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Marginalism and Discontinuity

Marginalism and Discontinuity: Tools for the Crafts of Knowledge and Decision

Copyright Date: 1989
Published by: Russell Sage Foundation
Pages: 208
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  • Book Info
    Marginalism and Discontinuity
    Book Description:

    Marginalism and Discontinuityis an account of the culture of models employed in the natural and social sciences, showing how such models are instruments for getting hold of the world, tools for the crafts of knowing and deciding. Like other tools, these models are interpretable cultural objects, objects that embody traditional themes of smoothness and discontinuity, exchange and incommensurability, parts and wholes.

    Martin Krieger interprets the calculus and neoclassical economics, for example, as tools for adding up a smoothed world, a world of marginal changes identified by those tools. In contrast, other models suggest that economies might be sticky and ratchety or perverted and fetishistic. There are as well models that posit discontinuity or discreteness. In every city, for example, some location has been marked as distinctive and optimal; around this created differentiation, a city center and a city periphery eventually develop. Sometimes more than one model is applicable-the possibility of doom may be seen both as the consequence of a series of mundane events and as a transcendent moment. We might model big decisions or entrepreneurial endeavors as sums of several marginal decisions, or as sudden, marked transitions, changes of state like freezing or religious conversion.

    Once we take models and theory as tools, we find that analogy is destiny. Our experiences make sense because of the analogies or tools used to interpret them, and our intellectual disciplines are justified and made meaningful through the employment of characteristic toolkits-a physicist's toolkit, for example, is equipped with a certain set of mathematical and rhetorical models.

    Marginalism and Discontinuityoffers a provocative and wide-ranging consideration of the technologies by which we attempt to apprehend the world. It will appeal to social and natural scientists, mathematicians and philosophers, and thoughtful educators, policymakers, and planners.

    eISBN: 978-1-61044-340-1
    Subjects: Sociology

Table of Contents

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  1. Front Matter
    (pp. i-vi)
  2. Table of Contents
    (pp. vii-viii)
  3. Preface
    (pp. ix-xii)
  4. Acknowledgments
    (pp. xiii-xvi)
    M. K.
  5. Introduction
    (pp. xvii-xxiv)

    Here I want to provide a fairly abstract epitome of the themes of toolishness, marginalism, and discontinuity. And then I want to look briefly at a countertheme, that of middles, mixtures, and transitionality.

    Taking the World Toolishly. Toolishness is a vital theme in twentieth-century thought, transforming the Kantian transcendental categories concerned with perception and cognition into categories of action, intervention, and construction and repair. Tools are modular, they get around the subject-object dichotomy much as do the transcendental categories, and they are instantiated in vivid examples that “everyone knows.” They provide a way of thinking about the task of constructing...


    • CHAPTER ONE Big Decisions
      (pp. 3-18)

      A recurrent theme in modem thought and institutions has been the transformation of things big into sets, sums, or sequences of things little.* The aim is to be analytical and methodical: break something down into its presumed parts, and then properly and automatically recompose them all. Neoclassical economics relies on a “Principle of Continuity,” as defined by Alfred Marshall in hisPrinciples of Economics(1890), to assure the possibility of both analysis and recomposition through the calculus: “ … that there is a continuous gradation” in preferences and time periods and “ … that our observations of nature, … relate...

    • CHAPTER TWO Adding Up the World
      (pp. 19-36)

      Making the world additive is a pervasive human theme. Can we find a scheme or algorithm which converts a series of steps into a process of arithmetic addition, their consequences into a sum? For the ancients there was arithmetic, mensuration, and harmonics. The modern mathematization of nature is a commitment to adding up the world as a way of putting together its presumed pieces, and an attempt to classify the cases, often about discontinuity, when that additive decomposition is not manifestly possible.

      Here I want to explore the following claims:

      1. Whatever else it is, mathematics is a tool. It is...

    • CHAPTER THREE Where Do Centers Come From?
      (pp. 37-50)

      A center is a marked place in space, or in time, or in a collection of objects. Such a center could be a point, an orientation, or an asymmetry. It could be an author or a style, around which an oeuvre or a collection is organized, or a prime object, which defines all others as derivative or anticipatory of it. Surrounding a center is a structure that in effect supports it and points to it, and that structure is exhibited through inhomogeneity or pattern. So, for example, if there is falloff toward the boundary, or the periphery arises from the...

