Juridical Coherence

Theory on framework issues

Sunday, September 7, 2014

24.0. Abstract construal is offline thinking

The foundation of construal-level theory doesn’t seem to be a “framework” matter (per this blog’s subtitle), but I will treat it so by contending the theory describes how two basic forms of human cognition differ; in fact, no less than how human cognition differs from that of nonhuman animals. To glimpse these underpinnings, we must descend beneath the experimental findings, which provide the semblance of a continuous dimension, to the ultimate binary opposition between online and offline cognition.

These two forms of cognition were distinguished by linguist Derek Bickerton. (Language and species (1990), Language and human behavior (1996), and others.) They refer to brain processes that depend for their elicitation on external stimulus (online), versus processes that can originate autonomously from internal processing (offline). Offline processing, an evolutionary product of language, originated in the long development of protolanguage—language-based concepts without syntax for their manipulation—by homo erectus; and marking the beginning of our species, the sudden emergence of syntax. Protolanguage provided the neural space for primitive offline processing, as when our ancestors could call up the thought of potential prey—without its having any particular empirical presence—by having learned the term for woolly mammoth. With syntax came the ability to think of anything. Thus, language evolved, more than as a tool for communication, as a vehicle for thought. (The most basic argument is that language could not have developed for communication because the ability to communicate depends on the listener’s ability to understand. A language mutation in a single organism, serving communication, would be useless.)

Online processing can be applied exclusively to matter that is immediately present. Only the offline variety of thinking, created by language—gradually through protolanguage and punctuatedly through syntax—enables abstraction. Distance and  abstraction are the fundamental facets of construal level.

One way that abstractness and psychological distance seem to differ from offline processing is that construal level is a continuum, whereas offline/online processing is a dichotomy. Intermediate construal levels must be generated from elemental proportions. The dichotomous underpinnings of construal level are apparent in absolutely extreme construal levels—pure expressions; some processes are entirely online, like scratching an itch, and others, like thinking about metaphysics, are entirely offline. This pattern differs from dimensions, such as intelligence or extraversion, which are unbounded, without maxima. Construal level reveals its dichotomous essence in its modelike quality: a concrete/near and abstract/far polarity, despite the presence—even predominance—of intermediates.

I’m aware of one interpretation alternative to construal level as degree of offline processing. It comes from economist Robin Hanson’s homo hypocritus theory, which, among other interesting claims, holds that abstract construal serves impression management. Hanson’s theory says that our ancestors evolved mental modes involving concrete and abstract construal (Hanson terms them “near-mode” and “far-mode”) under pressure for separating the functions related to representing things as they are, on the one hand, and on the other, representing the self as we would like to be perceived. For Hanson, abstract construal is mainly about our ideals. Accordingly, he identifies abstract construal with Freud’s super-ego (conscientious tendency) and concrete construal with the id (impulses for immediate gratification).

On the present offline-processing analysis, abstract construal serves foresight more than moral hypocrisy, although morality and moral hypocrisy do require offline processes; in fact, they seem particularly insulated from online processing, and practical offline processing generally depends on the testing of abstract intuitions against concrete facts. Thus harnessed, offline thinking serves foresight, the abstract construals capturing essential causal relations for the sake of accurate long-term prediction.

The critical concrete fact that may decide the issue in favor of online/offline processing is that efforts at impression management, termed signaling, typically occurs online, in direct communication with another person, based on immediate perceptions. If, as Hanson claims, humans evolved two modes because the knowledge needed to manipulate the world would contaminate human efforts to impress others, then these modes are richly contaminated, because social signaling, in the prototypical face-to-face interaction, relies heavily on “near-mode” processing.

The strongest argument for a moralistic/hypocritical adaptation behind abstract construal is the human practice of fashioning arguments opportunistically, not as a tool to reach correct conclusions, but only as justification, as if one were defending against accusers. My alternative explanation is the opinion/belief analysis. We form and defend opinions in deliberation, whereas we act on beliefs. Abstract construal developed (during the protolanguage stage) under selective pressure for good deliberators.

Wednesday, May 14, 2014

23.0. The death penalty and Hegel’s law of quantity into quality: The incoherence of executions

If the gruesome Oklahoma execution portends the death-penalty’s demise, the reason may have more to do with the obnoxious applause of apologists, satisfied that justice was done, than the righteous denunciations of opponents. The arguments against the death penalty have never been strong, mainly because, by equally impugning incarceration, they prove too much. While mass incarceration and executions both implement racism (for example), mass incarceration is the far greater racial injustice.

Folk-logical confusion

The public rationale for the death penalty is (necessarily) based on an implicit error of “folk logic”; this error underlies its ethically coarsening consequences.

My discussion is grounded in a few basic observations about the criminal-punishment system, which is three-tiered: fines, incarceration, and death. Each tier is supposed to correspond to a qualitative worsening of offense: malum prohibitum, malum in se, and heinous crime (minimally involving murder). The rationale, in short, is that taking a life is the ultimate crime, deserving loss of life, the ultimate punishment. Although we can question whether loss of life is really the worst that can happen to someone, that’s the way it’s presented, and it perhaps necessarily appears so to the mass mind.

But, accepting the premise, the rationale pretends a nonexistent symmetry, the asymmetry being in the capability of one person to inflict harm on others in great number. If death is the ultimate punishment, it doesn’t follow that taking life is the ultimate crime: a criminal is but a single person capable of harming many.

The 19th-century philosopher Georg Hegel diagnosed the cognitive bias of failing to see that change in degree (“quantitative” change), carried far enough, produces a change in kind (“qualitative” change). In this light, look at the banking collapse that led to the U.S. mortgage crisis, involving crimes by bankers that have yet gone unpunished and which would never be punished by execution. (If you need worse, consider the industrialists who funded Hitler’s ascent.) Ordinary “thin utilitarian” public-moral intuition tells us that knowingly causing suffering for millions is worse than even the sadistic murder of a single person; if there were a qualitative category of heinous crimes, at some tipping point sublethal mass crimes would become heinous. You might advise don’t stop executing murderers, rather expand execution to heretofore unpunished crimes of massive scale, but we find no point of qualitative inflection.

Moralistic misdirection

From this artificial abstraction of the act of individual murder stems the fundamental misdirection society incurs when it institutes a death penalty, which reinforces and accentuates the near-mode bias that carves, with the knife of extraordinary public vengeance, horrific individual acts out of their societal context. The social symbolism in capital punishment dwarfs (at most historical junctures) any specific deterrence effect. Capital punishment engineers a public mentality myopically preoccupied with vengeance against victims of far worse wrongs consequently ignored.

This analysis rests on the insight that public consciousness imputes a qualitative distinction between deeds where the law applies qualitatively different punishments, and it is confirmed by the fate of another potential tier of punishment. The deliberate infliction of pain is proscribed: we don’t flog criminals; but isn’t it curious that we regard killing as humane and flogging not—when we might execute for killing, but never for nonlethal flogging? Why the reversal of values when assessing crimes and their punishment? My explanation is that flogging competes with long-term incarceration, and they can’t easily co-exist, since we would then distinguish punishments without reciprocally distinguishing crimes.

