Goines On: A fundamental flaw of logic

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Goines was about to start reading a book he had borrowed from Duke University Library for Mrs. Goines. He knew that Apple’s iBooks probably had the book and he could download a free sample to start reading more easily on his iPad.

    Goines was amazed to find that the sample included the entire first three chapters of the book. Chapter 3 of the printed book ended on p. 30, and the last page of the electronic sample was also numbered 30. As a double check, Goines also quickly noted the book’s and the sample’s final word: they were the same. Goines valued such confirmations, because he was becoming more and more prone to error, and double checks helped him catch his mistakes.

Goines On: For the whiz-kids

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A not-so-simple formula…

Even after Goines realized that he had been drawing figures and assembling tables of yearly cyclical calendar patterns only to satisfy some obsession or compulsion within his own self, he continued working at it. But when he got done – or done enough, because more could be done – he decided to set that aside and be done with it. He’d wrap it all up by specifying the steps that a computer program could take to find the day of the week for any given date within the period covered by the Gregorian Calendar.

From “The Scratching Post”:Axioms

By Ken Marks

[Originally posted on The Scratching Post, September 18. Republished here by permission of the author.]

Mr. Dinkel taught me all about axioms in my high school geometry class. You begin with a set of self-evident truths – axioms – and from them you derive all the complex postulates of Euclidean geometry! I was astonished that so much knowledge could be derived simply by using logic.
    Much later it occurred to me that each person is a kind of Euclid. Each of us comes to see the world as a set of self-evident truths and, consciously or unconsciously, each of us extrapolates a worldview from them. The difference is only this: when Euclid stated that the shortest distance between two points on a flat surface is a straight line, he was irrefutably correct. Our axioms, however, are different. They are self-evident truths to each of us but not necessarily to our neighbors, who have their own sets of axioms. And here’s the fascinating bit: the lack of a consensus about personal axioms does nothing to weaken our convictions about their truth. That’s one of my axioms – what you might call a “meta-axiom.” It makes coexistence challenging.

[Read the whole thing on The Scratching Post.]

Copyright © 2021 by Ken Marks Ken Marks was a contributing editor with Paul Clark & Tom Lowe when “Moristotle” became “Moristotle & Co.” A brilliant photographer, witty conversationalist, and elegant writer, Ken contributed photographs, essays, and commentaries from mid-2008 through 2012. Late in 2013, Ken birthed the blog The Scratching Post. He also posts albums of his photos on Flickr.

13 Years Ago Yesterday: An ontological argument for the non-existence of god

A mid-17th century
engraving of Anselmn

By Moristotle

[Originally published, without an image, on December 6, 2007. Dawkins’ reference to the “ironic ‘proof’ ” he announces understates the pleasure it afforded me when I read it again this year.]

In the year 1078, St. Anselm of Canterbury (England) proposed an “ontological argument” for the existence of God:

Seven Years Ago Today: A funny from Bertrand Russell

By Moristotle

[Originally published on October 25, 2010, not one word different, but a better photo of Mr. Russell has been substituted.]

My wife didn’t laugh when I read her the following excerpt from Bertrand Russell’s 1909 essay, “Pragmatism,” but I did, and I hope you might too:

Ask Wednesday: Are there as many odd numbers as even?

No...but... yes...but....

By Morris Dean

[Originally published, under the title "More even than odd," on January 10, 2011.]

I was amazed one morning to discover a "proof" for something that is quite counter-intuitive. I mean, there are as many odd numbers as even numbers, right?

Thor's Day: Who and what is the supreme lama?

Thursday of the week is devoted to airing out religion and religions. The column's title, "Thor's Day," comes from the etymology of the word Thursday, literally "Thor's Day."

Last Thor's Day, I quoted the Dalai Lama (and also Saint Paul and Jesus).

