IMAGINARY NUMBERS ARE REAL. Pegasus is Not.

Technical language is derived from common language to allow more accurate and precise statements, and more penetrating and perceptive questions. Commonly, when we say “real” we mean “true”, independent of the observer, valid, or verifiable, actual; not imaginary or mythical. Pegasus was not a real animal.  Polyphemus the Cyclops was not real, though Odysseus may well have been. In mathematics, “real” numbers are the set that includes all integers, rational, and irrational numbers. “Imaginary” numbers are those whose square (or other “even” power) is a negative number; in other words, the square roots of negative numbers are imaginary. But imaginary numbers are real in the common sense.

Euler's Equation. As sin^2(x) + cos^2(x) = 1
this can be applied to the analysis of
alternating current electricity. 

Imaginary numbers are important to the design and analysis of alternating current circuits. (See, for instance, the Wikipedia article on Volt-ampere-reactive.)   Without imaginary numbers we could not have complicated electrical power systems, just as we could not have modern commerce without negative numbers.  Overcoming the confusion and ignorance about the reality of numbers has been a historical process.

The Golden Ratio seen in the Parthenon
has many applications.
Geometrically pleasing,
its algebraic expression
(1 + sqrt(5))/2 is irrational

It is said that the followers of Pythagoras killed one of their disciples for revealing that the square root of two is irrational. Apparently, until about 5^th century BCE, the Greeks accepted that every number must be rational, only that not all reductions were known. For example, the Egyptians chose to represent all fractions as sums of fractions with 1 in the numerator: ¾ = ½ + ¼ or 3/7 = 1/3 + 1/14 + 1/42.  

Diophantus of Alexandria (3^rd century CE) denied the reality of negative numbers.  The Nine Chapters on Mathematical Art (Jiu zhang suan-shu) of about the same time accepted their reality. Although early conceptions of zero as a placeholder are known from Babylonian and Egyptian texts, zero was not accepted as a number in the modern sense until about 500 CE.  What is nothing? And in the technical language of metaphysics, nothing is not a different kind of something. “Nothing exists beyond the universe” does not mean that “beyond the universe” is “something else.” The confusion over zero comes from the difference between “nothing” and “none.”  The number 207 has no tens; it does not have metaphysical “nothing” in the tens place. 

But we are not confused by that in daily life.  When Mom asked “What’s going on?” and you replied “Nothing!” she was not thrown into a metaphysical conundrum.

So, too, with imaginary numbers. They have an unfortunate etymology, but we use them every day. If the operators in control rooms of electrical power plants could not manipulate reactive power – expressed in imaginary numbers—with real controls, we would suffer blackouts. 

My motivation here is a post on the Galt’s Gulch Online discussion board.  On April 5, 2016, about 7:00 AM local time, frequent contributor ewv wrote: “Mathematics by itself doesn't describe reality. It is the means by which you relate in terms of concepts what can be measured. Mathematics is a science of method, not about things like physics does.” (Reply here in "What is Science?" here.)

Her keyboading error aside (“physics does” for “physics is”), she is usually a very adept student of Objectivism. As a quip, I once accused her of being Dr. Leonard Peikoff.  Her comment about mathematics was a direct derivation of statements by Ayn Rand in Introduction to the Objectivist Epistemology, as well as elucidations by David Harriman in The Logical Leap. However, mathematics does describe reality, as does any language. 

We can give expression to falsehoods using common language, as when we attempted to deflect Mom’s inquiry about our noisy play. Pegasus and Nike of Samothrace are other examples. They are mathematically impossible. Whatever the wings represent symbolically, they cannot function from the meager muscles on the back of the horse or the girl. Arguments about politics and religion, and Monday morning quarterbacking supply a surfeit of such falsehoods. That silliness is impossible in mathematics.

Patent for application
of the Moebius strip
to a power conveyor.

Can you have a sheet of paper with only one side? Can you have a container with only an inside? The Möbius Strip and the Klein Bottle were inventions of topology, a study in mathematics that contravenes common sense. But they do exist; and they do have practical applications. As an investigation of relationships, topology is based on qualities, not quantities. Topology is nonetheless a study within mathematics. Topology is rigorous and consistent. It does not allow for internal contradictions, just as integer arithmetic does not.  

