Formal Strategy and Philosophical Logic: Work in Progress

6 March 2011


Lately I have been returning to my books on philosophical logic in an attempt to clarify some of my ideas on formal systems and the concept of the formal generally speaking. (Yesterday’s post on unpacking an Einstein aphorism was a result of my recent return to thinking in this vein.) It has become my ambition to formulate strategic thinking in a formal context, and in order to do this I need to refine and extend my own conception of formalism. In fact, I have started a manuscript with the working title Strategic Thinking, in which I hope to give a formal exposition of strategy.

Frege is largely responsible for the logical innovations that made contemporary rigorous formalism possible.

Formal thinking is alien and unfamiliar to most people. What understanding of formalization there is usually derives from dimly-recalled mathematics, and especially from an encounter in school with axiomatization, usually by way of geometry. Euclid’s geometry is often the only experience that people have of formal thought. The rise of formalized languages in the twentieth century (though due to Frege’s innovations in the nineteenth century) provided a great impetus into research in formal reasoning, though the particular path this development took — formalized languages given symbolic expression — meant that these developments primarily influenced logic and mathematics. Ultimately these developments issued in computer science and a technology that is transforming our lives even as I write. But getting people to understand how central formal thinking is to our lives today is another matter.

Wittgenstein's Tractatus Logico-Philosophicus was part of the efflorescence of formal thinking focused on logic and mathematics.

Formal thinking need not take the form of a symbolic language. In some contexts symbolic languages make it possible to perceive at a glance the logical interrelationships of the elements that constitute a theory, but from a conceptual point of view, one can approach formalism in ordinary language so long as one understands what one is doing. I tried to point this out in my post Foucault’s Formalism. In other words, we can distinguish between a conceptual formalism that is embodied in a technique of reasoning and particular symbolic instances of formal reasoning, which have, to date, been the paradigm of formalism.

I tried to explain in my post on Foucault's Formalism how thought can be formal without being expressed in a symbolic language. A formalism after the fashion of Foucault would be a formalism that could give depth and precision to strategic thought.

While in logic and mathematics (which were at one time called the “formal sciences”) ordinary language is cumbersome and ultimately counter-productive to the elaboration of the ideas in question, in a field of thought as thoroughly humanistic as strategy a symbolic language, on the contrary, would be cumbersome and counter-productive. So the key to a formal grasp of strategy is to approach strategy by way of conceptual formalism, and this is what I intend to do, and in fact have started to formulate in my own, imperfect way.

An arbor porphyriana or Porphyrian tree, created by Porphyry, is a hierarchical (tree structured) ontology, construction in logic consisting of three rows or columns of words; the middlemost whereof contains the series of genus and species, and bears some analogy to the trunk. The extremes, containing the differences, are analogous to the branches of a tree.

Porphyry's tree is a semi-formal representation of the structure of knowledge; the axe-wielding figure represents a widespread rejection of formalism, about to chop down Porphyry's tree.

I briefly expressed my interest in formal strategic thinking in Precisification: Calibrating our Concepts. Mr. T. Greer, who formerly was responsible for the Scholar’s Stage blog (no longer a going concern), wrote this in response: “Economics: the dismal science, or the science that makes men dismal? I tend to believe the latter. Much of the precision and ‘science’ of economics is really nothing of the sort; I fear for the day strategy and politics follow its course. I find value in the humility that allows us to admit that we lack the capability to be precise in our (limited!) understanding of much of this Earth.” Thus we see that not only is formal thought unfamiliar and as a consequence often misunderstood, it is also at times vehemently rejected. I have no idea if more people share my point of view, and welcome innovations in formal thought that will allow us to extend our knowledge to areas of experience previously given over to Chaos and Old Night, or if more people share Mr. Greer’s view that there is a kind of “cosmic impiety” (a term I take from Bertrand Russell, of all people) that raises humility and limitation as epistemic virtues higher than formal precision.

Bertrand Russell said that John Dewey's philosophy presented the danger of “cosmic impiety” (A History of Western Philosophy, p. 828) though I suspect that far more people thought that it was rather Russell's thought that presented the danger of cosmic impiety. Russell, like Whitehead and Wittgenstein mentioned above, was instrumental in laying the foundations of contemporary formal thought.

Mr. Greer explicitly mentioned the example of mathematical economics, and this is, without question, one of the great triumphs of formal thought in our time. Economics was once as humanistic as history or strategy, but it is now pursued almost exclusively in terms of mathematical models. This is one approach to formalism, but not the only approach. It is an approach that emphasizes the quantification of variables and the formulation of equations to formally manipulate the values determined for the variables. This is very much in the spirit of mathematical physics. We recall that most of the laws of nature recognized by physics are expressed as equations. If you plug in the values of the actual world into the variables of the equations, you get predictions. This has obviously been stunningly successful, judging from the past couple of hundred years of scientific accomplishment, but it has its limitations.

The kind of mathematical formalism we find in physics and economics is vulnerable to what are sometimes called “finite dimension errors,” which are the compromises forced upon us whenever we quantify data that are in any way also qualitative. You can break the rainbow into red, orange, yellow, green, blue, indigo, and violet, but in fact color is a continuum that does not admit of discrete divisions. For purposes of the mathematization of thought we may choose to interpolate arbitrary divisions, and the disjunction between these arbitrary divisions and the reality of continuity are the source of finite dimension errors. Formal thought requires and enforces finitude as the price of precision. Formalism thus perfectly exemplifies Alfred North Whitehead’s aphorism, seek simplicity and distrust it. (And who would know better than Whitehead?)

There is already an example of strategic thought that has followed this quasi-economic lead. T. N. Dupuy, in his book Understanding War: History and Theory of Combat, approaches the study of war from a carefully quantified perspective. This is also evident in his other books (I have copies of The Evolution of Weapons and Warfare and A Genius for War, both of which have a similar conceptual approach). I don’t want to criticize Dupuy’s approach, which I think is very valuable, but it is also very different from the approach I will take.

I have a queue of unfinished posts on other topics to which I need to given exposition first before I can more on to a full exposition of the formalization of strategic thought — since one idea depends upon another, I must give my formulations of the more fundamental ideas first in order to show how I will apply them to strategy — but formal strategic thought is the longer term project that I have now set myself and am working toward.

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