Thor's Day: Suffer the little children

Thursday of the week is devoted to airing out religion and religions. The column's title, "Thor's Day," comes from the etymology of the word Thursday, literally "Thor's Day."

The Apostle Paul wrote in his first letter to the Corinthians (about 1,950 years ago):

Thor's Day: God, une belle hypothèse

Joseph-Louis Lagrange
(1736-1816)

Thursday of the week is devoted to airing out religion and religions. The column's title, "Thor's Day," comes from the etymology of the word Thursday, literally "Thor's Day."

Thor's Day: God's existence proved

Rene Descartes famously said,
"Cogito ergo sum."

Thursday of the week is devoted to airing out religion and religions. The column's title, "Thor's Day," comes from the etymology of the word Thursday, literally "Thor's Day."

Announcing: Thor's Day

Thursday of the week will be devoted to airing out religion and religions. The column's title, "Thor's Day," comes of course from the etymology of the word Thursday, literally "Thor's Day." In Norse mythology, Thor (from Old Norse Þórr) was a hammer-wielding god associated with thunder, lightning, storms, oak trees, strength, the protection of mankind, and also hallowing, healing, and fertility. [Characterization from Wikipedia.]

Today's Islamist oxymoron

Al Qaeda, according to The New York Times today (in "Bin Laden’s No. 2, Zawahri, Takes Control of Al Qaeda," by David Jolly and J. David Goodman), has announced that it will “seek with the aid of God to call for the religion of truth and incite the ummah to prepare and fight.” (Ummah is an Arabic word, in this context meaning the global community of Muslims.)
    If you're waiting for me to reveal the oxymoron, you weren't paying attention. Go back three sentences: "...aid of God...religion of truth," as though God and religion had anything to do with truth.
    It isn't clear whether the statement is cheap rhetoric to hoodwink (i.e., incite) gullible people or its author himself actually believes the pairing.

Sayyid Qutb, Bin Laden’s favorite philosopher, who spent most of 1949 in Greeley, Colorado, apparently terrified of women and fantasizing about American girls, made a similarly flawed pairing. He saw the sexuality of western teenage women as evidence of a spiritual banality that demanded the destruction of western civilization.
    In his 1951 book, The America I Have Seen: In the Scale of Human Values, Qutb wrote that

The American girl is well acquainted with her body’s seductive capacity. She knows it lies in the face, and in expressive eyes, and thirsty lips. She knows seductiveness lies in the round breasts, the full buttocks, and in the shapely thighs, sleek legs—and she shows all this and does not hide it.

    As Sam Harris noted Tuesday in his blog, in the entry "On Spiritual Truths, "What a relief it must have been [to Qutb] to know [from studying his holy book] that the Creator of the universe intended these terrifying creatures to live as slaves to men."
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See sequel: "A 'good' Muslim."

Theological fallout from "birthtime"

The ACLU directrix who proposed the "birthtime (b.t.) method" for calculating your next birthday ("When's your birthday time?") had trouble sleeping the next night. His dreams were haunted by profound theological rumblings, which, round about 3:30 a.m., gave rise to the following proof for the non-existence of God:

God, by definition, created the universe.
    But only a cruel God would have organized the clockwork of our planet around the sun in such a fashion that something as complicated as birthtime is needed to calculate accurate birthdays.
    Therefore, since God, also by definition, is not cruel, birthtime implies that there is no God and also implies that creation is the consequence of random happenstance.

This can't be right, can it? If you think you can refute this argment, please be so kind as to offer your refutation in a comment. Thanks in advance.

