Saturday, May 28, 2005

Our government knows what it is doing

In the great tradition of American government, only the truly important things get rushed though. Hence, the bankruptcy bill was the first thing herded through this year. It was an emergency. Credit card companies had recorded a mere 30 billion dollars in profits last year. Many of them, out of pure humanitarianism, were charging their customers a mere 29 to 34 percent after the inevitable late fees that did not have to be late fees on a specific card, but late on any payment. This is almost 0.5% percent less than the going rate Al Capone charged. We are, after all, talking about active Christians.

Then there were the earthshaking investigations into steroid use among home run hitters. America simply stopped in its tracks, since, as is well known, nothing effects every household in America like a distorted home run record. It causes little children to cry and grown men to hurl themselves from tall buildings.

But though grave issues require speed, other issues – like paying the trash that die or are wounded in Iraq and can’t figure out how to game the system like our President once did – can go on the backburner.

Here’s a story from the Boston Herald – a two bit paper obviously so desperate for news that it pays attention to a wounded military guy

“Winthrop Marine Lance Cpl. James Crosby's effort to give combat-wounded soldiers special pay while they recover moved closer to becoming law with a U.S. House vote last week.

``It will make such an impact,'' said Crosby's father, Kevin. ``My son is in constant pain 24 hours a day. No amount of money can ever make up for that, but at least there's something for these people and their families who have been torn apart.''

A rocket attack in Iraq last year left the younger Crosby, 20, paralyzed from the waist down. When he left Iraq, his combat pay was cut while he fought for his life.

The measure, sponsored by U.S. Rep. Edward Markey (D-Malden), would give $430 a month to soldiers who are wounded and evacuated from the combat zone.”

Supposedly, if it goes through in the House, the Senate might debate it in July, and who knows, Bush might even sign it by September, if he has nothing better to do. That will be after another, say, 800 to 1,000 are wounded in the war for our wonderful freedom lovin’ Iraqis, trusting the averages from the Iraqi coalition casualties page.

It is a bit much to give to the trash. On the bright side, what with the new tools given to the Credit card cos. in that Bankruptcy bill, it will probably be absorbed as late fee detritus by the investors in Discover, Visa, MBNA, Citibank and Bank of America who could really use it. Who says America isn’t still the land of opportunity? It's the ownership society, baby.

Friday, May 27, 2005

Atlas finally shrugs

Last night LI wrote Paul a semi apology. Starting this series of posts three days ago, we intended to obliquely angle into Paul’s post on ethical individualism. However, we admit the degree of obliquity seems a bit, well, excessive. An unkind critic might call it multitudinously losing the point. Paul wrote back:

“Yeah, I was gonna write you an email from work today, with the subject of "Atlas - start shrugging"! I'm not sure what crazy scheme you have in mind - neither, apparently, do you (though your daimon does!) - but I look forward to reading the resulting opus.”

LI will sniffily ignore the reference to that appalling novel and try to get down to brass tacks in this post. Paul’s post is an enthusiastic appreciation of a book by David L. Norton entitled Personal Destinies: a philosophy of ethical individualism. We thought this was among the best bits we’ve ever read on his site:

“Of especial interest is the fact that Norton understands his account to ground a kind of individualism - an "ism" in disrepute with both Left (collectivism) and Right (communitarianism). Those two poles are often likeminded in taking individualism necessarily to be of the "atomistic" (Hobbesian; sc., merely numerical) variety. Norton's eudaimonism claims to establish "qualitative" individualism: each person, ex hypothesi, is obliged to actualize an excellence uniquely his own; to live in truth to his daimon. The social entailment of this doctrine is the "complementarity of excellences," implying the need for counterparts. Hence an individualism is possible which at once celebrates independence and affirms interdependence and sociality of a kind.”

