Leibniz 1: Elemental Qualities of Hypotheses
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| Fred Williams not titled [Lysterfield landscape with pool] 1965 |
I also borrow, rebuild and sometimes invent ideal type concepts that accurately describe the phenomenon. Impersonal governance is an ideal type concept, as are concepts such as system, state, code, functional differentiation, and separation of power. Ideal types synthesise observed elements of complex realities with a pure abstraction that accentuates the special qualities of a generalisable phenomenon of social action. It facilitates comparisons across periods and places.
A basic function of hypotheses is to make all of the initial objectives of the investigation plain and understandable. When preparing a new theory, a new interpretation of history, or new terminology, a premium is placed on clarity. At a minimum, author and readers should be able to refer to the hypothesis to remind themselves of the purpose and direction of argument. All the definitions of concepts and interpretations of empirical data are made commensurable with the hypothesis.
The hypothesis and the ideal type are the two cardinal methods by which the social sciences create an initial heuristic structure upon which new knowledge is built. An objective standard for evaluating the quality of ideal types is set out clearly enough in Max Weber’s ‘The Methodology of the Social Sciences’ (1949). But though creations of ideal types can help in constructing and testing the hypotheses, the science in the social science starts with the creation of the hypothesis.
A universal standard for critically judging a hypothesis, its scope, what it should aim to achieve, and methods of testing it was formulated in the seventeenth century by another German thinker, Gottfried Wilhelm Leibniz [1646-1716]. The question of what constitutes a hypothesis was first addressed in early modern Europe on a number of fronts, but most comprehensively by Leibniz.
There are really three distinct levels at which Leibniz judged the quality of a hypothesis. These represent challenges of gradually increasing difficulty. In three separate entries I will describe the relatively easily-satisfied first level as the one of ‘intention’. The second more difficult level is the one of ‘method’. The third speculative level will be called ‘extrapolation’.
The focus of this entry is on elements of the first level which may be summarised as follows — A hypothesis has a higher chance of success if it is simple in construction, has wide applicability, can explain multiple phenomena, makes few assumptions, and is easy to understand.
The probability of the hypothesis being true is greater once all these conditions are met. A good hypothesis may even allow predictions about phenomena that cannot yet be tested. If it turns out to be an incorrect hypothesis it will at least have made the phenomena easier to remember.
Leibniz: “Phenomena are virtually contained in the hypothesis from which they can be deduced, so that anyone who remembers the hypothesis will more easily recall these phenomena when he wishes, even if he knows that the hypothesis is false and that certain other phenomena are known with which it conflicts.”
Leibniz: “Some hypotheses can satisfy so many phenomena, and so easily, that they can be taken for certain. Among other hypotheses, those are to be chosen which are the simpler; these are to be presented, in the interim, in place of the true causes.”
Leibniz: “The simpler a hypothesis is, the better it is.”
If the initial intention is to maximise the number of phenomena that can be contained within the hypothesis, then ours meets the Leibniz standard in spades. It includes most routine intra-state and state-society interactions over the course of a few hundred years of history in most of the countries that are now said to comprise the Western world.
The intentions of comprehensibility and simplicity largely look after themselves once a high level of abstraction is achieved, and once the concepts are defined in language or symbols to a sufficient level of satisfaction. Inevitably this is a subjective judgement. Among empirical social scientists the use of ideal type abstractions could raise the ire rather than clear the air.
The qualities just mentioned — multiple phenomena, understandability, and simplicity — can be easily achieved at the design stage by generalising to an extremely high degree, though at the risk of provoking incredulity. These qualities alone are not sufficient, since Leibniz had a special way of linking some of the essential criteria in defence of the method of hypothesis.
The linkages to be discussed in what follows are: the assumptions; the probability of truth; the role of symbols; the function of reducibility; the clarity of distinction between analysis and synthesis; and the requirement that the hypothesis encapsulate a single unambiguous contradiction as the binary foundation for a truly primitive concept, one that embodies knowledge that can be intuited.
Firstly, assumptions can be dealt with by ensuring every significant word in the hypothesis and its expository material runs the gauntlet of redefinition. The assertions in it are not taken for granted. It should be explicit, also, that some things are unseeable and may be proven in argument, if not by facts then by the allusions and logic of historically-founded ideal types.
There are perhaps only two really necessary assumptions. Firstly, sources of complexity in governance generate system imperatives to codify interactions of governance. Secondly, intelligent human agency recurrently regulates and reduces interactional complexity by institutionalising automaticity through coding solutions. These two assumptions are treated with caution, yet they do clearly meet the Leibniz standard for safe priori conjecture.
Leibniz: “The conjectural method a priori proceeds by hypotheses, assuming certain causes, perhaps, without proof, and showing that the things which now happen would follow from these assumptions. A hypothesis of this kind is like the key to a cryptograph, and the simpler it is, and the greater the number of events that can be explained by it, the more probable it is. But … the same effect can have several causes. Hence no firm demonstration can be made from the success of hypotheses. Yet … the number of phenomena which are happily explained by a given hypothesis may be so great that it must be taken as morally certain. Indeed, hypotheses of these kind are sufficient for everyday use. Yet it is also useful to apply less perfect hypotheses as substitutes for truth until a better one occurs, that is, one which explains the same phenomena more happily or more phenomena with equal felicity. There is no danger in this if we carefully distinguish the certain from the probable.”
A further task is to know a particular idea is possible. Among Leibniz’s many pleasing methodological provocations we find these:
Leibniz: “An idea is true when the concept is possible; it is false when it implies a contradiction”.
Leibniz: “There is a certain urge for existence or a straining toward existence in possible things or in possibility or essence itself; in a word, essence in and of itself strives for existence”.
The investigations begin with rational reason used to devise finite conjectural hypotheses and definitions based on what could be true in light of existing data and models. Clear definitions are essential because the investigation depends on the concept to produce knowledge of the possibility. If no contradiction appears, the concept is presumed to be possible.
Leibniz: “We know an idea a posteriori when we experience the actual existence of the thing, for what actually exists or has existed is in any case possible. Whenever our knowledge is adequate, we have a priori knowledge of a possibility, for if we have carried out the analysis to the end and no contradiction has appeared, the concept is obviously possible.”
Probability is a step higher than possibility on the epistemological ladder, the result of further simplification and reduction leading by the same process to predictive potential.
Leibniz: “A hypothesis becomes the more probable as it is simpler to understand and wider in force and power, that is, the greater the number of phenomena that can be explained by it, and the fewer the further assumptions.”
Finally, for a hypothesis to have potential predictive power it should be demonstrably consistent with what is already known of the whole sequence of society’s evolution.
Leibniz: “The most powerful criterion of the reality of phenomena, sufficient even by itself, is success in predicting future phenomena from past and present ones, whether that prediction is based upon a reason, upon a hypothesis that was previously successful, or upon the customary consistency of things as observed previously.”
If the probable chain of causation that produced emerging phenomena is known, then past and present phenomena are coherent and traceable to the same underlying cause. I extend application of the hypothesis at a later stage to conjecture about governance in an imagined future when there is already a fuller union of machine-human intelligence. In the present context all that matters is the initial tracing of past patterns and their probability, the ability to explain multiple comparable phenomena. The hypothesis cannot be “happily explained” until it is tested against histories and ideal types.
Michael G. Heller ©2021