An un-odd semantic solution

Last Monday, I reported my "insight" that there seemed to be more even numbers than odd numbers. I labeled the report humor to signal that my tongue was in my cheek. But I also labeled it parody to signal that I was seriously making fun of a certain way of trying to think (exemplified by numerology and astrology and, perhaps more often than not, by theology).
    Commenter Ken provided a serious, logical counter to the "proof" that there are more even numbers than odd. There's an infinite number of both, he pointed out, and one infinity is just as numerous as another. Actually, as Georg Cantor (1845-1918) theorized,

there are infinite sets of different sizes (called cardinalities). For example, the set of integers is countably infinite, while the set of real numbers is uncountably infinite. –Wikipedia

But Ken is right, because, with even and odd numbers, we're confining ourselves to "countably infinite" sets.
    Of course, I never thought for a minute myself that there were more even numbers than odd numbers. But the semantic example I contrived (the asymmetry of "even number of odd numbers" and "odd number of even numbers") did sort of make it look as though there might be more even than odd numbers.
    While Ken's logical objection is well and good¹, I've been waiting for my muse to provide a fitting semantic retort. Alas, I've been disappointed, and I've even had grapefruit almost every morning. I'm going to have to work to provide a proportional solution.

Many years ago (in the early seventies), I became interested in "creative problem-solving." One of the things I learned from my mentor, Moe Edwards ("Moe" was simply his initials; there's a reference on the web to a book titled Doubling Idea Power, by M.O. Edwards, Palo Alto), was to "ask provocative questions"—or to ask any question at all, to see whether it can spur a thought.
    Okay. What's going on when you (1) double an odd number and get an even number, but (2) take an odd number of even numbers and also get an even number?
    What this struck right off is the realization that when you double two things, you get an even number of them, and when you take an odd number of things, you get an odd number of them. So something fishy or sleight-of-hand seems to be going on in (2), taking an odd number [of something]...and getting "an even number."
    And the clue as to what's going on is that the phrase, "of them," was coyly omitted in Monday's "proof." That is, it didn't say "getting an even number of them," but "getting an even number."
    I'll go on and spell this out later (perhaps tomorrow), but for now, as a gift to my readers, I'll leave it to them to work it out for themselves, perhaps while eating a grapefruit.

Proof more odd than even

The proof "more even than odd" was semantic,
Playful, good-humored, a little pedantic,
    Done for good fun,
    As well as the pun,
And while not even odd, it was, flatly, antic².

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1. "Acceptable, all right, as in 'If you can get a better discount elsewhere, well and good.' [The] redundant phrase ['well and good'] was first recorded in 1699." –yourdictionary.com
2. antic. adjective: ludicrously odd
       Example: "Hamlet's assumed antic disposition."

More even than odd

I was amazed this morning to discover a "proof"¹ for something that is quite counter-intuitive. I mean, there are as many odd numbers as even numbers, right?
    Wrong. There are actually more even numbers than odd numbers. Here's the proof that came to me while I was eating my grapefruit half:
    If you add an even number of even numbers, you get an even number.
    But you also get an even number if you add an even number of odd numbers! And you don't conversely get any extra odd numbers when you add an odd number of even numbers. Rather, you seem to gain some even numbers—or lose some odd numbers, depending on how you look at.
    Therefore, there are apparently more even numbers than odd ones. And I haven't even tried to find other ways we might gain even numbers or lose odd ones.
    Isn't that amazing!

How can that be? Can that possibly be right?
    If true, it is so astounding, do you think maybe this might be a clue toward discovering a proof for the existence of God? Or maybe for the existence of two of them (God even rather than odd)? Or for their nonexistence? Wow.
    What if duotheism is the True Way, rather than monotheism? Or if atheists have to deny the existence of two Gods in order to be atheists? "Aduotheists" is hard to pronounce.

An odd God limerick

More even than odd...the truth about God?
Then let's swell the ranks of Their Squad,
    Double Their pronouns,
    Use King and Queen crowns,
And on Fridays eat twice as much cod.

Notes for further analysis:

1. The operator "even number of" is equivalent to "multiplied by two" (or "the numerical result made even").
2. The operator "odd number of" is not equivalent to "the numerical result made odd" (if the things there are an odd number of are even numbers).

