## Some thoughts concerning a general theory of business 26: a second round discussion of general theories as such, 1

This is my 26th installment to a series on general theories of business, and on what general theory means as a matter of underlying principle and in this specific context (see Reexamining the Fundamentals directory, Section VI for Parts 1-25.) I began this series with its Parts 1-8 with an initial orienting discussion of general theories per se, and then turned from there in Parts 9-25 to at least begin to outline a lower-level interpersonal interaction approach to businesses and to thinking about them.

My goal here is to step back to reconsider general theories per se, adding to the conceptual framework initially offered in Parts 1-8 as a basis for continuing my discussion of theories of business as special cases. And I begin this with a quote that is generally attributed to Bertrand Russell:

• “Everything is vague to a degree you do not realize until you have tried to make it precise”

My goal here is to shed light on at least some of the underlying assumptions that we all tend to make when thinking about businesses and how they do and do not function, and to do so with a measure of precision in analytical characterization and understanding. That approach applies, at least as a matter of intent in how I discuss both theories of business here, and general theories as a whole too.

I repeatedly make assumptions in what I write in this blog, just to step back and highlight them for explicit consideration. And I often and even usually do that in order to challenge those usually axiomatically presumed assumptions in order to expand the applicability of what I seek to offer here (and at least hopefully while at least marginally increasing its value and utility too.) So the first set of issues that I would address in this posting and in the progression of them that I begin here, is to reconsider axiomatic assumptions per se. And I begin doing so with the perhaps tritely obvious fundamentals:

• True axioms are underlying assumptions that are simply presumed to hold true as exception-free givens.

To cite an ancient historical source of examples for that, consider Euclidean geometry and its axiomatically presumed postulates. And consider Euclid’s famous (infamous?) fifth postulate in particular: often referred to as his parallel postulate. At least when considered within the dictates of Euclid’s system of geometric reasoning, this is presumed to hold true as an absolute given, but scholars began questioning its more general validity from very early on.

• Axiomatically based systems such as Euclidean geometry can be thought of as analytically reasoned presentations of specifically stated automatically presumed assumptions and their logical consequences.

That does not mean that axioms presumed in such a systematic analysis cannot be questioned or challenged at all. It just means that they remain unchallenged within the scope of the logically framed analytical reasoning that would explore their consequences, within the systems in which they are perhaps at least somewhat arbitrarily assumed to hold axiomatic value.

• What statements, realistically, should be considered as axiomatic and serve as such as a starting point for carrying out logical analyses that would not be burdened by what could become infinite regressions in background reasoning, foreclosing any more definitive attempted analysis going forward? What should simply be assumed as a collective starting point that all relevant logical deductive reasoning would be built from, in fleshing out an axiomatic theory?

• And how many such axioms should be presumed in any given logically developed axiomatic system?

A theory of business seeks to model and descriptively and predictively represent a very particular aspect of empirically grounded reality. So the What of that as touched upon in the first of those bullet points is empirically constrained in such theory systems, in ways that it might not be in more entirely abstract non-empirical systems. More specifically, axioms or rather proposed axioms that might be presume to be true and valid but that would posit as real, potentially observable states that differ from observable reality, would of necessity fall into question if used in a general theory such as a theory of business. They would not adequately, accurately serve to model empirically observable reality as presumably would be addressed in such a body of theory. And that certainly holds true if and when the observations themselves that would test and challenge those axiomatic assertions seem to be validly accurate and reliable. But what of the second of the above two bullet points? How many axioms should be included in any given system to adequately cover it for its intended scope of generality and inclusiveness?

This leads me to William of Occam and his meta-theory postulate: his axiomatic presumption as to how axiomatic systems should be framed and in this case constrained: Occam’s razor:

• The simplest resolution to any logically framed problem: the simplest solution to it, should be presumed to be true.

And when considering axiomatic systems and their best formulations as logically framed problems, this directly leads to an injunction dictating that these theories hew to a minimum possible set of axiomatic assumptions that can adequately meet their needs in supporting arguably valid conclusions (provable theorems) while invalidating arguably false ones.

