Logic

            "Logic" is a set of formal rules for examining ideas in order to determine whether they are true. Logic can be divided into two broad methods: deductive logic and inductive logic.

            Deductive logic reasons from statements about reality, called premises, to conclusions. Two or more premises may be combined in a syllogism to reach a conclusion.

            Deductive logic is often illustrated with the following example of a syllogism:

                        Premise 1: All men are mortal

                        Premise 2: Socrates is a man.

                        Conclusion: Therefore, Socrates is mortal.

             If the conclusion must follow from the premises - that is, if it is impossible for the premises to be true and the conclusion to be false - then the argument is valid. The above syllogism is valid because it's impossible for Socrates to be immortal if he is a man and if all men are mortal. Note that an argument being valid doesn't necessarily mean that its conclusion is true, only that it follows from the premises. It's possible to have a valid argument that's false:

                        Premise 1: All men are fish.

                        Premise 2: Socrates is a man.

                        Conclusion: Therefore, Socrates is a fish.

            The conclusion follows from the premises, so it's a valid argument. But premise one is false, so the conclusion is also false. It's important to remember that "valid" doesn't mean "true." Valid refers to the structure of an argument, not the truth of its premises or conclusion.

            To get conclusions that are true, an argument must be sound: it must both have true premises and be valid. Sound arguments always yield conclusions that are true.

            Common mistakes when constructing syllogisms are Affirming the Consequent and Denying the Antecedent. In an if-then statement, such as "If you are a man, then you are mortal," the antecedent follows "if," and the consequent follows "then."

Affirming the Consequent:

Premise 1: All men are mortal

Premise 2: My fish is mortal.

Conclusion: Therefore, my fish is a man.

            This argument affirms the consequent. Premise one says that if you are a man, then you are mortal. The argument mistakenly takes premise one to also say that if you are mortal, then you are a man. But, "If you are a man, then you are mortal," is not the same as, "If you are mortal, then you are a man." The mistake occurs when one takes the truth of the consequent, the "then" part of the statement, to mean that the antecedent, the "if" part of the statement, is also true. The "then" part of premise one says that "you are mortal," and this is true of my fish. The mistake is in thinking that the "if" part of premise one, "you are a man," is also true of my fish. It is a mistake because being mortal is an attribute of being a man, but being a man is not an attribute of being mortal. The consequent, being mortal, is dependent on the antecedent, being a man, but the antecedent is not dependent on the consequent. If you are a man, you must be mortal, but lots of things are mortal, so being mortal doesn't mean that you must be a man.

Denying the Antecedent:

Premise 1: All fish are mortal

Premise 2: Socrates is not a fish.

Conclusion: Therefore, Socrates is not mortal.

            This argument denies the antecedent. Premise one says that if you are a fish, then you are mortal. The argument mistakenly takes premise one to also say that if you are not a fish, you are not mortal. The mistake occurs when one takes the denial or falsehood of the antecedent to mean that the consequent is also false. "If you are a fish, then you are mortal," doesn't imply that, "If you are not a fish you are not mortal." It is a mistake because while if the antecedent is true, the consequent must be true, the falseness of the antecedent tells us nothing at all about the consequent. Knowing that something is not a fish tells us nothing at all about whether it's mortal. There may be many things that can cause the consequent. All we know is that the particular one described in the antecedent is not true. If you are a fish, then you are mortal, but lots of things are mortal, so not being a fish doesn't mean you're not mortal.

            Inductive logic is a method of reasoning in which an argument's premises show that the conclusion is probably true. Unlike deductive logic, where if the argument is sound, the conclusion must be true, in inductive logic even when the argument is sound, there is a possibility that the conclusion is false. Deductive logic takes the form, A and B, therefore C, while inductive logic takes the form, A and B, so probably C, too.

            Induction is used to make predictions about what is likely to be true based on our previous knowledge. Deduction reasons from the universal to the particular, from statements about all men to a statement about Socrates, a particular man. Induction extrapolates from the particular to the universal. We might look at Socrates and inductively come to conclusions about all men. The more evidence that points towards a conclusion, the stronger the inductive argument is and the more likely it is to be true. If we look at a hundred men, we can make better predictions about all men than if we only look at Socrates. Anything we see in Socrates might be peculiar to him, but if it is shared by a hundred other men, it is more likely that it is shared by all men. If we look at a million men, and the all share a feature, it is even more likely that it is shared by all men.