    Further disquisition
_______________

1. Note: This post is labeled "humor." I only added this note later when I suspected that some readers had not detected the post's parody of wishful or theological thinking, possibly because they'd noticed that I'd lately been taking myself so very seriously.

Theological space [is empty]

I often fall to musing while doing household or personal chores. Like cleaning up the kitchen after dinner, or bathing in the morning. This morning (or perhaps it was last night), I fell to contemplating the billions of hours that human beings have spent theologizing. If God doesn't exist (which I believe "he" doesn't), how could intelligent beings waste so much time that way?
    As often (if not invariably) happens when I muse, an idea came to me, prompted by musing's tendency to pose questions and thereby invoke the principle, Ask and ye shall receive.
    The idea provided by my muse (so to speak) was that humans have also spent billions of hours contemplating mathematics, or what might be called "logical space." Well, inventive minds can also posit theological entities (gods, angels, devils, sins, etc.) and amuse (or torture) themselves for hours puzzling over their conceptual implications. And they have.
    But, though mathematical entities (numbers, for example) don't exist in the way atoms and avalanches and alligators do, they have proven themselves in all sorts of theoretical and practical applications (science, economics, technology, everyday commerce).
    God hasn't.

A funny from Bertrand Russell

My wife didn't laugh when I read her the following excerpt from Bertrand Russell's 1909 essay, "Pragmatism," but I did, and I hope you might too:

The legitimate conclusion from [William James's] argument [that if we don't have the necessary information for deciding between, for example, "God exists" and "God doesn't exist," we ought to choose one anyway in order to have a 50% chance of being right] would be that, in such cases as William James has in mind, we ought to believe both alternatives; for in that case we are sure [emphasis mine] of "knowing" the truth in the matter. If it were said that to believe both is a psychological impossibility, we would rejoin that, on the contrary, it is often done, and that those who cannot yet do it need only to practice the "will to believe" until they have learnt to believe that the law of contradiction is false—a feat which is by no means as difficult as it is often supposed to be.

Who said philosophy couldn't be a barrel of laughs?
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Another passage a page further down:

To go about the world believing everything in the hope that thereby we shall believe as much truth as possible is like practicing polygamy in the hope that among so many we shall find someone who will make us happy.

Bertrand Russell was a great writer. Did you know that he was awarded the Nobel Prize in Literature in 1950? Well, he was. "..."in recognition of his varied and significant writings in which he champions humanitarian ideals and freedom of thought."

Why is there something rather than nothing?

The question, Why is there something rather than nothing?, has long haunted me, as it has haunted many if not most people. Could the answer be quite simply that the eternal truths of logic, whose nonexistence is impossible, require "something" to exist for them to be about, and "something's" existence as inexorably requires that it inter-react and reform itself, even becoming, over the course of millions and billions of years, creatures capable of being haunted by such questions?
    I'm reminded of my favorite short poem, by Howard Nemerov:

The world's just mad enough to have been made
By the being whose beings into being prayed.

Whether it's relevant or not, it nevertheless evokes a similar feeling in me. Awe at the weirdness of things. The mystery of being.
    Could the story by which to exult, to dance, be written as paeans to the mystery, like some weird novel by Flann O'Brien—say, The Third Policeman, which was written between 1939 and 1940 and published posthumously. In the book's frontispiece, O'Brien "quotes" his fictional philosopher De Selby:

Human existence being an hallucination containing in itself the secondary hallucinations of day and night (the latter an insanitary condition of the atmosphere due to accretions of black air) it ill becomes any man of sense to be concerned at the illusory approach of the supreme hallucination known as death.

As a teenage philosopher, I found The Gospel of John more appealing than the other Gospels. The very first verse of John suggests that existence derived from those eternal logical truths: "In the beginning was the Word...." As Wikipedia says, "The Gospel of John identifies the Logos, through which all things are made, as divine (theos), and further identifies Jesus as the incarnation of the Logos." While most of the Jesus myth simply borrows from the various pagan and other religious mythologies of the period [something I didn't realize as a teenager], logos is borrowed from Greek philosophy. Heraclitus (ca. 535–475 BC) used the term for the principle of order and knowledge in the universe.

