Does the hidden hand need to hold a stake in society?

As the father of a four year old daughter, I have been to the cinema to see the the Disney film, Tinkerbell and the Pirate Fairy.  When I took my daughter to the cinema I had taken an mp3 player as I anticipated I would need a diversion, however I became engrossed in the film.

The film tells the story of how a 'fairy scientist', Zarina,  undertook an experiment, which went wrong.  In response, Zarina left the fairy kingdom, taking pixie dust, and got involved with the young Captain Hook.  Hook had convinced Zarina that they were a team, but in fact the pirate was using the fairy so that he could use Zarina's knowledge of pixie dust to get his ship to fly in order that he could become the most powerful pirate. Eventually, other fairies, led by Tinkerbell, rescued Zarina, by showing who her friends really were, and she was bought back into the fairy-fold.

I saw the film around the time I spoke at the Circling the square: Research, politics, media and impact conference last year and there was coverage of the idea that U.S. high tech firms were considering going 'off-shore' so that they would escape regulation.  On the face of it, there seemed to be a connection between Captain Hook and the Seasteading Institute or Andreessen Horowitz.

These thoughts returned to me while reading Albert Hirschman's The Passions and the Interests: Political Arguments for Capitalism before Its Triumph on the advice of @tcspears.  From the back-cover

In this volume, Albert Hirschman reconstructs the intellectual climate of the seventeenth and eighteenth centuries to illuminate the intricate ideological transformation that occurred, wherein the pursuit of material interests - so long condemned as the deadly sin of avarice - was assigned the role of containing the unruly and destructive passions of man. Hirschman here offers a new interpretation for the rise of capitalism, one that emphasizes the continuities between old and new, in contrast to the assumption of a sharp break that is a common feature of both Marxian and Weberian thinking.

Hirschman begins his story with Machiavelli and highlights the following paragraph in Chapter 15 of The Prince

But since it is my [Machiavelli's] object to write what shall be useful to whosoever understands it, it seems to me better to follow the real truth of things than an imaginary view of them. For many Republics and Princedoms have been imagined that were never seen or known to exist in reality. And the manner in which we live, and that in which we ought to live, are things so wide asunder, that he who quits the one to betake himself to the other is more likely to destroy than to save himself; since any one who would act up to a perfect standard of goodness in everything, must be ruined among so many who are not good. It is essential, therefore, for a Prince who desires to maintain his position, to have learned how to be other than good, and to use or not to use his goodness as necessity requires.

In 1532 Machiavelli appears to be making precisely the same point as behavioural economists make today, it beggars the question: what progress have we made in almost 500 years?

 Hirschman identifies this passage as the start of the 'fact-value dichotomy' that features in Hobbes, Spinoza, Rousseau and, most famously (for English speakers?) in Hume. It reminded me that during the Enlightenment, when the consensus was on the dominance of the passions,  today  the fact-value dichotomy is invoked to ensure policy is guided by positivist, 'rational', arguments.

Before the nineteenth century the view was that humans, as they really are, are governed by their passions (in particular, lust, the excessive passion for love; pride, the excessive passion for honour, and avarice, the excessive passion for wealth) and during the seventeenth century there was discussion of how a damaging passion can be harnessed by another passion: a person sublimates their adulterous lust by their desire to be honoured.

Hirschman notes that these thought processes originate in political theory, where the entity in question is the state, but they become applied to individuals, or in the case of Mandeville, how a skilled politician should be able to harness the passions of the people to the benefit of the state.  In particular, Mandeville identifies how personal avarice can be used to temper the other passions.

In Hirschman's account 'Interests' become the main tamers of passions and by the nineteenth century they are equated with wealth, due mainly to Adam Smith  and from this point individual profit maximisation emerges as a virtue that results in public good. Interests guide the hidden hand.

Hirschman notes that the noun 'interest' is difficult, and this is covered in the current edition of the Oxford English dictionary:

There is much that is obscure in the history of this word, first as to the adoption of Latin interest as a noun, and secondly as to the history of the Old French sense ‘damage, loss’. No other sense is recorded in French until the 16th cent. As this was not the 15th cent. sense of English interess(e), it is curious that the form of the French word should have affected the English. The relations between the sense-development in French and English in 16–17th cent. are also far from clear.

