Quote of the Day

"What are the facts? Again and again and again - what are the facts? Shun wishful thinking, ignore divine revelation, forget what "the stars foretell," avoid opinion, care not what the neighbors think, never mind the unguessable "verdict of history" - what are the facts, and to how many decimal places? You pilot always into an unknown future; facts are your single clue. Get the facts!" - Lazarus Long (Robert Heinlein, Time Enough for Love)

Rhetorical Poison

The state of modern American political rhetoric is dismal. There is little logic or courtesy, and the following types seem to be the primary ones in use:

• argumentum per repetitio, or the Snark Syllogism, from the famous Lewis Carroll poem (which Carroll subtitled "an Agony in Eight Fits"):

  "Just the place for a Snark!" the Bellman cried,
  As he landed his crew with care;
  Supporting each man on the top of the tide
  By a finger entwined in his hair.
  
  "Just the place for a Snark! I have said it twice:
  That alone should encourage the crew.
  Just the place for a Snark! I have said it thrice:
  What I tell you three times is true."

  so named by Dafydd ab Hugh here.
  
  To this must be added others in common use:
  
  
• argumentum per clamo, or proof by volume -- the apparent belief that the louder an argument is made, the more validity it has. In the extreme this degenerates to shouting-down an opponent, never allowing them to speak, a favorite tactic of the left.
• argumentum per rumpo, or argument by interruption -- the discourteous practice of not letting anyone else complete even one of their sentences, destroying any continuity in their argument. This technique is often seen combined with the previous one. (I suspect it indicates the inability to remember parts of an argument, so they must be responded to immediately lest they be lost.)
• argumentum per ignarus quaero, or argument by ignoring the question and instead producing a non sequitur bearing small or no relation to the issue, argument, or question at hand. Most politicians are particularly adept at this technique.
• argumentum per a singulus refero, or the argument of a single answer to all questions, i.e., the daily talking point. This, of necessity, is often associated with the previous technique.
• argumentum per capitagium, or argument from polling -- the belief that because a majority of people, often ill-informed or totally ignorant of the issue, believe something, it therefore must be so. This logical fallacy has become so common that it is seldom even recognized, and is widely employed by all sides.
• argumentum ex affectus, or argument from emotion -- the belief that a good person's feelings must be a reliable guide to the truth of a matter, with the corollary that anyone who disagrees must be i) cold-hearted or unfeeling, or ii) emotionally disturbed, or, in the extreme, iii) evil -- in any case, not fully human, leading quite naturally to ad hominum attacks.

Unfortunately, I despair of any improvement in our political rhetoric -- the confrontational cable programs and the Internet only seem to be accelerating the decline.

Quote of the Day

Now, I have to change all the world democide totals that populate my websites, blogs, and publications. The total for the communist democide before and after Mao took over the mainland is thus 3,446,000 + 35,226,000 + 38,000,000 = 76,692,000, or to round off, 77,000,000 murdered. This is now in line with the 65 million toll estimated for China in the Black Book of Communism, and Chang and Halliday's estimate of "well over 70 million."

This exceeds the 61,911,000 murdered by the Soviet Union 1917-1987, with Hitler far behind at 20,946,000 wiped out 1933-1945.

For perspective on Mao's most bloody rule, all wars 1900-1987 cost in combat dead 34,021,000 — including WWI and II, Vietnam, Korea, and the Mexican and Russian Revolutions. Mao alone murdered over twice as many as were killed in combat in all these wars.

-- Rudy Rummel, a Professor Emeritus at the University of Hawaii

Models are not Reality

Mars Melt Hints at Solar, Not Human, Cause for Warming, Scientist Says, Kate Ravilious, National Geographic News, February 28, 2007 (h/t Orrin Judd)

Simultaneous warming on Earth and Mars suggests that our planet's recent climate changes have a natural—and not a human-induced—cause, according to one scientist's controversial theory.

Earth is currently experiencing rapid warming, which the vast majority of climate scientists says is due to humans pumping huge amounts of greenhouse gases into the atmosphere.

Mars, too, appears to be enjoying more mild and balmy temperatures. [...] In 2005 data from NASA's Mars Global Surveyor and Odyssey missions revealed that the carbon dioxide "ice caps" near Mars's south pole had been diminishing for three summers in a row. [See for instance, Mars Ski Report: Snow is Hard, Dense and Disappearing]

Habibullo Abdussamatov, head of the St. Petersburg's Pulkovo Astronomical Observatory in Russia, says the Mars data is evidence that the current global warming on Earth is being caused by changes in the sun. [...] "The long-term increase in solar irradiance is heating both Earth and Mars," he said. [...] Abdussamatov believes that changes in the sun's heat output can account for almost all the climate changes we see on both planets.

