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.


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


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. 


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."  

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