© Paul K. Davis 2009. All Rights Reserved.
Mission Peak Unitarian Universalist Congregation
December 6, 2009


Like Mr. Spock in Star Trek, I am emotionally attached to logic. To many, logic is a dull subject, but it can be very interesting and highly useful to understand common logical errors. Just listen to any current political debate and you will hear much fuel for logical analysis and criticism on all sides of an issue. I will attempt to spice up your critical abilities by explaining just a few common errors, and how to detect and avoid them.

Story for All Ages - from "Through the Looking Glass", by Lewis Carroll

Said the Queen, 'Were you ever punished?'

'Only for faults,' said Alice.

'And you were all the better for it, I know!' the Queen said triumphantly.

'Yes, but then I had done the things I was punished for,' said Alice. 'That makes all the difference.'

'But if you hadn't done them,' the Queen said, 'that would have been better still; better, and better, and better!' Her voice went higher with each 'better', till it got quite to a squeak at last.

Alice was just beginning to say 'There's a mistake somewhere--,' when the Queen began screaming, so loud that she had to leave the sentence unfinished. 'Oh, oh, oh!' shouted the Queen, shaking her hand about as if she wanted to shake it off. 'My finger's bleeding! Oh, oh, oh, oh!'

Her screams were so exactly like the whistle of a steam-engine, that Alice had to hold both her hands over her ears.

'What is the matter?' she said, as soon as there was a chance of making herself heard. 'Have you pricked your finger?'

'I haven't pricked it yet,' the Queen said, 'but I soon shall -- oh, oh, oh!'

'When do you expect to do it?' Alice said, feeling very much inclined to laugh.

'When I fasten my shawl again,' the poor Queen groaned out. 'The brooch will come undone directly. Oh, oh!' As she said the words the brooch flew open, and the Queen clutched wildly at it, and tried to clasp it again.

'Take care!' cried Alice. 'You're holding it all crooked!' And she caught at the brooch; but it was too late: the pin had slipped, and the Queen had pricked her finger.

'That accounts for the bleeding, you see,' she said to Alice with a smile. 'Now you understand the way things happen here.'

'But why don't you scream now?' Alice asked, holding her hands ready to put over her ears again.

'Why, I've done all the screaming already,' said the Queen. 'What would be the good of having it all over again?'

By this time it was getting light. 'The crow must have flown away, I think,' said Alice: 'I'm so glad it's gone. I thought it was the night coming on.'

'I wish I could manage to be glad!' the Queen said. 'Only I never can remember the rule. You must be very happy, living in this wood, and being glad whenever you like!'

'Only it is so very lonely here!' Alice said in a melancholy voice. And, at the thought of her loneliness, two large tears came rolling down her cheeks.

'Oh, don't go on like that!' cried the poor Queen, wringing her hands in despair. 'Consider what a great girl you are. Consider what a long way you've come to-day. Consider what o'clock it is. Consider anything, only don't cry!'

Alice could not help laughing at this, even in the midst of her tears. 'Can you keep from crying by considering things?' she asked.

'That's the way it's done,' the Queen said with great decision: 'nobody can do two things at once, you know. Let's consider your age to begin with -- how old are you?'

'I'm seven and a half, exactly.'

'You needn't say "exactly",' the Queen remarked. 'I can believe it without that. Now I'll give you something to believe. I'm just one hundred and one, five months and a day.'

'I can't believe that!' said Alice.

'Can't you?' the Queen said in a pitying tone. 'Try again: draw a long breath, and shut your eyes.'

Alice laughed. 'There's no use trying,' she said 'one can't believe impossible things.'

'I daresay you haven't had much practice,' said the Queen. 'When I was your age, I always did it for half-an-hour a day. Why, sometimes I've believed as many as six impossible things before breakfast. There goes the shawl again!'

The brooch had come undone as she spoke, and a sudden gust of wind blew the Queen's shawl across a little brook. The Queen spread out her arms again and went flying after it, and this time she succeeded in catching it herself. 'I've got it!' she cried in a triumphant tone. 'Now you shall see me pin it on again, all by myself!'

'Then I hope your finger is better now?' Alice said very politely, as she crossed the little brook after the Queen.

