In this post, I'm going to give two more examples of Occam's Razor and how it functions in the world. Sometimes using it actually leads one into a false conclusion. Sometimes an inductive argument involves a chain of reasoning that creates a disagreement as to which conclusion is supported by it. In cases such as these, each participant in a dialogue or polemic or debate believes that his or her conclusion is made preferable because of Occam's Razor. Thus, Occam's Razor itself would need to be examined.
For my purposes, we'll keep things simple.
Many years ago, a movie directed by Robert Zemeckis was released in the United States. Castaway told the story of a Federal Express cargo plane that, after attempting to divert around a large storm, crashes in the middle of the ocean. Given the location of the crash and the nature of ocean currents, recovery of the wreckage would be difficult, while recovery of human remains would be almost impossible.
Now in the movie, the audience stays with the character who survives not only the initial crash and sinking fuselage, but also luckily drifts into a land mass that can support his continued survival. Because the camera remains with this character, we, the audience, know that he is still alive. But have you ever wondered what is happening to his family and friends who are back at home? Obviously, they are mourning, but it is important to ask: why are they mourning? Because they believe that someone they cared about died in a plane crash. Of course, we, the audience, know that the proposition:
There were no survivors in the Federal Express cargo plane that crashed into the middle of the ocean--is false.
Some of the crew did die. The pilot, for example, died and the co-pilot as well. They have families too. So let's think about how Occam's Razor might work to analyze these two different chains of reasoning.
Premise 1. It is very very unlikely that any person could survive a plane crashing into the middle of the ocean.
Premise 2. The pilot in Castaway was in plane that crashed into the middle of the ocean.
Thus,
3. It is very very unlikely that the pilot survived.
By applying Occam's Razor we should prefer the following conclusion.
4. In fact, it is so unlikely that the pilot survived that as a matter of fact he did not survive.
And it turns out that this conclusion: The pilot did not survive is true.
Occam's Razor leads us to a true conclusion.
Now let's look at a similar reasoning chain.
1. It is very very unlikely that any person could survive a plane crashing into the middle of the ocean.
2. The protagonist in Castaway was in a plane that crashed in the middle of the ocean.
Thus,
3. It is very very unlikely that the protagonist in Castaway survived.
Now here things go against Occam's Razor. Remember Occam's Razor tells us that we should not multiply the number of causes to explain an effect, or to explain a data set, and that when one chain of inductive reasoning includes fewer un-evidenced assumptions than a competing conclusion, the former should be preferred.
What un-evidenced assumptions do we need in order to move from #3 to the following:
#4. The protagonist in Castaway did in fact survive not only the initial impact of a plane crashing into the middle of the ocean but also the sinking fuselage. In fact, the protagonist in Castaway is alive four years after the plane crash because he washed ashore on an island that allowed him to procure sustenance and shelter.
We would need a lot of un-evidenced assumptions to get there. But the story gets even more unlikely as the movie goes on.
But let's just think about #4. Since empirical data has established that surviving a plane crash is very unlikely, the following assumption would be un-evidenced:
a: The protagonist in Castaway survived the plane crash.
Since empirical data has established that surviving a plane crash away from medical care is even less likely than surviving a plane crash near emergency services, it would be even less likely that a person would survive a plane crash in the middle of the ocean. Thus, anyone back on land who concluded that--The protagonist in Castaway is not dead--would need another un-evidenced assumption, namely,
b: After surviving the initial impact of the plane hitting the ocean, the protagonist in Castaway did not suffer a severe injury that ultimately killed him.
Then we would need another un-evidenced assumption, namely,
c: After not being seriously injured during the initial impact of the plane hitting the ocean, the protagonist in Castaway was carried to a land mass that included within it both food and shelter.
The list would go on for maybe a hundred independent un-evidenced assumptions, and yet it does't affect the truth of the conclusion above.
Now, most of us, if we were in the situation of the protagonist's family and friends would not believe assumptions a,b,c, etc. In fact, Occam's Razor forbids us from doing so. But unlike in the case of the pilot's death, using Occam's Razor for this reasoning chain would lead us to a false conclusion.
Even though Occam's Razor is a powerful tool to assess the merits of competing inductive reasoning chains, it is not invariably reliable.
Showing posts with label Inductive Reasoning. Show all posts
Showing posts with label Inductive Reasoning. Show all posts
Friday, March 22, 2013
Friday, March 8, 2013
Induction and Occam's Razor
When you make an inductive argument or you encounter one, what method do you use to decide whether to believe the conclusion it draws? This process of winnowing the wheat from the chaff, so to speak, happens automatically when we walk to the store or cook our dinner.
But when you need to assess two chains of inductive reasoning, each of which was produced by a reputable thinker and contain contradictory conclusions, the process of assessing the principles that both arguments employ becomes more important.
Generally, what inductive arguments are trying to accomplish is provide the best explanation for a certain data set. The data set could come from any academic discipline; it could come from our personal experiences of the world..
This data set could be statistical in nature e.g., American men between the ages of 45-49 suffer 28% more heart attacks than Japanese men between the ages of 45-49; it could be sensory in nature--sensory in many different respects, for example, during a trial a jury might here the following piece of data delivered by a defense attorney., "On the night in question, three independent witnesses testified under oath that they saw John Doe at the party when the crime was committed." Likewise, for a scientist, sensory data generated from an experiment needs to be explained: "Over the past five years, during my research in Madagascar on the ring tailed lemur, I have observed a decline in the number offspring produced each mating season."
The data set does not need to be what we might typically think of as a data set.