The main meaning of the word 'interest' is

 1. The relation of being objectively concerned in something, by having a right or title to, a claim upon, or a share in.

  a. The fact or relation of being legally concerned; legal concern in a thing; esp. right or title to property, or to some of the uses or benefits pertaining to property;  

with the earliest example coming from 1450 "Noon of youre Liege peple hafuyng interest, right or title, of or in ony of the premisses." and in 1478 we have "He neuer knywe..þat I hadde any clayme or entrest in the maner off Heylesdon.".

Relevant to our discussion is the second definition

 2.a. The relation of being concerned or affected in respect of advantage or detriment; esp. an advantageous relation of this kind.

with a 1533 use "Without interest we commit sinne, seeyng peyne commyng withall."  This is significant as it highlights the role of interests in repressing sin.

 b. That which is to or for the advantage of any one; good, benefit, profit, advantage.

with a 1579 example "Caried with ambicious respectes touching their interests and desires particular."

The OED places the financial meaning as secondary, but older:

II. Senses related to medieval Latin interesse, as used by Matthew Paris a1259, and frequently from 13th c. (see Du Cange), in the phrase damna et interesse, in French legal phraseology dommages et intérêts, the indemnity due to any one for the damage and prejudice done to him. Cf. Old French interest (1290 in Godef.) in sense ‘damage’, also recompense for damage done or caused, ‘damages’. In sense 10   French interest (now intérêt) occurs in Rabelais, 1535.

9.a. Injury, detriment. 

 9.b. Compensation for injury, ‘damages’. (French dommages et intérêts medieval Latin damna et interesse.) Obs. rare.

and the examples are two hundred years older than the common meaning:  1259 Propter usuras, pœnas,et Interesse, or 1274   Tam super principali, quam super custibus, dampnis, et interesse refundendis

and the penultimate meaning is the technical, financial, meaning

10. a. Money paid for the use of money lent (the principal), or for forbearance of a debt, according to a fixed ratio (rate per cent.).

In medieval Latin interesse (Interest) differed from usura (Usury) in that the latter was avowedly a charge for the use of money, which was forbidden by the Canon Law; whereas originally ‘interesse refers to the compensation which under the Roman Law, was due by the debtor who had made default. The measure of compensation was id quod interest, the difference between the creditor's position in consequence of the debtor's laches and the position which might reasonably have been anticipated as the direct consequence of the debtor's fulfilment of his obligation’. This compensation was always permissible when it could be shown that such loss had really arisen (damnum emergens). At a later period, lucrum cessans—loss of profit through inability to reinvest—was also recognized as giving a claim to interesse; both cases appear to be included in the formula damna et interesse. The interesse was originally a fixed sum specified in the contract; but a percentage reckoned periodically, so as to correspond to the creditor's loss, was afterwards substituted (as sometimes in England in the first half of the 13th cent.). Interest in the modern sense was first sanctioned by law (though apparently under cover of the mediæval theory) by 37 Hen. VIII, c. 9 (see quot. 1545); this statute was repealed in 1552, but re-enacted in 1571.

1529   King Henry VIII Instr. Orator Rome,   Which money..shalbe truely repayde with interesse.

1545   Act 37 Hen. VIII c. 9 §3   Be it also enacted..that no person or persons..by way or meane of any corrupte bargayne, loone, eschaunge, chevisaunce, shifte, interest of any wares..accepte or take, in lucre or gaynes, for the forbearinge or givinge daye of payment of one hole yere of and for his or their money..above the sume of tenne poundes in the hundred.

Originally interest was the charge a debtor had to pay a creditor for non-repayment, it was a compensation payment.  In the Middle Ages, this damnum emergens became lucrum cessans, a payment from the borrower to the lender in compensation for the loss of investment opportunities available to the lender.  Over time interest came to indicate "a right or title to, a claim upon, or a share in" something.

It is here that I see the crux, interests imply a stake suggesting that the hidden hand will only work if an individual has a stake in society.

One aspect of Hirschman's account that had me thinking is that the implication was there is an internal dialogue taking place within individuals, there was no reference to the external, cultural pressures, on an individual.