When flogging and stoning reappear, they serve a corresponding false distinction in crimes, and crimes can be special by being no crime at all; theocracies have resurrected flogging and stoning to punish thought crimes. Legally manufacturing a spurious moral hierarchy—such as one including capital crimes—foments mass myopia.

Sunday, March 30, 2014

22.0. The concept of belief and the nature of abstraction: A social propensity account

Belief, puzzling to philosophy, is part of psychology’s conceptual framework. The present essay provides a straightforward yet novel theory of the explanatory and predictive value of describing agents as having beliefs. The theory attributes full-fledged beliefs exclusively to agents with linguistic capacities, but it does so as an empirical matter rather than a priori. By treating abstraction as an inherently social practice, the dependence of full-fledged belief on language resolves a philosophical problem regarding its possibility in a world where only concrete particulars exist.

The propositional character of belief

It can appear mysterious that the content of epistemic attitudes (belief and opinion) is conveyed by clauses introduced by that: “I believe that the dog is in his house.” If beliefs were causes of behavior, our success in denoting them gives rise to an apparently insurmountable problem: how do propositions—if they exist at all—exist independently of human conduct, so as to be fit for causally explaining it?

While belief ascriptions figure prominently in many behavioral explanations, their propositional form indicates that they pertain to states of information. My belief that my dog is in his house consists of the reliable use of the information that he’s there. Not only will I reply accordingly if asked about his location; in directing other my conduct, I may use that information. If I want the dog to come, I will yell in the direction of his house rather than toward his sofa. Yet, I won’t always use this information: I might absent-mindedly call to my dog on the sofa despite knowing (hence believing) that he is in his house. Believed information can be mistakenly disregarded.

Belief “that p” is a propensity to take p into rational account when p is relevant to the agent’s goals. But taking certain information into account involves also various skills, and it must be facilitated by the appropriate habits. The purposeful availability of believed information is also affected by, besides skills, inhibitions, habits, and desires.

What becomes striking on recognizing beliefs as propensities to use particular information is that behavior can be so successfully explained, when we know something of an agent’s purposes, by reference to the information on which we can predict the agent’s reliance.

Is this successful reliance a unique feature of human cognition? We can use belief ascriptions to describe nonhuman behavior, but we can do the same for machines. The concept of belief, however, isn’t essential to describing nonintelligent machine behavior. When my printer’s light indicates that it is out of paper, I might say it believes it is, particularly if, in fact, the tray is full. The printer’s “belief” that it is out of paper is expressed in two ways: it refuses to print and a light turns on, and I can refer to these directly, without invoking the concept of belief. Compare it to what is true of me when I run out of paper, where my belief that I have exhausted my supply can explain an indefinitely large set of potential behaviors, from purchasing supplies to postponing work to expressing frustrated rage—in any of an indefinitely large variety of manners.

Applying the concept of belief to nonhuman animals is intermediate between applying it to machines or to humans; it can be applied to animals more robustly than to machines. It isn’t preposterous to say that a dog believes his bone is buried at a certain location, particularly if it’s been removed and he still tries to retrieve it from the old location. What can give us pause about saying the dog believes arises from the severely limited conduct that’s influenced by the dog’s information about the bone’s location, as is apparent when the dog fails, except when hungry, to behave territorially toward the bone’s burial place.

Humans differ from canines in our capacity to carry the information constituting a belief’s propositional content to indefinitely many contexts. This makes belief indispensable in forecasting human behavior: without it, we could not exploit the predictive power of knowing what information a human agent is likely to rely on in new contexts.

This cross-contextual consistency in use of information seems to rest on our having language, which permits (but does not compel!) the insertion of old information into new contexts.

The social representation of abstractions

Explaining our cross-contextual capacities is the problem (in the theory of knowledge) of how we manage to mentally represent abstractions. In Kripke’s version of Wittgenstein’s private-language argument, the problem is expressed in the dependence of concepts on extensions that are not rule-governed. The social consensus engendered by how others apply words provides a standard against which to measure one’s own word usage.

Abstraction relies, ultimately, on the “wisdom of crowds” in achieving the most instrumentally effective segmentations. The source of abstraction—a form of social coordination—lies in our capacity to intuit (but only approximately) how others apply words.

The capacity to grasp the meanings of others’ words underlies the fruitfulness of using believed propositions to forecast human behavior. With language we can represent the information that another human agent is also able to represent and can transfer to all manner of contexts. But this linguistic requirement for full-fledged belief does not mean that people’s beliefs are always the beliefs they claim (or believe) they have. Language allows us our propositional knowledge about abstract informational states, but that doesn’t imply that we have infallible access to those states—obviously not pertaining to others but not even about ourselves. Nor does it follow that nonlinguistic animals can have full-fledged beliefs limited only by concreteness. Nonlinguistic animals lack full-fledged beliefs about even concrete matters because linguistic representation is the only available means for representing information in a way allowing its introduction to indefinitely varied contexts.

This account relies on a weakened private-language argument to explain abstraction as social consensus. But I reject Wittgenstein’s argument that private language is impossible: we do have propositional states accessible only privately. Wittgenstein’s argument proves too much, as it would impugn also the possibility of linguistic meaning, for which there is no fact of the matter as to how society must extend the meaning to new information. The answer to the strong private-language argument is the propositional structure of perception itself. (See T. Burge, Origins of Objectivity (2010).) What language provides is a consensual standard against which one’s (ultimately idiosyncratic) personal standard can be compared and modified. (Notice that this invokes a dialectic between what I’ve termed “opinion” and “belief.”)

This account language's role in abstraction justifies the early 20th-century Russian psychologist Vygotsky’s view that abstract thought is fundamentally linguistic.

Wednesday, October 30, 2013

21.1. Status inflation and deflation: Prestige, the essence of status, permits broad alliances

Is status a positional good?

As the concept of social status itself attains higher status (through employment in evolutionary psychology), class struggles over the material conditions of life are recognized as impregnated with status aspirations. The conclusion may be drawn or implied that these conflicts are inherently wasteful: we’d be better off if people accepted their lot, because status is a positional good—a zero-sum game—what is won by some is lost by others. (See, for example, Robin Hanson’s Inequality talk is about grabbing.) But it also seems that a society beset with severe status inequality will suffer status deflation.

One approach to the question of whether status is a positional good is whether status is (implicitly) measured using an ordinal scale of measurement or a higher scale, interval or ratio, where ordinal scales express only rank, whereas interval and ratio scales express degrees of difference. An example of an ordinal scale expressing social status is military rank. The status of the rank of major depends on the mass of soldiers a major outranks and the number who outrank the major, so, if half of the captains are promoted to major, the major’s status declines.

Social status can seem similar to military rank, but (I contend) this is a confusion: the social status of an entire population can rise or fall (inflate or deflate), because the main component of social status is prestige, which has ratio properties. The confusion results from conflating prestige with dominance, more primitive and prototypical, but prestige is a ratio scale, not an ordinal scale like dominance, because it results from summing over weighted dominance relations. Consider our major in contrast to a lieutenant under his command. The lieutenant may have received higher grades in the military academy, he may come from a wealthier family, and he may be the president of a nonmilitary club in which the major participates as an ordinary member. Which has more prestige? The point is that the question makes sense; we combine information about position in various separate dominance hierarchies with other information about their potential power to determine their prestige, the information’s additivity implying that prestige is at least an interval scale (probably a ratio scale), not a mere ordinal scale like dominance. Concern with prestige (as distinct from dominance) is a human-specific trait, with few roots other than dominance in our primate psychology.