Our personal experiences include an endless series of observations that we interpret in an inductive way. When I look out my window in the morning and see snow on the ground, I, assuming I have no reason to doubt the reliability of my sense of sight will instantaneously explain that sensory data in terms of temperature, i.e., it's cold outside.
Why do I conclude that it is cold outside before I actually go outside and feel the temperature? Well, because snow is, generally speaking, frozen rain. And rain is water. And water is subject to the laws of nature. More or less, one of these laws of nature, dictates that water freezes at a temperature that I know from past experience is "cold."
Now, from a meteorologist's point of view, the sensory data of snow on the ground might involve a much more complex physical process, but despite the added complexity of his explanation, seeing snow on the ground, he too will conclude: it's cold outside.
So, continuing with our example, we have this set of data: I look out my window and see snow on the ground. I explain, in a basic and narrow sense, this data with the following conclusion: "It is cold outside." It all seems fairly automatic, no? But now let's complicate things.
Suppose you have a roommate who is science fiction fan, suppose he just read a science fiction novel about an alien invasion of earth. Suppose he, upon seeing you reach for your galoshes, says: "What are you doing that for?"
You slide your eyes askance, and tilt your head as if aiming a weapon. Since you've already had your morning coffee, you decide to spare his life. "Well, uhhh, it snowed last night and I don't want my feet to get cold on the way to class."
"It's not cold outside," your roommate assures you as he digs into his bowl of Lucky Charms with a fork.
"No?" Have the folks at General Mills started adding something extra to their cereals?Magically delicious, indeed! "There's snow on the ground. But it's not cold outside?"
"Actually that white stuff on the ground only looks like snow."
You feel your eye begin to itch. "Huh?"
You roommate sets his bowl on the counter top in order to gain access to a vaster array of gestures. "My theory," he whispers in conspiratorial tones, "is that last night. While we slept. An alien race, maybe from Epsilon Eridani, maybe from Gliese 876, visited the planet earth. What you see out the window is the evidence of their visit."
"Evidence? Of their visit?"
"Like the litter campers leave in Jellystone National Park. And its definitely not cold but has a temperature consistent with the ashes of dying campfire."
You consider correcting his malapropism directly but opt to murmur your correction as you search for your chap stick, " I thought Ranger Smith executed litterers."
At this point, your other roommate walks in. You can't help yourself. "Tell him. Let's see what Mike thinks about our competing explanations."
It might not seem like it at first but Mike must now perform a detailed evaluation of two competing explanations. The first explanation concludes that the snow on the ground outside is frozen water and that frozen water requires a certain temperature. That certain temperature is felt by human beings as "cold."
The second explanation concludes that the snow on the ground, despite its appearances, is not actually snow. It is litter left by a race of super intelligent alien beings. He further concludes that this litter is not cold but warm.
Why do I classify these two explanations as being in competition with one another? Well, because they both explain the data set and neither one involves a contradiction. After all, the roommates's explanation is possible, if it weren't possible, in a basic sense of the word then all those sci-fi movies that people love would not be so riveting. Think about it--has there ever been a movie about a person discovering a square with three sides?
So, even though it seems counterintuitive, both explanations do in fact explain the data set. In other words, each explanation offers an answer to the questions: What is the stuff I see outside my window? and What caused it to appear?
Now let's get back to Occam's razor (just so you know Occam's razor is also known as the law of parsimony). Here's how The Shorter OED defines it: "the principle that in explaining a thing no more assumptions should be made than are necessary."
Now what does this actually mean for those of us who must act in the real world? When we must decide whether or not to wear galoshes or sneakers, shorts or pants, a skull cap or a baseball cap?
It means that we should prefer the first explanation not the second one.
Now investing the time to count the number of assumptions a particular chain of inductive reasoning uses can be a tedious process--unless you happen to be a philosopher, in which case the activity is considered an ideal Friday night--but in the example above we don't need to be overly scrupulous. Take the following assumption (in logic an assumption is an unstated premise)
Assumption #1: There exists a race of super intelligent aliens.
The first explanation does not require the truth of this assumption. The second explanation does require it. Thus, in regard to Occam's razor, the first explanation is winning: 0-1.
Assumption #2: There exists a race of super intelligent aliens from Gliese 876 and Epsilon Eridani.
Assumption # 2 is different from assumption # 1, you see that right? After all, #1 could be true and #2 could be false. Thus, in regard to Occam's razor, the first explanation extends its lead 0-2.
Assumption #3: There exists a race of super intelligent aliens that litter.
0-3
Assumption #4: There exists a race of super intelligent aliens whose litter has an uncanny resemblance to frozen water that English-speaking earthlings have connoted snow
0-4
Assumption # 5: There exists a race of super intelligent aliens who would travel a long distance through space time for the purpose to silently drop its litter on another planet.
Assumption #5 is tough even for the Klingon faction to believe. I mean surely if aliens visit us one night, the ruckus will disrupt our sleep.
0-5.
Okay that's a sizable lead. At this stage in the contest, Jordan can grab a towel and ice his knees.
Both explanations have assumptions, but the roommate's explanation requires more assumptions, none of which, and this is key, none of which have any evidence to support their truth. Now, of course, we know that an absence of evidence is not, logically speaking, the same thing as evidence of absence. Every one of the roommate's assumptions could be true--even #5--but simply unknown to those of us on earth.
But whether or not the assumptions could true or false is not the issue.
The issue, according to Occam's razor, is that in the present moment we have no evidence to support any of those assumptions. Thus, when we evaluate the two chains of reasoning, when we examine the suggested explanation for each one, Occam's razor, provides a way for us to judge which is better, which we should believe. Sometimes Occam's razor is interpreted as a measure of simplicity. Such a conceptualization has some merit. When we look at the above example, one way to explain our preference for the first explanation is say "It is just simpler."
