Monday, October 22, 2012

There is no such thing as 1 + 1 = 2

at 11 comments
Picture credit: SP-Studio

What runs through most of my writings is a subjectivist approach to life, springing from a deep and pervasive desire to emancipate myself from any cozy pattern of thought that has been established or greatly influenced by prejudices, political opportunism, hypocrisy and convention. I simply do not want to be cast into a mould or conform unwittingly with whatever others—all others—may hold dear. For that reason I proceed to question every shibboleth, practice or theory I find worth deconstructing, always with the tacit understanding that I may not necessarily be expounding on any sort of truth myself, but quite possibly on yet another profound fallacy or tissue of illusions. Concerns on truth per se notwithstanding, I often find myself arguing that "there is no such thing as ..." followed by the concept which I elaborate on.

One day over lunch, I was regaling (or testing the patience of) my friends with some unconventional ideas of mine on national sovereignty and identity, both of which I consider artificial to say the least. At some point a person whom I came to befriend in the most bizarre and unexpected of ways one could ever imagine, made a very valid joke over my attitude to question established truths and perceptions, which made me reply, in a similarly humorous fashion, that I even disagree with the mathematical proposition of 1 + 1 = 2. Of course the discussion was carried out in a light spirit and soon ran off into another tangent. My statement in that context was never meant to be substantive, but rather to exaggerate an accurate remark made by my friend on my tendency to criticize. Nevertheless my disagreement with the mathematical truism was not at all a joke; I really do believe that 1 plus 1 does not necessarily equal 2, or more fully, I often myself confronted with the realization that 1 + 1 ≠ 2.

Mathematics is considered to be a precise science, yet this may only hold true in a perfectly abstract province of thought, where again generalizations are prerequisites to any path in mathematical knowledge. The number 1 for instance is supposed to be an absolute and universal truth, yet this scarcely ever is the case in the complexity of the real world for 1 is in fact a constantly self-differentianing concept that may only be considered '1' after all epistemological concerns are sacrificed to the altars of expediency and practicality.

1 qua 1 does not exist. A more precise way of putting it is to claim that 1α ≠ 1β ≠ 1γ ≠ ... ≠ 1ν where ν = ∞. To put it in linguistic form, it is more correct and precise to suggest that 1 exists in an infinite array of 1 all of which are in a dynamic process of constant, even though marginal, differentiation from one another. I wish not tread on this purely theoretical insight, at least not for the time being, for it might prove too tedious a task for a mere blog post, yet I shall apply this simple syllogism to capital theory so as to illustrate my radically subjective approach to the topic now under discussion.

Economists use the generic term capital in almost every single piece of work they produce. The word may be applied to a variety of situations, with the function of providing a descriptive term to substantially different things. In modern macroeconomics "capital" is seen as yet another holistic aggregate which is, for the sake of mathematical convenience, considered homogeneous. As such we often witness economists propounding theories on how to increase the capital stock or to control and manipulate capital flows etc. As important as these issues may be to the politician and decision-maker, it is the task of the judicious theorist or economist to reject such aggregative conceptualizations as epistemologically erroneous and misleading.

Capital is heterogeneous and the capital structure is always dependent on time, or rather on the interrelations and complementarities that are formed in the passage of time. Different types of capital goods may not be summed up together as their use-values may be antithetical to one another. For instance a building may be considered 'capital' if it is deployed for certain uses. Its value qua capital exists in e.g. performing a number of specific functions, such as housing a production process. A cannon may also be considered 'capital' with its use-value being, inter alia to destroy buildings. Assuming a simple world these two together may not be valuable at the same time, for one may only have use-value at the expense of the other; the building has value for as long as it remains standing, while the cannon is valuable only if it demolishes buildings. Under these circumstances a macroeconomist or statistician with the task of measuring the capital stock, or otherwise the total amount of existing capital, will be committing an egregious error if she proceeds into lumping together the building with the cannon, for the two capital goods have value only as against one another, making their summation absurd and meaningless.

