Generality, Particularity, Singularity

Performing Sculpture. Small Feathers, 1931, by Alexander Calder

Marx’s Abstractions

and Dialectical Developments

On further listening to David Harvey’s analysis of Marx’s Capital, it becomes important exactly what the necessary kinds of Abstraction are, that are actually being used.

Previously, when revealing the significant and transforming content of the Greek Intellectual Revolution, somewhat earlier in these investigations, the key achievement turned out to be in the wholly new kind of Abstraction that they had developed in their study of shapes, but which, at that time, had also enabled the development of the very first intellectual discipline - Mathematics.

So, once again, within this current discussion on Marx’s Capital, it has to be the kinds-of-abstraction used, as well as both when, and to what extent, they can be effectively employed, that are the most important questions.

Now, Marx wasn’t a scientist, he was a philosopher and historian - and neither is David Harvey, who is a geographer by trade: so neither of them were intimately familiar with the methods and abstractions of ‘hard’ sciences such as Physics, or even their associated disciplines, such as Mathematics. So, they would not be immediately aware of the unavoidable limitations of idealistic Mathematics - for their focussings were very different in their own primary disciplines.

Now, Marx crucially talks about Generalities, Particularities and Singularities as the abstractions concerned with the Laws of Motion of Capital, and how he sees and uses them, turns out to be crucial, and also very revealing when related to their somewhat different uses in Science and Mathematics.

So, once again, I am pressed to use my analogue regarding Multiple-Chemical-Processes, to clarify what is involved. For there, though many active factors are involved (all acting simultaneously), the most frequently naturally- achieved Stability, in this type of system, will always be in an achieved persisting balance between all of these processes, characterised by a certain Dominance, as the apparent underlying determining “Law” of the situation.

And, that would be what Marx calls the Generality of the situation.

But, the other factors involved will vary, and though they cannot dislodge this Dominant Law, they can move it about - somewhat!

They would be the contingent Particularities of the situation.

Finally, something could happen which completely terminates the situation: so this Law ceases to apply!

That would be due to a Singularity of the situation. These are key Abstractions from the situation with different properties and effects.

Now these are necessarily considered somewhat differently in their varieties of use: and though my explanations, that lead to these differences, arise from my always-holistic stance, it is important to note that many other widely current uses, even in Science, are wholly pluralistic in their determining, underlying stance, and hence differ significantly! That is, they take all the laws involved as permanently fixed.

So, Marx’s strictly holistic methods will never be considered by those usually employing entirely pluralist methods - like the majority of both scientists and logicians for example.

Now, in any such, many-law, holistic context, as with both my favoured chemical analogue, and also the ones involved in Capitalist Economics, the simultaneously-acting laws will most certainly NOT interact pluraliatically, for then all would be of the exact same type. Indeed, within holism there will usually be a Generality - delivering the underlying fundamental Law, determined as such by the overall, dominating conditions, but always also (potentially) modified by a whole series of Particularities; which can adjust and vary the Generality. While there will always be, in addition, one or more Singularities, which can, in appropriate circumstances, terminate the Generality completely, by changing the underlying situation. And, there will be different reasons, which causally-determine all these natures, and their roles, in a given situation.

Once again, my revealing analogue can be used to expose all their various determining causes. In that case, the Generality will be described by the basic underlying Law, itself, caused by the relative abundance of its major required resource, more often than not, determined by the circumstances in which it occurs. While, the various Particularities, will never challenge that objective dominance, but could modify it contingently to some extent. Finally, the Singularities are totally independant influences, sometimes from without, that cancel the dominance of the Generality and facilitate its complete replacement.

NOTE: Now, the above constitutes only the briefest start in addressing such Holistic Changes and how we can deal with them, and, as we develop this discription, the significant differences and evident superiority to the consensus Pluralist Approach, will gradually, and excitingly, be revealed. For example, the conundrums and even impasses connected with Dichotomous Pairs of contradictory concepts will be fully explained - particularly via our revealing analogue, which will always include an opposite sub-dominant process, which, in certain circumstances replaces the prior Dominance, without significantly altering the overall Balance and Stability!

But, the very reason for the prior adoption of Plurality as the universal stance in investigating Reality, does have some sort of basis, in the evident relative predominance of long-persisting Stabilities within Reality: indeed Stabilities are frequent and persist for long periods, but can never deliver any significant Qualitative Change.

So, in spite of the always very short durations of Emergences, they are, nevertheles, the sole sources of all Development. And, the apparent “Truths” of Plurality are usually arranged-for, by artificially-constructing and actively-maintaining appropriate Stabilities, to ensure the possibility of applying such Pluralist Laws successfully.

But, of course, such a purely technological approach can never address any of the areas involving qualitative changes and their explanation - and these are evident in by far the widest ranging areas of study. Even Modern Physics and Cosmology have both been brought to existential crises by the limited pluralist appoach, and without a veritable revolution in these areas, they are effectively doomed as sources of Explanation for Reality. .

NOTE: It is interesting to consider Mathematical Singularities alongside Marx’s use of the term. The use of singularities in Mathematics means indisputedly that they are occurring wholly-within a legitimately pluralist context - namely Ideality. But, the infinities possible within Ideality, legitmises the positioning of a found “real” relation upon a graph of infinite possible extention, though for it is only a small locality within that graph, that maps onto a situation in Reality, and the rest of the space included in the graph necessarily constitutes what are, in that context, termed as Singularities - that is as aymptotes to Infinity, or swoops to Zero. They should just be the boundaries-of-Reality, but in idealist Modern Physics are instead suggested as portals to alternative Worlds!

