Burns & Novick's The Vietnam War #1

We have been watching the film series, The Vietnam War, Episodes 1-5 the latest 5 days, Sun-Thu. There will be 5 more episodes Sun-Thu next week. They can be viewed on PBS's website shortly after they are aired on television. The whole series is 18 hours.
http://www.pbs.org/kenburns/the-vietnam-war/home/

I didn't care much for Episode 1, maybe because of the time span covered. But 2-5 have been excellent. I learned quite a bit from them, especially the USA inside politics the press didn't report at the time. LBJ was an awful human being. Yet he was funny with the colorful Texan language and idioms he used. I found some scenes unpleasant, even gruesome. I am amazed at some of the scenes captured by video cameras -- how somebody managed to be filming in those particular circumstances and Burns et al got and used their film. Episode 5's time frame ends just before the 1968 Tet Offensive. Having been there during that peak period of the war, the next episodes will be interesting.

Back in the USA, a coincidence occurred without my being aware of it at the time. I visited some friends in St. Louis about 2 weeks ago. I was headed home at the St. Louis airport, walking from the central part to the gate where my flight was to be. Walking toward me was Ken Burns. I didn't do anything to show that I recognized him. I didn't know then about the film series. If I had known, I probably would have said something to him and that I was a Vietnam vet.

Infinitesimal #4

A intellectual war involving math and politics also occurred between Thomas Hobbes and John Willis. Near the end of the English Civil War (1642-1651) Hobbes wrote Leviathan. In it Hobbes argued for a social contract and rule by an absolute sovereign. He wrote that civil war and a brutal state of nature ("the war of all against all") could only be avoided by strong, undivided government.

Hobbes also was a geometer of some repute. Similar to the Jesuits, he believed that the answer to uncertaity and chaos was absolute certainty and eternal order. They believed the key to both was Euclidean geometry. He set about trying to "square the circle" and solve two other long-standing geometry problems. "Square the circle", or "quadrature the circle," means construct a square with area exactly equal to the area of a given circle. (It can be done with great, but not perfect, precision.) Under the traditional restrictions of using only a compass and straight edge, this had been proven impossible. Hobbes tried anyway. Mathematician John Willis was well prepared to discredit any solution Hobbes proposed. Willis' political attitudes also reflected the chaotic years in England, but he believed in a state that would allow for a plurality of views and wide scope for dissent. Willis also sided with those who supported the use of infinitesimals.

Hobbes was also a sharp critic of the mathematical works of Willis. For Hobbes the infinitely small was an unwelcome intruder in mathematics. In contrast Willis considered practically all the features of the infinitely small to be clear advantages. His math was for investigating the world as it is. The world could be a little mysterious, unexplored, and ambiguous, but it invited new investigation and new discovery (p. 287).

Infinitesimal #3

For centuries before the Reformation the Roman Catholic Church had reigned supreme in western Europe. Empires rose and fell. There had been invasions and occupations, heresies and plagues, but the Church had survived and thrived. The Church oversaw the lives of Europeans and gave order, meaning and purpose to their existence, and ruled on everything from the date of Easter to the motion of Earth and much else (p. 24). The Reformation was a challenge to all that.

The Jesuits, formed in 1540, were not much interested in mathematics in their first few decades. The founder, St. Ignatius, had little interest in mathematics. But as they built their education system, they became committed to Euclidean geometry. "It was the core of their teaching and the foundation of their mathematical practice. ... [T]he whole point of studying and teaching mathematics was that it demonstrated how universal truth imposed itself upon the world -- rationally, hierarchically, and inescapably. Ideally, the Jesuits believed, the truths of religion would be imposed on the world just like geometrical theorems, leaving no room for avoidance or denial by Protestants or other heretics and leading to the ultimate triumph of the Church. For the Jesuits, mathematics must be studied according to the principles and procedures of Euclid, or it should not be studied at all. A mathematics that ran counter to these practices not only was useless to their purposes, but it would challenge their unconquerable faith that truth, handed down through the hierarchy of the universal catholic Church, would inevitably prevail" (p. 74). Infinitesimals are not part of Euclid's Elements.