    • CHAPTER FOUR Sticky Systems
      (pp. 51-60)

      If we push on a part of the world, it may move smoothly enough in response, if not without a resistance. That resistance may be an inertia due to mass; or the viscous drag and friction of water, slime, or molasses; or the harmonic force of a spring or of an economy in equilibrium; or societal conservatism due to tradition, convention, and solidarity. Such resistance may be proportional to the mass or drag of what we are pushing, its speed or its acceleration, and how hard we push. This resistance might even be termed marginal.

      Yet the resistance is sometimes...

    • CHAPTER FIVE Economy, Perversion, and Fetishes
      (pp. 61-82)

      Economy is a story of exchange and property, a story that appears in commerce, kinship, and natural science. Conventionally, an economy is a means for allocating and valuing goods and resources through processes of comparison and exchange. It may employ monetary intermediates, and the prices assigned to goods treated as commodities tell how valuable they are in relation to each other. In market economies the prices are also signals indicating where we might make our investments and purchases, valuing alternative opportunities. Economy also provides a justification for alienation. Individuals, as alienated, achieve their best in a market economy. For it...


    • CHAPTER SIX The Horizon of Mathematics
      (pp. 85-96)

      Mathematicians know that a rigorous proof is only one aspect of actually doing mathematics. The challenge is to find a theorem, a mode of stating what must be the case, that is worth proving. And for that we must understand what is really going on. Then we can begin to construct a proof for the theorem, although at that point we will surely discover even more about what is really going on, modifying both proof and theorem. Sometimes a proof is crucial, in that our blindness is epitomized by the proof’s flaws or by a problematic passage. The pride of...

    • CHAPTER SEVEN The Physicist’s Toolkit
      (pp. 97-112)

      Natural science is often described in sacred terms, whether it be a search for the truth or an uncovering of Nature’s secrets. Yet the everyday life of scientists is surely mundane. They do their work mostly between breakfast and supper, within a complex bureaucratic system, they themselves being well trained in their field but are otherwise rather more ordinary people. We have already discussed some of the connections between mundane and sacred practice, how we set things up so that we may appreciate the wonders of nature. Still, everyday practice remains veiled to outsiders, perhaps because it is mystified by...

    • CHAPTER EIGHT The Possibility of Doom
      (pp. 113-128)

      Doomsday is judgment day. Stories of doom are moral descriptions, judgments of how we live now and claims about how we ought live. They are motivated by what seems least under our control and is most frightening, and they are meant to warn us of our wayward paths and to influence what we might do next. As worst-case scenarios, we pay attention to them not because they are likely but because the untoward consequences they describe are so very great.

      Science has perhaps succeeded religion and theology as the source of the most authoritative stories of doom, and consequently the...

    • CHAPTER NINE Los Angeles and the Frontier
      (pp. 129-136)

      Places become archetypes of their countries or regions, epitomizing larger themes and conflicts, mythifying a culture’s obsessions and taboos. For the United States, the West has been such a place, an other place compared to the East and the Middle West. And Los Angeles has come to be the place in which that otherness is crystallized—whether it be tinsel town Hollywood, or multiethnic world-city Los Angeles. How might the myth of a place be related to the actualities of life around it? For a place is not just a set of properties, whether they be demographic, spatial, or economic....

  8. EPILOG: Bringing Up Baby
    (pp. 137-140)

    If our world is marginal and may be added up, it is as well resistant to that strategy and is discontinuous, nonlinear, nonconservative, sacred, and historical. Even if Marshall was right in asserting that nature does not make jumps, notions of bigness, stickiness, fluctuation, perversion, and fetishism and taboo are not likely to be retired by smoothing out the world or by any straightforward reductionist program.

    These seemingly contradictory features are equiprimordially present in our world. We find ourselves within a dialectic of marginalism and discontinuity, mechanism and design, object and anima, and tradition and invention. We need all the...

  9. Notes
    (pp. 141-164)
  10. Bibliography
    (pp. 165-174)
  11. Index
    (pp. 175-182)