Our response to this has been to consider a certain set of adventures of the concept of the “ratio,” (oops -- the Germanic amplification of the genitive -- the curse of philosophical class. Sorry) insofar as the human individual is supposed to embody it. If one is to “live in truth” to one’s daimon, it is important to think about the various ways one usually lives – unlike some purists, we like Weber’s term, “lifestyle”, for this. The truth, here, seems to do double duty: it implies, on the one hand, some standard of authenticity to which one can compare one’s lifestyle, and on the other hand, it seems performative – the criteria of authenticity is not prefigured, but is constituted in the living. That doubleness isn't incoherent -- a set of truths can be constituted over time in such a way that future acts can be judged against it -- but it does imply a limit on one's liberty that may, in time, become onerous. No more lighting out for the territory, no more second acts.

One of the perennial philosophical worries is the degree of error inherent in these various lifestyles. This is why we think the match between Gigerenzer vs. Tversky and Kahnman is fascinating, and casts a certain light upon the qualitatively different points of view that are each haunted, in Paul’s view, by a daimon.

Now, this idea of the daimon is interestingly ambiguous in terms of its site. Where, exactly, is it? this parallels the question we have been pursuing – where exactly is the innate tendency to error – if there is one? Where, that is, is its systematic place?

The early moderns were all very anxious about error. However, until Kant, error was conceived as a thing exterior to the subject. Among other of his functions, Descartes malin genie embodied the exteriority of deception. Hume inflected this line of thinking in a way, insofar as he showed that induction was not logically grounded. However, his intent wasn’t to delegitimize induction – rather, it was to estrange us from our mania about the framework of error and falsity. Induction, being on the side of life or habit, couldn’t be turned off, or doubted in any practical way. All of which went into Hume’s project of showing that reason was and should be the slave of the passions. It is important to note that at the same time that the natural philosophers were worried so about the Pseudodoxia Epidemica, the rising merchant/professional class was increasing sensitive to original sin. But let’s bracket that circumstance.

It was Kant, I think, who first interiorized error as an inevitable formation of the reason itself. There’s a famous passage in the Critique of Pure Reason from the section on the transcendental semblence (Schein). That semblence is the idea that one can deduce how the world is (for instance, whether the world has a beginning or not) from what I would call logic – that is, a conceptual analysis of beginning. Kant writes:

“The cause [of the transcendental semblence (Schein)] is this, that in our Reason (perceived, subjectively, as the human capacity to know) lie fundamental rules and maxims of its use, which have the total appearance of objective principles, and through which it appears, that the subjective necessity of a certain conjunction of our concepts, supported by the understanding, can be maintained. This is an unavoidable illusion, as much one as the illusion, that the sea seems higher on the horizon than on the shore, because we see the former through higher beams of light than the latter; or, even more, so little as astronomer can keep the moon from seeming greater in its setting, even if he is not deceived by this appearance.”

It isn’t surprising that Gigerenzer, too, uses visual illusion as an analogy for cognitive illusion. In Gigerenzer’s work, the necessity he is looking for is ecological – what living function does illusion serve? – rather than metaphysical.

The notion of an error inside (the logical equivalent of Jim Thompson's Killer Inside Me) might seem, at first glance, to have nothing to do with Norton (and Craddick’s) qualitatively different demon. And yet that demon seems inherited from the most famous of all daimons – Socrates. And Socrates is definitely a corrective daimon – a negating spirit. It is not a constructive one:

In the Apology, Socrates says: “…something divine and spiritual comes to me, the very thing which Meletus ridiculed in his indictment. I have had this from my childhood; it is a sort of voice that comes to me, ("some divine (theîon) and spiritual (daimónion) [thing] comes to me...")
and when it comes it always holds me back from what I am thinking of doing, but never urges me forward. This it is which opposes my engaging in politics. And I think this opposition is a very good thing; for you may be quite sure, men of Athens, that if I had undertaken to go into politics, I should have been put to death long ago and should have done no good to you or to myself. And do not be angry with me for speaking the truth; the fact is that no man will save his life who nobly opposes you or any other populace and prevents many unjust and illegal things from happening in the state. A man who really fights for the right, if he is to preserve his life for even a little while, must be a private citizen, not a public man.”

If Socrates is speaking truly, then perhaps the daimon is insufficient to ground Paul’s desire that “an individualism is possible which at once celebrates independence and affirms interdependence and sociality of a kind.”