But when you need to assess two chains of inductive reasoning, each of which was produced by a reputable thinker and contain contradictory conclusions, the process of assessing the principles that both arguments employ becomes more important.
Generally, what inductive arguments are trying to accomplish is provide the best explanation for a certain data set. The data set could come from any academic discipline; it could come from our personal experiences of the world..
This data set could be statistical in nature e.g., American men between the ages of 45-49 suffer 28% more heart attacks than Japanese men between the ages of 45-49; it could be sensory in nature--sensory in many different respects, for example, during a trial a jury might here the following piece of data delivered by a defense attorney., "On the night in question, three independent witnesses testified under oath that they saw John Doe at the party when the crime was committed." Likewise, for a scientist, sensory data generated from an experiment needs to be explained: "Over the past five years, during my research in Madagascar on the ring tailed lemur, I have observed a decline in the number offspring produced each mating season."
The data set does not need to be what we might typically think of as a data set.
Our personal experiences include an endless series of observations that we interpret in an inductive way. When I look out my window in the morning and see snow on the ground, I, assuming I have no reason to doubt the reliability of my sense of sight will instantaneously explain that sensory data in terms of temperature, i.e., it's cold outside.
Why do I conclude that it is cold outside before I actually go outside and feel the temperature? Well, because snow is, generally speaking, frozen rain. And rain is water. And water is subject to the laws of nature. More or less, one of these laws of nature, dictates that water freezes at a temperature that I know from past experience is "cold."
Now, from a meteorologist's point of view, the sensory data of snow on the ground might involve a much more complex physical process, but despite the added complexity of his explanation, seeing snow on the ground, he too will conclude: it's cold outside.
So, continuing with our example, we have this set of data: I look out my window and see snow on the ground. I explain, in a basic and narrow sense, this data with the following conclusion: "It is cold outside." It all seems fairly automatic, no? But now let's complicate things.
Suppose you have a roommate who is science fiction fan, suppose he just read a science fiction novel about an alien invasion of earth. Suppose he, upon seeing you reach for your galoshes, says: "What are you doing that for?"
You slide your eyes askance, and tilt your head as if aiming a weapon. Since you've already had your morning coffee, you decide to spare his life. "Well, uhhh, it snowed last night and I don't want my feet to get cold on the way to class."
"It's not cold outside," your roommate assures you as he digs into his bowl of Lucky Charms with a fork.
"No?" Have the folks at General Mills started adding something extra to their cereals?Magically delicious, indeed! "There's snow on the ground. But it's not cold outside?"
"Actually that white stuff on the ground only looks like snow."
You feel your eye begin to itch. "Huh?"
You roommate sets his bowl on the counter top in order to gain access to a vaster array of gestures. "My theory," he whispers in conspiratorial tones, "is that last night. While we slept. An alien race, maybe from Epsilon Eridani, maybe from Gliese 876, visited the planet earth. What you see out the window is the evidence of their visit."
"Evidence? Of their visit?"
"Like the litter campers leave in Jellystone National Park. And its definitely not cold but has a temperature consistent with the ashes of dying campfire."
You consider correcting his malapropism directly but opt to murmur your correction as you search for your chap stick, " I thought Ranger Smith executed litterers."
At this point, your other roommate walks in. You can't help yourself. "Tell him. Let's see what Mike thinks about our competing explanations."
It might not seem like it at first but Mike must now perform a detailed evaluation of two competing explanations. The first explanation concludes that the snow on the ground outside is frozen water and that frozen water requires a certain temperature. That certain temperature is felt by human beings as "cold."
The second explanation concludes that the snow on the ground, despite its appearances, is not actually snow. It is litter left by a race of super intelligent alien beings. He further concludes that this litter is not cold but warm.
Why do I classify these two explanations as being in competition with one another? Well, because they both explain the data set and neither one involves a contradiction. After all, the roommates's explanation is possible, if it weren't possible, in a basic sense of the word then all those sci-fi movies that people love would not be so riveting. Think about it--has there ever been a movie about a person discovering a square with three sides?
So, even though it seems counterintuitive, both explanations do in fact explain the data set. In other words, each explanation offers an answer to the questions: What is the stuff I see outside my window? and What caused it to appear?
Now let's get back to Occam's razor (just so you know Occam's razor is also known as the law of parsimony). Here's how The Shorter OED defines it: "the principle that in explaining a thing no more assumptions should be made than are necessary."
Now what does this actually mean for those of us who must act in the real world? When we must decide whether or not to wear galoshes or sneakers, shorts or pants, a skull cap or a baseball cap?
It means that we should prefer the first explanation not the second one.
Now investing the time to count the number of assumptions a particular chain of inductive reasoning uses can be a tedious process--unless you happen to be a philosopher, in which case the activity is considered an ideal Friday night--but in the example above we don't need to be overly scrupulous. Take the following assumption (in logic an assumption is an unstated premise)
Assumption #1: There exists a race of super intelligent aliens.
The first explanation does not require the truth of this assumption. The second explanation does require it. Thus, in regard to Occam's razor, the first explanation is winning: 0-1.
Assumption #2: There exists a race of super intelligent aliens from Gliese 876 and Epsilon Eridani.
Assumption # 2 is different from assumption # 1, you see that right? After all, #1 could be true and #2 could be false. Thus, in regard to Occam's razor, the first explanation extends its lead 0-2.
Assumption #3: There exists a race of super intelligent aliens that litter.