The reason I thought about this is that when faced with a moral decision, I am not concious of sublimating one passion with another, rather I am concious of peer-pressure, what my friends and family might think of me.  I guess in the framework that Hirschman presents this would be covered by 'honour', and maybe  explicitly highlighting the fear of shame, a feature of Calvinism, might not be well received by an 'Enlightened' audience.  Another explanation could be that the likes of Montesquieu, Hume and Smith took it as given that an individual is a part of the society that they will improve by pursuing their personal interests.  None the less, it struck me that if the individual is set adrift from their society and culture, their morals are likely to be compromised (anyone who has experienced working as an ex patriate might be familiar with this phenomenon; I witnessed it working in Abu Dhabi in the 1990s, where adultery was the norm amongst westerners, not the exception).  This to me is a the heart of The Pirate Fairy, and a central risk of Seasteading.

One character whom one might expect to appear in Hirschman's account, but does not, is Hugo Grotius.  Grotius is widely regarded as setting the foundations of international relations in the modern era and Hedley Bull describes a contemporary interpretation of Grotius' theory of 'international society' as

A society of states (or international society) exists when a group of states, conscious of certain common interests and common values, form a society in the sense that they conceive themselves to be bound by a common set of rules in their relations with one another, and share in the working of common institutions. If states today form an international society . . . this is because, recognising certain common interests and perhaps some common values, they regard themselves as bound by certain rules in their dealings with one another, such as that they should respect one another's claims to independence, that they should honour agreements into which they enter, and that they should be subject to certain limitations in exercising force against one another. 

On the basis of Hirschman's claim that during the seventeenth and eighteenth centuries, philosophers adapted state-craft to individual behaviour, I think we can gain insight into the role of interests in guiding the hidden hand by replacing 'state' with 'individual' in the above quotation.

My intuition is that if people become alienated from society then we can't rely on their self-interest promoting the well-being of society, as proposed by Smith and others.  When Zarina becomes alienated from the other fairies she loses here good judgement.  Whether Seasteaders can construct a 'new Jerusalem', as the puritan immigrants to north America set out to do in the seventeenth century, remains to be seen.  But I am doubtful: the 'founding fathers' had a definite moral compass that bound them together, not an infantile desire to do as they see best justified by their personal wealth.

Mark Carney's recent Mansion House speech touches on some of these issues.  For example, when Carney argues that

The Bank of England’s general approach was consistent with the attitude of FICC markets, which historically relied heavily on informal codes and understandings. That informality was well suited to an earlier age. But as markets innovated and grew, it proved wanting. 

can the "informality was well suited to an earlier age" be interpreted as that when the City was less 'global', and market participants closer to each other, they shared 'common interests' which become diluted as traders become separated and potentially alienated (as in the case of Zarina).

Carney goes on to argue that "Real markets are resilient, fair and effective. They maintain their social licence." and "Real markets don’t just happen; they depend on the quality of market infrastructure."  Developing these themes, he highlights the final report the Fair and Effective Markets Review, noting that

Firms’ systems of internal governance and control that were incapable of asserting the interests of firms – let alone the wider market – over those of close-knit trading staff;

highlighting how market participants must share common interests that transcend the local interests of trading cliques.   Carney goes on to observe that the result was

All these factors contributed to an ethical drift. Unethical behaviour went unchecked, proliferated and eventually became the norm. Too many participants neither felt responsible for the system nor recognised the full impact of their actions. For too many, the City stopped at its gates, though its influence extended far beyond. 

I am fairly sure that these comments are relevant as much to those advocating Seasteading as Fixed Income, Currencies and Commodity traders cast adrift from broader society.

Finance and Mathematics: where is the ethical malaise?

This is a draft of an article that has been accepted by The Mathematical Intelligencer and offers an argument very similar to Romer's 'mathiness' argument as discussed in my previous post.

Discussions of the role of mathematics in finance appearing in The Mathematical Intelligencer can be split into two classes. Marc Rogalski [26] and Jonathan Korman [18] capture a widespread fury at a collapse in commercial ethics while Ivar Ekeland [6] and Peter Haggstrom [13] offer economic facts. The conclusions of Rogalski and Korman can be summarised as that mathematicians should spurn the financial world; Haggstrom and Ekeland point to technocratic solutions, characterised by better regulation. I do not buy into the argument that the problems of finance can be solved by regulations, it is, as both the U.K. and U.S. governments have identified¹, an ethical problem. But I also do not think it is virtuous for mathematicians to spurn finance, so I am not completely aligned with Rogalski or Korman. My position is that mathematicians should be forthright in presenting financial mathematics as a discipline centred on the concept of justice, making it explicit that successful finance must be moral finance.