So -- this is the end of this series of posts. A null-set end? An irony? Not really. LI is neither playing the village explainer or the answer guy, here, but simply responding to an interesting idea with a bunch of his own questions.

Thursday, May 26, 2005

clearing the table

Yesterday, we lined up things for Gigerenzer’s first shot.

Okay, to briefly reprise – although to follow this post, you will have to read yesterday’s post: Tversky and Kahnman claim to have shown a pattern of illogical response to problems that transform sets into the language of probability. The conjunction problem, or what’s wrong with Linda, was one of those conundrums.

Here’s the problem as T and K present it:

Linda is 31, outgoing, single. She majored in philosophy in college. As a student she was deeply concerned with issues of discrimination.

Which of the two alternatives is more probable:

Linda is a bank teller
Linda is a bank teller and is active in the feminist movement?

The b is, as Gigerenzer points out, rather like the question Piaget posed to children: here is a picture of flowers, 6 of which are daisies and four of which are not. Are there more daisies or flowers in the picture? In the Piaget case, by the time children are eight, they recognize that the daisies are flowers, and that the confusing thing in the question is really that it makes it falsely appear like daisies are categorially equal to flowers, instead of a subset of them. (well, they realize this in child-brain speech, as in, that’s a trick question). But T and K consistently found that college students would chose b. So what gives?

“I argue that the irrationality is not to be found in adult reasoning but in the logical norm. Consider what the norm is: the probability of an event A is larger than (or equal to) the probability of the events A and B, that is, p(A) > P(AAB). This conjunction rule is used as a
content-blind norm for judgment: the content of the As and Bs is not considered relevant to evaluating good reasoning. All that counts is the mathematical probability p and the logical '^ and correct judgment is attested when people use the English terms probable and and in this and
only this way. This amounts to a purely syntactic definition of rational reasoning, and therefore, of an error in judgment.”

Putting his money on the table, so to speak, Gigerenzer rearranges T and K’s question to this one:

“Consider the following version of the Linda problem. Here the polysemy of the word probable is eliminated by using the phrase how many:

There are 100 persons who fit the description above (that is, Linda's). How many of them are:

Bank tellers?

Bank tellers and active in the feminist movement? '^

This change is sufficient to make the apparently stable cognitive illusion largely disappear. In one experiment, every single participant answered that there are more bank tellers {Hertwig and Gigerenzer, 1999; for similar results see Fiedler, 1988; Tversky and Kahneman, 1983). The
experiment also showed that the majority of participants interpreted how many in the sense of mathematical probability, but more probable as meaning "possible," "conceivable," or one of the other nonmathematical meanings listed in the OED.”

If Gigerenzer is right, he is onto something major – like, Meno style major. Like, maybe education is actually possible – confounding the cynics among you. Alas, T and K have tinkered with rephrasing the question in terms of “how many,” discovering that simply changing the b phrase slightly (to “bank tellers and active feminists”) can again dramatically change the responses.

All of which leads Gigerenzer to ask whether the problem, here, is that T and K are abstracting the mind from our ecology. This is how the Great G puts it:

“What have we learned from some 20 years and hundreds of experiments on the conjunction fallacy? We have leamed more about the limits of logic as norms than about the workings of the mind. In fact, I do not know of any new Insight that this activity has produced. Logical norms distract us from understanding intelligent behavior.”

At this point, LI is tempted to go down the trail, shooting up the Bush age obsession with testing as education, and the foreseeable result (further cretinization of a vulnerable population) by the No Child having anything to think with but their Behind Act. But we will simply lay down a marker for future reference.

