Occam's Razor Continued

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.