But the argument does not stop at the level of capital goods with mutually-exclusive use-values, since even if we consider only two capital goods that superficially are the same, we may still be facing an impossibility in trying to add them up in some holistic indicator. The problem exists in the fact that value is an individualistic experience which is always time-related among others, meaning that the value of a capital good may have substantial inter- and intra- personal and temporal variations. A building, to use the same example of a possible capital good, may be of great value for a given use to person X in time T1, and of insignificant value to person Y also in time T1. In time T2 this may no longer be the case, as person Y might then find the capital good more valuable than before while person X might then consider it of less value to herself (time is only one of many factors influencing value – adding more such factors to the train of thought will be more pragmatic but will not change the substance of the argument, while it will add a great deal of unnecessary complexity).

To cut the long story short, the value of capital, just like all value in economics, is purely subjective as it is dependent on a complex, interweaving web of causes, all of which may at any point be altered in multiple ways, in the passage of time. Consequently it is in fact impossible to produce any genuinely accurate aggregate which refers to capital as such, for 'capital' as a homogeneous and unalterable entity does not and cannot exist; and even if it were homogeneous on the surface it still may be subject to irresistible forces of constant differentiation, especially related to time (for those with any serious interest in capital theory, I recommend you start reading Ludwig Lachmann, Capital and its Structure).

I hope the above application of the mathematical insight to capital theory has been of help in illustrating my argument that the proposition 1 + 1 = 2 is only true in the perfectly abstract, time-less sense for as we saw it can well happen that 1α + 1β ≠ 2 in time Tx, since the two capital goods α, β are not really the same even though both are 'buildings', 'cannons' or 'capital', as they either have constantly changing values over persons and time or retain use-values that are at any given point antithetical to one another or mutually-exclusive.

This short post does not even begin to reveal the full extent of what I have mind, perhaps because I myself have yet to untangle all the thoughts that are interwoven in varying and complex ways with one another in several stages of the thinking process. However I do believe that this rather straightforward insight can be applied to many areas of research, while the inferences to be derived from them can certainly be far reaching. My primary purpose here was to throw some light on certain fields of thought I have lately been treading in, even though I still have many inroads and intellectual tracks to make. I guess I also wrote this short piece with the aim of demonstrating my subjectivism and for satisfying a perhaps apocryphal desire to provide another source of inspiration to the lunchtime friend I mentioned earlier, who will now have the chance to use this article to produce yet more jokes of my armchair theories and impractical, aka useless, deductions :-) Cheers!
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Protesilaos Stavrou

I specialize in European Union politics and the political economy of the Euro area. I am a left libertarian, a subjectivist, a relativist and a Cynic in the original sense of the latter term. I was born in Greece in 1988 and since February 2012 I live in Brussels, where I work at the European Parliament as an assistant to an MEP. The opinions Ι express on this website and my other social media profiles are strictly personal and do not reflect the views of any employers, organizations or institutions that are, have been, or may be affiliated with me.

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11 comments:

  1. Agreed. Although subjectivism in probability theory has been around since Laplace (i.e end of the 18th and the beginning of 19th century) and even economists of the caliber of John Maynard Keynes have been struggling with it over the years, it seems like the idea has not caught up with the rest of the economists even since. As more areas of knowledge try to include more mathematics in them (with the rather stupid idea that something called an "art" is less important than something called a "science") more of what you describe as "precise science" will be visible albeit it will never be precise. Precision in mathematics appears only in the so called "pure" mathematics which have almost no resemblance with the real world. Even statistics, the main (perhaps the only nowadays) weapon in economists' arsenals is much more subjective than most people believe. As statistics necessarily need large samples to be more accurate, individual people are lost in the crowd. Thus, macroeconomic models using a "representative agent" are not representative at all. For this, we only have to blame economists' mania for order and equilibrium, terms derived from physics and mathematics, where laws are stricter, although more applied to those situations. To witness the great difference between economics and physics I quote John Maynard Keynes (although even he was not always right): "Professor [Max] Planck, of Berlin, the famous originator of the Quantum
    Theory, once remarked to me that in early life he had thought of
    studying economics, but had found it too difficult! Professor Planck
    could easily master the whole corpus of mathematical economics in a few
    days. He did not mean that! But the amalgam of logic and intuition and
    the wide knowledge of facts, most of which are not precise, which is
    required for economic interpretation in its highest form is, quite
    truly, overwhelmingly difficult for those whose gift mainly consists in
    the power to imagine and pursue to their furthest points the
    implications and prior conditions of comparatively simple facts which
    are known with a high degree of precision."

