Leibnizian inquiring systems

Combining insights of Descartes, Spinoza to grow fact nets

As I wrote in a previous post, “Churchman suggests that the history of epistemology can be used as a source of design models for learning systems and their justification. To this end he takes the renaissance of epistemology by Descartes in the seventeenth century as the starting point, followed by Spinoza, Leibniz, Locke, Kant, Hegel and the American pragmatists, Singer in particular.” In this post I will summarize the chapter on “Leibnizian inquiring systems” in Churchman’s book on “The design of inquiring systems”. In this chapter Churchman writes how he understands Leibniz’s contribution to systemic inquiry, which is fundamental to our thinking about systems. And the world is packed with systems, many of which in dire need of Wicked Solutions. What more proof of the practical utility of philosophy does one need?

Diagnostic framework       One of the great problems of philosophy is the absence of a common language among philosophers. For the case of the epistemologies of Descartes, Spinoza, Leibniz, Locke, Kant and Hegel Churchman solves this problem by first creating a unified diagnostic framework. He does so by using two basic learning models to create a 2 x 2 matrix, which provides 4 quadrants or options to associate the different philosophers with (see left hand part of the concept map below). The key aspect of the first learning model of input-process-output is that the input must be “given” (as in ‘data’), or not. The key aspect of the second, simple-to-complex learning process is that whatever it is that the process starts off with must be “clear”,  or not.

Clarity and “given”-ness       Locke is an exponent of empiricism: we are not born with innate ideas, so all our knowledge comes from experience, i.e. sensory data that are clear. He is in the upper-right quadrant number 1. On the opposite end (quadrant number 4) we find Leibniz, who argues that inquiry begins with unclear material which is not an input. In his metaphysics people are a higher class of monads. Very simply put, monads are indivisible entities such as atoms or persons. They lack a window for input, so perception of the outside world is mostly guesswork. This goes very well with Churchman’s pragmatist background. According to Churchman, all the other philosophers fail to prove their respective positions, including Descartes and Spinoza, of whom Leibniz nevertheless adopted some ideas. (Note: Locke and Kant are not discussed in detail in the chapter on “Leibnizian inquiring systems”).


Descartes        Inquiring systems process symbols. That’s why an inquiring system can also be called a processer. Symbols can be sentences, digital sets, images and so on. Descartes is well known for his method of radical doubt (“Cogito ergo sum”), hence the demand for any inquiring system to be able to determine and guarantee the status of symbols to be processed, i.e. determine and guarantee whether these symbols are simple or complex, clear or unclear, and above all: true or false. For the inquiring system to be able to do so, Descartes designs a three-step approach. In the first step, God is invoked to ensure that the inquiring system can do that, “if God exists”. In the second step, the existence of God must be demonstrated, and in the third step God must be shown to be trustful, not a deceiver. In Churchman’s eyes Descartes fails to prove the last step.

Spinoza       … is not a traditional theist, but rather a pantheist, who identifies God with Nature. Therefore, God can no longer be play the role of a transcendent guarantor as with Descartes. Instead, Spinoza argues that the inquiring system needs an executive function. This function, like a modern “executive”, does not look at the nitty-gritty of actual processing of the symbols. It just co-ordinates the action of guaranteeing whether symbols are true or false (and simple or complex etc.). It also judges whether this action of co-ordination is carried out correctly. Spinoza says that the executive function is ‘intuitively’ capable of doing so. That’s where, in Churchman’s eyes, he fail to provide adequate proof.

Leibniz’s turn        As mentioned above, Leibniz’s metaphysics is based on the monad. Much has been said about the monad and what it is, but it is easiest – for the moment – to think about it as a person that can be described using some of the same terminology as used above for outlining the ideas of Descartes and Spinoza. Monads can be equated with inquiring systems or processers. With Descartes, Leibniz acknowledges the need for some form of guarantee of the truth or falsity of the symbols to be processed, but he sees no direct role for a transcendental God. With Spinoza he agrees with the idea of an executive function for his monad, but the way it works is entirely different. Leibniz´s solution for the monad to come up with something approximating truth involves five steps.

The monad´s five steps       … are: (A) identifying and sequencing the symbols, i.e. sentences etc.; (B) using innate logic to classify the sentences etc. as tautologies, contradictions or contingent truths (these are by far the most important, because they are very common in natural languages); (C) using a logic processer to process the tautologies and contradictions; (D) loosely assembling contingent truths into so-called fact nets. Imagination is used to do so, causing the fact nets to proliferate endlessly; (E) limiting proliferation by seeking convergence of the fact nets on one optimal net. The executive function achieves this by striving towards broad coherence, involving such principles as simplicity, elegance, and concordance with the proof of God’s existence. As a consolation for atheists or agnostics, this may well be a naturalistic God or an atheistic approximation thereof (see this post). Let’s not forget that Leibniz was a 17th century German.

N.B. None of the new concepts in the final two paragraphs of this post have been used in above concept map.

Current practice of science          A large part of scientific practice can be considered a Leibnizian inquirer. Science is not entirely ‘objective’ in the sense that preference is given to results that fit earlier findings and mainstream theory, which forms a “fact net.” Results that lie outside the largest net are often ignored. Theoretical laws, the denial of which would entail reconstruction of the net, are apt to be safeguarded by various devices. Disciplines tend to keep control of their nets by trying to exclude the relevance of results generated by other disciplines. Whether all disciplines comply with step E – convergences on one optimal net – is not clear.

Leibnizian concept of a whole system         Two ideas will be explored in the next chapter (and so in a next post): “On whole systems: the anatomy of goal seeking”: (1) no optimal design of a part of a system is possible without prior knowledge of the “whole” system. This idea, if correct (but self-evident!), challenges almost all our conscious policy making. We “attack” poverty, inefficiency, national belligerence, crime, as though each were a blot on an otherwise pure white carpet, and as though we had no responsibility for showing how the whole system would improve if this part were changed in accordance with our plan. And: (2) all systems are fundamentally alike in the design of their components. The pre-Socratic Anaxagoras (510-428 BC) was the first with a known quote of similar intent: “The seed of everything is in everything else.

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