Mathematics does have unsolved challenges. Science always has frontiers.  However, anything that is proved to be mathematically true must be realizable, even if we have not found one or built one yet.

ALSO ON NECESSARY FACTS

The Man Who Loved Only Numbers 
U.S. Patent Law Does Not Add Up  
Patent Nonsense  
Visualizing Complex Data  
Knowledge Maps 

Ayn Rand versus Conservatives

Ayn Rand said that labor unions are the only decent group today and hold the greatest potential for saving our society from economic collapse. She suggested that any business that offers unsafe working conditions should be punished under law, whether or not any actual injury occurs. Ayn Rand also said that the only purpose of a handgun is to kill another human being, and no one has that right.

From Ayn Rand:
A Sense of Life
by Michael Paxton

Ayn Rand continues to be popular. Sales of her books always were steady over the past 50 years. None went out of print. Then, the tallies spiked in 2008-2009 with economic crisis and the Bush-Obama bailouts. Between the release of the movies Atlas Shrugged Part 1 and Part 2, Paul Ryan accepted the Republican Party nomination for the vice presidency in 2012. Although he previously had been a guest of the Atlas Society (February 2, 2005), Ryan told National Review (April 26, 2012) that he is a practicing Roman Catholic who rejects Ayn Rand’s atheistic philosophy. 

Ayn Rand would have predicted that. However, because of the obvious political message in the movie, many conservatives continue to be drawn to websites and discussion boards hosted by committed Objectivists. New to the works of Ayn Rand, they do not know of her animosity toward their deepest beliefs.

Ayn Rand’s own published works include four novels and seven collections of essays taken from her three newsletters. Over 40 more books by and about Ayn Rand have appeared. Of these, Anthem, The Fountainhead, Atlas Shrugged, and The Virtue of Selfishness are easily the most visible, while the others remain obscure or apocrypha.

So, many of the Christians and constitutionalists who claim to admire her do not know of “Conservatism: an Obituary.” That essay began as a speech at Princeton University, December 7, 1960, and was reprinted first as a pamphlet by the Nathaniel Branden Institute in 1962; and then was added to the anthology, Capitalism: the Unknown Ideal published by New American Library in 1966. 

In that she said: “There are three interrelated arguments used by today’s ‘conservatives’ to justify capitalism, which can best be designated as: the argument from faith – the argument from tradition – the argument from depravity.
[…]“Intellectually, to rest one’s case on faith means to concede that reason is on the side of one’s enemies—that one has no rational arguments to offer. The “conservatives’ ” claim that their case rests on faith means that there are no rational arguments to support the American system, no rational justification for freedom, justice, property, individual rights, that these rest on a mystic revelation and can be accepted only on faith—that in reason and logic, the enemy is right, but that men must hold faith as superior to reason.”

Rand explained that the argument from tradition ignores the truly radical nature of the American Revolution. Moreover, arguing from tradition grants all claims to progress and the future to the very people who would return us to primitive, village collectivism. She called it “grotesque” that conservatives offer stagnation as a defense of capitalism which is the one truly dynamic economic system.

She said: “The plea to preserve 'tradition' as such, can only appeal to those who have given up or to those who never intended to achieve anything in life. It is a plea that appeals to the worst elements in men and rejects the best: it appeals to fear, sloth, cowardice, conformity, self-doubt – and it rejects creativeness, originality, courage, independence, self-reliance.”

The argument from depravity says that no one can be trusted to rule. People are weak, capricious, and fallible: “since men are depraved, they are not good enough for a dictatorship; freedom is all that they deserve; if they were perfect, they would be worthy of a totalitarian state.”  Thus, the conservatives grant the premise that dictatorship is based on human potential. From that it follows that it is wrong to enslave the depraved, but morally proper to enslave the virtuous. Moreover, the conservatives claim that the disasters and horrors of the 20^th century were the punishment we suffered for the sin of attempting to devise a rational society. Ultimately the argument from depravity rests on the argument from faith, of course.