During the Financial Crisis of 2007-2009 I was the U.K. Research Council's ‘Academic Fellow' in Financial Mathematics, meaning my background is, like Ekeland and Haggestrom, that of a financial mathematics ‘insider'. In this role I was expected to explain the discipline I represented to U.K. policy makers, both in government and in the media. As I attempted to meet these expectations I took an unconventional step for a mathematician and started looking into the origins of mathematical probability, both technically and the cultural context. I noticed that in solving the Problem of Points, in 1654, Pascal and Fermat were pricing a derivative contract on a binomial tree, and their solution would today be recognised as the Cox-Ross-Rubinstein option pricing model, published in 1978. There was a difference between the 1654 and 1978 models, CRR give a methodology for identifying the branch probabilities on the tree, Pascal and Fermat assume they are a half. This raised the question: how did Pascal and Fermat conceive the probabilities they used?

The answer came, initially, in some work the historian Edith Dudley Sylla did in the process of translating the Ars Conjectandi. Sylla observes that

equity among associates or partners rather than probabilities in the sense of relative frequencies provided the foundation for the earliest mathematical probability theory.[28, p 13]

and that

the foundations (...) [were] not chance (frequentist probability), but rather sors (expectation) in so far as it was involved in implicit contracts and the just treatment of partners.[28, p 28]

Intrigued by this point, I followed the path of mathematical probability from the origins of western mathematics in Fibonacci's text on financial mathematics, the Liber Abaci, to contemporary mathematics' Fundamental Theorem of Asset Pricing. The Fundamental Theorem is a consequence of Black and Scholes' paper on pricing options [2] that is based on the arbitrage argument, which originates in Aristotle's discussion of justice in commercial exchange in Nicomachean Ethics and features in the Liber Abaci. The novelty of contemporary financial mathematics is not in the techniques used, or the products traded², but in the fact that, today, mathematicians approach the problem of one of ‘positive' science, not ‘normative' ethics. For example, Black and Scholes opens with the observation that “it should not be possible to make sure profits”³, appealing to a consequentialist argument that if you get your price wrong⁴ someone will bankrupt you, where as medieval merchants were conscious of the Catholic Church's injunction that a riskless profit was turpe lucrum (filthy money).

Back in 2009, at the start of this journey, I took a position similar to Ekeland: there are economic laws that “outweigh the puny might of mathematicians” and the solution is in the hands of regulators. Today I have a darker view of the role of mathematics in the markets.

European science is often distinguished from other cultures' science by the fact that it is mathematicised and there is an argument, first offered in 1934⁵ but developed more recently [12, 17], that this came out of Aristotle's examination of ethics in commerce. Justice in exchange is distinguished from distributive and restorative justice by Aristotle as being characterised by equality, “there is no giving in exchange”, it is a reciprocal arrangement essential in binding society together and for social cohesion [17, p 51; 3, 1133a15-30]. It is notable that Aristotle approached this ethical problem mathematically, since he rarely applied mathematics to the physical world elsewhere [12, p 75; 4, p 13; 3, 1094b15-28]. On this basis, the medieval Scholastic scholars realised that money was a universal measure, up until then Hellenic thought (including Islamic scholarship of the time) had considered different physical properties, such as time and space, to be ‘incommensurable' - it was impossible to represent momentum, mass x length/time, mathematically - and it was this property of money as a universal measure that enabled the development of modern physics based on mathematics [4, 17]. To appreciate the point, Copernicus wrote on money before he wrote on the planets; Stevin, founder of the influential Dutch Mathematical School, was a financier; the financier Gresham endowed the first chair of mathematics in England and laid the foundations for the Royal Society. Recently, Bernard Bru has explained the significance of Bachelier's experience of stock-markets in the development of Kolmogorov's ideas on probability [30, pp 20-21]. The close relationship between mathematics and finance is born out of the fact that finance is concerned with relations, measured as prices, between objects. Finance informs mathematics on measurement and uncertainty while mathematics is critical to finance because we cannot perform experiments in the economy. It might not be possible to divorce the two disciplines, even if we wanted to.