            I might make an inductive argument about the probability of my friend sharing his lunch:

1. Every time I've told my friend that I'm hungry, he offered to share his lunch.

2. If I tell him I'm hungry now, he'll probably offer to share his lunch.

            This is an inductive argument because the conclusion, while probable, is not certain. Perhaps today my friend is especially hungry, or perhaps I've offended him in some way, and so today he won't offer to share. But given that every other time I've told him I'm hungry, he offered to share his lunch, it's likely that he'll offer to share this time, too.

            The greater my experience, the more probable it is that my conclusion is correct. If my friend has offered to share two or three times, then his generosity in those instances may not be indicative of his usual behavior. If he has shared with me every day for the past year, then I can be pretty sure that he will share today, too.

            Most of science relies on inductive logic. If something is tested and we get the same result over and over, then we can be reasonably confident that we will always get that result. If it is tested by different people in different conditions and they also get the same result, then our confidence grows stronger. It's unlikely that the conclusion is false, but there is always the possibility that our conclusion will be overturned by new evidence that shows our inference was mistaken.

Book Review: Cut Me Loose

                I was in the library on Friday picking out books and was about to go to check out when I noticed "Cut Me Loose" sitting by itself at the end of a half-empty shelf. I took it out and read it over the weekend. It was not what I expected.

                I had some idea of what it was about, having read some reviews when it came out. I knew that the book chronicled Leah Vincent's journey away from the religion of her Yeshivish upbringing, and that part of that journey had included clashes with her family and ill-advised sexual encounters. I was expecting a story about how she had become disenchanted with her religious upbringing, had made some mistakes learning to integrate with general society, and had ultimately been successful in doing so. I was expecting to root for her against the forces of religious fundamentalism that had wronged and alienated so many of us. Instead, I found myself saddened by what Leah had experienced, but also sympathetic to the people around her who were dealing with a clearly unstable person.

                The book is well-written and engaging. I didn't want to put it down. The book is published by Doubleday and seems intended for a general audience, but there were many nuances that I think would be lost on someone who had never been a part of the Yeshivish community. Not because one had to be a part of the community to understand, but because these things weren't explained. Nor would it have been difficult or cumbersome to include explanations. Here and there, the author does explain. For instance, when she writes that her father was often invited to speak at the Agudah conventions, she adds that Agudah is a powerful Orthodox lobbying group. It's an addition of half a sentence that gives the reader context. Yet in many other places that addition is missing. For instance, she describes her brothers running up and down the stairs shouting Hebrew words (which she transliterates), but neglects to mention that they were singing a song (easily recognizable to anyone familiar with Jewish music of the era), instead leaving the impression that the little boys in her crazy religious family shouted Hebrew incantations while playing. In another place she describes having day-dreamed about having Rabbi Matisyahu Solomon officiate at her wedding, but neglects to explain his stature (easily done: "dean of the largest graduate-level Jewish school in the United States"), leaving a typical reader without any understanding of the daydream's significance.

                For much of the first half of the book, I felt angry as her family over reacted to her transgressions. She's banned from the post-high-school religious school of her choice when it's discovered she's been corresponding with a boy. Her parents cut off her allowance when she spends a month's worth of money on a borderline-immodest sweater. Her sister, who she is staying with, hides letters Leah's friend sends to her, and only pretends to mail the letters Leah writes. When she moves to New York, she can barely afford necessities on her minimum-wage income, and often goes without meals. When she calls her mother, desperate for help, her mother tells her to stop being so dramatic, and sends her only twenty dollars.

                As the book progresses, and she describes more and more of her dysfunctional behavior, I began to suspect that rather than the victim of circumstance and religious extremism her narrative implies, she was instead someone with a serious clinical disorder. I'm not qualified to make a diagnosis, and even if I were, you can't diagnose someone without having evaluated them in person, but what she describes seems like a textbook case of Borderline Personality Disorder (BPD). People who leave their religion are too often dismissed as unbalanced, and I'm loathe to perpetuate the stereotype, but in this case I think it may be accurate.

                The diagnostic criteria for BPD include: "A pervasive pattern of instability of interpersonal relationships, self-image, and affects, and marked impulsivity beginning by early adulthood and present in a variety of context."