For Ayn Rand, faith and force were reflected images. She explained that in detail in an essay “Faith and Force: Destroyers of the Modern World” which was originally a set of lectures delivered at Yale, Brooklyn College, and Columbia University in 1960, and republished after her death in the anthology Philosophy: Who Needs It? (New American Library, 1982). In the very first issue of The Objectivist Newsletter, January 1962, and reprinted in The Virtue of Selfishness and again in Capitalism: the Unknown Ideal Ayn Rand wrote: “We are not conservatives. We are radicals for capitalism.”  She meant it.

Beyond condemning the mystics, Ayn Rand also proposed, considered, and reflected on many issues, some of which were tangential for her. She was a philosopher.

In 1972, Edwin Newman interviewed Ayn Rand for his show “Speaking Freely” on NBC-TV. Among other statements, Ayn Rand said: “I am not an enemy of labor unions. Quite the contrary. I think that they are the only decent group today, ideologically. I think they are the ones who will save this country, and save capitalism, if anybody can.”  She went on to say: “But the one flaw is that labor unions are government-enforced and become a monopoly and can demand higher wages than the market can offer. This union power creates the unemployable. It creates this vast group of people, the unskilled laborers who have no place to go for work. The artificial boosting of the skilled laborer’s income causes unemployment on the lower rungs of society. Every welfare measure works that way. It doesn’t affect the so-called rich, if that the humanitarians are worried about it, always affects the poor.”

A few minutes earlier, on the same show, speaking of the proper role of government, she said: 

“But on the matter of protecting people from physical danger, if certain conditions of employment, let us say, are unsafe and it can be proved that there is a physical risk – I don’t say that we have to wait until somebody dies – then the employer who is creating this risk can be sued, and can be severely punished financially. In other words, there can be a law protecting a man from physical injury by another man. In this case, the employer who puts men into conditions of danger – not accidentally, but intentionally or carelessly – can be penalized because he is infringing the right of his workers not to be injured physically.”  

The entire interview and many others are collected in the anthology Objectively Speaking: Ayn Rand Interviewed, edited by Marlene Podritske and Peter Schwartz (Lexington Books, 2009).

Ayn Rand did not cite Max Weber or John Stuart Mill when she said that the government holds a legal monopoly on force. It is a subtle point. John Locke, David Hume, Thomas Hobbes, Aristotle, and Plato, (among many others) all suggested different reasons for the origin of government, and its purpose today. For Aristotle, the state was a union of families. Max Weber spoke in language closest to Rand’s when in a speech to the Free Student Union at the University of Munich in 1919, he said that the government holds a monopoly on force. If the government holds a monopoly on retaliatory force, then why do you want a gun?

From Ayn Rand Answers: the Best of Her Q&A, edited by Robert Mayhew (New American Library, 2005) come two questions and answers.

Q: What is your opinion of gun control laws?A: I do not know enough about it to have an opinion, except to say that it is not of primary importance. Forbidding guns or registering them is not going to stop criminals from having them; nor is it a great threat to the private, non-criminal citizen if he has to register the fact that he has a gun. It is not an important issue, unless you're ready to begin a private uprising right now, which isn't very practical. [Ford Hall Forum, 1971]Q: What's your attitude toward gun control?A:  It is a complex, technical issue in the philosophy of law. Handguns are instruments for killing people -- they are not carried for hunting animals -- and you have no right to kill people. You do have the right to self-defense, however. I don't know how the issue is going to be resolved to protect you without giving you the privilege to kill people at whim. [Ford Hall Forum, 1973]”

When I cited this, some of my conservative comrades online insisted that handguns can be used for hunting, even deer, and for all I know, perhaps even for killing elephants and dinosaurs, but that evades the salient problem. According to Ayn Rand, it is perfectly reasonable for the government to know who owns a handgun. Ownership of an unlicensed handgun would be a crime in Ayn Rand’s perfect capitalist society.

Ayn Rand believed that a woman has a right to terminate a pregnancy. Conservatives disagree. Among them are Congressman Ron Paul, MD, and his son, Senator Randal H. Paul, MD, who introduced a “Life at Conception Act” to make abortion a federal crime.