Why prestige?

Evolutionary psychologists propose that prestige (usually referred to simply as status, a convention I will abide) reflects a person’s value as an ally: a high-status person is a powerful ally. (The person with the highest prestige is God, the most powerful ally.) Other primates appear to have only dominance, which suffices for simian calculations because apes, living in a single hierarchy, don’t need to sum over different hierarchies. Humans live embedded in multiple social hierarchies—at root, dominance relations—which must be weighted and added to appraise an individual’s value in alliances.

If primordial alliances were exclusively alliances pitted against other allied humans, prestige could still be a zero-sum game despite its ratio scaling. But the alliances formed primordially weren’t exclusively competitive alliances: alliances were presumably formed for foraging and child care. Ratio-scaled prestige, a currency spanning dominance hierarchies, allows more and broader alliances.

Two distinct explanatory tasks regarding prestige concern its evolutionary function and its individual motivation. Evolutionary psychologists hypothesize that status derives from the differential value of persons as allies. The quest for prestige aligns the individual’s efforts with adaptation: by pursuing prestige, one becomes a more powerful ally, deriving the corresponding social (and reproductive) advantages. But the mechanism is more complex and itself provides additional clues about function. Prestige is a reaction formation against envy. This agrees with the observation that we accord prestige to those we would otherwise envy. (See Theodor Reik, Love and Lust: On the Psychoanalysis of Romantic and Sexual Emotion regarding the idealization process—rooted in unconscious envy—in romantic love. “Reaction formation” is a psychodynamic mechanism involving experiencing the opposite of certain thoughts, to deny them conscious access.)

Since status is commonly perceived value as ally, status deflation means decreased willingness to rely on—to ally with—others. In 11.3, I discussed opinionation as a pathology of belief-opinion confusion: we are opinionated when we fail to rely sufficiently on the opinions of experts. Status deflation causes irrational opinionation (as well as other adverse societal effects, including some relating to macroeconomics). The modern expression of the tendency toward excessively narrow alliances is lack of regard for the opinions of most others, including experts. At the same time, (one's own) status deflation increases the experienced envy. In societies where status is most deflated (typically, traditional agrarian societies), this two-pronged attack on the sublimation of envy results in the bullheadedness of the peasant.

Countering status deflation and generating inflation.

Economic inequality is a manifestation of status deflation as well as one of its causes (as I maintained in 21.0.) In modern capitalist societies, the main ways of reducing inequality have been restricted immigration (to reduce the supply of labor and increase its price) and progressive taxation. But these policies have been applied sporadically and are only practiced weakly in most advanced countries. Within Europe, the Common Market has opened borders, and in the United States, wealth inequality is so high it rivals some third-world countries. The reason stringent immigration control and progressive taxation are only sporadically applied is that these methods don’t correspond to any humanly valued relational model—which as Alan P. Fiske (Structures of Social Life (1991)) shows, enable the moralization of social practices and, as John Bolender elaborates (The Self-Organizing Social Mind (2010)), correspond to the four scales of measurement. (Communal/Sharing is nominal, Authority/Ranking is ordinal, Equality/Matching is interval, and Market/Pricing is ratio.) A flat tax employs a ratio scale, a fact that helps account for its ideological popularity despite its practical infirmity. To human intuition, progressive tax rates are arbitrary. As to immigration control, absolute restriction would correspond to Communal/Sharing, but like the flat tax rate, mere reduction of immigration rates doesn’t form an intuitively compelling public policy. (This is not to disparage the instrumental use of either immigration control or progressive taxation.)

State socialism, on the other hand, can be grounded in intuitive metrics: equality matching (interval scale) embedded in communal sharing (nominal scale). It has proven not only to provide a greater degree of status equality (thus status inflation) but also to be more durable.

Saturday, August 10, 2013

21.0. The dismal employment picture: A social-status-theory explanation

Most economists agree automation costs jobs, but the reason it does is unclear. Economists had theorized that automation would create more jobs than it eliminates. This essay sketches a novel theory explaining why, today, automation costs jobs, whereas introducing machinery into production once created jobs and continues to create them in some economically backward countries, particularly China. I’m not an expert on the subject, and I confine myself to basing my theory on a few facts and principles of economics that are widely accepted, to which I apply the nascent social-status theories from evolutionary psychology. (Economist Robin Hanson’s blog, Overcoming Bias, which has influenced my thinking regarding social status, contains numerous novel applications of social-status theory.) This explanation is independent of my previous theorizing that the tendency of rate of profit to decline is a source of economic decline. The point of this essay is to propose that social-status theory is relevant to macroeconomics.

Aggregate demand and the industrial revolution

The concept taken from economics is aggregate demand. Rising aggregate demand allows the economy to grow in the long-term, furnishing the reason economists had believed automation would create jobs. By creating wealth more efficiently, automation permits the employment of more workers, whose increased buying power supports their employment.

This logic can collapse if workers doing the new jobs are paid less than the workers replaced in the labor force. Profits will then rise, and while profits contribute to aggregate demand, they do so less than wages because the profit-takers are wealthier than workers and spend less of the increase than workers would spend. Investments in machinery increase aggregate demand, but the profitability of these investments depends on unreliable technological opportunities. Every modern society that has been economically expansive long-term has raised the standard of living of the masses of people.

The fundamental reason the industrial revolution allowed vast expansion of the economy is that expansion of the labor force occurred primarily by turning peasants and farm workers into manufacturing workers. Workers were paid low wages and worked as much as 14 hours a day before they organized into unions, but still, at least in long historical perspective, their income was better than that of the peasants they had replaced. Even today, agricultural workers throughout the world get much lower wages than do manufacturing or personal-service-sector workers. The creation of an urban working class meant an expanding economy with expanding employment. The process is observed today in fast-motion in China, where an expanding economy is powered by converting very poor peasants into better-off workers, creating rising aggregate demand. This isn’t the only tendency in the early and middle industrial revolution. In a countervailing tendency, much emphasized in the popular imagination, skilled workers are replaced by unskilled workers. The first tendency is stronger.

During the past hundred years, another trend came to dominate: the growth of the personal-service sector. “Personal-service sector” (from which I exclude the “producer services,” which aren’t “personal”) is an amorphous term  including well-paid occupations, such as physicians, but most advanced-country workers not employed in manufacturing goods are employed in distributing goods (wholesale and retail sales), restaurants and hotels, and the nonprofessional health-care sector, and these workers are everywhere paid more poorly than those employed in manufacturing. Hence the worry about the “disappearing manufacturing jobs.” Replacing manufacturing jobs with service-sector jobs entails slower growth in aggregate demand.