The orbiting teapot

I'm parsing a statement that recently came across my desk (so to speak):

I have religious duties to perform at my church. I cannot say for sure that God exists, but if he does exist, he wants me to be doing these things.

Whatever the content might be, it has to reside in that final indicative, "He wants me to be doing these things [i.e., performing my religious duties at church]."
    The question of course is, how does the speaker know what God, "if he does exist," wants him to be doing? How can he know that if he doesn't even know whether God exists?

My dear Watson! In a trivial sense, it's elementary. He knows because his conception of the God that might exist is of a God who wants him to be doing those very duties. That is, the speaker's statement, "unpacked"—as Professor Wildrid Sellars liked to say—amounts to this:

If God (defined as a being who, if he existed, would want me to perform these religious duties) exists, then he wants me to be doing these things.

It's as if I were to say (to use Bertrand Russell's famous example¹):

If an undetectably small china teapot were revolving about the sun, I know that it would be undetectably small.

Among other things, this sort of statement is called a tautology. The predicate doesn't add anything not already contained in the subject. If you assume that God exists, then (in your world) God exists, and he wants you to be doing whatever you specify that he wants you to be doing.
    Welcome to your world!
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1. Wikipedia conveniently quotes the passage from Russell in which the teapot is specified:

   In an article entitled "Is There a God?" commissioned, but never published, by Illustrated magazine in 1952, Russell wrote:
       If I were to suggest that between the Earth and Mars there is a china teapot revolving about the sun in an elliptical orbit, nobody would be able to disprove my assertion provided I were careful to add that the teapot is too small to be revealed even by our most powerful telescopes. But if I were to go on to say that, since my assertion cannot be disproved, it is an intolerable presumption on the part of human reason to doubt it, I should rightly be thought to be talking nonsense. If, however, the existence of such a teapot were affirmed in ancient books, taught as the sacred truth every Sunday, and instilled into the minds of children at school, hesitation to believe in its existence would become a mark of eccentricity and entitle the doubter to the attentions of the psychiatrist in an enlightened age or of the Inquisitor in an earlier time. [emphasis mine]

A house built on sand

When I wanted to include in yesterday's post on Autosuggestion an ironic allusion, I googled on jesus house built on the sand for the precise gospel source, and the very first item on Google's list (of 341,000 items) was "A house built on sand - Testimonies of Ex-Christians," a coincidentally corroborating post from M in Helsinki (December 11, 2003):

Jesus teaches in the Sermon on the Mount to build the houses of our faith on the solid rock of his teachings (Mt 7:24-27). Too bad that the religion based on his teachings is a house built on sand. [emphasis mine] However strong you make the internal structure of your faith, there is no external rock that it is anchored to. So when the flood of rational thinking hits it, it will fail.
    My parents became born again Christians when I was 5. They started in Pentecostal and Lutheran circles, but soon ended in charismatic and Word of Faith (you know, the name-it-and-claim-it bunch, e.g. Hagin, Copeland, Oral Roberts) connections, though there were no such churches in the area we lived. As the only child I grew up with the faith, starting to speak in tongues at 7 and getting baptized at 14.
    ...[skipping to M's concluding sentence:] It just happens that the rock is reason and the sand Christianity.

That final sentence of course expresses my own affiliation with reason rather than blind faith in primitive doctrines. However, the "internal structure" of these doctrines is decidedly not strong, however much apologists over the years have tried to shore up the doctrines. I take exception with M on that. But he may well have revised this opinion, expressed as it was before the appearance of the books of Sam Harris, Christopher Hitchens, and Richard Dawkins that I occasionally cite here to elaborate various problems of religion.