The classicist Richard Seaford offers some insight into this account when he goes into the roots of western thought and argues that Greek philosophy, including democracy and mathematics, are a consequence of Archaic Greece's use of money [27]. He notes that other ancient civilisations were based on centralised re-distribution, where as pre-Socratic Greek society was based on exchange, reliant on a conception of equality and reciprocity. He suggests that when the Pythagoreans assigned a number to every object, they were, in fact, pricing the object.

The view that finance is socially corrosive is more novel than the practices of finance. One way of approaching Shakespeare's The Merchant of Venice is as a study of the four natures of love - erotic, familial, friendship and the highest form of love - charity/caritas/agapi - and Shakespeare personifies charity in the form of Antonio, the merchant of Venice. Throughout the seventeenth and eighteenth century, commerce was considered a civilising influence, in The Rights of Man (1792) Thomas Paine writes “commerce is a pacific system, operating to cordialise mankind” following a path laid by Montesquieu, Hume, Condorcet and Adam Smith [15, 8].

After the Industrial Revolution, these attitudes all but disappeared and today it would be inconceivable to personify Christian love in the form of a merchant. An explanation for this cultural shift can be found in Dialectic of Enlightenment [1] where it is argued that the Enlightenment led to the objectification of nature and its mathematisation, which in turn leads to ‘instrumental mindsets' that look to optimally achieve predetermined ends in the context of an underlying need to control external events. Where as during the seventeenth and eighteenth centuries public spaces emerged, the public sphere, which facilitated rational discussion that sought the truth in support of the public good, through the nineteenth century, mass circulation mechanisms came to dominate the public sphere and these were controlled by private interests. As a consequence, the public became consumers of information rather than creators of a consensus through engagement with information [11].

One aspect of this process of alienation for the public is the attitude that mathematics is an almost mystical pursuit that can reveal hidden truths, but only for the initiated, a recurring theme in the presentation of mathematics in popular culture. This is nicely captured in a documentary film on the development of the Black-Scholes-Merton equation where the economist Paul Samulelson describes how he ‘discovered' Bachelier's thesis, much as Indiana Jones might discover a magical artefact,

In the early 1950s I was able to locate by chance this unknown book by a French graduate student in 1900 rotting in the library of the University of Paris and when I opened it up it was as if a whole new world was laid out before me.⁶

This trope might seem benign in the context of popularising mathematics, but when combined with the idea that mathematics is immutable and indubitable, themes of traditional histories and philosophies of mathematics, we are given the impression, to paraphrase William Tait, that

A mathematical proposition is about a certain structure, such as financial markets. It refers to prices and relations among them. If it is true, it is so in virtue of a certain fact about markets. And this fact may obtain even if we do not or cannot know that it does. [29, p 341]

While mathematicians themselves might not make this claim explicitly, mathematics has been used by many to obscure and legitimise financial activity, passing over any consideration of the ethical implications of those activities. Ekeland might see mathematics as ‘puny', but others value its authority and there are too many examples of how mathematics has been employed to prevent democratic oversight of the markets. In their submission to the Parliamentary Commission on Banking Standards in 2013 the Bank of England was highly critical of how some firms have used advanced mathematical techniques to ‘pull the wool' over the eyes of the regulator [22, v. II, para. 89] while U.S. authorities identified that this type of mathematical sleight of hand played a part in the ‘London whale' episode [23, p 14]. The existence of the Gaussian copula as a ‘'truth-teller' of the value of complex debt portfolios played a central role in the Crisis of 2007-2009, justifying the actions of banks, despite its short-comings being known to mathematicians [31, 21, 9]. In the early 1970s, the Black-Scholes-Merton framework played an important part in legitimising the re-emergence of financial derivatives markets [20, p 158]. As long ago as 1877 a large, corporate, insurer defended their actions in undermining fraternal/mutual insurers to legislators with the argument that

There are certain fundamental rules †which can only be understood by actuaries, and it is impossible for me to go into here [19, p 198]

An antidote to the causes and consequences of ‘instrumental mindsets' identified above is to turn away from the philosophical paradigm of Foundationalism, which sees language as being made up of statements that are either true or false and complex statements are valid if they can be deduced from true primitive statements. This approach is exemplified in the standard mathematical technique of axiom-theorem-proof. An alternative approach is to shift the focus from what language says (true or false) to what it does. Specifically, the function of language is to enable different people to come to a shared understanding and achieve a consensus, this is defined as discourse⁷ [10]. Because discourse is based on making a claim, the claim being challenged and then justified, to be successful discourse needs to be governed by rules, or norms. The most basic rules are logical and semantic, on top of these are norms governing procedure, such as sincerity, and finally there are norms to ensure that discourse is not subject to coercion or skewed by inequality. This is why reciprocity is central to financial mathematics, it is a norm of market discourse, embedded in the language of mathematics.