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  2. Thanks for the comment. Yours are very valid points. Indeed Keynes himself was concerned with subjectivism. The 'animal spirits' concepts is after all a theme of subjectivism if seen naked (I mean without any policy concerns).


    The argument here could have been presented in a more technical way, to illustrate such themes as time preference or even originary interest (though this is secondary), but I shall do so in a more systematic way in the (near) future.

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  3. Indeed, 'animal spirits' is a theme of subjectivism. Nevertheless, I do not believe that your arguments could have been presented better in a technical way, as arguments of this sort appear better in words ('philosophically' if you prefer) rather than symbols. In economics, as in many aspects of life, although we crave for the security of certainty, the distinction between qualitative and quantitative issues is occasionally hard and measuring the former even harder. In searching for 'certainty' and 'nice' mathematical equations is where most rationale and subjectivity is lost.

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  4. Yes you are right. Personally I do not cling on to mathematics or quantitative methods per se, as a consider them tools for research, or more fully the prolegomena to economic knowledge, not knowledge as such (this does not mean that I necessarily reject them of course, or that I find them unimportant).


    Economists all too often obfuscate reality or get lost in elegant geometric portrayals and complex formulas that look very attractive and "scientific".
    Indeed the use of words is more effective than that of symbols in elaborating on such themes. Thanks for that remark.

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  5. Even as a late reply, I have recently discovered another Keynesian Quote which I think is suitable for our discussion:
    "The study of economics does not seem to require any specialised gifts of
    an unusually high order. Is it not, intellectually regarded, a very
    easy subject compared with the higher branches of philosophy and pure
    science? Yet good, or even competent, economists are the rarest of
    birds. An easy subject, at which very few excel! The paradox finds its
    explanation, perhaps, in that the master-economist must possess a rare combination
    of gifts. He must reach a high standard in several different directions
    and must combine talents not often found together. He must be
    mathematician, historian, statesman, philosopher—in some degree. He must
    understand symbols and speak in words. He must contemplate the
    particular in terms of the general, and touch abstract and concrete in
    the same flight of thought. He must study the present in the light of
    the past for the purposes of the future. No part of man's nature or his
    institutions must lie entirely outside his regard. He must be purposeful
    and disinterested in a simultaneous mood; as aloof and incorruptible as
    an artist, yet sometimes as near the earth as a politician"

    P.S. Have a look at this short article I had written some time ago. I think you will agree with some of it:
    http://euronomist.blogspot.com/2012/08/economists-and-real-life-economy.html

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  6. This is an indeed very accurate remark from Keynes, which in effect states what many other prolific economists have at times suggested or practiced.


    On a general note on him, I believe he did offer a refreshing tendency to criticize the classical economic traditions and shibboleths. However I think that Keynes did not go as far as he ought to, for him to be consistent with his critical approach, nor did he truly manage to emancipate himself from the errors of previous modes of economic thinking, effectively falling back into the slough of fallacies that comprised earlier systems of thought.


    For instance he absorbed many of the tenets of reasoning of the mercantilists, while his circular flow theme was in principle a recrudescence of the physiocratic tableau. Meanwhile many of his underlying assumptions and methods were similar to those of his predecessors many of whom he detracted.