Meditation - Mistaken Assumptions

I would ask you to meditate, during a few moments of silence ending with the bell sound, on mistaken assumptions you have made, or almost made. Perhaps small ones in conversation. Perhaps larger ones at work. How easy it is to slip into an error through implicit assumption.


In the play, Harvey, by Mary Chase, which was made into a movie with Jimmy Stewart, the character Elwood P. Dowd explains, "One night...I was walking...along Fairfax street -- between 18th and 19th...when I heard a voice saying, 'Good evening, Mr. Dowd'. I turned and there was this great white rabbit leaning against a lamp-post. Well, I thought nothing of that, because when you have lived in a town as long as I have lived in this one, you get used to the fact that everybody knows your name." [p. 55]

However, this event had greatly disturbed his sister, Veta Louise, who engaged in a desparate effort to deal with the utterly embarrassing problem that her brother sees a great white rabbit, which is rarely, if at all, seen by anyone else. She decides to have him treated with an injection by the renowned Dr. Chumley. In making this decision, she commits a common logical error. From a dramatic point of view, this error is an essential part of the compelling nature of the script. Of course, matters are set right, just in time.

The purpose of this sermon is to insist on the importance of logic, both in our own thinking and in our discussions with others, and to explain how to recognize, avoid and correct some very common logical fallacies. Besides Harvey, I will be drawing on an example from the play, Dial M for Murder, from the opera Gianni Schicchi, from the book Through the Looking Glass, and other sources.

We derive the word "logic" from the Greek word "logos" which, like a number of Greek words used by the ancient philosophers and the authors of the Christian New Testament, has a variety of related meanings or, if you prefer, a broad meaning. In the New Testament, for example, it is variously translated "account", "cause", "doctrine", "reason", "speech", "treatise", "utterance" or "word". It occurs in the first verse of John's Gospel, where the King James Version translates it "word", as follows: "In the beginning was the word, and the word was with God, and the word was God." This verse is the inspiration for the first line of the version of "Joy to the World!" in our hymnal, namely, "Joy to the World! the Word is come." The recent British philosopher Bertrand Russell sees here a connection between classic Greek philosophy and Christianity, writing in his "History of Western Philosophy", "It was this intellectual element in Plato's religion that led Christians - notably the author of John's Gospel - to identify Christ with the Logos. "Logos", Russell continues, "should be translated 'reason' in this connection." [p. 289]

Indeed, I might sing, "Joy to the World! logic has come", for I am joyful about logic. I realized something about my own attitude toward logic from the first two Star Trek series - that is, the original "Star Trek" and "Star Trek the Next Generation", specifically in comparing the characters of Mr. Spock and Mr. Data. They are two different takes on logic. Mr. Spock seemed the epitomy of logic until compared with Data. The difference is, that Mr. Spock is emotionally attached to logic - he is angered when people are illogical, while Data is simply perplexed when people are illogical. I am more like Spock, and I feel it is right to be joyful about logic, and angry about illogic.

To me, logic is a fundamental principle, along with truth and love. When the term "god" is defined as a person's highest guiding principles, I identify the trio of logic, truth and love as my god. I have noticed that each of these is sometimes identified with God in the first Christian writings, and this is one of my enduring consonances with the message of Jesus.

Logic did not, of course, originate with Jesus or the ancient Greeks nor even, I think, with humans. Though they did not, of course, express it in words, logic was being performed hundreds of millions of years ago, when a bottom-feeding creature first evolved eyes and saw another, larger, creature above it, with sharp teeth. I believe they quickly evolved the ability to realize this meant they would be eaten if they did not promptly hide. Recent experiments have shown more complex logical abilities in animals long recognized as intelligent, such as the ability to conclude an opaque box is empty, if an item has first been placed in it, and then later removed.

The first book that I know of on the topic of logic was written by Aristotle, but I was struck a week ago, listening to our reverend Barbara Meyers' sermon, that an excellent two-word definition of logic was given over a century before Aristotle by the Buddha. The second element of his "eight-fold way" is "right thinking", which is what logic is all about.

There is more to right thinking than the mathematical manipulation of symbols. I was also struck, a few weeks ago, in our reverend Joy Atkinson's class on the transcendental philosophers, when she cautioned us that when Ralph Waldo Emerson speaks of Reason he is speaking of Spirit and intuition, not reason or logic, which he calls understanding. Emerson is not the only thinker who has used these words in unexpected ways, and I believe it is because there is a close relationship between what we usually call "intuition" and the narrow meaning of "logic".