These are the most visible problems that conservatives face when attempting to assume that Ayn Rand supported their cause. Whether they can support hers is for each of them to decide.

PREVIOUSLY ON NECESSARY FACTS

The Influence of Ayn Rand's Objectivism

Leonard Peikoff's Understanding Objectivism

That goddam Ayn Rand book

Libertarians and Racism

Objectivism and the Gold Standard

Harriman's Logical Leap Almost Makes It

The root of the problem with his presentation is that the audience is not defined.  If he were writing only for others in his peer group – he holds master’s degrees in physics and philosophy – then much of Harriman’s narrative could have been deleted.  That the book is mass-marketed indicates a wider audience for whom more or better explanation is needed. Rather than trying to replace the accepted meaning of the inductive method, Harriman should simply call his the objective (or Objectivist) method. 

The Logical Leap: Induction in Physics by David Harriman, with an introduction by Leonard Peikoff. New American Library, July 2010. Paperback, 279 pages + vi, illustrations. $16.00.

Despite some flaws in the presentation, David Harriman’s proposal for a new method of scientific methodology is interesting, valuable, and important.  Harriman’s thesis is that induction is actually the integration of a new experience with the totality of all previous experience for the purpose of creating a new generalization.  One example is enough for a generalization, if it is validly composed.  According to Harriman, to be valid, an induction must be derived from a first-level generalization.  To demonstrate the truth of his claim, Harriman provides examples from the works of Galileo, Newton, and Dalton, among others. 

[edited and shortened February 8, 2016]

In philosophy the “problem of induction” is defined by the question “How much evidence is enough?”  David Harriman’s answer is provocative on several grounds.  One fact is enough to validate a theory, if that fact is properly integrated with everything else known to be true.  That much alone would be challenging.  The back cover of this book credits Ayn Rand’s theory of epistemology as the starting point for Harriman’s work.  That flag is necessary for those who do not know Leonard Peikoff as Ayn Rand’s appointed “intellectual heir.”  Peikoff wrote the introduction, and, it is revealed, tutored Harriman in the use of induction in physics.  But Peikoff is a philosopher (doctorate from NYU) and so Harriman attempts the technical proof. 

The root of the problem with his presentation is that the audience is not defined.  If he were writing only for others in his peer group – he holds master’s degrees in physics and philosophy – then much of Harriman’s narrative could have been deleted.  That the book is mass-marketed indicates a wider audience for whom more or better explanation is needed. 

David Harriman is not the only working physicist to blunder about orbital mechanics.  It is an easy error to say that the path of a projectile is a parabola (p. 50).  Later, discussing Newton he does note that the path of an object in orbit under an inverse-square law of central force motion can be any conic section (though he leaves out the line). However, in this part he is explicit about the parabolic path of a projectile. Thirty years ago, I caught Scientific American in this same error; and for them, I photocopied a page from The Wonders of Physics by Irving Adler (Golden Books, 1966).

The Wonders of Physics:
an Introduction to the Physical World
by Irving Adler 
( Illus. by Cornelius De Witt); New York,
Golden Press [1966].

We take the parabola as an approximation for projectile motion by assuming that the Earth is flat. 

This is helpful to students for whom the mathematics of this curve is easier than that of an ellipse.  The ellipse is the most common orbital path in our immediate experience.  Harriman does not distinguish this.

If projectile motion can be explained to a child, then it should stated correctly in a technical treatise on the epistemology of science. 

This oversight is especially significant as the author claims to be explaining how the scientific revolution of the Renaissance replaced earlier mysticisms.  Galileo knew that the Earth is round; that fact was known to Aristotle.  The diameter of the Earth was measured by Eratosthenes. 

Galileo failed to make the logical leap that Newton finally did when he demonstrated via his calculus why an inverse-square force results in orbits that are conic sections.  In fact, in his introductions to editions of the Principia, Newton credits the ancients (“Chaldeans”) who “long ago believed that the planets revolve in nearly concentric orbits, around the sun and that comets do so in extremely eccentric orbits…” (Cohen/Whitman translation, 1999).