0-3
Assumption #4: There exists a race of super intelligent aliens whose litter has an uncanny resemblance to frozen water that English-speaking earthlings have connoted snow
0-4
Assumption # 5: There exists a race of super intelligent aliens who would travel a long distance through space time for the purpose to silently drop its litter on another planet.
Assumption #5 is tough even for the Klingon faction to believe. I mean surely if aliens visit us one night, the ruckus will disrupt our sleep.
0-5.
Okay that's a sizable lead. At this stage in the contest, Jordan can grab a towel and ice his knees.
Both explanations have assumptions, but the roommate's explanation requires more assumptions, none of which, and this is key, none of which have any evidence to support their truth. Now, of course, we know that an absence of evidence is not, logically speaking, the same thing as evidence of absence. Every one of the roommate's assumptions could be true--even #5--but simply unknown to those of us on earth.
But whether or not the assumptions could true or false is not the issue.
The issue, according to Occam's razor, is that in the present moment we have no evidence to support any of those assumptions. Thus, when we evaluate the two chains of reasoning, when we examine the suggested explanation for each one, Occam's razor, provides a way for us to judge which is better, which we should believe. Sometimes Occam's razor is interpreted as a measure of simplicity. Such a conceptualization has some merit. When we look at the above example, one way to explain our preference for the first explanation is say "It is just simpler."
Friday, March 1, 2013
Induction as Scientific Investigation: An Attempt
In my last post, I wrote about a certain kind of inductive argument. Appealing to the authority of a legitimate expert is a common way we construct arguments. All of us rely on this kind of argument to make decisions about all sorts of issues: who to vote for, which charity to contribute to, which movie to see, which book to read, which college to attend, and so on.
For this post, I'm still going to write about inductive reasoning, but I'm going to connect it, as best as I can, to the scientific enterprise. You've probably heard of the Scientific Method before. When considered as a method of reasoning, the Scientific Method is an empirical form of inductive reasoning.
A scientist's curiosity (I guess, given human history, an aspiring scientist's curiosity would be just as dynamic. After all, before Einstein won his Nobel Prize for Physics, he was a Swiss patent clerk wondering what would happen if a person were to travel at the speed of light.) is piqued. Suppose our wondering scientist works as a zoologist at Lincoln Park Zoo.
"I wonder," the scientist might say to herself after watching a late-night showing of Stand by Me, "if non-human mammals can experience "friendship" either within their own species or outside of it?" (This was the subject of a recent episode of Nature. If anyone is interested, here is the link: http://www.pbs.org/wnet/nature/episodes/animal-odd-couples/full-episode/8009/
The zoologist would then go beyond mere wondering. She would create a hypothesis and then create an experiment to test her hypothesis. In the Nature episode, the zoologist closely observed a troop of macaques and then would test their feces for a chemical, I think it was cortisol, that is released when a macaque experiences stress. Thus, there would be two fundamental sets of data for the zoologist to analyze.
The behavior of the macaques, in particular behavior that indicated "friendship" would be one set of data. For example, macaques groom each other. Thus, grooming might indicate "trust" between two macaques.
The level of cortisol would be the second set of data.
Even before the zoologist examines her data sets, she has performed thousands of inductive reasoning chains. Most of these inductive reasoning chains involve the following basic structure:
X has happened repeatedly in the past, thus X will continue to happen in the future e.g.,
-In the past, the sun has always risen in the East; thus the sun will rise in the East tomorrow.
-For the past 10,000 years , the tropical island (I think it was Costa Rica) that the macaques live on has not experienced a blizzard; thus, the tropical island that the macaques will not experience a blizzard during the zoologist's research
-For the past 1000 years, most of the members of a troop of macaques in Costa Rica have not died simultaneously from natural causes; thus, most of the members of the troop of macaques she observes on a Monday will still be alive on Tuesday.
-For as long as macaques have inhabited Costa Rica, they have pooped. Thus, macaques will continue to poop in the future.
-In the past, other scientific research has established beyond a reasonable doubt that cortisol is a chemical that is released by macaques when they experience stress; thus, in the future, when a macaque is experiencing stress, its body will release cortisol.
In the past, other scientific research has establish beyond a reasonable doubt that zoologist's can accurately measure the amount of cortisol in a macaques body, thus in the future, when a zoologist measures the amount of cortisol in a macaques' body it will be accurate.
And so on.
Once the two sets of data have been collected, it will carefully examined. The zoologist will see if a correlation exists between, say, lower levels of cortisol and number of grooming events.
Suppose, for the sake of simplicity, there were a 100 macaques in the troop that our zoologist was observing. Suppose further that the 10 macaques that participated in the most grooming events had much lower levels of cortisol in their bodies. Here the zoologist would produce an inference to explain the data.
1. "During my observations of macaque troop #1, I observed 10,000 grooming events."
2. "For the purposes of my experiment, each "grooming event" will be interpreted as indicating an episode of "monkey-trust" between two macaques."
3. "For the purpose of my experiment, each episode of "monkey-trust" will be interpreted as indicating evidence for a macaque's ability to experience "monkey-friendship."
Assumption 1: "Experiencing less stress gives any mammal an evolutionary advantage to survive and procreate."
Assumption 2: "Monkey-friendship is analogous to human friendship in that it reduces the amount of stress the body produces."
Assumption 3: "If a pair of macaques experience "monkey-friendship," then that pair of macaques will each experience less stress than a macaque that does not experience "monkey-friendship."
Hypothesis 1: "If a pair of macaques experience "monkey-friendship," then each of those macaques will produce lower levels of cortisol than any macaque that does not experience "monkey-friendship."
Hypothesis 2:"If hypothesis 1 is true, then macaques can experience friendship in a way analogous to the way that human's experience friendship."