Controller of the Universe, 2007, Damián Ortega

Singularities and Emergences

Now, of course, even the role of Singularities, as so far merely described, can never explain any consequent real development, but only individual qualitative changes: and where they lead is also never-supplied, at such a level of analysis.

What is actually needed is a causal-mechanism for “system-change”, wherein a mutually-affecting collection of many different, and even contradictory, processes actually dismantles the old order, and generates a wholly New System. And, such an event, has a name within this Holist View of Development: it is called an Emergence.

And, it is certainly not a mere fixed-causality, with a given single outcome at all! Indeed, it is not even a consistent, co-ordinating system of coherent, related processes, naturally coalescing into a consequent final outcome. It is, remarkably, a balancing system of contradictory factors, which ordinary Logic would see as merely inhibiting, or even cancelling, one another, and hence leading nowhere!

And, it should be clearly contrasted with such co- ordinated systems, whhich can never lead to real, entirely-original qualitative changes.

An Emergence is always a remarkable Event, which produces purely temporary Stabilities, which almost always involve the same self-restoring balance of contradictory factors, while displaying an apparently resultant Dominance (which, superficially, certainly looks like a pluralist law).

Now, this turns out to be a surprising entity, for though it appears to be, and usually is, a conservative arrangement, ensuring its Status Quo for long periods of time, it can, in certain circumstances, become undermined. And yet, though that cause undermines - in one area of the balance, it mostly restores the situation - in another area, to counter that undermining. Such a contradictory Stability, therefore, includes the wherewithal to correctingly deal with Crises most of the time.

But, if pushed too far, it not only precipitates a wholesale dissociation - a total Collapse - it also always delivers an unexpected outcome. The produced intermediate situation no longer perpetuates anything. New subsytems can now begin to come together, relatively unhindered - though many just as quickly dissociating again in their own Crises. But, finally they come together in a new balance of contradictory factors, which constitures yet another new Stability! And, that new system could never have been predicted from the prior Stability. This is how the Wholly New emerges!

But, how is the necessary variety first produced, and then maintained in any given context? The engine of our Solar System is clearly The Sun, but different parts of a planet, presenting different angles of incidence of the Sun’s Rays at its surface will receive different amounts of heat, and consequent differential heating of the local atmosphere, causing Winds and hence differential evaporation from any liquid water available in seas or lakes.

And as the planet spins, it will also at every point on its surface by alternately be illuminated, and then plunged into darkness, causing differences in heating over time!

So, already, just considering the ‘stable’ Sun and Earth, we get diverse conditions including precipitation and even worldwide small particle distibution, via moving winds. And the more things that are considered, the more variabilities are involved.

The point is, how do they co-exist in some maintained, or regularly repeatable mix? Clearly, conditions can vary enough to promote opposite processes in extreme situations, the results of which can be moved about by winds and currents. Yet, some planets in our Solar System do seem to exhibit restricted ranges of prpocesses, and continuing as such for seemingly vast periods of time. While others, like Earth, seem to be in relatively constant change: which appears to be largely due to Life.

And Life itself must have once been some kind of Emergence: what else could it have been?

So, why no evident Life elsewhere in the Solar System?

We can deal with a variety in conducive circumstances, but what triggers the crucial event that enables everything that can consequently emerge? Clearly, once we abandon the fictional simplicity of a Pluralist World, we find ourselves in a much more complex Reality, requiring a wholly new approach when attempting to understand it.

Postscript:

Clearly, there is still a great deal to yet be addressed, but I feel some brief foray into that waiting world should be addressed here, as a sample of what is to come.

Let us consider Causality!

For, our idea of Causality is significantly distorted by not only the premise of Plurality upon its nature, but also in the consequences of that stance for how we see, explain and use Causality.

The Principle of Plurality has all elements extracted from Reality as permanently-fixed: not only categories and concepts but also extracted Natural Laws too. And, consequently, our tools for dealing with these were obviously also “tailored-to-fit” such fixed entities and relations.

Primarily, if Plurality were true, it would be entirely valid to deliberately restrict, or even “farm” investigated situations to effectively isolate a given relation: for, if that relation were naturally eternal, our manipulations would never affect it: it would remain the same.

Also, we could never effectively use that relation, if we didn’t similarly simplify the context for use, as with “only one Law free to act”, we could easily apply it to achieve predictable ends. And any complex production would have-to-be organised as a series of productions, one for each pluralist Law evidently involved.

We would never attempt to apply them all simultaeously! Yet, of course, simultaneously, is exactly how Reality works with its “Laws”, when left to itself! So, because of our subscription to Plurality, we purposely prohibit, for ourselves, any knowledge whatsoever of how simultaneous “Laws” might actaully affect one another, or even follow particular natural sequences over time.

The natural selection of such sequences is NEVER available to us, as it must have been in totally unfettered Reality. Indeed, Plurality is NOT true in either Reality, or even in Reasoning. In fact, it is only true in Mathematics, because of its simplified relatable abstractions, on which it was constructed. But, they don’t form the abstractions upon which Reality and Reasoning are constructed!

So, in making Plurality the basis where it does not apply misleads what we can do with what we obtain by such means: and, in addition, limits the conditions we can apply them in to severely restricted and unnatural contexts.

This essay is taken from the latest issue of SHAPE Journal called Changing Dialectics