Mathematics has not been passive in recent financial crises and I would argue that if mathematicians are not part of the solution, they are part of the problem. For me, the correct response of mathematicians to the financial crises is to work in support of those who wish to redirect finance from regarding markets as competitive arenas to seeing them as centres of cooperative, democratic, discourse⁸. In this vein I have developed the argument [16] that reciprocity is the central message of financial mathematics and it is one of three norms of market discourse, the others being sincerity and charity. For this case to be coherent I have followed Putnam [25] and abandoned the idea of mathematics being a value-neutral truth-teller, rather it is a means of discourse. This is a significant step if you perceive mathematics as being monogamous with the natural and physical sciences, or even celibate. I believe certain twentieth century mathematicians, such as Poincaré⁹ [14], Ramsey [5] and Putnam, would have sympathy with the approach I take, particularly in the cases where mathematics is employed in the social and human sciences.

Notes

¹In the U.S. Financial Crisis Inquiry Commission’s report of 2011 and the U.K. ‘Changing Banking for Good’ report of 2013.

²Most of these products existed in medieval times, the ‘Triple Contract’ shares the features of ‘structured products’ prominent in the crisis. ‘Mortgage Backed Securities’ were introduced in the U.S. in the late nineteenth century — see [19, Ch 5] for an enlightening account. It is not in the interests of well dressed bankers to tell their clients that what they are charging fat fees for existed before Columbus.

³This is the basis of Ekeland’s argument.

⁴Ramsey’s ‘Dutch book’ argument, which has been described as a modern version of the ‘Golden Rule’, “Do unto others as you would have them do unto you”, Luke 6:31.

⁵By the Marxist theoretician Borkenau in The Transition from the Feudal to the Bourgeois World View.

⁶The programme is ‘The Midas Formula’ also known as ‘The Trillion Dollar Bet’ and is available on YouTube. The relevant section is around 12:20/48:53 minutes. A transcript is available at http://www.bbc.co.uk/science/horizon/1999/midas_script.shtml.

⁷According to a recent translator of Fibonacci, a key feature of the techniques given in the Liber Abaci was that they enabled ideas to be transmitted and improved upon [7, Introduction].

⁸An I.M.F. paper on the crisis, Resolution of Banking Crises: The Good the Bad and the Ugly (WP/10/146) reveals that countries with a significant proportion of ‘not for profit’ mutual banks (e.g. Germany, France, Italy) did not require the public bailouts needed in the U.K. and U.S. — finance is not necessarily capitalist.

⁹Poincaré’s approach is captured in his observation “these two propositions ‘the earth turns round,’ and ‘it is more convenient to suppose that the earth turns round,’ have one and the same meaning” [24, p 91].

References

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[2]    F. Black and M. Scholes. The pricing of options and corporate liabilities. Journal of Political Economy, 81(3):637-654, 1973.

[3]    S. Broadie and C. Rowe. Aristotle: Nicomachean Ethics: Translation, Introduction, Commentary. Oxford University Press, 2011.

[4]    A. W. Crosby. The Measure of Reality. Cambridge University Press, 1997.

[5]    D. Edgington. Ramsey and Pragmatism: Probability, conditionals and truth. Cambridge Workshop on Pragmatism, May 2012.

[6]    I. Ekeland. Response to Rogalski. The Mathematical Intelligencer, 32(2):9-10, 2010.

[7]    L. Fibonacci and L. Sigler. Fibonacci's Liber Abaci: A Translation Into Modern English of Leonardo Pisano's Book of Calculation. Springer, 2003.

[8]    M. Fourcade and K. Healy. Moral views of market society. Annual Review of Sociology, 33:285-311, 2007.

[9]    M. B. Gordy. A risk-factor model foundation for ratings-based bank capital rules. Journal of Financial Intermediation, 12(3):199-232, 2003.

[10]    J. Habermas. The Theory of Communicative Action: Reason and the rationalization of society. Beacon Press, 1985.

[11]    J. Habermas. The Structural Transformation of the Public Sphere: An Inquiry Into a Category of Bourgeois Society. MIT Press, 1991.