Conclusion: "The macaques that participated in the most "grooming events" had the lowest levels of cortisol, thus macaques do experience friendship analogously to humans."
Now here things may get a little confusing. In fact, this entire reasoning process as its stated above is deductive. If the premises and the assumptions and the hypothesis are all true, then the conclusion would also be true.
But every one of the premises and assumptions and hypothesis would itself rely on an inductive argument. For example, (2) simply stipulates that "grooming events" will be "interpreted" in a certain way. But why think that "grooming events" should be interpreted in this way? Well, by way of induction, a grooming event would seem to more consonant with an explanation that postulate "trust" than one that postulate "dominance," but no one can be sure this intuitive relationship actually holds.
Thus, the beauty and the curse of inductive reasoning.
For this post, I'm still going to write about inductive reasoning, but I'm going to connect it, as best as I can, to the scientific enterprise. You've probably heard of the Scientific Method before. When considered as a method of reasoning, the Scientific Method is an empirical form of inductive reasoning.
A scientist's curiosity (I guess, given human history, an aspiring scientist's curiosity would be just as dynamic. After all, before Einstein won his Nobel Prize for Physics, he was a Swiss patent clerk wondering what would happen if a person were to travel at the speed of light.) is piqued. Suppose our wondering scientist works as a zoologist at Lincoln Park Zoo.
"I wonder," the scientist might say to herself after watching a late-night showing of Stand by Me, "if non-human mammals can experience "friendship" either within their own species or outside of it?" (This was the subject of a recent episode of Nature. If anyone is interested, here is the link: http://www.pbs.org/wnet/nature/episodes/animal-odd-couples/full-episode/8009/
The zoologist would then go beyond mere wondering. She would create a hypothesis and then create an experiment to test her hypothesis. In the Nature episode, the zoologist closely observed a troop of macaques and then would test their feces for a chemical, I think it was cortisol, that is released when a macaque experiences stress. Thus, there would be two fundamental sets of data for the zoologist to analyze.
The behavior of the macaques, in particular behavior that indicated "friendship" would be one set of data. For example, macaques groom each other. Thus, grooming might indicate "trust" between two macaques.
The level of cortisol would be the second set of data.
Even before the zoologist examines her data sets, she has performed thousands of inductive reasoning chains. Most of these inductive reasoning chains involve the following basic structure:
X has happened repeatedly in the past, thus X will continue to happen in the future e.g.,
-In the past, the sun has always risen in the East; thus the sun will rise in the East tomorrow.
-For the past 10,000 years , the tropical island (I think it was Costa Rica) that the macaques live on has not experienced a blizzard; thus, the tropical island that the macaques will not experience a blizzard during the zoologist's research
-For the past 1000 years, most of the members of a troop of macaques in Costa Rica have not died simultaneously from natural causes; thus, most of the members of the troop of macaques she observes on a Monday will still be alive on Tuesday.
-For as long as macaques have inhabited Costa Rica, they have pooped. Thus, macaques will continue to poop in the future.
-In the past, other scientific research has established beyond a reasonable doubt that cortisol is a chemical that is released by macaques when they experience stress; thus, in the future, when a macaque is experiencing stress, its body will release cortisol.
In the past, other scientific research has establish beyond a reasonable doubt that zoologist's can accurately measure the amount of cortisol in a macaques body, thus in the future, when a zoologist measures the amount of cortisol in a macaques' body it will be accurate.
And so on.
Once the two sets of data have been collected, it will carefully examined. The zoologist will see if a correlation exists between, say, lower levels of cortisol and number of grooming events.
Suppose, for the sake of simplicity, there were a 100 macaques in the troop that our zoologist was observing. Suppose further that the 10 macaques that participated in the most grooming events had much lower levels of cortisol in their bodies. Here the zoologist would produce an inference to explain the data.
1. "During my observations of macaque troop #1, I observed 10,000 grooming events."
2. "For the purposes of my experiment, each "grooming event" will be interpreted as indicating an episode of "monkey-trust" between two macaques."
3. "For the purpose of my experiment, each episode of "monkey-trust" will be interpreted as indicating evidence for a macaque's ability to experience "monkey-friendship."
Assumption 1: "Experiencing less stress gives any mammal an evolutionary advantage to survive and procreate."
Assumption 2: "Monkey-friendship is analogous to human friendship in that it reduces the amount of stress the body produces."
Assumption 3: "If a pair of macaques experience "monkey-friendship," then that pair of macaques will each experience less stress than a macaque that does not experience "monkey-friendship."
Hypothesis 1: "If a pair of macaques experience "monkey-friendship," then each of those macaques will produce lower levels of cortisol than any macaque that does not experience "monkey-friendship."
Hypothesis 2:"If hypothesis 1 is true, then macaques can experience friendship in a way analogous to the way that human's experience friendship."
Conclusion: "The macaques that participated in the most "grooming events" had the lowest levels of cortisol, thus macaques do experience friendship analogously to humans."
Now here things may get a little confusing. In fact, this entire reasoning process as its stated above is deductive. If the premises and the assumptions and the hypothesis are all true, then the conclusion would also be true.
But every one of the premises and assumptions and hypothesis would itself rely on an inductive argument. For example, (2) simply stipulates that "grooming events" will be "interpreted" in a certain way. But why think that "grooming events" should be interpreted in this way? Well, by way of induction, a grooming event would seem to more consonant with an explanation that postulate "trust" than one that postulate "dominance," but no one can be sure this intuitive relationship actually holds.
Thus, the beauty and the curse of inductive reasoning.