"The Jesuits valued mathematics for the strict rational order it imposed on an unruly universe. Mathematics, particularly Euclidean, represented the triumph of mind over matter and reason over the untamed material world, and reflected the Jesuit ideal not only in mathematics but also in religious and even political matters" (p. 91).

"Euclidean geometry was the embodiment of order. Its demonstrations began with the universal self-evident assumptions, and then proceed step by logical step to describe fixed and necessary relations between geometrical objects: the sum of the angles in a triangle is always equal to two right angles ... These relations are absolute, and cannot be denied by any rational being" (p. 119). A group of five Jesuits, the Rectors, had a strong control over what was taught, and it issued prohibitions on the teaching and promotion of infinitesimals (p. 122).

Cavalieri's and Galileo's ideas ran counter to that. They held that lines were comprised of indivisible points, planes of indivisible lines, and solids of indivisible planes. Thus these geometrical objects  were little different from the material objects we see around us (p. 91). Instead of mathematical reason imposing order on the physical world, pure mathematical objects are created in the image of physical ones. They wanted to study the world and find the order within. They were willing to accept some ambiguity and even paradox as long as it led to a deeper understanding (p. 177).

In Discourses (or Two New Sciences) Galileo made use of Aristotle's wheel paradox (link) to arrive "at a radical and paradoxical conclusion: a continuous line is composed of an infinite number of indivisible points separated by an infinite number of minuscule empty spaces. This supported both his theory of the structure of matter and his view that material objects are held together by the vacuum that pervades them" (p. 89-91). How Galileo thought about the wheel paradox is described here.

Infinitesimal #2

What are infinitesimals? That term was coined around 1670. A related term is indivisibles.  The author of Infinitesimal says: "To understand why the struggle over indivisibles became so critical, we need to take a close look at the concept itself, which appears deceptively simple but is in fact deeply problematic. In its simplest form the doctrine states that every line is composed of a string of points, or "indivisibles," which are the line's building blocks, and which cannot themselves be divided" (p. 8-9).

Some mathematicians, especially Cavalieri, held that a line is composed of an "infinite" number of points, a plane is composed of an "infinite" number of lines laid parallel and a solid is composed of an "infinite" number of planes laid parallel. Of course, for any polygon, sets of parallel lines can be drawn in different directions, e.g. vertical or horizontal or diagonal, which gives a different number of lines.

Infinitesimal mentions that the math symbol used for infinity, ∞, was invented by John Wallis (who has a prominent role in the book). Wikipedia confirms this. Wallis used 1/∞ for an infinitesimal.

One conundrum is how many indivisibles (or points) there are in a given line and how small they are. Assume a given line has a huge, yet finite, number, we can call a gazillion. That suggests each indivisible is 1/gazillion in size. Problems start arising when considering other lines of different length. A "deep" problem -- discovered by the Greeks -- is that some lines can not be subdivided into an integer number of uniform-sized units, no matter how small they are. For example, the square root of two length units (e.g. inches) cannot be converted to an integer number of anything, because the square root of two is an irrational number. Ditto for pi, the circumference of a circle with a diameter of 1 length unit, and Euler's number e, the base base of natural logarithms.

A related topic is the continuum. The usual meaning of continuous is “unbroken” or “uninterrupted.” Thus a continuous entity—a continuum—has no “gaps.” Aristotle addressed it in book 6 of his Physics. He concluded that the concept of infinitesimals was erroneous, and that continuous magnitudes can be divided ad infinitum (p. 10). The Jesuit Benito Pereia proposed the thesis that a line is composed of separate points and presented all the arguments in its favor by others. He then demolished them one by one, and concluded, like Aristotle, that the continuum is infinitely divisible, and not composed of  indivisibles (p. 121). The Jesuits thought Cavalieri's were untenable.

The Epilogue of Infinitesimal describes how the use of "infinitesimals" later grew to have a prominent part of mathematics. I believe it would have been improved if it explained the concept of a limit as used in math, such as in calculus. Said concept was developed in the 19th century. It involves, but is not identical to, "infinitesimals" as described in the book. The similarity is stronger in integral calculus.

A much longer history of infinitesimals and related topics is here. The historical period the book is mainly about is a very small part of it.