[12]    R. W. Hadden. On the Shoulders of Merchants: Exchange and the Mathematical Conception of Nature in Early Modern Europe. State University of New York Press, 1994.

[13]    P. Haggstrom. Mathematicians in the world of finance. The Mathematical Intelligencer, 34(1):6-7, 2012.

[14]    G. Heinzmann. Henri Poincaré and his thoughts on the philosophy of science. In E. Charpentier, E. Ghys, and A. Lesne, editors, The Scientific Legacy of Poincaré. American Mathematical Society / London Mathematical Society, 2010.

[15]    A. O. Hirschman. Rival interpretations of market society: Civilizing, destructive, or feeble? Journal of Economic Literature, 20(4):1463-1484, 1982.

[16]    T. C. Johnson. Reciprocity as a foundation of Financial Economics. The Journal of Business Ethics, Forthcoming, doi: 10.1007/s10551-014-2257-x.

[17]    J. Kaye. Economy and Nature in the Fourteenth Century. Cambridge University Press, 1998.

[18]    J. Korman. Finance and mathematics: A lack of debate. The Mathematical Intelligencer, 33(2):4-6, 2011.

[19]    J. Levy. Freaks of Fortune: The Emerging World of Capitalism and Risk in America. Harvard University Press, 2012.

[20]    D. MacKenzie. An Engine, Not a Camera: How Financial Models Shape Markets. The MIT Press, 2008.

[21]    D. MacKenzie. The credit crisis as a problem in the sociology of knowledge. American Journal of Sociology, 116(6):1778-1841, 2011.

[22]    PCBS. Changing Banking for Good. Technical report, The Parliamentary Commission on Banking Standards, 2013.

[23]    Permanent Subcommittee on Investigations. JPMorgan Chase Whale Trades: A Case History of Derivatives Risks and Abuses. Technical report, Committee on Homeland Security and Governmental Affairs, 2013.

[24]    H. Poincaré. Science and Hypothesis. In S. J. Gould, editor, The Value of Science: Essential Writings of Henri Poincaré. Modern Library, 1902 (2001).

[25]    H. Putnam. The Collapse of the Fact/Value Dichotomy and Other Essays. Harvard University Press, 2002.

[26]    M. Rogalski. Mathematics and finance: An ethical malaise. The Mathematical Intelligencer, 32(2):6-8, 2010.

[27]    R. Seaford. Money and the Early Greek Mind: Homer, Philosophy, Tragedy. Cambridge University Press, 2004.

[28]    E. D. Sylla. Commercial arithmetic, theology and the intellectual foundations of Jacob Bernoulli's Art of Conjecturing. In G. Poitras, editor, Pioneers of Financial Economics: contributions prior to Irving Fisher, pages 11-45. Edward Elgar, 2006.

[29]    W. W. Tait. Truth and proof: The Platonism of mathematics. Synthese, 69(3):341-370, 1986.

[30]    M. S. Taqqu. Bachelier and his times: A conversation with Bernard Bru. Finance and Stochastics, 5(1):3-32, 2001.

[31]    G. Tett. Fools' Gold. Little Brown, 2009.

Mathiness: not just a problem of macro-economics

I was aware of the "mathiness" discussion initiated by the macro-economist Paul Romer, but have only recently read the articles because while the discussion was taking place I was finishing of an article for The Mathematical Intelligencer that presents a remarkably similar argument (noting that mathematicians consider a coffee cup and doughnut to be the same).

Romer's concern is in the field of economic growth - an area I am unfamiliar with -  but two related statements caught my attention

For the last two decades, growth theory has made no scientific progress  toward a consensus. ... The question posed here is why the methods of science have failed to resolve the disagreement between these two groups.

and, postulating on why science has failed to come to a consensus, Romer offers an explanation as "mathiness"

Like mathematical theory, mathiness uses a mixture of words and symbols, but instead of making tight links, it leaves ample room for slippage between statements in natural versus formal language and between statements with theoretical as opposed to empirical content.