Friday, February 22, 2013
Induction and Writing Papers
In my previous blog post, I made a sincere, if imperfect, effort to draw some basic distinctions between deductive and inductive reasoning. Although deductive reasoning is an essential part of our cognitive framework, much of the reasoning we do when we write essays or research papers is inductive. A key part of completing many writing assignments, not to mention an infinite number of non-writing tasks, is to generate and defend conclusions based on the words or the testimony of an expert.
Obviously, the concept of "expertise" is complex. When does a person become an expert in some field? How do we decide when to bestow that title on an "expert?"
To give an example of this complexity, consider the legal career of Thurgood Marshall. I would imagine that most people presume that a lawyer is an expert on the law because of the education that he completed. Colloquially speaking, the concept of "education" would basically reduce to the following two questions:
"When did you graduate from law school?"
"What law school did you graduate from?"
Thurgood Marshall earned his Juris Doctor from Howard University Law School in 1933, graduating first in his class. He then went on to become the first African American appointed to The United States Supreme Court. It's an impressive resume, isn't it?
While every lawyer doesn't have such a sterling profile, most of us assume that a person who earns a Juris Doctor degree from an American Bar Association accredited law school is an "expert" about, if not the entire American Legal Code, then at least some particular aspect of it. One lawyer could be an expert on the criminal legal code; another lawyer could be an expert on the U.S. Constitution. Thurgood Marshall, being a Supreme Court justice, would be an expert on both the criminal legal code and on the U.S. Constitution.
The point is that if I'm writing an essay in my composition class about the FCC and its policies toward censoring the f-word on the public airwaves, I would, if he were still alive, ask Thurgood Marshall for his assessment of the issue. The answers he articulates for me would provide a well-forged link in my reasoning chain. The link would be well-forged because, as an expert in the U.S. Constitution, Thurgood Marshall would have knowledge about it that can trusted by all reasonable non-legal experts.
My reasoning chain might be constructed in the following way:
1. Some people believe that XYZ is true about the First Amendment
2. Thurgood Marshall believes that X is true and Y is true about the First Amendment, but he disputes that Z is true.
3. Thurgood Marshall is an expert about the First Amendment.
4. Thus, I have a good reason to doubt the truth of Z.
In the same way that a lawyer is an expert on certain legal topics, someone with a Ph.D. in particular academic discipline would be an expert in that discipline. This is why many of your professors want you to consider the author of text when you look for research sources. The author of a book or the author of a peer reviewed academic journal probably has a Ph.D. in a particular field thus we can justifiably assume that he/she is an expert in that field. Appealing to that expert's authority to justify a conclusion is an acceptable way to construct a chain of reasoning.
Complexity will almost always arise when you write a paper. For example, what happens when two experts disagree? When experts disagree, it actually allows you to carefully consider each person's position and then ask yourself which one is the more cogent. If you're writing a paper about Psychology, obviously the research (its methodology, for example) would be a good place to consider which expert you find more persuasive.
Of course, there are ways for a person to achieve expertise in a particular discipline without earning an advanced degree. For example, while a person could become an expert in journalism by earning a Ph.D in Journalism, there are many professional journalists who attain expertise on a topic by carefully researching a topic as an employee for a news organization like The New York Times or PBS.
If a journalist from The New York Times spends six months writing a series of feature length articles about the pros and cons of hydraulic fracking, many of us would justifiably consider that journalist, if not an "expert," then certainly someone who's opinion about hydraulic fracking is more informed, more nuanced than, say, the owner of my local Seven Eleven.
The journalist's stories become reliable sources because of the expertise he/she has achieved. When you write an argumentative paper, you might appeal to the journalist's authority about hydraulic fracking to make your case. When you appeal to a relevant authority in an argument, you are arguing inductively.
All this talk about becoming an expert or achieving an expertise is relevant because most of our inductive arguments rely on the authority of experts. Much of the article by the journalist in The New York Times will be quotes and paraphrases from experts in geology and petroleum engineering. The article will also probably include the testimony from people who've been deeply affected by agreeing to lease their land to a natural gas drilling company.
In this sense, whatever the journalist concludes, his/her reasoning will be inductive in nature.
To give an example of this complexity, consider the legal career of Thurgood Marshall. I would imagine that most people presume that a lawyer is an expert on the law because of the education that he completed. Colloquially speaking, the concept of "education" would basically reduce to the following two questions:
"When did you graduate from law school?"
"What law school did you graduate from?"
Thurgood Marshall earned his Juris Doctor from Howard University Law School in 1933, graduating first in his class. He then went on to become the first African American appointed to The United States Supreme Court. It's an impressive resume, isn't it?
While every lawyer doesn't have such a sterling profile, most of us assume that a person who earns a Juris Doctor degree from an American Bar Association accredited law school is an "expert" about, if not the entire American Legal Code, then at least some particular aspect of it. One lawyer could be an expert on the criminal legal code; another lawyer could be an expert on the U.S. Constitution. Thurgood Marshall, being a Supreme Court justice, would be an expert on both the criminal legal code and on the U.S. Constitution.
The point is that if I'm writing an essay in my composition class about the FCC and its policies toward censoring the f-word on the public airwaves, I would, if he were still alive, ask Thurgood Marshall for his assessment of the issue. The answers he articulates for me would provide a well-forged link in my reasoning chain. The link would be well-forged because, as an expert in the U.S. Constitution, Thurgood Marshall would have knowledge about it that can trusted by all reasonable non-legal experts.
