is not formal deductive inference although it presupposes it - its plausibility as such depends on integrating all facets of a subject in a coherent and consistent way, without this however necessarily having only one particular implication or end-state. Reasoning may be non-arbitrary, yet not amenable to formal proof. The transition from a plausible interpretation to a provable interpretation depends on whether (some or all of) the particular elements in the dialectical story can be logically proved or empirically proved. The strongest dialectical story would obviously seek to combine, synthesize and integrate a series of logical and empirical proofs, in order to reveal the total meaning of those proofs (what it all adds up to, or implies) in a very compelling way. So in a sense, dialectical story-telling is meta-theoretical.

Marx does use, refer or imply fairly simple algorithmic techniques in his narrative, but they are a sub-element of the dialectical story as a whole. However I think a dialectical proof is never a formal proof or an empirical proof. It proves only the plausibility, coherence or possibility of an explanation or interpretation, the capacity of a certain vantage point to make coherent sense of the facts and arguments pertaining to a reality. Dialectics is primarily concerned with "what things mean", what their significance ought to be understood as, for which formal inference is only an aid - formal inference cannot ultimately stipulate what concepts mean, it presupposes the meaning of certain concepts, or else refines what they can possibly mean or apply to, by specifying necessary implications or limits.

Quantification offers the greatest possibility of the most refined definable/identifiable distinctions, but this involves either abstracting from qualities or assuming qualities. I think it can be proved that dialectical reasoning is involved in inventing categorical distinctions, and therefore that dialectical thinking is always implied in the creative processes of concept formation. These processes go beyond formal logic, although they might assume it, because they involve both analysis and synthesis of a type which moves between different logical levels. This can be easily studied and verified (as educationists do in researching cognitive development) by examining what people actually behaviourially do, when they form new categorizations to describe a particular facet of reality.

Jurriaan

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