    In saying so I am not of course trying to be a nihilist or to downplay his importance in the history of economic thought. Finally I must note my belief that Keynes as a person, is not at all the same as the hagiographic, tutelary figure of keynesianism; or in other words, the work of Keynes and the works of the keynesians are not necessarily along the same lines.


    Concerning the growing chasm between the methods of economists and reality, which you correctly point out in your article, I must say that I fully agree with your proposition. I myself have a lot of trouble in accepting such manifestly unreal concepts such as the Walrasian general equilibrium, the static state, perfect competition, indifference curves etc. These fictions and figments are in my view only hindering our ability to be as close to reality as possible, rather than assist us in understanding the world which environs us.

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  7. Personally, I do not consider myself a Keynesian, (although I share some opinions with that school of thought) and I obviously hope never to become a classicist! Adhering to mathematical symbols to prove issues which can not even be well understood is idiotic: symbols (or in general mathematics) can prove anything you want them to prove, and I have done even as a student. Obviously, most of my professors would not accept that mathematics might be at fault for most (if not all) of the problematic issues in economics nowadays. Although I have stated that I do not consider myself a Keynesian another quote springs to mind:

    The famous "in the long run we are all dead". In lieu of the common understanding of this phrase, Keynes did not mean that we should not look at the long term. What he meant was simply that policies which harm the short-run in favour of the long-run (one might think of the disastrous Troika-imposed austerity measures which are bound to never let Greece grow) have no sense. What the long-run is saying is that the sea will be calm after the storm. The problem is what goes on during the storm and how can we get out of it unscathed? And unfortunately, no economist has the answer.

    Thus, using the false logic of people who have never seen how the world really works, as they have always observed the economy from the inside of a university office leads us to deep trouble. Austerity is not the answer for example. Yet a persistence in ideologies is very visible now. The Troika cannot accept that their measures are wrong and thus they push more through. Again with Keynes "were are slaves of a deceased economist".

    Having read your latest article, I could not help but agree with you. German obsession with control can only result to a totalitarian regime, which will mean the end of Europe. (as long as Golden Dawn in Greece and other nationalist parties in Europe don't do it first). I was optimistic at first that the situation would grow to be better. And yet, just as positive signs emerge, they seek to destroy them with more negative.

    The situation resembles (too much) with the state of the Weimar Republic in the early 1920's. You may recall what happened by the end of 1930's when that recession ended and who came to power. I really hope that history does not repeat itself.



    Our only hope is youth. Not yet succumbed to the brain-washed ideologies, ethics and values of the older generation, they should lead change. The problem is that they will face great resistance. Let us hope that they can overcome it.

    Unfortunately, we are only as good as the people who govern us. Too bad we cannot all have a Mario Monti (the only European economist thinking at the moment)

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  8. Good points. Indeed many (most) professors are not prepared to accept that mathematics is not the best tool for all topics. The problem fundamentally exists in a profound misunderstanding of mathematics as such, which is falsely considered as an intrinsically scientific organon. It clearly is not. Mathematics is just another language, resting on a number of logical 'truism' and basic axioms. Therefore I find the term "scientism" quite accurate in describing this epistemological misunderstanding.

    Agree with your remark on the meaning of the long run. No need for further comment there.

    The troika is indeed quite ideological – in the negative sense of the term 'ideological'. However it also serves a very specific political agenda, which is to shape the EU in accordance with the understanding of the powers that be. You see in a crisis, under extreme or desperate conditions, it is easier to propose such preposterous schemes as e.g. the Commissioner to veto national budgets which I discussed recently.

    On the issue of Golden Dawn, yes I agree that there are many things in common with the 1920's and 1930's. I am very worried about it as well. You might be interested in an extensive article I wrote on GD and Greek nationalism, though I must tell you that my views are a bit idiosyncratic: http://www.protesilaos.com/2012/09/golden-dawn-greece.html



    Concerning the youth, I agree in principle that the new generation is always the harbinger of change, however I would add that knowledge is also necessary –apart from the desire for change– so that we do not end up in a mere change of forms. But yes the youth is what brings hope.