My reasoning chain might be constructed in the following way:
1. Some people believe that XYZ is true about the First Amendment
2. Thurgood Marshall believes that X is true and Y is true about the First Amendment, but he disputes that Z is true.
3. Thurgood Marshall is an expert about the First Amendment.
4. Thus, I have a good reason to doubt the truth of Z.
In the same way that a lawyer is an expert on certain legal topics, someone with a Ph.D. in particular academic discipline would be an expert in that discipline. This is why many of your professors want you to consider the author of text when you look for research sources. The author of a book or the author of a peer reviewed academic journal probably has a Ph.D. in a particular field thus we can justifiably assume that he/she is an expert in that field. Appealing to that expert's authority to justify a conclusion is an acceptable way to construct a chain of reasoning.
Complexity will almost always arise when you write a paper. For example, what happens when two experts disagree? When experts disagree, it actually allows you to carefully consider each person's position and then ask yourself which one is the more cogent. If you're writing a paper about Psychology, obviously the research (its methodology, for example) would be a good place to consider which expert you find more persuasive.
Of course, there are ways for a person to achieve expertise in a particular discipline without earning an advanced degree. For example, while a person could become an expert in journalism by earning a Ph.D in Journalism, there are many professional journalists who attain expertise on a topic by carefully researching a topic as an employee for a news organization like The New York Times or PBS.
If a journalist from The New York Times spends six months writing a series of feature length articles about the pros and cons of hydraulic fracking, many of us would justifiably consider that journalist, if not an "expert," then certainly someone who's opinion about hydraulic fracking is more informed, more nuanced than, say, the owner of my local Seven Eleven.
The journalist's stories become reliable sources because of the expertise he/she has achieved. When you write an argumentative paper, you might appeal to the journalist's authority about hydraulic fracking to make your case. When you appeal to a relevant authority in an argument, you are arguing inductively.
All this talk about becoming an expert or achieving an expertise is relevant because most of our inductive arguments rely on the authority of experts. Much of the article by the journalist in The New York Times will be quotes and paraphrases from experts in geology and petroleum engineering. The article will also probably include the testimony from people who've been deeply affected by agreeing to lease their land to a natural gas drilling company.
In this sense, whatever the journalist concludes, his/her reasoning will be inductive in nature.
Friday, February 15, 2013
Deductive Vs. Inductive Reasoning
The spring semester has brought with it new challenges for us writing center consultants. Aside from trying to stay healthy during a merciless flu season, many of us are moving to the classroom as teaching apprentices. A couple weeks ago, I discovered, during two separate conversations with two different colleagues, that they would soon be giving a lecture explaining the difference between deductive and inductive reasoning.
After discussing with each colleague his/her teaching strategy, I asked myself how I might distinguish deductive reasoning from inductive reasoning, then I asked myself how I might give this information to a freshman composition student. This blog post will be the abbreviated version of my cerebral labors.
Let me begin by asking you a question: What can you conclude from the following two premises?
1. All men are mortal.
2. Socrates is a man.
I would imagine many of you have seen these two premises before. Lots of introductory philosophy or critical reasoning books include this example to illustrate the features of a valid chain of deductive reasoning.
Now if we assume that (1) and (2) are true, we can conclude--conclude without any doubt, without any qualification the following:
3. Socrates is mortal.
Part of what makes deductive reasoning distinct from inductive reasoning is that first premise. How many men does it say are mortal? All of them. And given the fact that (1) and (2) are related to each other in a specific linguistic way, and given the fact that we are assuming both to be true, the conclusion is guaranteed to be true. In other words, if (1) and (2) are true, then it is impossible for (3) to be false. In a world full of doubt and uncertainty, a sound deductive argument is a bastion of knowledge.
Other kinds of deductive reasoning move from some universal statement to a particular one. The valid forms of such reasoning chains would be called syllogisms.
Here is another example:
4. No book on my shelf has a pinstriped cover.
5. Catch-22 is a book on my shelf.
Therefore,
6. Catch-22 does not have a pinstriped cover.
(6) is entailed by (4) and (5). Part of what makes this chain of reasoning deductive is the content of (4). How many books on my shelf have a pinstriped cover? That's right, none of them. To show how (1) and (4) effect the nature of the reasoning chain lets slight modify these two examples.
1* 99 percent of men are mortal.
2* Socrates is a man.
Now if we assume that both 1* and 2* are true, what can we conclude? Or maybe the better question is to ask, what can't we conclude?
Because 1* is probabilistic, because it leaves that 1% of men floating around who could be immortal, even if both 1* and 2* are true, we would not be able to conclude, for certain, that "Socrates is mortal."
Instead, what we could cogently conclude would be something like, "It is very very probable that Socrates is mortal." Or maybe, to express the same basic idea in a different way, we could conclude, "Any rational person would believe that Socrates is, in fact, mortal." Even if both 1* and 2* are true, the conclusion "Socrates is mortal" might still be false, thus this chain of reasoning would not be deductive.
Let's look at our second modified argument:
4*Out of 250 books on my shelf 249 do not have a pinstriped cover.
5*Catch-22 is a book on my shelf.
4* gives information about the number of books on my shelf--I have 250 books on my shelf.
4* also gives information about a characteristic that 249 of the books do not possess--a pinstriped cover.
But even if 4* and 5* are true, it is still possible that 6* "Catch-22 does not have a pinstriped cover" is false. Maybe it's the one book that actually has a pinstriped cover. For those of you who believe that you've seen the cover of Catch-22 and know that it doesn't have a pinstriped cover, my edition is very special. So special, in fact, there is only one in existence. Since it's so special, I've never shown it to anyone, thus no one, at least no one who hasn't had some supernatural assistance, could possibly know about the features of its cover.
Just like in the other example, most of us would believe, given the truth of 4* and 5* that Catch-22 does not have a pinstriped cover" is true, but since the truth of the premises do not guarantee the truth of the conclusion, it would be an inductive chain of reasoning, not a deductive one.
