Precisification: Calibrating our Concepts

14 August 2010


The Antikythera mechanism: the origins of precision.

One of the points of contact between the scientific revolution and the industrial revolution was the development of precision instruments, which in turn made precision calibration possible, which in turn made precision engineering possible. None of the technological marvels we use in our daily lives today would be possible without precision engineering. There is evidence of limited precision engineering in the past (for example, the famous Antikythera mechanism), but before the industrial revolution the feedback loop between science, engineering, and technology had not developed into the industrial concern that it is today, and that limited its availability and its usefulness.

Today we are surrounded by precision; it is widely available and has proved its usefulness in countless ordinary activities. Despite the sophistication of our technology and the engineering the produces it, we tolerate a high degree of imprecision with the concepts that we use in our everyday life. As mentioned above in relation to ancient engineering, so too with ancient philosophy: there is evidence of the limited development of precision concepts (Aristotle’s logic, for example), but very little was made systematic. There are many within the analytical philosophy community today who share the common goal of bringing this kind of systematic precision to our philosophical thought. These efforts are not well known, in the same way the the efforts of precision engineers are not well known. Moreover, the work has not progressed to the level that would make it possible to produce articles for mass consumption. In fact, I can’t imagine an application of precision concepts that would ever produce articles for mass consumption.

But there could be. That is the tantalizing thought. There has been a partial precisification of economics as the dismal science has been mathematicized over the past century. Imagine politics, strategy, and diplomacy transformed through the use of precision concepts. Perhaps more to the point in the lives of most people, imagine the software and operating systems that you use every day on computers and cell phones transformed by the use of precision concepts. This is not happening. In fact, the opposite is happening. One of the few developments in contemporary logic possibly known to the general public is the recent work on fuzzy logic. There is a presumption that human beings think in such vague and imprecise terms that if we are going to produce usable machines then these machines will need to share in our vagaries. I do not dismiss this out of hand, but it is not the whole story.

A precisification of our ideas would enable the calibration of the concepts we employ, which would in turn enable more precise thinking. More precise thinking would clear up many muddles that make lives miserable, unpleasant, and uncomfortable. I am not suggesting that conceptual precision is a panacea, only that it offers certain benefits to the society that embraces them, and that we are not enjoying these benefits at present, or we are only doing so on a very limited basis.

In the spirit of precisification and the calibration of our concepts, here are some aphorisms that I posted to Twitter today:

1. A precise concept is a precisely delimited concept.

2. The precise delimitation of a concept prescribes tertium non datur for that concept, if for nothing else (e.g., the object for which the concept stands).

3. In so far as conceptual precision implies tertium non datur, precision is non-constructive (in the intuitionistic sense).

4. However precisely delimited a concept is in one respect, there will be other respects in which the same concept is not precisely delimited.

5. Even precision itself must admit of delimitation.

6. A perfectly simple concept might be made precise with no imprecise remainder, but perfectly simple concepts are few and far between.

7. Our concepts are as complex as the lives that generate them, and life is no simple matter.

8. Simple concepts capable of precision constitute a small subset of all concepts, and thereby again reveal the limitations of precision.

9. Either a concept reflects the complexity of life and cannot therefore be made perfectly precise, or a concept can be made perfectly precise but its application to the complexity of life is limited by this simplicity.

10. If you want to be precise, you must accept limitation.

11. If you will not accept limitation, you cannot be precise.

12. Imprecision as a consequence of defying limitation implies a commitment to the actual infinite, making imprecision as non-constructive as precision (cf. 3 above).

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2 Responses to “Precisification: Calibrating our Concepts”

  1. T. Greer said

    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.

    • geopolicraticus said

      Dear Mr. Greer,

      I was interested to see that the link that you provided included an epigraph of one of my favorite Einstein quotes, to which I often refer:

      “As far as the laws of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality.”

      In fact, when I was writing this post I almost included this quote because it is so closely relevant to the topic. Elsewhere I have written about “the tension between intuition and formalization” that one finds in all the formal sciences, including formal economics as it has emerged over the past hundred years.

      For my part, I find economics to be rather exciting, and I don’t feel that it makes me at all dismal (readers and acquaintances may disagree). In middle age, I find that economics, along with ontology and strategy, is able to retain my interest when little else can, and not least because these disciplines provide the most concrete relationship between theory and practice. This relationship is part of the tension between intuition and formalization.

      That being said, my own book on economics, Political Economy of Globalization, explicitly adopts a conceptual approach because I believe that the concepts that lie at the foundation of contemporary mathematical economics are deficient, and their deficiency can only be addressed by further conceptual work; in other words, model building with deficient concepts is only going to dig us deeper into a conceptual rut.

      So on this we will have to respectfully disagree: I welcome the day that strategy and politics will be given formal expression, and I hope to contribute to this development. I will admit to the value of intellectual humility to which you allude, but I also insist upon following the path of precision as far as it can take us — how else can we learn humility? — and it has quite some way to take us yet.

      Your formulation of your position, by the way, reminds me a little of Colin McGinn’s contention that the mind-body problem cannot be solved in his Problems in Philosophy: The Limits of Inquiry, a particular application of a thesis that he calls transcendental naturalism.

      Best wishes,


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