Newton’s works are prominent in this book, and rightfully so.  Newton was arguably the greatest scientist of all time.  However, Newton maintained that light consists of corpuscles; but Newton’s own experiments with optics argued against his theory of light.  Newton maintained faith in a hypothesis that he could not prove.  Harriman glides past this problem (pp. 50-67).  Later, Harriman derides the “wavicle” of modern physics.  He also denigrates Rene Descartes.  As an Objectivist, Harriman is opposed to Cartesian rationalism.  However, Descartes is credited with proving that light refracts according to the ratio of the sines of the angles of incidence and refraction.  In American schools, we call this “Snell’s Law” but Willebrord Snellius did not publish it.  So, Descartes is credited with the independent discovery that sin(I)/sin(R) = k.  Pierre de Fermat also proved this mathematically (rationalistically) from the principle of least time. 

Just as we speak too easily of parabolic motion, so, too, do we accept “white light.”  No such thing exists.  All electromagnetic phenomena exist in discrete wavelengths and white is not one of them.  It is true that if we project a mix of colors (red, blue, green; magenta, cyan, yellow) on a white screen, the screen remains white.  Projecting only a beam of red light on a white screen, the illuminated area appears red.  The perception of “white” is a consequence of perceiving several colors at once.  Harriman uses vernacular English to praise Newton for discovering that white light is composed of colors.

Attempting to explain the development of the atomic theory, Harriman offers an erroneous simile comparing a hydraulic pump to a lever (pp. 123-124).  Explaining the theory of the fluid barometer, he writes: “It is similar to the action of a lever; the weight of the air will raise the same weight of water (per unit surface area).  Here the weight of the entire atmosphere above a particular surface must be equal to the weight of thirty-four feet of water over the surface.”  It is true that all simple machines -- wedge, lever, wheel, axle, and screw – allow us to trade force, distance, time, speed, or work.  Considering conservation of energy, the liquid barometer could be likened to any of them, but it would be stretching the analogy.  A lever works by trading force and distance: the fifty-pound child at the end of a teeter-totter lifts the 150-lb. man sitting on the other side but closer to the center.  The hydraulic lift is not a lever any more than a screw is a pulley.

Harriman states in words what would be easier given as symbols.  Numbers are written out.  This reflects the lack of a defined audience.  Harriman explains some things but glosses over others; and it is hard to know when he is being technical or vernacular. 

Consider the allusions to elastic and inelastic collisions.  “… [Newton] deliberately varied the mass of the bobs and thereby proved that his law applied to both elastic and inelastic collisions.” (p. 127)  Referring to the standard college textbook by Sears and Zemansky (now 
Young and Freedman, Sears and Zemansky’s University Physics), in a perfectly inelastic collision the two bodies stick together, their kinetic energies before and after are not conserved, and the difference lost is converted to heat.  I believe that here Harriman is using the word “elastic” in its vernacular sense: balls of yarn or wood were deformed more or less by the impacts, having negligible consequences to the experiment.  However, discussing the kinetic theory of gases, Harriman uses elastic and inelastic in their proper technical senses (p. 166).

Kepler suggested that perhaps the sun attracts the planets with some kind of magnetism.  Newton ruled out magnetism in Corollary 5 to Proposition VI Theorem VI in the Principia.  However, magnetism had to be considered.  Newton’s measurements suggested that the power of magnetic attraction diminishes at a proportion between an inverse-square and an inverse-cube.  Today, we know that the field of a magnetic dipole diminishes as the inverse-cube, but that the force of attraction toward either pole follows the inverse-square rule.  Thus, gravity, static charge, and magnetism all were contenders to explain the motions of the moon and the falling apple.  As Harriman notes:  “Different causes can lead to qualitatively similar effects (e.g., a magnet with an electric charge on its surface will attract both straw and iron filings, but for different reasons” (p. 137).  But Harriman is in error when he continues: “However, when Newton proves that the moon and the apple fall with rates that were precisely in accordance with a force that varies as the inverse square of the distance from Earth’s center – then there can be no doubt that the same cause is at work” (p. 137).  Strictly on the basis of the inverse-square attraction, both magnetism and electric charge could have been the cause. 