Let’s consider my purposefully challenging wording there: “an injunction dictating.” One way that Occam’s razor can be, and has been pushed for its underlying logic to a reductio ad absurdum degree can be found in what is sometimes called Occam’s Procrustean bed. First some background: Procrustes (Προκρούστης) or the stretcher if you will, was a mythological Greek character, said to have come from Attica who was less than favorably known for his hospitality. It seems that he had a guest bed of his own construction that he reserved for visiting travelers, that was made of iron. And if a guest who fell into his hands was too short to perfectly fit his bed he had them stretched until they did fit it; if they were too tall to fit he had them cut down to size until they did too. Occam’s Procrustean bed arises when the same brute force approach is taken to enforce a specific set of axioms, with no additions, subtractions or reconciliations or adjustments between them possible, and exactly as arose in the “logic” of Procrustes’ iron bed and in how his guests were “adjusted” to fit its dictates.

Geometers who questioned the empirical validity of Euclid’s fifth postulate as an absolute, universally valid given, avoided or transcended if you prefer, the restrictions of Occam’s Procrustean bed by positing a geometry that held to all of Euclid’s other, unquestioned axioms as valid, but that left out the fifth, devising what is referred to as absolute geometry, or neutral geometry as it is also called. And going beyond that, geometers who questioned that fifth postulate also created non-Euclidean geometries that held as axiomatic, alternative postulates that explicitly deviated from and violated Euclid’s fifth, and in very specific and precise ways. They developed alternative geometries that simply set aside the issues of Euclid’s fifth postulate, or that explored alternatives to it and in precise analytical detail.

And this brings me to the issues of empirically grounded theories and the models of understanding that can be developed from them, as their axiomatic starting points are selected and logically explored for their consequences. I am going to continue this narrative in a next series installment where I will consider an empirically based approach to arriving at a meaningfully valid set of axioms for a specific general theory such as a theory of business. And I will base that conceptually on a set of approaches that have come to be known as reverse mathematics. For a reference on that field of study, which I will cite in that posting, see:

• Stillwell, J. (2018) Reverse Mathematics: proofs from the inside out. Princeton University Press.

I highly recommend that book as a fascinating read. I will also at least begin a discussion of the number of axioms that would best be pursued and included in any given general theory, where the reasoning behind Occam’s razor can only provide a lower limit to that. This will mean adding consideration of completeness and consistency to this narrative, and certainly for any significantly scaled body of theory that can be enumerably represented, as applies for essentially any theory of or modeling of business systems.

I conclude this posting by pointing out the specific title to this series and a phrase in it, that appears in each of its installments: “some thoughts concerning a general theory of business.” I approach and label this at least series-long endeavor that way, precisely because I do not start out presuming a finalized, absolutely valid, completely inclusively adequate set of foundational axioms in what I offer. So what I offer here is of necessity a step in what can only be considered a larger and more ongoing work in progress that neither I nor any other individual can be expected to fully conclude. I began this series with a discussion of compendium and axiom-based theories in its Parts 1-8. Those two conceptual approaches are of necessity related, where every basic compendium model element: every specific phenomenon that would be offered in it that could be descriptively and predictively represented through a body of potentially observable findings, carries with it its own axiomatic assumptions. There, developing a more inclusive and ideally more universal single rules based theory, means arriving at a single overarching set of axiomatic starting point assumptions and understandings that would apply to all compendium approach puzzle pieces that would be included and covered within it. And with this, I explicitly link this posting and what will immediately follow it regarding general theories per se, to Parts 1-8 of this series, as a single framework for developing and exploring general theories of business as a special case.

Meanwhile, you can find this and related material about what I am attempting to do here at About this Blog and at Blogs and Marketing. And I include this series in my Reexamining the Fundamentals directory and its Page 2 continuation, as topics Sections VI and IX there.

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