Mars and Earth, for instance, have experienced periodic ice ages throughout their histories. [...] By studying fluctuations in the warmth of the sun, Abdussamatov believes he can see a pattern that fits with the ups and downs in climate we see on Earth and Mars.

Abdussamatov's work, however, has not been well received by other climate scientists. [...] "His views are completely at odds with the mainstream scientific opinion," said Colin Wilson, a planetary physicist at England's Oxford University.

"And they contradict the extensive evidence presented in the most recent IPCC [Intergovernmental Panel on Climate Change] report." (Related: "Global Warming 'Very Likely' Caused by Humans, World Climate Experts Say" [February 2, 2007].) [...] Amato Evan, a climate scientist at the University of Wisconsin, Madison, added that "the idea just isn't supported by the theory or by the observations."

All planets experience a few wobbles as they make their journey around the sun. [...] These fluctuations change the tilt of Earth's axis and its distance from the sun and are thought to be responsible for the waxing and waning of ice ages on Earth. [...] Mars and Earth wobble in different ways, and most scientists think it is pure coincidence that both planets are between ice ages right now.

So let us examine the theory and observations as Mr. Evan suggests. The majority of heat for the Earth's surface undoubtedly comes from the Sun, with a small portion produced geothermally. It has long been suspected that a decline in Solar radiation coupled with increased volcanic activity was responsible for the Little Ice Age. While many studies claim to find no variation in Solar output, a recent study, Sun's Output Increasing in Possible Trend Fueling Global Warming, reanalyzing satellite data indicates that Solar output has been increasing for the last 20-30 years. The IPCC report, whose primary evidence is the Mann Hockey-stick graph, has been questioned by statisticians, since the methods used produce the same Hockey-stick shape when fed random data, and there are discrepancies between the proxy temperature data sets used and historic temperature data. Nor can the IPCC computer climate models accurately reproduce the last 10 or 20 year temperature records. As for humans producing "huge" amounts of greenhouse gases: "NOAA research estimates that 97% of atmospheric CO₂ created each year is from natural sources and approximately 3% is from human activities." Nor are present levels abnormally high: "Although contemporary CO₂ concentrations were exceeded during earlier geological epochs, present carbon dioxide levels are likely higher now than at any time during the past 20 million years and at the same time lower than at any time in history if we look at time scales longer than 50 million years." (source), and see also this graph ("Both measurements and models show considerable uncertainty and variation; however, all point to carbon dioxide levels in the past that have been signifcantly higher than they are at present.")

Finally, "mainstream scientific opinion" is never the sole criterion of truth - there are too many counter-examples in history for this argument to be more than merely suggestive. What is certain is that many climatologists are heavily invested in promoting research and grant money, which is easier if there is an imminent crisis. And arguing that the same phenomenon occurring on two planets is pure coincidence is surely a rather lame one.

Quote of the Day

"A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it." -- Max Planck

Quote of the Day

"There are no hard distinctions between what is real and what is unreal, nor between what is true and what is false. A thing is not necessarily either true or false; it can be both true and false." -- Harold Pinter, explaining leftist logic

Quotes of the Day

It is amazing how complete is the delusion that beauty is goodness. - Leo Tolstoy

Only those things are beautiful which are inspired by madness and written by reason. - Andre Gide

Quote of the Day

"If you torture the data long enough, it will confess, even to crimes it did not commit."
Or, as Karl Popper might have said,
"If you are looking for evidence to confirm an hypothesis, you'll always find it."

Quote of the Day

Nobody before the Pythagoreans had thought that mathematical relations held the secret of the universe. Twenty-five centuries later, Europe is still blessed and cursed with their heritage. To non-European civilizations, the idea that numbers are the key to both wisdom and power, seems never to have occurred. - Arthur Koestler

Dodgson's Eight - A Heap of Sorites

This concludes my analysis of the hitherto unsolved Eight Problems from Part II in the appendix to Dodgson's Symbolic Logic. Links to all the articles are collected here for easy reference:

