Platt Perspective on Business and Technology

Zeno’s paradox, Moravec’s paradox and rethinking how we project forward in our planning 4

Posted in business and convergent technologies, reexamining the fundamentals by Timothy Platt on January 26, 2015

This is my fourth posting to a series on paradoxes, and both as philosophical constructs and as the concept of paradox is applied to business and technology contexts (see Ubiquitous Computing and Communications – everywhere all the time 2, postings 305 and loosely following for Parts 1-3.)

So far in this series I have presented and at least briefly discussed two specific paradoxes:

• An historically ancient example of this phenomenon with one of Zeno’s paradoxes (see Part 1), and
• A modern technology-oriented example what has come to be called Moravec’s paradox (see Part 2.)

And I have offered and discussed four reasons by which a statement might seem to be paradoxical, developing them in terms of these working examples. And in the course of that, and in Part 3 in particular, I have begun discussing axiomatic systems per se, there focusing on the issues of completeness and consistency and how these properties cannot be presumed to hold for any axiomatic system of any real complexity – and certainly if it can be represented in more rigorous abstract mathematical or mathematical logic terms.

My goal for this posting is to more fully discuss what my four (so far) stated reasons for evaluating possible paradoxes actually are, and as a starting point for that I begin with:

• A direct continuation of my Part 3 discussion of axioms and axiomatic systems,
• And as they might be applied to provably valid and provably invalid statements,
• And more particularly in how they might be applied to truth-indeterminate and seemingly paradoxical statements.

And as a starting point for that, I repeat my list of paradox-analysis criteria by repeating the four that I have already discussed up to here:

1. A seeming paradox can arise when a logically consistent and formally valid line of reasoning is offered in description of an empirically observable circumstance, but where its underlying axiomatic assumptions are not applicable to the circumstances or conditions for which it is being applied.
2. Alternatively, a seeming paradox can arise and even when the application of its reasoning to a specific empirically observable circumstance would seem valid, when there are perhaps subtle and unobvious but still significant flaws or gaps in its underlying logic.
3. A seeming paradox can also arise when axiomatic assumptions are made that simply reflect the limitations of some current state of the art and for the technology available, for current practices in using that technology, or both. And this can, among other things arise because of implicit assumptions that the particular path that technology is developed in historically, could be the only one possible.
4. A statement or assertion might appear to be paradoxical if it can only be understood and explained by either altering or generalizing an axiom already in place in new and unexpected directions, or by adding in one or more new supporting and validating axioms to the logically framed system of understanding that they are evaluated within.

And I add a fifth to that here, that is also explicitly grounded in the reasoning that entered into Part 3 of this series:

5. A truly truth-indeterminate statement of the type that Gödel proved to exist in his incompleteness theorems would be fundamentally indistinguishable from a paradox and as such could be seen as presenting itself as one if arrived at and analyzed – in an axiomatic system where its validity could not be established and within the limitations of provability imposed by those incompleteness theorems.

And I start from there with a simple question: what do these five points hold in common beyond the obvious detail that they all seek to in some way describe how a statement can at least appear to be paradoxical?

• All five of them, and I add an undoubtedly open-ended number of potential additions to that list can be considered axioms – in a logical framework that is intended to analyze other axiomatically-based logical systems.
• As such they are axiomatic metalogical statements – automatically assumed logical statements about what are at least in principle validatable logical statements,
• And their level of validatable truth when considered in the specific logical frameworks that they are stated within has to be considered a significant discussion thread of this series too.

And with that in place in developing the discussion of this series, I come to the issues that I stated at the end of Part 3, I would focus on next and that I will at least begin to more fully discuss in my next series installment:

• Smoothly developing evolutionary and discontinuity-defined disruptive change, and
• Descriptive and predictive understandability from the perspective of the conceptual framework that I have been developing in this series up to here.
• And I add here to that list, a discussion of formal and heuristic axiomatic systems as up to here, I have fairly thoroughly blurred an important distinction there.
• And I also add that after discussing these points and the issues that they represent, I will address a topic area that I have been building up to throughout this series: the validity and capacity for validation of the type of system of axiomatic assumptions and emergent statements that I have developed in assembling this blog itself, as a descriptive and recommendational model of business and technology, and from the level of the individual employee, the single business functional area, the business as a whole, systems of businesses, and entire economies.

Meanwhile, you can find this and related postings at Ubiquitous Computing and Communications – everywhere all the time 2 and in my first Ubiquitous Computing and Communications directory page. I also include this in my Reexamining the Fundamentals directory as an entry to a new Section V: Rethinking Underlying Assumptions and Their Logic.

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