Social-status theory from evolutionary psychology

The question seldom addressed is why service-sector workers, such as retail clerks, food preparers, and nursing aides, are so poorly paid. Lower skill requirements may be part of the reason, but the fact that service-sector jobs remain unskilled may itself be best explained by their inherently lower status, which is the answer I propose. Socially stratified societies allocate social status to the various occupations based on criteria rooted in instinct. The personal-service occupations are accorded lower status because these occupations carry indicia of servitude and servility.

Modern social-status theory derives from evolutionary psychology, which emphasizes our continuity with chimpanzees, whose social life is characterized by dominance hierarchies. But evolutionary psychology also recognizes that bands of hunter-gatherers were usually egalitarian: “primitive communist” societies resisting any attempts by strongmen to dominate them or establish material or other status-based inequalities. With the agricultural revolution, the accrual of social surpluses and the need for large-scale social coordination both intensified and unfettered the striving for social dominance—power, prestige, wealth—from the group control that held them in harness throughout 90% of humankind’s span of existence, producing societies divided into social classes.

Allocation of status depends on instinctual triggers, including the marks of servitude: all else being equal, one who serves has less status than the one served.

Indicia of servitude aren’t the exclusive basis for awarding status to occupations, as demonstrated by the vast range of incomes among occupations in the personal-service sector. Anything associated with power increases status. Status theory can explain the higher incomes of manufacturing workers compared to peasants and farm workers by the prestige of cities, associated with urban power. The link between status and power might also explain why economists of the early industrial revolution, such as Ricardo and Marx, underestimated the ability of manufacturing workers to sustain wages higher than the price of bare necessities: the economists could not foresee the consequences of the comparatively high social status of workers in manufacturing, or perhaps, the relative status of manufacturing workers wasn’t evident to them. Even today, farm workers have far lower incomes than either manufacturing or personal-service workers. Physicians have high status because they command medical technologies that afford power over life or death. Consequently, the large incomes of physicians are a new development: 19th century physicians weren’t affluent and highly respected, since they didn’t command the powers of modern chemistry. Occupations that require considerable skill and demonstrate intelligence are high status. But the trend is proliferation of personal-service jobs in retail sales, hotels and restaurants, and health-care, where workers have low status based on bearing indicia of servitude.

Status inheres in making useful goods that does not inhere in providing useful services. Dwell, for a moment, on the concept “the dignity of labor.” Even unskilled work has a dignity that is absent in personal service; think of the fake smile a sales agent or nurses’ aide must present. Insincerely agreeable affect is demeaning, compared even to unskilled manual labor, which may be boring but isn’t humiliating. This is only an example—and not the most obvious example.

The whole of society may conspire to bring about the low wages of service-sector workers. Laws protecting full-time workers often don’t extend to part-time workers, who are more common in the personal-service sector. But since wages are set primarily by market pricing, the assertiveness of the workers, especially their collective assertiveness, is probably the main proximal mechanism by which status influences income. High status produces confidence and sense of entitlement, a collective refusal to accept conditions below their due, because of their station in life.

Prospects

These trends paint a bleak picture: rising inequality, growing unemployment, and social-status deflation. Not only are the macro-economic trends unfavorable, but the means to resist them politically diminishes as the assertiveness of the downtrodden declines with their loss of self-confidence and sense of class entitlement. The analysis does point to a public policy that might slow or reverse these trends. Although no great cause for optimism in the absence of any practical means of effecting change, I’ll end on that note of relative optimism: we must ask how the social status of personal-service workers might be raised. 

If the triggers for low status are inevitably the signals of servitude inherent in these occupations, upgrading their status entails adding high-status signals. Statizing personal-service industries would accomplish this. Government, being powerful, is high status, and all else being equal, workers employed by government will enjoy higher status than those working in the private sector. The evidence includes the strength of unions in the public sector despite their obliteration elsewhere. Statization of personal services, regretably, isn’t today’s trend.                     

Sunday, July 7, 2013

15.3. Why ideology types and the political spectrum match: The theory of ideological concealment


The correspondence problem in general

The unanticipated correspondence between ideology types and segments of the left-right political spectrum posed an unexpectedly difficult theoretical problem. The solution is now at hand: you must consider not only what the types each tell but also what they conceal. But first, a review of the basics of construal-level theory and the theory of ideology types.

Construal-level theory from social psychology deals with abstract construal (or far-mode) and concrete construal (or near-mode), where abstract means lower granularity achieved by deeper cognitive processing and far means distant (primarily) in time. The alternative names for these perspectives on reality correspond to two facets of construal level, which are correlated but can diverge. Managerialism is concrete and present-oriented, Utopianism abstract and future-oriented; but Demagogism is abstract and present-oriented, Monomaniacalism concrete and future oriented.

The unexpectedly difficult problem is to explain why the far political right fits the Demagogist pattern, the far left the Utopianist, the broad center Managerialist. To understand why, first notice that construal-level theory can seem to contradict an earlier claim: ideologists view abstract or far components of ideologies as more important than concrete or near components. How can this be, when construal-level theory informs us that the concrete and near seem more important? The key to resolving the apparent contradiction is that what’s ideologically most important isn’t the same as what’s simply most important. In fact, what’s most important ideologically serves to conceal what’s really more important to typical individuals espousing the ideologies.

Explaining the correspondence of each ideology type

In Managerialism, the typical ideology of modern, stable regimes, the low commitment to both components of ideology conceals the strength of its nonideological commitment to practical policies favoring particular interests. Managerialists portray themselves as flexible, as carrying their ideologies lightly, because they want the population to think they are more open to input and pressure than they are. President Obama, the complete Managerialist, concealed his political commitment to the survival of the banking monopolies, under a pragmatic rhetoric according to which the old bank “regulators” were simply the most capable candidates available. Managerialism corresponds to a broad centrism because powerful interests support the status quo and must look flexible to appear less powerful than they are. The commitment to the status quo is paramount.

Utopianism shows the opposite pattern where intransigence is exaggerated rather than downplayed. Utopianism is often the ideology of those of the downtrodden who have the capacity to resist by collective action. While powerful individuals must try to appear flexible, those in a position to offer contest should appear implacable. They must downplay what is really most important to them, concrete improvements, since by concealing their willingness to compromise they can extract better compromises. The Social Democratic Parties of the Second International often emphasized their Maximum Program, which was socialism, while in practice pursuing concrete, less ideological concrete measures. The Maximum Program improved their bargaining position in pursuing their Minimum Program.

Demagogists are ideologically committed to abstract means and seem to choose issues without concern for consistency, but their commitment to abstract means conceals their opportunistic orientation to immediacy. Demagogists are on the far right because Demagogism appeals to peasants and small businessmen who, in their social isolation, flounder and are unable to resist. They lack the raw collective strength of the workers or the individual power of the capitalists and high managers, so they desperately want immediate relief. The issues may vary, but they always deal with the immediate. The Tea Party campaigned under an abstract ideology of privatization of government services, but when it came to their own benefits, they were grasping; aged Tea Partiers wanted above all to preserve their Medicare “entitlements.” Demagogists must conceal their real concern about their narrow and immediate self-interest because even the transitory political coalitions they enter would come apart if the narrowness of its components was understood.