To return, however. Our topic, in our last post, was supposed to be the individual, considered as an autonomous thing – the person, in short. Since Kant – at least, that is how the intellectual history story goes, but in actuality Kant simply codified what was in the child-speak of the Western mass mind for a long time – we’ve operated on the assumption that the autonomy of the individual is the bedrock of ethics. Philosophy’s safecrackers – Schopenhauer, Nietzsche, Freud, Heidegger, etc, etc – have found it pretty easy to break into that concept and show up its flaws, just as Marx found it easy to point to the historical trajectory of class interest that produces the “character mask” of the subject under capitalism. Old Kant’s original formulation of the autonomy thesis is notably eccentric, since it excludes the sensibility – the animal collective that howls around the noumenal X that we proudly bear through our trials and temptations. While Gigerenzer is no overt Kantian, his theory does lend credence to the idea that the sensibility can, indeed, breach our autonomy – or, to put it another way, that the way in which we perceive things is so framed by elements given by the sensibility that “logical norms distract us from intelligent behavior.” To illustrate which, Gigerenzer cites a psychological experiment created from a cliché:

“Consider an experiment in which a full glass of water and an empty glass are put in front of a participant (Sher and McKenzie, 2003). The experimenter asks the participant to pour half of the full glass into the other glass, and then asks the participant to hand him the half empty glass. Which one does the participant pick? Most people picked the previously full glass. When they were asked, however, to hand over the half-full glass, most participants picked the previously empty one. This experiment reveals that the two statements are not pragmatically equivalent (see also McKenzie and Nelson, 2003). People extract surplus information from the framing of the question, and this surplus information concems the dynamics or history of the situation, which helps to guess what is meant.”

Okay, one more post on this topic, tomorrow.

Wednesday, May 25, 2005

Linda you sly fox

Lately, LI has been a little baggy and disorganized. Unfortunately, I foresee this post straying into chaos too – I can feel its edges, even now, being pulled towards some strange attractors -- but I will try to be a bit more disciplined.

See, I want to write about two different things. I want to write about my web pal Paul’s post on the daemonic interpretation of the person – which rings some bells with me. And I also want to write about Gerd Gigerenzer’s essay in the new issue of Social Theory, I think, therefore I err. And at some point I wanted to use Schopenhauer’s image of the Veil of Maya to talk about traffic fatalities.

Uhh, right. Okay. Three things.

As fans of prospect theory know, Gigerenzer plays Moriarty to Kahneman and Tversky’s Holmes and Watson. Prospect theory – which takes the datum from psychological testing to understand patterns in how people make decisions according to their perspective of the probabilities involved in adopting a course of behavior – has busily revamped the way economists think of the rational agent. Kahneman and Tversky found that certain patterns of logical error occur across groups. For instance, given a constant probability of a course of action, one can manipulate responses to that course by framing it in terms of gain or loss. K and T developed what is called the Asian disease problem. Using students and professors as their pool of respondents, they posed this problem:

Imagine that the US is preparing for the outbreak of an unusual Asian disease, which is expected to kill 600 people. Two alternative programs to combat the disease have been proposed. Assume that the exact scientific estimates of the consequences of the programs are as follows:

If Program A is adopted, 200 people will be saved.

If Program B is adopted, there is 1/3 probability that 600 people will be saved, and 2/3 probability that no people will be saved.

72 percent chose A, 28 B. Then they proposed this problem:

Problem 2
If Program C is adopted 400 people will die.
If Program D is adopted there is 1/3 probability that nobody will die, and 2/3 probability that 600 people will die.
Which of the two programs would you favor?”
22 percent went for C, and 78 percent went for D.

The first question was framed in such a way that it brought out risk averseness: “the prospect of certainly saving 200 lives is more attractive than a risky prospect of equal expected value, that is, a one-in-three chance of saving 600 lives.” The second question brought out risk taking: “the certain death of 400 people is less acceptable than the two ­in­ three chance that 600 will die.”

Gigerenzer’s essay begins by showing that the paradigm within which Kahneman and Tversky are working is one that assumes that the brain is a logic machine. This goes back, according to G., to Piaget’s work. Piaget showed that children, as they get older, get better at answering questions that are, basically, about sets. For instance, children are shown a picture with ten flowers, of which five are daisies. They are asked if there are more daisies or more flowers in the picture. Eventually, by the age of eight or nine, they click to the fact that daisies are a subset of flowers, and thus, naturally, there are more flowers. But K. and T., those devils, upset this neat pattern by transposing the terms into probability terms with the famous Linda problem. Linda is 31 years old. Linda was a philosophy major. Linda is outspoken. Now, which one of the two is more probable? A. Linda is a bank teller. B. Linda is a bank teller and is active in the feminist movement? People match Linda’s characteristics to b., and so choose b, even though – by the laws of probability – the conjunction of the probability of two states is less than their separate probabilities.