                Leah's relationships with men, to which she devotes a lot of space, are highly unstable and frequently end abruptly. She often makes impulsive decisions with negative consequences, like blowing a month's worth of money on a sweater, going to a club and allowing a man to have sex with her on the dance floor, or suddenly deciding to stop eating.

                "Frantic efforts to avoid real or imagined abandonment."

                 Leah's narrative is one of constant abandonment, first by her family, then by her community, and then by the string of men she throws herself at in a desperate attempt to find self-worth in her sexuality.

                "A pattern of unstable and intense interpersonal relationships characterized by alternating between extremes of idealization and devaluation."

                This is an accurate description of Leah's relationships with her family and especially with her "boyfriends," each of whom is described as wonderful, life changing, and the love of her life while she is dating him, but is reduced to his basest traits as soon as they break up.

                "Impulsivity in at least two areas that are potentially self-damaging (e.g., spending, sex, Substance Abuse, reckless driving, binge eating)."

                She engages in impulsive, damaging sex on almost every page. Several times she describes impulsively spending money she needed for food or other necessities on things like the sweater mentioned above or high-priced cocktails at a bar. And sprinkled though the book are accounts of binge-eating in an attempt to control her emotions or fill an emotional emptiness.

                "Recurrent suicidal behavior, gestures, or threats, or self-mutilating behavior."

                Through much of the second half of the book Leah regularly cuts herself to relieve her psychological distress, and several times describes imagining killing herself, including an incident where she actually swallows a bottle of painkillers and another where she almost slashes her wrists, stopping only after she had already made a cut deep enough to leave a scar.

                "Chronic feelings of emptiness."

                Leah describes such feelings after her estrangement from her family. These feelings led her to constantly look for another man as each of her relationships failed, and, as mentioned above, she sometimes attempted to fill the emptiness with food.

                Leah recounts a childhood conversation with her mother in which her mother dismissed mental disorders as a scam dreamt up by pharmaceutical companies to sell drugs. Yet her father has claimed in a publicly published letter that Leah had been under the care of a psychiatrist since she was thirteen. I don't know which is the more accurate version of events, but if it is true that Leah has BPD, and that she has been treated since she was a young teenager, it implies a story very different than the one she is trying to tell.

                When her parents decide not to give her attention when she acts out, this is not an indication that they are cruel and distant. It is the reasonable (if perhaps mistaken) reaction of people who have for years been dealing with their daughter's destructive outbursts. Her mother dismissing her plea for help when she can't make ends meet isn't an indication that her mother is a callous and uncaring woman. It is the reaction of someone who is used to dramatic pronouncements and irresponsible behavior. Her description of her final encounter with her father, and his refusal to engage when she tearfully asks him why he cut her off and no longer expresses love is not an indication that he has tossed his daughter aside for small infractions of religious law. It is the reaction of a father who has long ago reached the end of his rope and is refusing to be dragged yet again into the toxic quagmire that experience has taught him engaging with his daughter inevitably leads to.

                I don't doubt that Leah's description of events is how she perceived them, and that she experienced them that way makes me sad for her. I want to go back in time and comfort the lonely, miserable girl she was. And yet, I can't help but think that if I could, it would be the beginning of yet another toxic relationship for her during which she would try to seduce me and build an ultimately destructive relationship if she was successful, or berate herself as disgusting undesirable garbage if she failed.

                At the end of the book, where in a few pages Leah describes how she finally turned her life around, got into Harvard, got married, and had a child, she mentions that her family still regards her as crazy and toxic. It's heavily implied that this is because she's no longer religiously observant. Maybe. Or maybe they regard her that way because, for most of her life, that's what she was.

History's Stories

                I think that history is often taught the wrong way. Kids learn history as unconnected chunks of stuff they have to memorize, as boring lists of names and dates - as stuff that happened once upon a time a long time ago.

                I recently read "The Last of the Doughboys" by Richard Rubins. The book is a history of the American involvement in WWI told through interviews with American veterans of the war. The author conducted the interviews in the early 2000s. One interview I found particularly interesting was done in 2003 with a man who was then 110 years old. He talked a bit about his experiences as a combat engineer in 1918, repairing railroads for the Allies and blowing up German bridges. He also talked about his parents, who had been born slaves in the antebellum south and had been married, as free people, just after the Civil War ended.