My article for the Intelligencer is titled "Finance and Mathematics: where is the ethical malaise" and was written in response to a series of articles  about the role of mathematics in financial crises.  I begin my piece

Discussions of the role of mathematics in finance appearing in The Mathematical Intelligencer can be split into two classes. Marc Rogalski and Jonathan Korman capture a widespread fury at a collapse in commercial ethics while Ivar Ekeland  and Peter Haggstrom off er economic facts. The conclusions of Rogalski and Korman can be summarised as that mathematicians should spurn the financial world; Haggstrom and Ekeland point to technocratic solutions, characterised by better regulation. I do not buy into the argument that the problems of finance can be solved by regulations, it is, as both the U.K. and U.S. governments have identified, an ethical problem.

I go onto to explain that mathematics has not been neutral in recent financial crises

In their submission to the Parliamentary Commission on Banking Standards in 2013 the Bank of England was highly critical of how some fi rms have used advanced mathematical techniques to 'pull the wool' over the eyes of the regulator [para. 89] while U.S. authorities identified that this type of mathematical sleight of hand played a part in the 'London whale' episode [p 14]. The existence of the Gaussian copula as a 'truth-teller' of the value of complex debt portfolios played a central role in the Crisis of 2007-2009, justifying the actions of banks, despite its short-comings being known to mathematicians. In the early 1970s, the Black-Scholes-Merton framework played an important part in legitimising the re-emergence of financial derivatives markets. As long ago as 1877 a large, corporate, insurer defended their actions in undermining fraternal/mutual insurers to legislators with the argument that

 "There are certain fundamental rules . . . which can only be understood by actuaries, and it is impossible for me to go into here [p 198]"

 In my piece, for the mathematics community, I note that while mathematicians might see these abuses, which I am fairly certain could be ascribed to 'mathiness' as coined by Romer, as being abuses of mathematics, we do bear some responsibility.

Many mathematicians, but probably only a minority, argue that there is an issue with mathematics in that it is often used to obscure rather than enlighten.  Part of this trope is the presentation of mathematics as a mystical key that can unlock hidden truths:
In economics, my favourite example is Samuelson's account of how he 'discovered' Bachelier's thesis, much as Indiana Jones might uncover a magical artefact

(From the BBC programme "The Midas Formula/The Trillion dollar Bet")

This all might seem benign in to context of encouraging people to engage with mathematics, but when combined with he dominant philosophical paradigm of Foundationalism and finance, problems emerge.

Foundationalism sees language as being made up of statements that are either true or false and complex statements are valid if they can be deduced from true primitive statements. This approach is exemplified in the standard mathematical technique of axiom-theorem-proof and so arguments presented mathematically are automatically imbued with the quality of 'truth' and so hold authority.

I then give a Habermasian explanation of what happens when mathematics and finance come together.

the Enlightenment led to the objectification of nature and its mathematisation, which in turn leads to 'instrumental mindsets' that look to optimally achieve predetermined ends in the context of an underlying need to control external events. Where as during the seventeenth and eighteenth centuries public spaces emerged, the public sphere, which facilitated rational discussion that sought the truth in support of the public good, through the nineteenth century, mass circulation mechanisms came to dominate the public sphere and these were controlled by private interests. As a consequence, the public became consumers of information rather than creators of a consensus through engagement with information.

Habermas, and Pragmatic philosophy more generally, offer an antidote by switching the emphasis of what language says (whether it is true or false) to what it does

Specifically, the function of language is to enable different people to come to a shared understanding and achieve a consensus, this is de fined as discourse. Because discourse is based on making a claim, the claim being challenged and then justified, to be successful discourse needs to be governed by rules, or norms. The most basic rules are logical and semantic, on top of these are norms governing procedure, such as sincerity, and finally there are norms to ensure that discourse is not subject to coercion or skewed by inequality.

This is the basis of my claim that Reciprocity is a Foundation of Financial Economics.

With regard to the 'mathiness' discussion it is interesting to see that Romer argues the issues are in the collapse of 'economic norms', so are diagnosis and treatment appear aligned.  My criticism of Romer is mild, and it is that he has not presented his case in the context of Pragmatism, which would provide him with a firmer foundation for his case (I recommend Haack and Misak  as bedrocks).

However, I do not see my contribution as calming the criticism there has been for Romer, because my suggestion is the issue is not with one, or another, local mis-understanding but a fundamental issue with the dominant pardigm supporting science.  Economists might disagree on their growth models but they are likely to agree that science is based on Foundationalism.  This said, the problems Romer, and I, identify are pervasive, with science being unable to resolve many problems ranging from finance to climate change.