(The conjunction fallacy, by the way, was rife during the early days of the Iraq occupation, as LI liked to point out at the time. But I’m not going off in that direction today.)

So: what? Tomorrow I will write about Gigerenzer’s problem with the Linda problem.

Tuesday, May 24, 2005

Doing our share

LI has been contemplating one of the latest developments in the War.

“In a joint statement at the end of a three-day visit by the Iranian foreign minister, Kamal Kharazi, the new Shiite-led Iraqi government said that Saddam Hussein, the overthrown Iraqi leader, and other officials in his government must be put on trial for committing "military aggression against the people of Iraq, Iran and Kuwait," as well as crimes against humanity and war crimes.”

Given this statement by our ally officially making that war a criminal offense, and given LI's well known sense of patriotism, we thought we'd start the ball rolling by fingering a few collaborators that the Iraqis might want to pick up in this country.

For instance: Weinberger, Caspar W. Description: lunatic, former Secretary of War under Ronald Reagan (president, U.S.A.). In his memoirs, written in 1990 “Weinberger holds the Ayatollah responsible for the war with Iraq, even though Iraq attacked first. Moreover, he asserts that Iran was able to hold its own in the war only because Iraq had decided it did not want to commit the substantial resources required for a military victory. The former secretary conveniently forgets that Iraq resorted even to chemical weapons.”

There’s a rundown of the dog’s criminal activities here.

Current resorts: “Cap” has been seen in Washington D.C. Method of capture suggested: ambush at meeting of the Forbes magazine board of directors, of which he is chairman; also can be picked up at the Winston Churchill Memorial Fund annual pigsticking hunt, or, if 20 to 30 thousand dollars is available, can be lured to speak at any event involving making money from the commerce of mass murder, i.e. defense related industry.

Rumsfeld, Donald. Description: lunatic, current secretary of War. Record: There's a rundown of beast's criminal role here.

Method of capture suggested: Rumsfeld, known to his associates as Babbling Don, is known to frequent a building on 1000 Defense, where he hangs out with various shady cronies. Warning: suspect is armed and should be considered dangerous.

Bush, George Herbert. Description: records show that the suspect may have been president of the United States. Information is considered highly unreliable, as it is unlikely a person so egregiously unpleasant could have been elected to position of dogcatcher, even among kaf'r. Record: partial list of crimes committed in La Times article here

Method of Capture suggested: last seen looking like prune went wrong way down windpipe in tsunami aid photo-op in Thailand. Likely to be anywhere wife is not in vicinity. May be lured by set up involving search for new spokesman for viagra related product, for which see Dole, Robert.

PS - Since we are doing our share in the Great Bush War Effort, we felt like sharing some more of the good news in Iraq.

Ali Hameed quit his job as a taxi driver because he no longer felt safe on Baghdad's streets. Increasingly desperate for money to help him get married, he hit on a once-in-a-lifetime business opportunity - selling one of his kidneys.

Last week, in a shabby ward in the city's Al Karama hospital, he lay bandaged on a bed, one kidney lighter and $1,400 (about £765) richer after a three-hour operation.

In a nearby room, his body similarly bandaged, lay the man who had paid for it - the other player in a grim new black market trade in organs that is one of Iraq's few growth industries.

Monday, May 23, 2005

LI read a fascinating article by Mary Morgan in the Winter Philosophy of Science journal, and we want to write about it. Mary Morgan, Margaret Morrison, Nancy Cartwright, and Ronald Giere form, in LI’s mind, a sort of collective that bridges the distance between the Latourian Science in Action school and the last gasp tradition of the Popperians. Significantly, many come out of the London School of Economics, long a stronghold of the late Popperian school.