Monomaniacalists are unique in spanning the ideological spectrum, and they correspond to amorphous class interests. What they conceal is the rigidity of their very outlook, its obsessional quality, which can preclude getting serious support. Ron Paul’s ideological emphasis on abstract liberty concealed the primacy of his fetishistic support of the gold standard and his mechanical negative votes on any tax bills.

The two sources of ideology

Not one singly but two bases in practical life jointly support ideologies: the interests of social classes and the habitual thought patterns of occupations. These don’t always correspond. Engineers are prone to Monomaniacalist thinking, but if an engineer becomes very wealthy, Managerialist ideology will better express his interests. As his interests won’t support his Monomaniacalist tendencies and his Monomaniacalism doesn’t support his Managerialist interests, he is an unlikely ideologist.

Monday, May 20, 2013

11.6. Belief–opinion confusion and the contradictions of capitalist investment markets: Fictional-market socialism

(Part 7 of Belief-versus-opinion series.)

Economic recessions, like the one we hope we’re recovering from, have varied causes, but any causes inhering in capitalist markets are fundamental in that they won’t be eliminated without basic systemic change. My theory of belief-opinion confusion explains a fundamental cause of business cycles: investment markets necessarily rely on beliefs at places in social-decision processes where opinions are appropriate.

Belief and opinion: Two kinds of judgments

With mild regimentation of ordinary language, belief and opinion name two distinct entity types—dispositions versus occurrent mentation—derived from two perspectives on reality: abstract construal and concrete construal. This chart summarizes the differences between belief and opinion:



Belief and opinion ideally correspond to ways of participating in decisions in groups, including entire societies: action and deliberation; deliberation concerns figuring out what ought to be done, and action concerns doing it. Confusion is rife in electoral democracies with deeply opposed interests, since one forum serves both purposes.

“Deliberation” by capitalist markets defectively supplants opinion with belief

But if the political arena is the scene for opinion-belief confusion, the investment markets are where belief completely supplants opinion. Markets are mechanisms for societal decision-making: in a democracy of the dollar, your purchases figure into the determination of what is produced. In markets for use, the buying decisions follow from the buyer’s opinion, which—being personal—translates smoothly into belief, without deliberation. Whose opinion but your own should you consult? Markets for commodities and other easily comparable items effectively combine the opinions of buyers, since they can decide independently.

Investment markets are fundamentally different because investors must rely on the past financial performance of an enterprise; usually that’s the most important information available, so they must mainly extrapolate from an investment's past market results. In the societal deliberative process, investors express their beliefs rather than opinions, and these beliefs are heavily laden with others’ judgments (although from a personal standpoint, they express their opinions, since they value most what is original in the judgment).

The investment process can be viewed as forgoing opinion formation prior to deliberation, where the decision to invest should be based on independent opinion if the “deliberative process”—consisting of the “decisions” issued by the market—is to function properly.

The cost of this type of dysfunctional substitution of belief for opinion in deliberation is conformism, and when decisions are made sequentially, a consequence is information cascades, where random variations are amplified into large swings. This results from extrapolation, the result of investors using the previous judgments of other investors—expressed as stock or bond prices—as guide. Judgments by investors are essentially expressions of investors’ beliefs, primarily based on others’ judgments previously given. Obscuring the role of extrapolation is the apparent paradox that profits are made on the market by betting against the consensus, but extrapolating from investment-market gains is to extrapolate based on outperforming the crowd.

Purified fictional markets under socialism

Conceptualization of belief-opinion confusion suggests that the solution is to obtain independent opinions, which investments don’t reflect because investors know their beliefs are more veridical than their opinions, which are based on very limited data. Opinions can be obtained only if personal gain is divorced from investment decisions. Not only can’t capitalist investors be expected to invest according to opinion; they won’t even disclose their true opinions because they benefit from the ignorance of other investors.

Opinions could be obtained in an economy where capital is state owned—probably in such an economy exclusively. The model suggested is a fictional market where numerous government functionaries make investment decisions based on their opinions but don’t lose or profit because of their decisions: those incentives would cause them to “invest” based on beliefs. The fictional investments regulate the economy, which is state owned despite being controlled by a market purified of cascades and the other distortions due to correlated judgments.

Such a society requires a high level of material well-being and a high level of social consciousness, so the functionaries will afford concern with following instructions for which they won’t be rewarded or punished. These requirements may illuminate the ultimate failure of the socialistic experiment that was the Soviet Union, where slow growth set the stage for a pro-capitalist coup. In a society still materially poor, fictional use of the market would degenerate into a real capitalist market.

Monday, April 15, 2013

11.5. Why do we confuse belief and opinion?: A construal-level-theory analysis. THE CONFUSION BETWEEN BELIEF AND OPINION AND THE NATURES OF FANATICISM AND PHILISTINISM. PART 6.

Why do we confuse the epistemic attitudes opinion and belief, which—to serve the distinct functions of deliberation and action—should be based, respectively, on our own thinking or on that of our epistemic superiors and peers? We confuse them because we’re prone to see our own beliefs as being more like original opinions than they are, so we forgo the distinction, treating these epistemic attitudes identically whether as opinion or belief. Construal-level theory provides the explanatory concepts. We use a distinctively global way of thinking—abstract construal or far-mode—when we contemplate the future and the psychologically distant; and we use a distinctively narrow way of thinking—concrete construal or near-mode—when we act for the present and on the psychologically near. Appraisals of belief, unlike opinion, result from abstract construal, but when we think of our own (hence psychologically near) beliefs, we construe concretely, eliminating construal level as a cue to distinguish belief and opinion to assess each on its proper grounds.

Belief is more psychologically distant than opinion because one’s own person is near, others’ distant, and belief incorporates (averages) others’ opinions, which are disregarded in rational opinion formation. Construal-level theory would indicate that we perceive others as acting for their beliefs and ourselves as acting for our opinions, that is, we see ourselves as engaged in deliberation when we see our counterparts engaged in action. The spiral ensues in which parties to deliberation misperceive the other as advancing an agenda rather than engaging in good-faith deliberation, forcing each to reciprocate because the party engaging in action controls through benefiting from the distraction.

Beliefs and opinions are different entities, not just different functions that entities serve. We typically ascribe beliefs to others to describe and predict their conduct. Beliefs are far-mode constructions that must be grounded in an inbuilt template—since belief ascription is humanly universal—an idealization, which reality only approximates. If you believe that “She’s telling the truth,” your actions will comport with the absence of suspected untruthfulness but only to a point. Belief is a matter of degree, based on how close the template and reality match.

Belief is a primitive intuition regarding others, but applying the concept of belief to oneself doesn’t come naturally. Ferreting out the contours of unarticulated belief is what gives insight-based psychotherapy its power. Although the thinking comes easily that another agent is deceiving himself about what he really believes—others’ beliefs proven by behavior more than words—the agent himself often rejects belief ascriptions contradicting the words he tells himself. Those words are usually his opinions: our ordinary unwillingness to attribute an opinion to someone who can’t express it shows that opinions are closely tied to particular words. Opinion is the construct more suitable for possible neurobiological reduction, whereas belief is a family-relations concept, not a sharply delineated entity.

