Objections to Objectivity

I start with a warning that this is a synthesis-in-development of some thoughts about mathematics, economics, objectivity and justification.  As a work in progress it might be a bit incoherent.  I have been thinking about "justification" having read Cheryl Misak's Truth, Politics and Morality on the advice of the pragmatist Matthew Festenstein when giving me feed-back on my Reciprocity paper.  Matthew had identified a relationship between the influence on seventeenth century commerce on politics (his field) and finance (my interest) and given it takes place in the seventeenth century there is a third node: science.

Following reading Misak I went to Susan Haack's Putting Philosophy to Work that discusses science in the context of pragmatism.  Misak and Haack got me thinking that fundamental to the pragmatic conception of politics and science, and by induction, finance, is the idea that in making a claim you put it up for criticism, if there is no criticism the claim passes but if it challenged the claim needs to be justified in a discursive manner.  Eventually a consensus is reached.  The problem for philosophy is under what conditions can the consensus be regarded as truth.  Clearly a "democratic" conception that 51% signifies truth is inadequate, and this opens the door to wondering if 90% of "scientists" signifies truth or if the "market" determines truth.

With this in mind I attended a workshop on Mathematical Cultures during which Norma Beatriz Goethe gave a talk on Leibnitz.  What caught my attention was in the pre-amble Norma discussed how in the mid-seventeenth century there was a tradition of representing the scientist as a spectator at a theatre, with nature being what occurred on the stage.  This was interesting to me because one of the cornerstones of pragmatism is the rejection of the Cartesian belief that the scientist can be an objective observer of the world.  This is a reasonable working hypothesis for the physical sciences, but begins to break down in the natural sciences (the "anthropocene"), is dubious in the social sciences and untenable in the human sciences.

However, what really caught my attention was an illustration in this vein which had the "scientist" in a room that enabled them to eavesdrop on those around them, with massive "hearing horns" and spyglasses observing activities in a public space.  What struck me was a correspondence between these prototypical conceptions of science, the scientist as the observer, and recent crises of mathematicians working for security services monitoring the public's activity.

My talk, in order to justify its place in a discussion of Mathematical Cultures, centred on financial mathematics as a language to facilitate discourse rather than the more popular conception as the key to unlocking the secrets of financial markets.  A concern I share with many applied mathematicians - and regulators - is that contemporary financial mathematics has become too complex to be useful.  However, more pertinent is the fact that research mathematicians might become irrelevant because in the markets there seems to be a paradigm shift away from sophisticated models to simpler models that incorporate  CVA - a basic accounting tool abhorrent to a PhD trained quant.  Though I am sure us mathematicians could, given time, make CVA incomprehensible to the uninitiated as well.  I note with interest that Mark Davis (my mathematical grandfather) is questioning mathematicians' objections to VaR as a risk measure and re-poses the mathematical question: "Instead of asking whether our model is correct, we should ask whether our objective in building the model has been achieved."  I suggest we can interpret this as a statement that we do not require objective justification for the validity of the model, rather we need a subjective, i.e. relative to our aims, assessment. The mathematician is an actor on the stage of finance.

Twitter alerted me to two posts by @MarkThoma.  One from last year makes the observation that

We like to think or ourselves as scientists, but if data can’t settle our theoretical disputes – and it doesn't appear that it can – then our claim for scientific validity has little or no merit.

while one from yesterday is titled 'Pretending To Do Something Like Science'??? and is a quote from Paul Krugman

Were the freshwater guys always just pretending to do something like science, when it was always politics? Is there simply too much money and too much vested interest behind their point of view?

Both these posts, and Mark's presentation, (implicitly) ask the question "what is science", a question that dominates much of my thinking as a "scientist" working in finance.

With regard to Mark Thoma's 2013 post, Poincare was always sceptical of the Anglo-Saxon obsession with "facts", "facts are to science what bricks are to houses: a collection of facts is no more science than a pile of bricks is a house".  In this setting mathematics has the role of mortar or cement, identifying the relationships between facts and linking them together.  Something else I learnt from Poincare is that mathematics is essential when you cannot perform an experiment: Higgs' mathematics being proved by the Large Hadron Collider is an example.  This is why mathematics is essential for economics and finance: because we cannot experiment in economics because the system is so dynamic we need a way of disentangling the myriad of facts that we are presented with.

The main point of the 2013 post is that economic mathematicians cannot agree on "one model" for the economy.  I would suggest is that Thoma is wishing to place economists in the audience where they can objectively deduce the "true" model for the economy that enables its control.  I would suggest a better aim is to follow Mark Davis' lead and evaluate different models on the basis of the aim in mind, different aims will require different models, but now single model can accomplish multiple aims.  Anyone who recognises Mark Thoma's predicament could do worse than read three of Poincare's essays: "The Mathematical Sciences" and "The Objective Value of Science" from The Value of Science and "The Scientist and Science" from Science and Method.

I think Paul Krugman's frustration with the "freshwater guys" more troubling because it is a symptom of a general degradation of science.  I worry that scientific discourse has degenerated into the accumulation of publications.  For example. I have been critical of an important (because it is cited) paper on financial stability.  My issue is that the authors - physicists - construct a discrete-time/finite state economy that they show becomes unstable when the number of assets traded is four times the number of possible states.  Cramer's Rule tells me that as soon as the number of states equals the number of assets, the economy becomes deterministic (it is 'complete'). One of the authors responded to my criticism, which was nice.  But what troubled me was this attitude

As for any paper, there is a time to defend it, which is when it is submitted to a journal and it goes to the referees. Once published, it should defend by itself. 

This implies to me that the author believes that a claim is "justified" if two or three (like minded) individuals   agree with what is claimed.  My criticism need not be considered, and if I have a criticism I should not raise it publicly, but privately.

I think beliefs like these are at the root of Krugman's concern.  If my friends and I can come up with a coherent set of claims that we can get peer-reviewed and published, they justified. I do not have to justify my claims to criticism, particularly external criticism.  This is not a problem of economics but much of what is currently perceived as science: it is a feature of the climate debate and pharmaceutical research.  It is damaging to science but corrosive to society as a whole where politics is dominated by the sound bite and "fact" with little effort or interest of many politicians to justify themselves.  I believe the popularity of UKIP, the 'Tea Party' and Front National are the consequences of  mainstream political leaders to justify their claims in any meaningful way.

My objection to objectivity is that it elevates the scientist to a position of authority that cannot be challenged by non-scientists, or scientists that you do not disagree with.  Suggesting that scientists accept they acknowledge they are on the stage diminishes their authority, they become fallible, but in doing so I think we can actually solve problems rather than fail to control situations.