Infinitesimal #1

I read the book Infinitesimal: How A Dangerous Mathematical Theory Shaped The Modern World. In mathematics, infinitesimals are things so small that there is no way to measure them. I thought the history in Infinitesimal – both political-religious and mathematics from about 1500 to 1675 – was very interesting. I believe the author makes the tie between them stronger than what they actually were, but there were parallel ideas - parties opposing one another in two very different realms.

The Society of Jesus, more commonly called the Jesuits, has a prominent role. Before Martin Luther initiated the Protestant Reformation, the Catholic Church was the dominant power in society. Kings and their lower ranking brethren depended on approval by the Catholic clergy. The anti-Reformists believed that the Reformation would bring about disorder and war. The Jesuits became the leading defenders of Catholicism. In large part their success was due to their building of educational institutions.

A leading Jesuit, Christopher Clavius, was almost single-handedly responsible for the adoption of a rigorous mathematics curriculum – Euclidean based -- in an age where mathematics was often ridiculed by philosophers and religious authorities. While Clavius clearly opposed the heliocentric model of Copernicus, it was mainly other Jesuits who opposed infinitesimals.

A leading proponent of infinitesimals was mathematician Bonaventura Cavalieri. He was a Jesuat, which is different from a Jesuit.

Except as noted below, the author summarizes the book's thesis very well as follows.

"Why did the best minds of the early modern world fight so fiercely over the infinitely small? The reason was that much more was at stake than an obscure mathematical concept. The fight was over the face of the modern world. Two camps confronted each other over the infinitesmal. On the one side were ranged the forces of heirarchy and order – Jesuits, Hobbesians, French royal courtiers, and High Chuch Anglicans. They believed in a unified and fixed order in the world, both natural and human, and were fiercely opposed to infinitesmals. On the other side were comparative "liberalizers" such as Galileo, [John] Wallis, and the Newtonians. They believed in a more pluralistic and flexible order, one that might accommodate a range of views and diverse centers of power, and championed infinitesmals and their use in mathematics. The lines were drawn, and a victory for one side or the other would leave its imprint on the world for centuries to come" (p. 8).

Most of the history presented in the book happened before Isaac Newton published his revolutionary Principia  in 1687, so Cavalieri instead of "the Newtonians" arguably fits better.

The Cost of Rights

In my August 27 post I said Passions and Constraint was unclear about where the author stood on controversial rights and how far government can go to reach its goals. I said maybe his answer is in another book, The Cost of Rights: Why Liberty Depends on Taxes, co-authored with Cass Sunstein. It wasn't there.

The Introduction holds that there are two kinds of rights – moral rights and legal rights. It has little to say about moral rights and says they are "toothless by definition." There is nothing about natural rights along the lines of John Locke. In contrast legal rights have "teeth." They are defined and enforced by governments. The authors claim that legally enforcing rights costs money, but this is "ignored by almost everyone." Really? Is almost everyone ignorant of total government spending is now about 36% of GDP, was 41% in 2009, and 40% in 2010-11? Is almost everyone ignorant about taxes?

The authors continually confound rights with enforcement of rights.

Chapter 1 claims that all rights are positive, and that the common distinction between negative rights and positive rights is inadequate because “all legally enforced rights are necessarily positive rights.” Usually negative rights are meant to prohibit what others can do to you. Positive rights are meant to require actions by others on your behalf. They portray the views of others correctly: “Negative rights ban and exclude government; positive ones invite and demand government.” “Negative rights protect liberty; positive rights typically promote equality.” However, these and others are only  “storybook distinctions” in the authors’ opinion (p. 41). They belittle the difference between rights as limiting the actions of government and limiting the actions between private persons. Co-author Holmes in Passions and Constraint wrote about factions and the Founding Fathers’ great concern about the encroachment of government on the rights of citizen. The book says nothing about Founding Fathers, Madison, or Jefferson.

As I expected, the authors laud welfare rights as they construe them. The Cost of Rights reads like a puff piece for Progressivism. I was not surprised to find more 1-star reviews than 5-star reviews on Amazon.

On Peikoff's ‘Fact and Value’

I wrote the following 28 years ago. At that time I gave copies to a few people, but did not publish it. The forthcoming book referred to in the last paragraph is Objectivism: The Philosophy of Ayn Rand. 'Fact and Value' had the lead role in the Objectivist schism of 1989. Most other comments about the schism have been about whether Objectivism is closed or open, or about sanctioning. I considered that a mere "turf war" then, and still do.