Friday, March 29, 2013

20.0. Buridan’s ass and the psychological origins of objective probability

The medieval philosopher Buridan reportedly constructed a thought experiment to support his view that human behavior is determined rather than “free”—hence rational agents can't choose between two equally good alternatives. In the Buridan’s Ass Paradox, an ass finds itself between two equal equidistant bales of hay, noticed simultaneously; the bales’ distance and size are the only variables influencing the ass’s behavior. Under these idealized conditions, the ass must starve, its predicament indistinguishable from a physical object suspended between opposite forces, such as a planet that neither falls into the sun nor escapes into outer space. (Since the ass served Buridan as metaphor for the human agent, in what follows I speak of “ass” and “agent” interchangeably.)

Computer scientist Leslie Lamport formalized the paradox as “Buridan’s Principle,” which states that the ass will starve if it is situated in a range of possibilities that include midpoints where two opposing forces are equal and it must choose in a sufficiently short time span. We assume, based on a principle of physical continuity, that the larger the bale of hay compared to the other, the faster will the ass be able to decide. Since this is true on the left and on the right, at the midpoint, where the bales are equal, symmetry requires an infinite decision time.  Conclusion: within some range of bale comparisons, the ass will require decision time greater than a given bounded time interval. (For rigorous treatment, see Buridan’s Principle (1984).)

Buridan’s Principle is counterintuitive, as Lamport discovered when he first tried to publish. Among the objections to Buridan’s Principle summarized by Lamport, the main objection provides an insight about the source of the mind-projection fallacy, which treats probability as a feature of the world. The most common objection is that when the agent can’t decide it may use a default metarule. Lamport points out this substitutes another decision subject to the same limits: the agent must decide that it can’t decide. My point differs from that of Lamport, who proves that binary decisions in the face of continuous inputs are unavoidable and that with minimal assumptions they preclude deciding in bounded time; whereas I draw a stronger conclusion: no decision is substitutable when you adhere strictly to the problem’s conditions specifying that the agent be equally balanced between the options. Any inclination to substitute a different decision is a bias toward making the decision that the substitute decision entails. In the simplest variant, the ass may use the rule: turn left when you can’t decide, potentially entrapping it in the limbo between deciding whether it can’t decide. If the ass has a metarule resolving conflicts to favor the left, it has an extraneous bias.

Lamport’s analysis discerns a kind of physical law; mine elucidates the origins of the mind-projection fallacy. What’s psychologically telling is that the most common metarule is to decide at random. But if by random we mean only apparently random, the strategy still doesn’t free the ass from its straightjacket. If it flips a coin, an agent is, in fact, biased toward whatever the coin will dictate, bias, here, means an inclination to use means causally connected with a certain outcome, but the coin flip’s apparent randomness is due to our ignorance of microconditions; truly random responding would allow the agent to circumvent the paradox’s conditions. The theory that the agent might use a random strategy expresses the intuition that the agent could turn either way. It seems a route to where the opposites of functioning according to physical law and acting “freely” in perceived self-interest are reconciled.

This false reconciliation comes through confusing two kinds of symmetry: the epistemic symmetry of “chance” events and the dynamic symmetry in the Buridan’s ass paradox. If you flip a coin, the symmetry of the coin (along with your lack of control over the flip) is what makes your reasons for preferring heads and tails equivalent, justifying assigning each the same probability. We encounter another symmetry with Buridan’s ass, where we also have the same reason to think the ass will turn in either direction. Since the intuition of “free will” precludes impossible decisions, we construe our epistemic uncertainty as describing a decision that’s possible but inherently uncertain.

When we conceive of the ass as a purely physical process  subject to two opposite forces (which, of course, it is), then it’s obvious that the ass can be “stuck.” What miscues intuition is that the ass need not be confined to one decision rule. But if by hypothesis it is confined to one rule, the rule may preclude decision. This hypothetical is made relevant by the necessity of there being some ultimate decision rule.

The intuitive physics of an agent that can’t get stuck entails: a) two equal forces act on an object producing an equilibrium; b) without breaking the equilibrium, an additional natural law is added specifying that the ass will turn. Rather than conclude this is impossible, intuition “resolves” the contradiction through conceiving that the ass will go in each direction half the time: the probability of either course is deemed .5. Confusion of kinds of symmetry, fueled by the intuition of free will, makes Buridan’s Principle counter-intuitive and objective probabilities intuitive.

How do we know that reality can’t be like this intuitive physics? We know because realizing a and b would mean that the physical forces involved don’t vary continuously. It would make an exception, a kind of singularity, of the midpoint.  

Thursday, March 7, 2013

14.2.1. The habit theory of morality, moral influence, and moral evolution

Contrasting with all forms of moral realism, the habit theory of morality recognizes no “terminal moral values,” since it holds that transgression of an agent’s principles of integrity is necessary to allow their adjustment to circumstances. By conceiving moral principles as principles of integrity, prosocial habits serving as indispensable self-control devices in a psychological economy where willpower is an exceedingly scarce resource, it uniquely explains—without recourse to group selectionism—how humans could evolve a group-minded morality.

Group selectionism is the minority view among evolutionists that natural selection in humans occurs in the manner of eusocial species, at the level of groups, not just genes. Eusocial species comprise primarily the social insects, whose hives’ genetic commonality permits group selection, which in their case—unlike the human—reduces to the gene level. Social psychologist Jonathan Haidt in his recent book The Righteous Mind (2013) frames the case for human group selection with the aphorism “Humans are 90% chimpanzee and 10% bee.” Haidt observes that most moral arguments are hypocritical, aiming to impress or control others, agents often ignoring standards when they can avoid punishment for transgressions. Yet Haidt acknowledges that humans occasionally behave selflessly, as when a soldier takes huge personal risks for his fellows or zealots lose themselves in moral or political causes. Haidt thinks these phenomena inexplicable at the gene or individual level because it would subject agents to strongly adverse selection pressures, since their altruism fails to serve their individual interests. Group selectionism is subject to a standard objection: inevitable exploitation by free riding, which group-selectionist theory must contain a mechanism to punish. Human societies curtail free riding by social approval and disapproval, including material rewards and punishments.

According to Haidt (and other strict-adaptationist theorists), the proclivity to reward and punish transgression against group interest must arise through group selection because otherwise approval and disapproval meted out in the group interest would be another form of self-sacrifice. The habit theory of morality treats moral approval and disapproval as expressing the same habit set used for self-control, illustrated by the habit theory of civic morality: U.S. citizens practice habits of frugality in their personal lives by demanding the government cut spending. The same equivalence describes moral suasion directed toward individuals.

Ironically, moral hypocrisy provides evidence that self-control and moral suasion practice a unified moral habit. If hypocritical demands are seen as purely deceptive, it’s hard to see how they would serve as a costly signal; carrying no costs, moral hypocrisy would have no value as a signal. Hypocrisy has no point if anyone can be a hypocrite cheaply. But if engaging in moral suasion agents rehearse (practice) principles of integrity that they habitually apply to themselves, the cost of demanding more morality than you want to give is becoming more moral than you wish.

