Archive for the ‘language’ Category

Revisiting The Federalist Paper No. 31 by Alexander Hamilton: An Analogy from Geometry

July 10, 2018

[John Platt’s chapters on social chain reactions in his 1966 book, The Steps to Man, provoked my initial interest in looking into his work. That work appears to be an independent development of themes that appear in more well-known works by Tarde, Hayek, McLuhan, Latour, and others, which of course are of primary concern in thinking through metrological and ecosystem issues in psychological and social measurement. My interest also comes in the context of Platt’s supervision of Ben Wright in Robert Mulliken’s physics lab at the U of Chicago in 1948. However, other chapters in this book concern deeper issues of complexity and governance that cross yet more disciplinary boundaries. One of the chapters in the book, for instance, examines the Federalist Papers and remarks on a geometric analogy drawn by Alexander Hamilton concerning moral and political forms of knowledge. The parallel with my own thinking is such that I have restated Hamilton’s theme in my own words within the contemporary context. The following is my effort in this regard. No source citations are given, but a list of supporting references is included at bottom. Hamilton’s original text is available at:  ]


Communication requires that we rely on the shared understandings of a common language. Language puts in play combinations of words, concepts, and things that enable us to relate to one another at varying levels of complexity. Often, we need only to convey the facts of a situation in a simple denotative statement about something learned (“the cat is on the mat”). We also need to be able to think at a higher level of conceptual complexity referred to as metalinguistic, where we refer to words themselves and how we learn about what we’ve learned (“the word ‘cat’ has no fur”). At a third, metacommunicative, level of complexity, we make statements about statements, deriving theories of learning and judgments from repeated experiences of metalinguistic learning about learning (“I was joking when I said the cat was on the mat”).

Human reason moves freely between expressions of and representations of denotative facts, metalinguistic instruments like words, and metacommunicative theories. The combination of assurances obtained from the mutual supports each of these provides the others establishes the ground in which the seeds of social, political, and economic life take root and grow. Thought itself emerges from within the way the correspondence of things, words, and concepts precedes and informs the possibility of understanding and communication.

When understanding and communication fail, that failure may come about because of mistaken perceptions concerning the facts, a lack of vocabulary, or misconceptions colored by interests, passions, or prejudices, or some combination of these three.

The maxims of geometry exhibit exactly this same pattern combining concrete data on things in the world, instruments for abstract measurement, and formal theoretical concepts. Geometry is the primary and ancient example of how the beauty of aesthetic proportions teaches us to understand meaning. Contrary to common sense, which finds these kinds of discontinuities incomprehensible, philosophy since the time of Plato’s Symposium teaches how to make meaning in the face of seemingly irreconcilable differences between the local facts of a situation and the principles to which we may feel obliged to adhere. Geometry meaningfully and usefully, for instance, represents the undrawable infinite divisibility of line segments, as with the irrational length of the hypotenuse of a right isosceles triangle that has the other two sides with lengths of 1.

This apparently absurd and counter-intuitive skipping over of the facts in the construction of the triangular figure and the summary reference to the unstateable infinity of the square root of two is so widely accepted as to provide a basis for real estate property rights that are defensible in courts of law and financially fungible. And in this everyday commonplace we have a model for separating and balancing denotative facts, instrumental words, and judicial theories in moral and political domains.

Humanity has proven far less tractable than geometry over the course of its history regarding possible sciences of morals and politics. This is understandable given humanity’s involvement in its own ongoing development. As Freud put it, humanity’s Narcissistic feeling of being the center of the universe, the crown of creation, and the master of its own mind has suffered a series of blows as it has had to come to terms with the works of Copernicus, Darwin, and Freud himself. The struggle to establish a common human identity while also celebrating individual uniqueness is an epic adventure involving billions of tragic and comedic stories of hubris, sacrifice, and accomplishment. Humanity has arrived at a point now, however, at which a certain obstinate, perverse, and disingenuous resistance to self-understanding has gone too far.

Although the mathematical sciences excel in refining the precision of their tools, longstanding but largely untapped resources for improving the meaningfulness and value of moral and political knowledge have been available for decades. “The obscurity is much oftener in the passions and prejudices of the reasoner than in the subject.” Methods for putting passions on the table for sorting out take advantage of the lessons beauty teaches about meaning and thereby support each of the three levels of complexity in communication.

At this point we encounter the special relevance of those three levels of complexity to the separation and balance of powers in government. The concrete denotative factuality of data is the concern of the executive branch, as befits its orientation to matters of practical application. The abstract metalinguistic instrumentation of words is the concern of the legislative branch, in accord with its focus on the enactment of laws and measures. And formal metacommunicative explanatory theories are the concern of the judicial branch, as is appropriate to its focus on constitutional issues.

For each of us to give our own individual understandings fair play in ways that do not give free rein to unfettered prejudices entangled in words and subtle confusions, we need to be able to communicate in terms that, so far as possible, function equally well within and across each of these levels of complexity. It is only to state the obvious to say that we lack the language needed for communication of this kind. Our moral and political sciences have not yet systematically focused on creating such languages. Outside of a few scattered works, they have not even yet consciously hypothesized the possibility of creating these languages. It is nonetheless demonstrably the case that these languages are feasible, viable, and desirable.

Though good will towards all and a desire to refrain so far as possible from overt exclusionary prejudices for or against one or another group cannot always be assumed, these are the conditions necessary for a social contract and are taken as the established basis for what follows. The choice between discourse and violence includes careful attention to avoiding the violence of the premature conclusion. If we are ever to achieve improved communication and a fuller realization of both individual liberties and social progress, the care we invest in supports for life, liberty, and the pursuit of happiness must flow from this deep source.

Given the discontinuities between language’s levels of complexity, avoiding premature conclusions means needing individualized uncertainty estimates and an associated tolerance for departures from expectations set up by established fact-word-concept associations. For example, we cannot allow a three-legged horse to alter our definition of horses as four-legged animals. Neither should we allow a careless error or lucky guess to lead to immediate and unqualified judgments of learning in education. Setting up the context in which individual data points can be understood and explained is the challenge we face. Information infrastructures supporting this kind of contextualization have been in development for years.

To meet the need for new communicative capacities, features of these information infrastructures will have to include individualized behavioral feedback mechanisms, minimal encroachments on private affairs, managability, modifiability, and opportunities for simultaneously enhancing one’s own interests and the greater good.

It is in this latter area that our interests are now especially focused. Our audacious but not implausible goal is to find ways of enhancing communication and the quality of information infrastructures by extending beauty’s lessons for meaning into new areas. In the same way that geometry facilitates leaps from concrete figures to abstract constructions and from there to formal ideals, so, too, must we learn, learn about that learning, and develop theories of learning in other less well materialized areas, such as student-centered education, and patient-centered health care. Doing so will set the stage for new classes of human, social, and natural capital property rights that are just as defensible in courts of law and financially fungible as real estate.

When that language is created, when those rights are assigned, and when that legal defensibility and financial fungibility are obtained, a new construction of government will follow. In it, the separation and balance of executive, legislative, and judicial powers will be applied with equal regularity and precision down to the within-individual micro level, as well as at the between-individual meso level, and at the social macro level. This distribution of freedom and responsibility across levels and domains will feed into new educational, market, health, and governmental institutions of markedly different character than we have at present.

A wide range of research publications appearing over the last several decades documents unfolding developments in this regard, and so those themes will not be repeated here. Some of these publications are listed below for those interested. Far more remains to be done in this area than has yet been accomplished, to say the least.



Sources consulted or implied

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