As philosophers of science know, the first thing that scientists will mention when asked for a philosophy of science is falsification. This is less a thoughtful judgment of the practice of science as they have observed it than boilerplate. As is well known, the falsification criteria comes from the Logical Positivist school in the twenties. More specifically, it comes from Karl Popper, as a leading thesis in the investigation of the “logic of discovery.” What those scientists usually don’t know is that the leading thesis was part of a program that claimed to offer a devastating and final refutation of induction in science.

The idea that science could be captured in a logic is an essential move in the logical positivist program of reducing all salient questions of knowledge to questions of formal language. This inflation of the notion of language signals the lineage of the philosophy: language functions, here, much as Kant’s reason functions in the Critiques. We won’t go over the adventures and impasses of this program. Suffice it to say that Popper’s picture of science was confessedly abbreviated. It didn’t tell us much about how statistics decisively changed the practice and meaning of experimentation in science. It didn’t tell us much about models. It made assumptions about hypothesis building that isolated that activity from science practice. But, mainly, it was aimed at telling us about the truth – with the idea that science is ultimately constructed around the truth. Other Popperians – Lakatos, Feyerabend, Kuhn, etc – extended to Popperian impulse to larger views of research programs, and in the process destroyed Popperian rationality. It was self mined from the very beginning. But the essential idea – that at the heart of science there is a wholly deductive program that is theoretically capturable in a formal language – still remained, yearly becoming much worse for wear. As, indeed, the original and simple thesis of falsification proved itself unable to account for large swatches of science, and fell into logical difficulties of its own (Hempel’s White Raven paradox).

Actually, in LI’s eyes, the logical positivists simply encoded, in a new form, the reaction of philosophy to science that arose during the early modern period – notably, the Cartesian idea that science advances by the hypothetico-deductive method. It was that idea which Newton fought against from the correspondence around his first paper, the great 1676 letter on light and color, to the Opticks which he published after the death of his inveterate enemy, Robert Hooke. Newton’s entire seriousness in not “framing hypotheses” was a great step towards separating, utterly, physics from metaphysics. It is a step the philosophers have never wholly forgiven him – or even wholly understood in him. Hence, the perennial urge to annex the natural sciences as a branch of logic.

Where does this leave philosophy of science, then? PoS has an uneasy relationship with Sociology of Science, insofar as it gives up the pretence of deducing the principles of science and applies itself to the observation of scientific practice. In one way, this makes PoS a very exciting field. Where other branches of philosophy amuse themselves with dubious thought experiments, PoS observes real ones.

Morgan’s paper takes a case from Economics – a model called the Edgeworth Box – and shows how it permutated over the course of a century, as economists mathematized their discipline. The Edgeworth Box (see this history by Humphrey ) was invented by Francis Edgeworth in “his now famous Mathematical Psychics ([1881] 2003), a book of almost impenetrable erudition from this Irish economist. For Edgeworth, mathematics was a form of expression, a language, and because of its special qualities it was a tool or instrument both for expression of economic ideas and for reasoning about them. But in Edgeworth's mind it was also an instrument of imagination.”

Edgeworth imagines two individuals with two goods to exchange. The world of these individuals is closed, to an extent: the traders do not have competitors. But they are free to contract or not. In other words, the Robinson Crusoe story so savaged by Marx. As Morgan puts it, the Edgeworth box “defines the locus of points at which exchange might be contracted as those where, whichever direction a move is made away from that set of points, one trader gets more and the other less utility. This set of points is termed the "contract curve.’” From Morgan: “Edgeworth's diagram refers to individual traders alongside their goods, and provides an indifference curve for each individual and their contract curve. And while it seems initially that the whole space is open for trade as in Marshall, the argument defining the contract curve in conjunction with the indifference curves through the origin (i.e., points at which utility is equivalent to that obtained from zero exchange) rules out some areas of the ninety-degree total space. Edgeworth is so impressed by his own diagram and the way that it allows him to work out some results which had previously failed to yield to general analysis, that he writes that his figure "is proved to be a correct representation" and that the diagram provides "an abstract typical representation" of a process (Edgeworth [1881] 2003, 36; my underlining).”

Now, the interesting thing about this abstract typical representation is that it represents a dynamic – although Morgan doesn’t mention it, surely there is some slight reference, here, to Maxwell’s fields, which are also constructed to capture trajectories. Morgan, instead, references Marshall’s theory of trade between two countries as the template for Edgeworth. LI notes this as a limit to exploring model building with an exclusive endogenous focus.