The workings become clearer and more plausible with more concreteness about the structure of the moral habits (or principles of integrity), and Alan P. Fiske’s relationship-regulation theory integrates well with the habit theory. According to Fiske’s model, systems of moral principles are activated when their associated social relationships are “constituted,” where the systems of moral principles are Unity, Hierarchy, Equality, and Proportionality. (T.S. Rai and A.P. Fiske, Moral psychology is relationship regulation (2011) Psychological Review, 118: 57 ‒ 75.) Hierarchical principles, for example, are activated when the appropriate social relations of Authority/Ranking are constituted, so when an agent is involved in an authoritarian relationship, such as between employees and their boss, the corresponding Hierarchical principles of unconditional submission and conditional protection dominate. To restate in habit-theory terms, negotiating hierarchical relationships motivates agents to form habits based on Hierarchical principles. Most importantly, the Hierarchical structure is a coherent whole, including facets involving regulation of both self and others. In the habit theory, other-directed morality is a spandrel deriving from the primary adaptive value of self-control.

Monday, February 18, 2013

14.1.1. Utilitarianism twice fails

It seems almost self-evident that (barring foreign subjugation) a government will care about the wants of (some of) its citizens and nothing else: no other object of concern is plausible. If governments concern themselves with the wants of noncitizens, that will be only because citizens desire their well-being. The now platitudinous insight that the only possible basis for government policy is people’s wants can be attributed to utilitarianism, which gets credit in its stronger form for the apparent success of weaker claims. 

Another reasonable claim derives from utilitarianism: citizens’ wants should count equally. This seems only fair in a democracy, where one citizen gets one vote. Few today would deny the principle that public policy should serve the most good of the greatest number, which may seem to contradict my claim that no general moral principle governs public policy, but in practice, the consequences of this limited utilitarianism are thin indeed, leaving ample room for ideology. I’ll call thin utilitarianism this public-policy formula: the greatest good for the greatest number of citizens, weighting their welfare equally. 


First, I’ll consider whether thin utilitarianism succeeds on its own terms by providing a practical guide to public policy. Second, I’ll examine how this deceptively appealing guide to public policy transmogrifies into the monster of full-blown utilitarianism, a form of moral realism. The first constrains even casual use of thin utilitarianism; the second impugns utilitarianism as a general ethical theory.


1. Non-negotiable conflicts between subagents undermine thin utilitarianism

Although simple economic models attributing conduct to rational self-interest require that agents assign consistent utilities to outcomes, agents are inconsistent. One example of inconsistent utility assignment is the endowment effect, where agents assign more value to property they own than  to the same property they don’t own. The inconsistency considered here is stronger than the endowment effect, which we can surmount with effort, as professional traders must do. Despite the endowment effect, there is an answer to how much utility an outcome affords, the endowment effect being a bias, which willpower or habit may neutralize.

The conflict between subagents within a single person, on the other hand, can’t be resolved by means of a common criterion, such as market price, since two subagents pursue different ends. Which of these subagents dominates depends on situational and personological factors that elicit one or the other, not on bias. Construal-level theory reveals a conflict between intrapersonal subagents, near-mode and far-mode, integrated mindsets applied to matter experienced at fine or broad granularities. Modes (or “construal levels”) differ in that far-mode is more future-oriented and principled, near-mode, present-oriented and contextual. Far-mode and near-mode are elicited by the way social choices are made: voting elicits far-mode and market choices, near-mode; the utility of a choice depends on construal level.

Take a policy choice: how much wealth should be spent on preventive medicine? There are two basic ways allocating resources to medical care, political process and the market, socialized medicine being an example of political process, private medicine, the market. Socialized medicine makes allocating funds for the medical care a political decision; the market makes it each consumer’s personal choice. When you compare the utility of the choices by political process with those on the market, you should expect to find that when people choose politically, they use far-mode thinking encouraged by voting; whereas when they make purchases, they use near-mode thinking encouraged by the market. The preventive-care expenditure will be higher under socialized medicine because political process elicits far-mode, which is concerned with future health. People will be more miserly with preventive care under private medicine, where the decision to spend is made by consumer choice in near-mode, where we care more about the present. People favor spending more on preventive care when they vote to tax themselves than when they buy it on the market. Which outcome provides the greater utility—more preventive care or more recreation—is relative to construal level.

The same indeterminacy of utility occurs when comparing decisions made under different political processes, such as local versus central. Local decisions will be near-mode, central decisions far-mode. Assuming socialized medicine, less funding would be available if it were subject to state rather than federal control. Which provides more utility depends on whether the consequences are evaluated in near-mode or far-mode; no thin-utilitarian criterion applies.

Some utilitarians will protest that we should measure experiences rather than wants. The objection misses the argument’s point, which is that utility is relative to mode, a conclusion easiest to see in the public-choice process because the alternatives may be delimited. If the conclusion that utility depends on construal level holds, the same indeterminacies occur in evaluating experience. That apart, when utilitarianism is applied to public policy, present wants rather than experienced satisfaction is the criterion; agents necessarily choose based on present wants whether on the market or the political process.

2. Full-blown utilitarianism stands convicted of moral realism

Full-blown utilitarians are necessarily moral realists, but increasingly they are seen to deny it. While moral realism is widely recognized as absurd, utilitarianism seems to some an attractive ethical philosophy. For the sake of intellectual respectability, utilitarians can appear to reject anachronistic moral realism while practicing it philosophically.

Full-blown utilitarianism often obscures its differences with thin utilitarianism, which is a questionable doctrine but in accord with ordinary common sense. It emerges from thin utilitarianism by the misdirection of subjecting ethical premises to the test of simplicity, a test appropriate to realist theories exclusively, because simplicity serves truth. A classic illustration: Aristotle theorized that everything on earth that goes up goes down; Newton set out the gravity theory, which applies to all objects, not just those terrestrial, and which predicts that objects can escape the earth’s gravitational field by traveling fast. Scientists confidently bet on Newton well before rockets were invented, and their confidence was vastly increased by the simplicity of Newton’s theory, which made correct predictions concerning all objects. Although philosophers have explained variously the correlation between simplicity and truth, they generally agree that simplicity signals truth. Unless utilitarians can otherwise justify it, searching for a simple moral theory means searching for a true theory.

The full-blown utilitarian seeks a misplaced simplicity by insisting that all entities that can experience happiness, a much simpler criterion than “current citizens,” serve as the beneficiary reference group—including future generations of humans and even beasts, whose existence depends on policy; whereas, thin utilitarianism is a democratic convention, serving only the wants of the currently existing citizens. Because they must incorporate future generations into the reference group, utilitarian philosophers have had to accept that using a policy-dependent reference group entails a dilemma regarding interpretation of full-blown utilitarianism, with unattractive consequences at both horns, which realize radically different ideals.  In one version, you maximize the average utility obtained by the whole population; in the other, you sum the utilities. These interpretations seem almost equally unattractive: the averaging view says that one supremely happy human is better than a billion very happy ones; the adding approach implies that a hundred trillion miserable wretches is better than a billion happy people. 

To apply a utilitarian standard to scenarios so distant from thin utilitarianism, accepting their consequences because of simplicity’s demands, is to treat moral premises as truths and to practice moral realism, despite contrary self-description. Those agreeing that moral realism is impossible must reject full-blown utilitarianism.