Symbolic Logic, Eight Problems from Part II, p. 185
Don't ask Alice, I don't think she'll know	Symbolic Logic, p. 186
Don't ask Alice - Part the Second	Symbolic Logic, p. 187
Don't ask Alice - Part the Third	Symbolic Logic, p. 188
Don't ask Alice - Part the Fourth	Symbolic Logic, p. 190
Don't ask Alice - Part the Fifth	Symbolic Logic, p. 191
Don't ask Alice - Part the Sixth	Symbolic Logic, p. 192
Don't ask Alice - Part the Seventh	Symbolic Logic, p. 193
Don't ask Alice - Part the Eighth	Symbolic Logic, p. 194
And an analysis of an old nursery rhyme not composed by Dodgson:
Don't ask Alice - Part the Rhyme	Symbolic Logic, p. 194

The purpose of these articles is to provide the solutions for the first time, and to demonstrate that a relatively simple, yet powerful, boolean algebra is capable of solving these advanced problems easily. In the process, it was discovered that the premise set of Problem 2 was redundant, that Dodgson begged the question in Problem 7, and that the nursery rhyme is not a vallid syllogism. Problems 6 and 8 are, by far, the most difficult ones.

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My strange journey to these topics began in 1972 with the acquisition of Laws of Form by G. Spencer Brown. The book is a very difficult read, and I do not recommend it - Brown's literary style is eclectic and obscure, his unusual notation and interpretation are deficient, and he has a decidedly mixed reputation. However, he suggested a very simple method for solving Dodgson's last example sorites (No. 60, p. 124) in Appendix 2, Interpretative Theorem 1, p. 123, which caught my interest and led me to read and re-read the book over a period of several years, trying to understand it. [Note: I am an Electrical Engineer with training in Boolean algebra, logic design, and symbolic logic, and still I found the book exceptionally difficult.] Eventually, I reformulated Brown's system into a more conventional notation while retaining Brown's basic structure and axioms/initials. In the process of studying Aristotlean Logic and Syllogism, I discovered the proper form (Syllogistic Theorem below) for Brown's Interpretative Theorem 1 which did not have Brown's difficulties with invalid syllogisms (which he tried unsucessfully to explain away), and the proper form for the Existential Syllogisms (see below), making all 24 valid Aristotlean syllogisms substitutional instances of only two fundamental forms. As mentioned in Problem 2, I first encountered Dodgson's Eight Problems on a blog, applied my newly discovered methods to it, solved it in 30 minutes, asked the blog writer if the answer was correct, and was surprised to learn no one apparently knew the answers to these eight problems.

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For those wishing to follow the calculations in the analysis of Dodgson' Eight Problems, I here present that part of my formal system necessary for understanding. There are only two operations: disjunction, indicated by the concatenation of symbols, and complementation, indicated by a postfix tilde "^~".

The binary logical operations are defined as: [X1 ∨ X2] = [X1 + X2] = X1X2 Disjunction (Or) [X1 ∧ X2] = [X1 · X2] = (X1~X2~)~ Conjunction (And) [X1 ⇒ X2] = X1~X2 Material Implication [X1 - X2] = (X1~X2)~ Difference [X1 ≡ X2] = (X1X2)~(X1~X2~)~ Material Equivalence [X1 ^ X2] = [X1 ⊕ X2] = (X1~X2)~(X1X2~)~ Exclusive Or [X1 | X2] = X1~X2~ Stroke (Nand)

Syllogistic Inference

For all substitutions of real variables R1, R2 and R3 : a)  ρ(R1R2)~ρ(R2~R3)~ρ(R1R3) = U    or, written as an implication:      ρ(R1R2) · ρ(R2~R3) ⇒ ρ(R1R3)    Hypothetical Syllogism and, by appropriate substitution and re-arrangement, the corollary:      ρ(R1R2) · ρ(R2R3)~ ⇒ ρ(R1~R3)~ b)  ρ(R1R2)~ρ(R2R3)~ρ(R1~R3~)~ρ(R2) = U    or, written as an implication:      ρ(R1R2) · ρ(R2R3) · ρ(R2)~ ⇒ ρ(R1~R3~)~    Existential Syllogism

The propositional operator ρ(...) is defined as ρ(R) = U if R = U, and ρ(R) = U~ otherwise, converting the class or set content of the distinction R to a binary propositional value.

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This theorem is the tool which was used in the solution of Dodgson's eight problems (with the exception of Problem 6) - its repeated application eliminates all terms which appear both complemented and uncomplemented. The interested reader should now be able to follow, in detail, the calculations in the eight articles on Dodgson's sorites.

Dodgson had three such rules (Fig. I, II, and III here), but his notation was so peculiar that he failed to realize that his Fig. I and II were equivalent. Brown, on the other hand, failed to explain the Existential Syllogisms at all, and had difficulties with invalid syllogisms because of his defective formulation and interpretation, confusing classes and propositions..