This can be illustrated from the history of mathematics. The Greek philosophers applied logic to mathematics quite zealously. Their greatest success in the use of logic was in geometry, culminating in the textbook Elements by Euclid, which was the standard text for millenia. However, one item in the Elements did disturb philosophers, logicians, and mathematicians. This was Euclid's "parallel postulate." It seemed more complex than a fundamental postulate should be. Many attempts to prove it from the other postulates failed. Eventually this failure led to the realization that other geometries than Euclidean are self-consistent, and potentially even relevant to our actual universe. This came about because mathematicians had the intuition that the parallel postulate was somehow different from the others, and they had the deductive ability to prove it.

I feel that intuition and formal logic are two aspects of the same thing, which ought to work together. Our intuition is better at discerning a problem, and our formal logic is better at solving problems. Another example can be seen in the excerpt above from Lewis Carroll's Through the Looking Glass. When presented with the White Queen's strange behavior and explanations, Alice's first response is to exclaim, "There's a mistake somewhere". Only later does she make the definitive objection, "One can't believe impossible things."

I might also liken formal logic to the intricate and precise relationships of the musical lines in a piece by Johann Sebastian Bach, yet such a piece also relies on the intuitive feeling of beauty of the melodies which are woven together. Similarly, from time to time in mathematics, a proposition long-proved will be blessed with a new proof, and the author praised for having accomplished the goal more beautifully.

Perhaps I've now held the suspence long enough about the fate of Elwood Dowd in the play Harvey. In the final scene a taxicab driver tries to get his tip in advance, and explains, "I've been drivin' this route fifteen years. I've brought 'em out here to get that stuff and drove 'em back after they had it. It changes 'em.... On the way out here they sit back and enjoy the ride. They talk to me. Sometimes we stop and watch the sunsets and look at the birds flyin'. Sometimes we stop and watch the birds when there ain't no birds and look at the sunsets when it's rainin'. We have a swell time and I always get a big tip. But afterward -- oh -- oh.... They crab, crab, crab. They yell at me to watch the lights, watch the brakes, watch the intersections. They scream at me to hurry. They got no faith -- in me or my buggy -- yet it's the same cab -- the same driver -- and we're goin' back over the very same road. It's no fun -- and no tips." [p. 69]

Veta Louise realizes, for the first time, what her choices actually are. Neither option is perfect, but she chooses Elwood, the mellow spreader of joy though delusional, over a potentially more sane but crabby and stingy version of Elwood.

The logical principle involved was well-stated by Charles Darwin, in the introduction to his Origin of Species as follows: "A fair result can be obtained only by fully stating and balancing the facts and arguments on both sides of each question."

It is very easy to fall into this error, especially when we are passionate for one alternative. I see this error committed almost compulsively in political debate. For example, in the current national health care reform debate, options are criticized mercelessly for every flaw, without any comparison to the status quo - without asking whether we are currently experiencing more and greater flaws.

Returning now to fictional plots, in the play, Dial M For Murder, by Frederick Knott, which Alfred Hitchcock made into a movie starring Grace Kelley, the inspector, investigating the killing of a captain Lesgate by Margot Wendice in her home, is quite careful to avoid the error Veta Louise fell into. He compares the possibility that the dead guy is the culprit with the possibility he is the victim. There is no sign of forced entry, as one would expect if he were a burglar who was killed in self defense. There is evidence that Margot was being blackmailed. In fact, her former lover was actually at a stag party with her husband at the very moment she kills the intruder. Margot is convicted of murder, it being apparent that the dead man knew about the affair and was blackmailing her. There is, however, one piece of evidence that still disturbs inspector Hubbard - there were no keys on the dead man. This does not seem to point either direction, in regard to the two possibilities, but is still unsettling. The inspector investigates further, and realizes the logical error -- there are actually more than two possibilities. The truth, that the husband is the culprit with both wife and intruder being victims, is proved when he is tricked into revealing that he knows where to find the missing key. The death is now seen to have been Margot's successful defense from an intricate murder plot concocted by her husband.