Friday, January 25, 2013

19.2. Infinitesimals: Another argument against actual infinite sets

Argument
My argument from the incoherence of actually existing infinitesimals has the following structure:

1. Infinitesimal quantities can’t exist;
2. If actual infinities can exist, actual infinitesimals must exist;
3. Therefore, actual infinities can’t exist.

Although Cantor, who invented the mathematics of transfinite numbers, rejected infinitesimals, mathematicians have continued to develop analyses based on them, as mathematically legitimate as are transfinite numbers, but few philosophers try to justify actual infinitesimals, which have some of the characteristics of zero and some characteristics of positive numbers. When you add an infinitesimal to a real number, it’s like adding zero. But when you multiply an infinitesimal by infinity, you sometimes get a finite quantity: the points on a line are of infinitesimal dimension, in that they occupy no space (as if they were zero duration), yet compose lines finite in extent.

Few advocate actual infinitesimals because an actually existing infinitesimal is indistinguishable from zero. For however small a quantity you choose, it’s obvious that you can make it yet smaller. The role of zero as a boundary accounts for why it’s obvious you can always reduce a quantity. If I deny you can, you reply that since you can reduce it to zero and the function is continuous, you necessarily can reduce any given quantity—precluding actual infinitesimals. When I raise the same argument about an infinite set, you can’t reply that you can always make the set bigger; if I say add an element, you reply that the sets are still the same size (cardinality). The boundary imposed by zero is counterpoint for infinitesimals to the openness of infinity, but actual-infinitesimals’ incoherence suggests that infinity is similarly infirm.

Can more be said to establish that the conclusion about actual infinitesimal quantities also applies to actual infinite quantities? Consider again the points on a 3-inch line segment. If there are infinitely many, then each must be infinitesimal. Since there are no actual infinitesimals, there are no actual infinities of points.

But this conclusion depends on the actual infinity being embedded in a finite quantity—although, as will be seen, rejecting bounded infinities alone travels metaphysical mileage. For boundless infinities, consider the number of quarks in a supposed universe of infinitely many. Form the ratio between the number of quarks in our galaxy and the infinite number of quarks in the universe. The ratio isn’t zero because infinitely many galaxies would still form a null proportion to the universal total; it’s not any real number because many of them would then add up to more than the total universe. This ratio must be infinitesimal. Since infinitesimals don’t exist, neither do unbounded infinities (hence, infinite quantities in general, their being either bounded or unbounded).

Infinitesimals and Zeno’s paradox
Rejecting actually existing infinities is what really resolves Zeno’s paradox, and it resolves it by way of finding that infinitesimals don’t exist. Zeno’s paradox, perhaps the most intriguing logical puzzle in philosophy, purports to show that motion is impossible. In the version I’ll use, the paradox analyzes my walk from the middle of the room to the wall as decomposable into an infinite series of walks, each reducing the remaining distance by one-half. The paradox posits that completing an infinite series is self-contradictory: infinite means uncompletable. I can never reach the wall, but the same logic applies to any distance; hence, motion is proven impossible.

The standard view holds that the invention of the integral calculus completely resolved the paradox by refuting the premise that an infinite series can’t be completed. Mathematically, the infinite series of times actually does sum to a finite value, which equals the time required to walk the distance; Zeno’s deficiency is pronounced to be that the mathematics of infinite series was yet to be invented. But the answer only shows that (apparent) motion is mathematically tractable; it doesn’t show how it can occur. Mathematical tractability is at the expense of logical rigor because it is achieved by ignoring the distinction between exclusive and inclusive limits. When I stroll to the wall, the wall represents an inclusive limit—I actually reach the wall. When I integrate the series created by adding half the remaining distance, I only approach the limit equated with the wall. Calculus can be developed in terms of infinitesimals, and in those terms, the series comes infinitesimally close to the limit, and in this context, we treat the infinitesimal as if it were zero. As we’ve seen, actual infinity and infinitesimals are inseparable, certainly where, as here, the actual infinity is bounded. The calculus solves the paradox only if actual infinitesimals exist—but they don’t.

Zeno’s misdirection can now be reconceived as—while correctly denying the existence of actual infinity—falsely affirming the existence of its counterpart, the infinitesimal. The paradox assumes that while I’m uninterruptedly walking to the wall, I occupy a series of infinitesimally small points in space and time, such that I am at a point at a specific time the same as if I had stopped.

Although the objection to analyzing motion in Zeno’s manner was apparently raised as early as Aristotle, the calculus seems to have obscured the metaphysical project more than illuminating it. Logician Graham Priest (Beyond the Limits of Thought (2003)) argues that Zeno’s paradox shows that actual infinities can exist, by the following thought experiment. Priest asks that you imagine that rather than walking continuously to the wall, I stop for two seconds at each halfway point. Priest claims the series would then complete, but his argument shows that he doesn’t understand that the paradox depends on the points occupied being infinitesimal. Despite the early recognition that (what we now call) infinitesimals are at the root of the paradox, philosophers today don’t always grasp the correct metaphysical analysis.

Distinguishing actual and potential infinities
Recognizing that infinitesimals are mathematical fictions solidifies the distinction between actual and potential infinity. The reason that mathematical infinities are not just consistent but are useful is that potential infinities can exist. Zeno’s paradox conceives motion as an actual infinity of sub-trips, but, in reality, all that can be shown is that the sub-trips are potentially infinite. There’s no limit to how many times you can subdivide the path, but traversing it doesn’t automatically subdivide it infinitely, which result would require that there be infinitesimal quantities. This understanding reinforces the point about dubious physical theories that posit an infinity of worlds. It’s been argued that some versions of the many-worlds interpretation of quantum mechanics that invoke an uncountable infinity of worlds don't require actual infinity any more than does the existence of a line segment, which can be decomposed into uncountably many segments, but an infinite plurality of worlds does not avoid actual infinity. We exist in one of those worlds. Many worlds, unlike infinitesimals and the conceptual line segments employing them, must be conceived as actually existing.

[Edit September 15, 2013.] Corrected claim that many-worlds theories of quantum mechanics posit an infinity of worlds. Some many-worlds theories do, and some don't. This argument applies only to those versions positing infinite worlds.

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SUPPLIER OF LEGAL THEORIES. Ghostwriter of legal briefs, motions, arguments, and analyses, serving all U.S. jurisdictions. Former Appellate/Law & Motion Attorney at large Los Angeles law firm; J.D. (University of Denver); American Jurisprudence Award in Contract Law; Ph.D. (Psychology); B.A. (The Johns Hopkins University). E-MAIL: srdiamond@gmail.com Phone: 760.974.9279 Some other legal-brief writers research thoroughly and analyze penetratingly, but I bring two more merits to bear. The first is succinctness. I spurn the unreadable verbosity and stupefying impertinence of ordinary briefs to perform feats of concision and uphold strict relevance to the issues. The second is high polish, achieved by allotting more time to each project than competitors afford. Succinct style and polished language — manifested in my legal-writing blog, Disputed Issues — reverse the common limitations besetting brief writers: lack of skill for concision and lack of time for perfection.