ON PEIKOFF’S ‘FACT AND VALUE’

by Merlin Jetton        July 27, 1989

The series of articles by Peter Schwartz, David Kelley, and Leonard Peikoff was both interesting and disappointing to read. It amazes me that such a heated exchange could arise from the mere event of David Kelley making a speech.

I have come to expect such behavior from Schwartz. He has a history of making straw men and burning them. He sometimes makes bizarre judgments. He did that in this instance, operating under the principle that one should judge a speech by its audience and its content is irrelevant. But to me Peikoff’s article ‘Fact and Value’ was the most disturbing part of the exchange. It was not just that he put words in Kelley’s mouth and was unfair in judging him. There are probably many people who would agree with that. There will probably be much said and written about it, so I shall, for the most part, leave that subject for others. The most disturbing part of Mr. Peikoff’s article was the illogical statements. He is the most prominent living spokesman for Objectivism, a philosophy which is committed to reason and logic. As such, I would expect from him a more acute attention to logic.

I considered calling this article “The All or Nothing Syndrome”, which is an affliction of Mr. Peikoff’s. It refers to the tendency to obliterate the distinction between “some” and “all” (or between “none” and “some”), which is an extremely important one in logic. There are several instances of it in Peikoff’s article.

He says, “In my judgment, Kelley’s paper is a repudiation of the fundamental principles of Objectivism.” Kelley and Peikoff clearly have different views about the relationship between fact and value. But did Kelley repudiate “A is A”? Does disagreement on just one principle imply disagreement on all of them?

He argues for the principle: Every “is” implies an “ought”. Note that the first word is “every”, not “some”. The word “every” makes it an overstatement. It baffles me to hear that any trivial, irrelevant fact implies an “ought.” There is the always applicable one that I ought to regard it as a fact, but that is far from the principle’s intended meaning.

He claims that the good is a species of the true and that evil is a species of the false. This is an apparently profound idea, so I did not take it lightly. Consider the logic of this statement. It says if X has the attribute “good”, then X necessarily also has the attribute “true”, and that if X has the attribute “evil”, then X necessarily also has the attribute “false”. I have a few comments:

Some X being both good and true does not imply that any X which is good is also true; similarly for both evil and false.

Hitler was evil. Would Peikoff also say he was “false”? If so, that is bizarre.

It implies there is no such thing as an evil truth. Is the fact that Hitler and the Nazis murdered millions of people not an evil truth? And Peikoff later gives examples of bad truths, such as too much exposure to the sun is bad and getting caught in a tidal wave is bad, which are inconsistent with the claim.

Similarly, it implies there is no such thing as a good falsehood, for which a counterexample easily comes to mind. Suppose A tells a lie to B to protect C, where B has malicious intent and C is innocent of wrongdoing.

It is muddled. There are truths about what is good for us and about what is bad for us. It is good for us to know these truths. There are falsehoods about what is good for us and what is bad for us. It may be or is (the right verb depends on the case) bad for us if we believe these falsehoods. This makes sense, but it is far from what he wrote.

I checked Ayn Rand’s writing for an idea having any resemblance to it and found nothing. And Peikoff exhorts the reader to not rewrite Objectivism!

He correctly paraphrases Kelley as saying: Truth and falsity apply primarily to ideas, and good and evil primarily to actions. Note that Kelley uses the word “primarily”, not “exclusively” or “only”. Yet Peikoff launches an extended polemic as if Kelley had said one of the latter. Admittedly Kelley gave a couple of poor examples in discussing the subject. Kelley also failed to make it clear that no dichotomy can be drawn between a man’s ideas and his actions. But did Peikoff deliberately misrepresent Kelley to set up his polemic? Or did he fail to note the logical import of the word “primarily” means there are exceptions? Either way, it does not speak well for Mr. Peikoff.