Harriman says that Newton experimented with magnets floated on wood in a tub of water.  According to Harriman, that the magnets were mutually attracted without causing a net motion of the tub proved that the attractions were directed equal and opposite to each other (pp. 127-128).  That experiment proves nothing of the sort.  Placing the magnets in a tub of water and measuring their motions, one might discover several facts, for instance, that some materials magnetize more strongly than others or (counterfactually) that different objects are attracted with unequal accelerations.  But there is no way that they could move the tub, even if they banged into the sides.  It is a standard problem in freshman physics to determine whether a person standing on a (frictionless) rail car could move it by firing a bullet at an opposite wall. 

Harriman goes on to say

“Since Earth attracts all materials on its surface, it was reasonable to suppose (and it would later be proven) that every part of Earth attracts all other parts.  So consider the mutual attraction, say, of Asia and South America.  If these two forces were not equal and opposite, there would be a net force on Earth as a whole – and hence Earth would cause itself to accelerate.  This self-acceleration would continue indefinitely and lead to disturbances in Earth’s orbit” (p. 128).

  Again, Asia might be more strongly attracted to South America than that continent is to Asia.  All actions would take place on the “tub” of the Earth within the same inertial frame of reference.

Denigrating ancient and medieval astronomy, Harriman claims that the relative sizes of the orbits of the planets could not be computed (pp. 88-86).  This was not true; and Harriman must know that because he says that Ptolemy estimated the distance to the stars (p. 88).  Moreover, if it is true that the geocentric model prevents such calculations, then the ancient astronomers must have used some other model, because the relative sizes of the orbits were computed.  The ancients did not believe that all of the celestial lights were spread on a single sphere.  They knew that the moon is much closer than Saturn.  On the other hand, (more reasonably) the geometry and observations of the time did, indeed, allow them to make those calculations, even assuming the geocentric model.  In fact, because of the religious viewpoint, the very scale of the measurable universe and the comparatively small size of the (spherical; not flat) Earth, were substantiating evidence of the relative unimportance of Earthly affairs.  (See Astronomies and Cultures in Early Medieval Europe by Stephen McCluskey, Cambridge, 1998.)

Measurement was always important to the medieval astronomers who welcomed the new astrolabe imported from the Muslims.  Thus, it is no surprise that measurement of the Earth’s diameter and the distance to the moon were important to Sir Isaac Newton.  Harriman says that Newton accepted the numerical approximation of 60 Earth radii as the distance to the Moon (pp. 136-137).  In fact, Newton was not comfortable with these approximations, but he had to settle for them.  He was being stonewalled by John Flamsteed, the Royal Astronomer who also was working out the celestial mechanics of the Earth-Moon system and did not want to share his data.  These facts about Newton are in the standard modern biographies by Richard Westfall (Never at Rest), Michael White (Isaac Newton: the Last Sorcerer), and David Berlinski (Newton’s Gift: How Sir Isaac Newton Unlocked the System of the World.). 

Harriman has his own new theory of science, dismissing the accepted scientific method. 

“Today, it is almost universally held that the process of theory creation is nonobjective.  According to the most common view, which is institutionalized in the so-called “hypothetico-deductive method,” it is only the testing of theories (i.e., comparing predictions to observations) that gives science any claim to objectivity.  Unfortunately, say the advocates of this method, such testing cannot result in proof – and it cannot result even in disproof, since any theory can be saved from an inconvenient observation merely by adding more arbitrary hypotheses.  So the hypothetico-deductive method leads invariably to skepticism” (pp. 145-146). 

 Thus, to Harriman, Newton’s experiments did not validate Descartes’ (more correct) theory of light.

Harriman would do well to heed his own words.  “Introspection is clearly an indispensable source of data, since philosophy studies consciousness and an individual has direct access only to his own” (p. 233).  We have the introspective reports of Richard Feynman, Kary Mullis, Albert Einstein, Francis Crick and James D. Watson, and many others, all of whom report something different in their heads than what Harriman claims must be true of all humans, based, we can assume, on his own introspection. 