To sum up some of what I've tried to illustrate with the above examples, a chain of deductive reasoning includes a couple of key features that are distinct from a chain of inductive reasoning. The first one is that, in a deductive chain of reasoning, if the premises are true, then the conclusion must also be true. A chain of inductive reasoning does not, even if its premises are true, entail the conclusion. The second one is that all the valid syllogistic forms (all of which contain a universal modifier like All or No) use a deductive chain of reasoning to draw their conclusions.
If you see a valid argument that contains only premises that itself includes either the term All or No, without some qualifying distinction, (For example, in the following proposition: All the penguins that have ever been seen by human beings..., the part in bold print qualifies the All), then it will be using a deductive chain of reasoning.
On the other hand, an inductive chain of reasoning will base its premises on a series of observations that will always fall short of universality. It's for this reason that, powerful as it may be, the scientific method only generates conclusions through a chain of reasoning that is inductive. Because a set of data collected by human observation will always be qualified by the natural limitations of either human faculties or the instruments we create, the conclusions generated by the scientific method are always inductive.
Induction and deduction are both essential ways of reasoning. In all honesty, we would be lost without either one.
After discussing with each colleague his/her teaching strategy, I asked myself how I might distinguish deductive reasoning from inductive reasoning, then I asked myself how I might give this information to a freshman composition student. This blog post will be the abbreviated version of my cerebral labors.
Let me begin by asking you a question: What can you conclude from the following two premises?
1. All men are mortal.
2. Socrates is a man.
I would imagine many of you have seen these two premises before. Lots of introductory philosophy or critical reasoning books include this example to illustrate the features of a valid chain of deductive reasoning.
Now if we assume that (1) and (2) are true, we can conclude--conclude without any doubt, without any qualification the following:
3. Socrates is mortal.
Part of what makes deductive reasoning distinct from inductive reasoning is that first premise. How many men does it say are mortal? All of them. And given the fact that (1) and (2) are related to each other in a specific linguistic way, and given the fact that we are assuming both to be true, the conclusion is guaranteed to be true. In other words, if (1) and (2) are true, then it is impossible for (3) to be false. In a world full of doubt and uncertainty, a sound deductive argument is a bastion of knowledge.
Other kinds of deductive reasoning move from some universal statement to a particular one. The valid forms of such reasoning chains would be called syllogisms.
Here is another example:
4. No book on my shelf has a pinstriped cover.
5. Catch-22 is a book on my shelf.
Therefore,
6. Catch-22 does not have a pinstriped cover.
(6) is entailed by (4) and (5). Part of what makes this chain of reasoning deductive is the content of (4). How many books on my shelf have a pinstriped cover? That's right, none of them. To show how (1) and (4) effect the nature of the reasoning chain lets slight modify these two examples.
1* 99 percent of men are mortal.
2* Socrates is a man.
Now if we assume that both 1* and 2* are true, what can we conclude? Or maybe the better question is to ask, what can't we conclude?
Because 1* is probabilistic, because it leaves that 1% of men floating around who could be immortal, even if both 1* and 2* are true, we would not be able to conclude, for certain, that "Socrates is mortal."
Instead, what we could cogently conclude would be something like, "It is very very probable that Socrates is mortal." Or maybe, to express the same basic idea in a different way, we could conclude, "Any rational person would believe that Socrates is, in fact, mortal." Even if both 1* and 2* are true, the conclusion "Socrates is mortal" might still be false, thus this chain of reasoning would not be deductive.
Let's look at our second modified argument:
4*Out of 250 books on my shelf 249 do not have a pinstriped cover.
5*Catch-22 is a book on my shelf.
4* gives information about the number of books on my shelf--I have 250 books on my shelf.
4* also gives information about a characteristic that 249 of the books do not possess--a pinstriped cover.
But even if 4* and 5* are true, it is still possible that 6* "Catch-22 does not have a pinstriped cover" is false. Maybe it's the one book that actually has a pinstriped cover. For those of you who believe that you've seen the cover of Catch-22 and know that it doesn't have a pinstriped cover, my edition is very special. So special, in fact, there is only one in existence. Since it's so special, I've never shown it to anyone, thus no one, at least no one who hasn't had some supernatural assistance, could possibly know about the features of its cover.
Just like in the other example, most of us would believe, given the truth of 4* and 5* that Catch-22 does not have a pinstriped cover" is true, but since the truth of the premises do not guarantee the truth of the conclusion, it would be an inductive chain of reasoning, not a deductive one.
To sum up some of what I've tried to illustrate with the above examples, a chain of deductive reasoning includes a couple of key features that are distinct from a chain of inductive reasoning. The first one is that, in a deductive chain of reasoning, if the premises are true, then the conclusion must also be true. A chain of inductive reasoning does not, even if its premises are true, entail the conclusion. The second one is that all the valid syllogistic forms (all of which contain a universal modifier like All or No) use a deductive chain of reasoning to draw their conclusions.
If you see a valid argument that contains only premises that itself includes either the term All or No, without some qualifying distinction, (For example, in the following proposition: All the penguins that have ever been seen by human beings..., the part in bold print qualifies the All), then it will be using a deductive chain of reasoning.
On the other hand, an inductive chain of reasoning will base its premises on a series of observations that will always fall short of universality. It's for this reason that, powerful as it may be, the scientific method only generates conclusions through a chain of reasoning that is inductive. Because a set of data collected by human observation will always be qualified by the natural limitations of either human faculties or the instruments we create, the conclusions generated by the scientific method are always inductive.
Induction and deduction are both essential ways of reasoning. In all honesty, we would be lost without either one.
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