    Yes Monti is an indeed very practical man.

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  9. Although I would not go as far as discarding mathematics, I would advocate "use with caution". This is the time where economics need more "philosophers" than mathematicians.


    It has been obvious throughout history that during times of crises and/or catastrophes many preposterous schemes have been proposed and accepted. One only need to remember the rise of Benito Mussolini or Adolf Hitler to power.

    As for Golden Dawn, I would agree with your article: just like any nationalist party, GD has build its arguments, policies and actions after taking into consideration the prejudices of the Greek people. I would especially agree with the part of the Greeks being overly idealistic and indeed the term banal patriotism is excellent for describing their obsession with the past.

    Unfortunately, it is not just the Greeks who face this problem. Most of the nations of the EU cannot accept the fact that the past is over. I have called this obsolete illusions in an article I have written more than 2 months ago: http://euronomist.blogspot.com/2012/08/obsolete-illusions.html
    On the subject, another quote that I particularly enjoy is that the person who can only brag about his/her ancestors is like a potato: all about him/her that is worthwhile are under the earth.

    Knowledge is indeed a prerequisite for meaningful change, as is political will and drive. My point is that many politicians nowadays do not possess neither of the aforementioned three and thus a change in the South's political setting need to be done. Greece's Prime Minister Antonis Samaras has shown signs of will and drive towards pursuing the necessary changes in the country, nevertheless, after being forced by Troika and the Germans he has very little margin to maneuver. Hopefully he will realize that GD is not just a fad as politicians in the last century thought of Fascism of Nazism. Democracy's inherent fault is that sometimes it not optimal (to use economic slang) for everyone to make a decision...

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  10. Yes agree on mathematics, "use it with caution" and always with the tacit understanding that it is a tool for science, not science as such.

    Indeed the economic schemes of Hitler/Mussolini are something to make note of. Especially the so-called syndicalist state of Mussolini or the "harmony of the classes" propounded by the Nazis. Both of course required a great deal of coercion to even be 'operational' and both ended up being corporatist to the core, even though they were supposed to be 'socialist'.

    Read your article and I certainly agree with it. Of course it is not just Greece. Nationalism broadly understood, is widespread in Europe, which in my view also explains the inter-governmental, incrementalist approach to European integration. I touched upon this in an article on early August: http://www.protesilaos.com/2012/08/eurocrisis-of-nationalism.html



    Agree with the last paragraph and I also hope everyone realizes the potent threat Golden Dawn poses, before it is too late (if it is not already...).

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  11. Nice article on nationalism. I would agree that if we are divided we shall plunge into misery. The euro was a somehow strange idea to promote federalism and solidarity. Had this crisis occurred 50 years from now, I do believe that we would have been more united against it.

    Yet, as the majority of the population was born and raised in circumstances which promoted nationalism, fortunately not in extreme forms, they are now cautious of "friendships" with neighbouring nations. This can be seen from the attitude of most people over the age of 50 (and, notably, many of the EU leaders). This was one of the reasons I had stated that youth should be more involved in politics, as they are less prone to obsolete ideals (in a negative connotation). Nationalism should be forgotten: In the words of House MD: "Nationalism is just property rights" and those of George Bernard Shaw: "Nationalism is the extreme form of egoism. Your nation is better than all the rest because YOU were born it". A clear distinction is need here: being proud of your origins, nation and country is one thing, and believing you are better than all the rest is another

    The notion that capitalism is to be blamed for all of our mishaps (even nationalism) is indeed not recent. Capitalism has been accused of many problems, nevertheless it is the only system which has prevailed. (Even China is more capitalistic than socialist) Would not for a moment propose that capitalism is a perfect system. Far from it. It is a system which need constant monitoring and severe changes from time to time. Alas, changes can only occur if we correctly understand the challenges and needs of our times.

    Antonis Samaras has the attitude of German and Italian leaders of the 20's and 30's. History proved them wrong. Hopefully history will prove us wrong too Protesilaos....

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