Richard Feynman’s The Character of Physical Law delivers an outstanding explanation of why the hypothetico-deductive method works.  Norman W. Edmund, the founder of Edmund Scientifics Corporation, created a superb website at www.scientificmethod.com/.  He teaches a 14-step process which touches on philosophy.  Any public school science teacher knows the many posters and other aids that present a 5 or 9-step method.  Regardless of the specifics, Harriman mischaracterizes the scientific method when he claims that it indulges in rationalist fantasies (p. 142). It is true that you can “make up” any airy explanations you want, but the only ones that count are the ones that can be tested.  Harriman ignores that. 

Arguing in the grand style of Ayn Rand he broadly accuses an unnamed collective of committing evils, and then draws his own conclusions about what they really believe.  “Today, it is almost universally held that the process of theory creation is nonobjective [p. 142].”  He does later resort to the Randian device of naming evil professors such as Paul Feyerabend, but nowhere does Harriman provide any support for his claim that what he opposes is “almost universally held.” 

For Ayn Rand, a person’s fundamental existential choice – to be or not to be – is to think or not to think.  Choosing to think is the essence of being human.  That raises the challenge, “Are you not thinking when you choose not to think?”  Rand’s answer came via psychologist Nathaniel Branden (at first an Objectivist himself, then developing his own Biocentric theories).  Psychological suppression is an avoidance mechanism to prevent unpleasant thoughts.  The thought process is abandoned before the thought can be fully formed.  This can begin as denial, justification, or rationalization, but typically is an emotional precognitive response to a potentially painful identification. 

Similarly, Harriman’s Objectivist theory of induction apparently rests on the very hypothetico-deductive method that he denies: in order to make a logical leap, do you not first carry out a series of experiments, any one of which could falsify the previous work until a better theory explains both?  Harriman praises Galileo and Newton both for their careful and repetitive work.  Then, he denies the repetitive aspect of induction, claiming that these scientists “leapt” to valid conclusions.  Harriman needs a meta-explanation. 

Is it inherent in human nature to think by induction?  Is this why we have superstitions as well as science because we leap to general conclusions based on single instances?  If so, what is the nature of this abstracting?  Where in the brain does it occur?  What chemicals cause it?  Can you go through life never doing it?  Or must you always do it?

Moreover, the hypothetico-deductive method is how we validate and verify the works of others.  Explanatory theories are easy to devise.  To be scientific an explanation must be tested.  The claim, no matter how compelling it seems, must be tried against new data, not in the original set.  And, best of all, a valid theory leads to new predictions not in the original data.  

Harriman requires that to be valid an induction must be integrated with all previously known truths.  If that alone were enough, then any theory might be falsified by the discovery of a new phenomenon.  That brings us back to the very problem Harriman claims to solve.  He wants to avoid the debilitating skepticism that hobbles philosophers of science.  We can never be sure of anything (they say) because something new might come along.  Thus, (it is claimed) science leads not to truth but to ignorance.  

Harriman’s beast is personalized by Paul Feyerabend.  Having recently completed a bachelor of science degree in criminology, I was assigned to read similar “post modernist” claims that there is no such thing as science, but only a “scientistic discourse” that excludes women and minorities, that criminology is only ideology in service to oppression.  Fortunately, our courts do not work on that theory any more than researchers in physics adhere to the "fashionable nonsense" of post-modernism.

While these shortcomings are bothersome, they are not fatal.  Harriman’s thesis deserves more than mere consideration.  Properly taught, it would be a revolution in science.  

Rather than trying to replace the accepted meaning of the inductive method, Harriman should simply call his the objective (or Objectivist) method. 

Objectivism (with or without the capital-O) is rational-empiricism and both sides of that equation are required.  Ayn Rand taught that existence exists, that reality is real, that A is A, entities have identities: to be is to be something.  Therefore, contradictions do not exist.  

Truth is rational and empirical, logical and evidentiary, analytic and synthetic, theoretical and experimental, ideal and practical, deductive and inductive, and even imaginary and experiential. Harriman’s book rests on those truths.  In that, its value cannot be overestimated.

ALSO ON NECESSARY FACTS
Is Physics a Science?
The Problem of Induction: Karl Popper and His Enemies
The Sokal Affair
The Structure of Scientific Revolutions