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fandomhigh2009-10-01 06:36 am
clevermsbennet.livejournal.com) wrote in fandomhigh2009-10-01 06:36 am
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Logic, Reason and Critical Thinking, Class 5: Period 4, Thursday, October 1
"Today, class," Miss Bennet said, cheerfully, "we shall be talking of two important principles of logical thinking, both of which discuss probability, but from opposite yet complementary viewpoints.
"The first is known as Occam's Razor. William of Ockham was a medieval philosopher and friar, from England in the fourteenth century. In one of his books, he stated, Numquam ponenda est pluralitas sine necessitate. For those of you who do not speak Latin, which I would imagine to be most of you, this translates, loosely, into, Plurality must not be posited without necessity. In this case, we are talking of reason and rationality. One should not introduce new elements or causations without good reason. The saying is frequently restated as The simplest answer is usually correct.
"For example, let us imagine that you return from class and discover that your fish-bowl has been overturned. There is water on the floor, your fish are missing, and your cat is wet. One solution suggests itself: your cat knocked over the fish-bowl and ate your fish. A second: there was a terrible earthquake, and your fish-bowl fell over; your cat tried to resuscitate the fish, but they crawled down his throat instead. A third: fairies flew into the room, abducted your fish, threw water onto your cat, and knocked the bowl over just to be horrid little creatures. Explanations two and three, while differing in their degree of absurdity, are both clearly impractical. They have added new elements -- an earthquake, roaming fairies -- as well as unlikely motivations -- your cat trying to help the beleaguered fish, and the fairies being mischievous for no discernible reason. Occam's razor suggests that one shave away the unnecessary and choose an answer that covers the facts as simply as possible. Which means one would presume Fluffy responsible for the crime in question.
"There are some important caveats, here. Let us start with the first one, which is that Ockham himself specified sine necessitate, without necessity. Elements can and should be added if they are required. If you left the cat locked in the bathroom before class, and Fluffy is now sleeping on your bed, your explanation must add in some element to account for that: a faulty lock, a sympathetic roommate. If there was a severe earthquake this morning, and all of your bookshelves are overturned, then the first half of theory number two improves considerably. Simplicity is good, but oversimplification is just as dangerous as adding rogue elements into a straightforward situation.
"The other is that Occam's razor is a suggestion. It is a heuristic, that is, a rule-of-thumb for examining and assessing the likelihood of events. Occam's razor does not ever say that the simplest answer is correct; only that it is usually the case that it is. It is far more likely that your cat upset the bowl and ate your fish, but it is not impossible that that was not the case. Perhaps there was a minor earthquake, or a sharp gust of wind. For that matter, we do live on this strange island; one cannot rule out the fairy theory out-of-hand.
"Which brings me to the other important principle, which would be the matter of black swans. It was considered a truism in Europe that all swans were white; black swans were used metaphorically to mean something that was impossible and ridiculous, the way fairies or unicorns might be. All of this changed in the seventeenth century, when a Dutch explorer named Willem de Vlamingh discovered swans in Australia that were jet black. Language is fluid, and the metaphor adapted with this new reality. "Black swans" were no longer impossibilities; they were now used to represent the idea that the highly improbable may, from time to time, come to pass.
"Occam's razor asks that we remember simplicity, and black swans remind us that the extraordinary and unthinkable do happen, in this strange world of ours. Even when one lives in a far more mundane reality than that which can be found on this particular island."
Miss Bennet finished talking, at last, and smiled at her students. "Before we begin today's discussion, I should like for all of you to know that I will be holding office hours this weekend. Parents and guardians are warmly invited to stop in for tea, as are any of you, yourselves."
"The first is known as Occam's Razor. William of Ockham was a medieval philosopher and friar, from England in the fourteenth century. In one of his books, he stated, Numquam ponenda est pluralitas sine necessitate. For those of you who do not speak Latin, which I would imagine to be most of you, this translates, loosely, into, Plurality must not be posited without necessity. In this case, we are talking of reason and rationality. One should not introduce new elements or causations without good reason. The saying is frequently restated as The simplest answer is usually correct.
"For example, let us imagine that you return from class and discover that your fish-bowl has been overturned. There is water on the floor, your fish are missing, and your cat is wet. One solution suggests itself: your cat knocked over the fish-bowl and ate your fish. A second: there was a terrible earthquake, and your fish-bowl fell over; your cat tried to resuscitate the fish, but they crawled down his throat instead. A third: fairies flew into the room, abducted your fish, threw water onto your cat, and knocked the bowl over just to be horrid little creatures. Explanations two and three, while differing in their degree of absurdity, are both clearly impractical. They have added new elements -- an earthquake, roaming fairies -- as well as unlikely motivations -- your cat trying to help the beleaguered fish, and the fairies being mischievous for no discernible reason. Occam's razor suggests that one shave away the unnecessary and choose an answer that covers the facts as simply as possible. Which means one would presume Fluffy responsible for the crime in question.
"There are some important caveats, here. Let us start with the first one, which is that Ockham himself specified sine necessitate, without necessity. Elements can and should be added if they are required. If you left the cat locked in the bathroom before class, and Fluffy is now sleeping on your bed, your explanation must add in some element to account for that: a faulty lock, a sympathetic roommate. If there was a severe earthquake this morning, and all of your bookshelves are overturned, then the first half of theory number two improves considerably. Simplicity is good, but oversimplification is just as dangerous as adding rogue elements into a straightforward situation.
"The other is that Occam's razor is a suggestion. It is a heuristic, that is, a rule-of-thumb for examining and assessing the likelihood of events. Occam's razor does not ever say that the simplest answer is correct; only that it is usually the case that it is. It is far more likely that your cat upset the bowl and ate your fish, but it is not impossible that that was not the case. Perhaps there was a minor earthquake, or a sharp gust of wind. For that matter, we do live on this strange island; one cannot rule out the fairy theory out-of-hand.
"Which brings me to the other important principle, which would be the matter of black swans. It was considered a truism in Europe that all swans were white; black swans were used metaphorically to mean something that was impossible and ridiculous, the way fairies or unicorns might be. All of this changed in the seventeenth century, when a Dutch explorer named Willem de Vlamingh discovered swans in Australia that were jet black. Language is fluid, and the metaphor adapted with this new reality. "Black swans" were no longer impossibilities; they were now used to represent the idea that the highly improbable may, from time to time, come to pass.
"Occam's razor asks that we remember simplicity, and black swans remind us that the extraordinary and unthinkable do happen, in this strange world of ours. Even when one lives in a far more mundane reality than that which can be found on this particular island."
Miss Bennet finished talking, at last, and smiled at her students. "Before we begin today's discussion, I should like for all of you to know that I will be holding office hours this weekend. Parents and guardians are warmly invited to stop in for tea, as are any of you, yourselves."