Tabyla Rosa Systems Blog 11/23/19 - Explanation of the Fallacy of Division

by Austin Cline
Austin Cline, a former regional director for the Council for Secular Humanism, writes and lectures extensively about atheism and agnosticism. 
Updated July 22, 2017
In critical thinking, we often come across statements that fall victim to the fallacy of division. This common logical fallacy refers to an attribution placed onto an entire class, assuming that each part has the same property as the whole. These can be physical objects, concepts, or groups of people. 
By grouping elements of a whole together and assuming that every piece automatically has a certain attribute, we are often stating a false argument. This falls into the category of a fallacy of grammatical analogy. It can apply to many arguments and statements we make, including the debate over religious beliefs.
Explanation of the Fallacy of Division
The fallacy of division is similar to the fallacy of composition but in reverse. This fallacy involves someone taking an attribute of a whole or a class and assuming that it must also necessarily be true of each part or member.
The fallacy of division takes the form of:
X has property P. Therefore, all parts (or members) of X have this property P.
Examples and Discussion of the Fallacy of Division
Here are some obvious examples of the Fallacy of Division:
The United States is the richest country in the world. Therefore, everyone in the United States must be rich and live well.
Because professional sports players are paid outrageous salaries, every professional sports player must be rich.
The American judicial system is a fair system. Therefore, the defendant got a fair trial and was not executed unfairly.
Just as with the fallacy of composition, it is possible to create similar arguments which are valid. Here are some examples:
All dogs are from the canidae family. Therefore, my Doberman is from the canidae family.
All men are mortal. Therefore, Socrates is mortal.
Why are these last examples valid arguments? The difference is between distributive and collective attributes.
Attributes which are shared by all members of a class are called distributive because the attribute is distributed among all members by virtue of being a member. Attributes which are created only by bringing together the right parts in the right way are called collective. This is because it is an attribute of a collection, rather than of the individuals.
These examples will illustrate the difference:
Stars are large.
Stars are numerous.
Each statement modifies the word stars with an attribute. In the first, the attribute large is distributive. It is a quality held by each star individually, regardless of whether it is in a group or not. In the second sentence, the attribute numerous is collective. It is an attribute of the entire group of stars and only exists because of the collection. No individual star can have the attribute "numerous."
This demonstrates a primary reason why so many arguments like this are fallacious. When we bring things together, they can often result in a whole which has new properties unavailable to the parts individually. This is what is often meant by the phrase "the whole is more than the sum of the parts."
Just because atoms put together in a certain way constitutes a living dog does not mean that all atoms are living - or that the atoms are themselves dogs, either.
Religion and the Fallacy of Division
Atheists often encounter the fallacy of division when debating religion and science. Sometimes, they may be guilty of using it themselves:
Christianity has done many evil things in its history. Therefore, all Christians are evil and nasty.
One common way of using the fallacy of division is known as "guilt by association." This is clearly illustrated in the example above. Some nasty characteristic is attributed to an entire group of people - political, ethnic, religious, etc. It is then concluded that some particular member of that group (or every member) should be held responsible for whatever nasty things we have come up with. They are, therefore, labeled guilty due to their association with that group.
While it's uncommon for atheists to state this particular argument in such a direct manner, many atheists have made similar arguments. If not spoken, it's not unusual for atheists to behave as if they believed this argument were true.
Here is a slightly more complicated example of the fallacy of division which is often used by creationists:
Unless each cell in your brain is capable of consciousness and thinking, then the consciousness and thinking in your brain cannot be explained by matter alone.
It doesn't look like the other examples, but it is still the fallacy of division - it's just been hidden. We can see it better if we more clearly state the hidden premise:
If your (material) brain is capable of consciousness, then each cell of your brain must be capable of consciousness. But we know that each cell of your brain does not possess consciousness. Therefore, your (material) brain itself cannot be the source of your consciousness.
This argument presumes that if something is true of the whole, then it must be true of the parts. Because it is not true that each cell in your brain is individually capable of consciousness, the argument concludes that there must be something more involved - something other than material cells. 
Consciousness, therefore, must come from something other than the material brain. Otherwise, the argument would lead to a true conclusion.
Yet, once we realize that the argument contains a fallacy, we no longer have a reason to assume that consciousness is caused by something else. It would be like using this argument:
Unless each part of a car is capable of self-propulsion, then self-propulsion in a car cannot be explained by the material car-parts alone.
No intelligent person would ever think to use or accept this argument, but it's structurally similar to the consciousness example.
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Air gapping is a security measure that involves physically isolating a computer or network to prevent it from connecting directly or wirelessly to other systems that can connect to the Internet. Air gapping is used to protect many types of critical systems, including those that support the stock market, the military, the government and industrial power industries. To prevent unauthorized data extrusion through electromagnetic or electronic exploits, there must be a specified amount of space between the air-gapped system and outside walls and between its wires and the wires for other technical equipment. In the United States, the U.S. National Security Agency TEMPEST project provides best practices for using air gaps as a security measure. For a system with extremely sensitive data, a Faraday cage can be used to prevent electromagnetic radiation (EMR) escaping from the air-gapped equipment. Although such measures may seem extreme, van Eck phreaking can be used to intercept data such as key strokes or screen images from demodulated EMR waves, using special equipment from some distance away. Other proof-of-concept (POC) attacks for air- gapped systems have shown that electromagnetic emanations from infected sound cards on isolated computers can be exploited and continuous wave irradiation can be used to reflect and gather information from isolated screens, keyboards and other computer components. As of this writing, the Defense Advanced Research Projects Agency (DARPA) is awarding grants for prototype hardware and software designs that will keep sensitive data physically isolated. The grants are made possible under the Guaranteed Architecture for Physical Security (GAPS) program. Enhancing air-gapped security measures The problem with physical separation as a security technique is that, as complexity increases in some system or network to be isolated, so does the likelihood that some unknown or unauthorized external connection will arise. Perhaps the most important way to protect a computing device or network from an air gap attack is through end user security awareness training. The infamous Stuxnet worm, which was designed to attack air-gapped industrial control systems, is thought to have been introduced by infected thumb drives found by employees or obtained as free giveaways. The software-defined perimeter (SDP) framework is another tool network engineers can use to create a type of "virtual air gapping" through policy enforcement. SDP requires external endpoints that want to access internal infrastructure to comply with authentication policies and ensures that only authenticated systems can see internal IP addresses.

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