It may seem odd that I am deriving most of my examples about logic, whose function is to discern the truth, from fiction, but this too illustrates something about what logic is. Logic is a matter of the self-consistency of a story, not its truth, and this can be seen in the various translations of the Greek "logos", including "reason" and "account".

For example, Jesus' parables were examples of a logos, a logically self-consistent statement. It did not matter whether Jesus knew of an actual Samaritan who had cared for a victimized Jew. Probably there were many. What mattered was the possibility of the story, which pointed to an important moral conclusion. Similarly the plots I have drawn from in my examples illustrate their points whether or not the actual events occured. It is the function of other processes, including observation and science, to elucidate truth. Our values, expressed through our love, are yet a further matter. Logic restricts both of these, but it does not perform their functions.

Yet a third common logical error is committed by various characters in Guiseppi Verdi's comic opera, Gianni Schicchi, libretto by Giovacchino Forzano. The heirs of the wealthy Buoso Donati, frustrated and angry that he has left his fortune to a monastery, employ the clever but disreputable Gianni Schicchi to impersonate Donati and dictate a new will. All goes well, until Schicchi leaves most of the fortune to himself. Each of the heirs have assumed that Schicchi will steal from everyone else, but not from them. This is a foolish assumption when stated, which shows that most false assumption sneak in without the realization that an assumption is being made. While it is not a function of logic to tell the truth or falsehood of an assumption, it is a function of logic to analyze exactly what your assumptions are.

Though Gianni Schicchi does not satisfy the greed of Donati's family, he does provide for the fulfillment of love. His daughter, Lauretta, in love with Rinuccio Donati, now has the dowry which will enable her to marry him.

I would also not have you believe that logic is perfect. Let's follow the history of mathematics a bit further. Once mathematicians had become somewhat comfortable with non-Euclidean geometries, they forged ahead to found their logical edifice on set theory. Flaws were found in the logic, but a phalanx of thinkers set about correcting them. The ultimate product, entitled Principia Mathematica, was written by Alfred North Whitehead and Bertrand Russell and published in three volumes in 1910, 1912 and 1913. Further problems were fixed in a second edition in 1927. Had we finally proved, beyond a reasonable doubt, that two plus two is four? Alas for the seekers after absolute certaintly, in 1931 Kurt Goedel published an article entitled "On formally undecidable propositions of Principia Mathematica and related systems". Not only had he found a remaining flaw in the system, he had proved that you simply cannot prove everything that's true, even in a restricted subject such as arithmetic. As the second verse of "The Star of Truth," our hymn of reflection, states, "The certainty for which we crave, no mortal ones can ever know."

While logic is highly valuable, it is still not absolute or perfect. On the other hand, though it is not complete or perfect, the avoidance of logical fallacies is still highly advantageous.

We have recounted examples of three specific common logical fallacies, namely failure to compare all options with the same degree of care and criticism, failure to outline all the actual options, and failure to understand what assumptions one is making. While I do not offer you as complete a catalog of fallacies as even Aristotle listed, I would also like to warn you about such errors as: making unwarranted generalizations, engaging in circular reasoning, taking a disproof of the opposite as a proof of your proposition, shifting among the meanings of a word, argument ad hominum, which means assuming the value of a statement depends on the worth of the person making the statement, and, lastly, the non sequitur. This last, basically means, no logic at all. Just because someone says or writes something in the form of logic, that does not mean it actually is a logical argument.

One wishes to know, of course, where can we get this "right thinking" which we need in order to avoid logical fallacies. I hope I've shown how we can learn from works of fiction, as well as textbooks. Sometimes it's easier to learn from a negative example, and it's definitely better to encounter that negative example in fiction than in daily life. Our conversations and interactions with others are also important. We should purposely test our ideas and our contemplated actions by discussion with friends. But I believe these only refine our logical abilities. I believe, with the Buddha and many others, that the source is within us.

I conclude now, by saying again that logical fallacies may add significantly to the plot of a play, movie or opera, whether comic, dramatic or tragic, but our real lives usually benefit from avoiding them. Search inside yourselves for your guiding light, and develop your logical intellect.


Go in peace,
Go watch a play or movie,
Ask yourself what logical fallacies underly the plot,
Return more enlightened,
And return in love.

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