He devotes a substantial part of his article to his ideas about the connection between fact and value, between cognition and evaluation. He summarizes his view in a single principle -- cognition implies evaluation -- which he says is the main point of his article. In my opinion, when he was writing this, he was so eager to railroad Kelley that he let his emotions interfere with his reasoning and clear communication. (Does this mean that his evaluation implied his cognition?) This is a topic on which I have not spent sufficient time to articulate well my own ideas, but I shall not let that stop me from making a few comments:

I found it difficult understanding clearly what he said and I attribute it to his lack of clarification of key concepts. For example, “evaluation” may mean a judgment about true/false or about good/bad. Ayn Rand more than once said that to properly evaluate what someone says or writes, look for the definitions. Well, I found none in Peikoff’s exposition.

I will presume that he meant by his principle something like this: one should properly understand the phenomena or idea (Objectivist epistemology), then decide whether it is good or bad based on one’s understanding (and act accordingly). If this is even close, then I believe he made a poor choice of words by using “imply”. This is a term of logic and generally means the consequence follows necessarily from the premise(s). But cognition and evaluation are volitional, so evaluation is not a necessary, automatic consequence of cognition. Cognition and evaluation can only be connected logically by thinking, which is volitional.

Mr. Peikoff said “every cognition implies an evaluation”, using “evaluation” in the sense of good/bad. If he really believes that, then I say his belief is seriously flawed. It would be a gross overstatement. If the instance of cognition were one of learning a new subject or idea and the knowledge gained were not instantaneously integrated, it would be a gross mistake to make such an evaluation. Facing reality and making good judgments also requires proper recognition of one’s state of knowledge.

Now imagine a person who believes that every cognition demands moral evaluation and who is afflicted with the all-or-nothing syndrome. That person would be overzealous to pass moral judgment and would do so on a fragment of evidence, evading any evidence which would indicate a different judgment.

Mr. Peikoff may have impressed a few readers by pointing out the contrapositive of his principle, i.e. that non-evaluation implies non-cognition, but I saw it as a misuse of logic. One of my previous comments was about the use of “imply” in this context. Another pointed out an obvious counterexample to ‘all cognition implies evaluation’. His contrapositive applied to that counterexample is: If the person did not pass moral judgment, then the person learned nothing!

Mr. Peikoff tries to posit a much more extensive connection between true/false and good/evil, between “is” and “ought”, and between fact and value than can be reasonably substantiated. It was both innovative and revolutionary for Ayn Rand to hold that there was such a connection, considering that Hume and many later philosophers held that there was absolutely no connection. However, the negation of “none” is “some”, not “all”.

Peikoff says “Kelley’s viewpoint is an explicit defense of a dichotomy between fact and value, or between cognition and evaluation, and thus between mind and body.” Here is misrepresentation and a non sequitor in the same sentence! Kelley defended a difference or distinction between fact and value, but hardly a dichotomy. Even if Kelley had defended a dichotomy between cognition and evaluation, it would be a dichotomy between two functions of mind, which clearly would not imply a dichotomy between mind and body.

Mr. Peikoff says, “a proper philosophy is an integrated whole, any change in any element of which would destroy the entire system.” I have two comments:

It implies no one philosophical principle is stronger than any other. In other words, every philosophical principle is equally important. I find this notion totally contrary to Peikoff’s often repeated claim that knowledge is hierarchical.

It seems to say you either have it all right or none of it right. It is another instance of the all-or-nothing syndrome.

He did not discuss the Libertarians like Schwartz did, but he did say he completely agreed with Schwartz, who is also much afflicted with the all-or-nothing syndrome. An example is: Some Libertarians are anarchist-subjectivists. They are morally reprehensible. Therefore, any Libertarian is morally reprehensible.

Mr. Peikoff’s all-or-nothing syndrome appears again in his closing paragraphs. He tells readers, in effect, to agree with him totally or disassociate themselves with Objectivism. This article makes me wonder how Objectivism will flourish with him carrying the torch. Logical flaws and the all-or-nothing syndrome make poor impressions. The all-or-nothing syndrome may come in handy in polemics and politics, but it is anti-logic and anti-reason. I believe it is inappropriate for anyone who considers himself/herself to be objective.

I have made some strong criticisms of Mr. Peikoff here, so it seems appropriate that my closing be tolerant, and I shall not pass judgment on him solely on the basis of ‘Fact and Value’ and be guilty of the all-or-nothing syndrome. I did agree with parts of his description of Objectivism. I have appreciated his past lectures. I shall probably be tolerant enough to buy his forthcoming book.