Morgan points out that Edgeworth’s original representation is not a box: “What might now be taken as the irreducible shape of the Box--namely, a closed set of two amounts of exchangeable items represented by the sides of the box, and two traders at opposite corners, each with two axes of potential commodities to trade with--are not there from the beginning.” Yet by 1950, the standard form of the Edgeworth diagram was a box. LI won’t reproduce Morgan’s history. But we are interested in the conclusion of that history: “For the economists in my case, learning to represent the economy in new ways was drawing new things. The mathematically expressed economic elements inside the Edgeworth Box--the indifference curves, the contract curve, the points of tangency and equilibrium, etc.--are new, mind's eye, conceptual elements, not old, body's eye, perceptual elements. Scitovsky's 1941 use of the diagram provides an excellent example of this point. The critical point of his article is the difference between allocative efficiency in which the total resources in the economy are fixed (denoted by a fixed size box) and those in which the resources change (denoted by a change in box size). The representation of the effect of this change proves to be quite difficult to understand for the modern user of such boxes. It is tempting for the reader of the diagram to suppose that, by expanding the box, there are just longer axes, more goods (for example, cheese and wine) to be exchanged for given indifference maps (representing tastes, which have no reason to alter). But of course these indifference lines represent contours in conceptual space, and increasing the total resources effectively expands the box from the middle. As the axes are lengthened, perceptual space expands, but so does the conceptual space, so that the original contract curve opens out to provide a region in the middle through which the new contract curve runs. This distinction between conceptual space and perceptual space also helps us to distinguish when a diagram is doing any work in the argument. If the diagram is about perceptual space but the argument about conceptual space, the reasoning will take place, as Mahoney describes it, "off the diagram" and the diagram will be, at best, an illustration, rather than a tool for experimentation and demonstration. (9)
Yet, as we know from Humphrey's 1996 history, during the early-twentieth-century period, the Edgeworth Box diagram was a creative tool used to derive propositions and prove theorems in economics. It was indeed a tool for reasoning about the economic world using the conceptual resources of the diagram.”

To evoke an entirely different philosophical tradition – the notions at play here, in Derridian terms, subsist in the gap between language and text. Those who read Derrida as collapsing text into language – as a run of the mill social constructionist, with the usual language idealism -- don’t understand him at all. The Edgeworth box is an excellent example of the trajectory of signs that constitutes a “text”, in Derrida’s terms. And what Morgan says, finally, about the ontological status of the Box is exactly what deconstruction would predict:

“I should be careful here to point out that when the Edgeworth Box is described as a mathematical model, it is not only made of mathematics. We can illustrate this best by considering the allowable movements or manipulations which can be made in the model. The notion that the two traders will be at some kind of optimum when their indifference curves meet at a tangency makes use of mathematical concepts and logic. But the apparatus of offer curves, indifference curves, and so, for example, the spaces in which trade is ruled out, depends on understanding the conceptual content of the elements in the model. Thus, Scitovsky's diagram showing the implications of increasing the resources requires manipulations of the diagram which are determined by the economic meaning of these curves, not by the logic of geometry. Both mathematical and subject-matter conceptual knowledge constrain the details of the representation and define the allowable manipulations. This is surely not particular to models in the form of diagrams, and indeed it seems likely that most if not all "mathematical" models in economics depend on economic subject information to constrain or define their rules of manipulation. From this point of view, there would be as much difficulty in "translating" the Edgeworth Box into "just mathematics" with no subject content as into "just words" with no mathematical content. The Edgeworth Box diagram carries an independent representational function: (10) it contains conceptual apparatus which could not be represented, or manipulated, in verbal form and indeed cannot be entirely expressed in purely mathematical terms.”

Which last sentence opens up a few too many vistas.

Elia meets Karl Marx at the South Sea House

    When Charles Lamb, a scholarship boy at Christ’s Hospital, was fifteen, one of his patrons, Thomas Coventry, had a discussion with a...