                My personal connection to history only goes back as far as the 1920s, to the depression in Germany after WWI. My grandfather often told the story of how he got a million marks for his birthday, and that was just enough money to buy a candy bar in the store around the corner. Yet in 2003, while I was in college, there was a man in this country who could remember his parents stories, the experiences of people who were adults when Lincoln was elected. I've been to a few Civil War battlefields. I've read the markers and looked at the memorials and cannon and tried to imagine what it was like to have been on those fields when those guns were firing. As recently as 2003, there was someone who could remember his parents telling him what it was like to wait for news of those battles.

                That's what history is - and how it should be taught. History is memories; the stories told by our parents and grandparents and great-grandparents. Anyone who could have talked to this man about his life would have listened to his stories. When people get together, that's what we do. We trade stories about our lives, about our personal histories. The older the stories and the more different than our own, the more interesting they are. People who found it boring to memorize who Lincoln and Davis were, to remember names and dates like Fort Sumter, 1861 and Appomattox Court House, 1865 would have found it easy and interesting to listen to this man talk about his parents.

                As a rule, the best histories are the ones that, like novels, focus on the experiences of a handful of main characters and tell the story of the events through their experiences. When history is, "This happened at this place to these people on this date, and then this happened to these people on this date, and then…" it's artificial and boring. When history is used as a tool for moralizing,  such as the apocryphal story about Washington and the cherry tree, it becomes a fairy tale: something that happened once upon a time a long time ago to story characters who aren't like us or anyone we know. When history is the stories people tell about themselves, their family and their friends it's real things that happened to real people, anecdotes that we would happily spend an afternoon trading with friends.

The Olden Days

                Steam shovels. Choo-choo trains. Horses and wagons. The stories of my childhood happened in Olden Days settings full of quaint technologies. The Little Engine that Could was a steam locomotive. The Berenstain Bears drove an old touring car. Even Mike Mulligan and his Steam Shovel, a book about an old technology becoming obsolete, was full of romantic elements of the Olden Days. Alongside pictures of rusting steam shovels put out of work by the shiny new gasoline and electric and diesel shovels were pictures of horse-drawn buggies, a milkman's cart, and a horse-drawn fire engine with a clanging bell.

                Stories from my own culture were even more removed from the reality I knew. These were invariably stories of life in the shtetle (the small rural towns of Eastern Europe), tales of rubles and poretzes and innkeepers. A ruble, I gathered, was some kind of money, and a poretz was a landlord who was mean just because. I had no notion of the transitions from slavery to serfdom to tenancy that had produced the social conditions of rural nineteenth-century Russia. Nor did I have any notion that these stories were limited in time and place, products of the accidents of history that had produced the Pale of Settlement. To me, all of it was the Olden Days: a blurry monolithic mass that encompassed everything that had happened before I was born.

                The stories in all my favorites books were set in some sort of Olden Days. The magical worlds of the fourteen Oz books, the Chronicles of Narnia, The Chestromanci books, the universe of The Five Children and It by E Nesbitt and Edward Eager's excellent imitation. The semi-magical worlds of the haunted mansion at Green Knowe and the anthropomorphized animals of the Redwall series. Historical fiction, like The Little House on the Prairie series. And the classics, Little Women, The Secret Garden, Tom Sawyer, Hans Brinker, and all the rest. All were set in the Olden Days.

                These stories were removed from mundane everyday life. In the Olden Days, anything was possible. I expected stories to happen in the magical past, and was mildly surprised when one was set in the present.

                I grew up, and I realized that there were no Olden Days, only earlier eras, populated by people not much different than me. Fantasy stories still occupied a world where anything was possible, but stories set in the real world had to conform to the same rules that I was subject to. It's one thing for Dorothy to travel by magical silver slippers. It's another for someone in the real world to magically travel to a far-away town.

                Mike Mulligan and his Steam Shovel was written in 1939, when steam shovels were fading into the past. When I was a kid, everything it described was part of the Olden Days. Not anymore. There are no more quaint steam shovels. Only backhoes.

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About Me

Mr. Shragy Lowenstein has been an active writer for over a decade. He has written numerous articles and blog posts on various forums and has published a non-fiction book. Readers have described him as, "erudite and insightful," and his writing as, "some of the most thoughtful, balanced, and intelligent," that they have read.