Archive for the ‘logic’ Category

Logical fallacy of division

September 27, 2006

I found something on wikipedia.com that is enragingly stupid: the fallacy of division.

A fallacy of division occurs when one reasons logically that something true of a thing must also be true of at least some of its constituents.

An example:

1. A Boeing 747 can fly unaided across the ocean

2. If a Boeing 747 can fly unaided across the ocean, then one of its jet engines can fly unaided across the ocean.

3. One of its jet engines can fly unaided across the ocean

This is so wrong I don’t know where to begin. First, the example doesn’t even correctly demonstrate the stated definition:”A fallacy of division occurs when one reasons logically that something true of a thing must also be true of at least some of its constituents.” The example picks a specific part of the plane, and just happens to pick the wrong part. So, let’s reword the example carefully.

1. A Boeing 747 can fly unaided across the ocean

2. If a Boeing 747 can fly unaided across the ocean, then some part of a Boeing 747 can fly unaided across the ocean.

3. Some part of a Boeing 747 can fly unaided across the ocean

Is there some part of a Boeing 747 that can fly unaided across the ocean? Yes — the part that flies! Remove the passenger seats, the landing gear, the radio equipment, and what are you left with: the constituent part of the jet that can fly unaided across the ocean. Good luck landing it, though.

We have to look for a better example. Is there some object where no constituent part has a property that the whole object has? How about the mass of a rock?

1) A rock has a mass of 100 grams.

2) If a rock has a mass of 100 grams, some part of the rock has a mass of 100 grams.

3) Some part of the rock must have a mass of 100 grams.

Obviously the last statement is untrue — if we take away any part of the rock, the resulting part will have a mass of less than 100 grams. But do you see the problem here? We’re confusing a property with the value of the property. Since the definition of a fallacy of division says nothing about values of properties, let’s reword the example without referring to values.

1) A rock has mass.

2) Since a rock has mass, some part of the rock must have mass.

3) Some part of the rock has mass.

Now we have a true statement. Maybe we should get rid of the fallacy of division and replace it with The Fallacy of Confusing a Variable and its Value.

Another problem with the “fallacy” of division is that most properties are reducible into other properties. When you simply reword an argument to refer only to component properties, the fallacy disappears. Look at the example of a Boeing 747. Flight is not just a property; it’s a combination of other properties: the ability to generate thrust and the ability to generate lift.

1. A Boeing 747 can generate enough lift and thrust for an unaided flight across the ocean

2. If a Boeing 747 can generate enough lift and thrust for an unaided flight across the ocean, then some part of it can generate enough thrust for an unaided flight across the ocean, and some part of it can generate enough lift for an unaided flight across the ocean.

3. Some part of a Boeing 747 can generate enough thrust for an unaided flight across the ocean, and some part of it can generate enough lift for an unaided flight across the ocean

So, while no constituent part of a 747 must logically have two properties of a 747 (both thrust generation and lift generation), some part of the jet must have one (and that’s true — the engines generate thrust and the wings generate lift). As long as you divide the properties and the object, no fallacy of division occurs. So the definition of the fallacy of division should be worded thusly: A fallacy of division occurs when one reasons logically that two things true of a thing must also be true of at least one of its constituents. However, since a simple rewording usually fixes the problem, the issue is pedantic.

My conclusion is this: a fallacy of division is not made if values of properties are not mentioned. Otherwise, the logic simply needs rewording.

Now, why do I get so upset about this? Well, I’ve used arguments based on logic like this: In physics, every property of any object is the sum of the properties of every particle within that object. I’ve also said: Nothing that exists is created from nothing, but instead built from smaller pieces that already exist. I think these statements are demonstrably true, and theories of emergence (that objects or properties magically appear) are demonstrably false. “Emergence” is just a pansy way for physicist to claim that mind is physical without being able to explain the phenomenon with physics. Either explain it with physics, or admit that it might be metaphysical.

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