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Fallacies: Fallacy of Division

In this video, Paul Henne describes the fallacy of division, the informal fallacy that arises when we assume that the parts of some whole must have the same properties as the whole they make up. He also discusses why water molecules aren't wet. 

Speaker: Paul Henne, Duke University.
Created by Gaurav Vazirani.

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  • male robot hal style avatar for user Yisrael F
    Is it fair to say that the division fallacy will not occur if the first premise is an "All" statement?
    (15 votes)
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    • leaf red style avatar for user Noble Mushtak
      That last argument is in the following form:
      P1: All things with quality A also have quality B.
      P2: Thing C has quality A.
      C: Thing C has quality B.
      This argument will always be true regardless of what you plug in for quality A, quality B, and thing C as long as the premises are true.

      Judy's argument, on the other hand, is in this form:
      P1: All things with quality A have quality B.
      P2: All things with quality A are made of things with quality C.
      C: All things with quality C have quality B.
      This is the Fallacy of Division as discussed in the video because it assumes that the parts that make up the things with quality A have the same qualities as the whole.

      In general, you probably shouldn't assume things about arguments because of one little thing, but instead, describe arguments in full using some kind of form. This makes more sense because often, arguments can be worded in multiple ways so statements like "the first premise is an 'All' statement," might have a different truth value for equivalent arguments that are worded differently.

      I hope this helps!
      (11 votes)
  • sneak peak green style avatar for user Sivens Glaude
    Where can I learn how to describe any argument in the correct philosophical form?
    (2 votes)
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  • mr pants teal style avatar for user Anthony Natoli
    What is he saying at time point ? He says "it could be the case that Sally is sort of a lay, and she hardly uses any appliances or devices that use electricity". What is "a lay"? The closed captioning tries to translate it as "sorta 18", which does not make sense.
    (1 vote)
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  • old spice man green style avatar for user Petrie (Peter S. Asiain III)
    The Fallacy of Composition and the Fallacy of Division both seem so similar.
    Can someone please differentiate and clarify the differences between these two informal fallacies?
    (1 vote)
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    • leaf red style avatar for user Noble Mushtak
      They are similar, but in a sense, they are opposites of each other.

      The Fallacy of Composition is an assumption about the whole based on the parts.
      Example:
      P1: Atoms are invisible to the human naked eye.
      P2: Elephants are made of atoms.
      C: Therefore, elephants are invisible to the human naked eye.

      In contrast, the Fallacy of Division is an assumption about the parts based on the whole.
      P1: Elephants are visible to the human naked eye.
      P2: Elephants are made of atoms.
      C: Therefore, atoms are visible to the human naked eye.

      I hope this helps you differentiate these fallacies!
      (11 votes)
  • spunky sam blue style avatar for user Cogito, ergo sum
    The Universe is Dark and Dangerous. People are part of the Universe, therefore people are Dark and Dangerous. Is this an example of the Fallacy of Division?
    (4 votes)
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  • starky ultimate style avatar for user Luka Agres
    There is a lot of mathematics(logic) in these videos. Could someone connect this topics to the existing topics in Math sections in Khan academy? Does mathematics and philosophy ever divide?
    (3 votes)
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  • spunky sam blue style avatar for user josefrichardtyler
    I was thrown by one of the questions that follows this video.
    In essence, it said a band is composed of A, B, and C. A is talented, B is talented and C is talented. I assumed that's enough to believe that the band as a whole is talented, but it was wrong.

    Can it be that every part of a whole can have a certain attribute, but the whole itself not have that attribute?
    (3 votes)
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    • hopper cool style avatar for user MickeyRich
      Yes, your question is very true. Remember, what's true of the parts may not true of the whole. For example, A, B, and C may be talented playing their own individual instruments, but that doesn't mean they're talented when they are playing in their band. This is a composition fallacy:

      P: A spark plug is light.
      P: A spark plug is part of an engine.
      C: Therefore, an engine is light.

      Spark plugs all share the same attribute because they are light, but the engine itself does not share it because it is heavy from the weight of everything that it is composed of. This is why the composition fallacy is a fallacy. The same thing can be said for division:

      P: An engine is heavy.
      P: A spark plug is part of an engine.
      C: Therefore a spark plug is heavy.

      This is why these arguments do not work. I hope this was helpful for you :D
      (1 vote)
  • leaf green style avatar for user nerdygirlie42
    Are you going to be explaining other fallacies? I am teaching these to my children and there is a surprising lack of entertaining and clearly explained content for children.
    (1 vote)
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    • blobby green style avatar for user admin
      Hi,
      We definitely will be! We have a long list that we hope to get through. Over the course of the summer we should be building these videos and releasing them. Glad to hear you are finding them valuable!
      (4 votes)
  • blobby green style avatar for user Микола Винницький
    In example with indestructible computer Paul finds out that of the hard drive is outside of computer it can be destructible. I have a doubt if here is really a case of fallacy of division.
    The hard drive is a destructible part so the whole computer can not be indestructible.
    It seems that Paul have made the fallacy of composition constructing this example, doesn't he?
    (2 votes)
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    • purple pi teal style avatar for user Maria
      I think that the hypothetical indestructible computer is a bit like a water bottle. Water will run all over the place if you take off the lid and throw it. But it you don't remove the lid, the water won't leak out.
      (1 vote)
  • spunky sam blue style avatar for user Cogito, ergo sum
    So, water molecules are NOT wet?
    (2 votes)
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Video transcript

(intro music) Hello, I'm Paul Henne, and I'm a philosophy graduate student at Duke University. And in this video I'm gonna talk to you about an informal fallacy called the "fallacy of division." And I'm also going to[br]discuss why it's wrong to conclude that water molecules are wet. The fallacy of division[br]is a defect in reasoning that arises when someone[br]infers that what is true of something must also be[br]true of that thing's parts. So, the fallacy is kind of like saying that because a university[br]has some qualities, then all of that university's departments must also have those qualities. And that's a fallacy[br]because even if a university is good all around, it doesn't necessarily mean that the university[br]has a good taxidermy program, for instance. So, sounds problematic, right? But let's represent the[br]logical error more formally. The reasoning is something like this. Premise (1): Whole A has[br]properties A, B, and C. Premise (2): P is a part of A. Conclusion: Therefore,[br]P must have properties A, B, and C. The argument seems attractive, but the style of argument will not always lead to true conclusions, for it might not be the case that the parts and the whole[br]have the same qualities. You may now be able to see what's going wrong with[br]this line of reasoning. So, let's look at a few examples. Suppose that I have a car, and I made this argument about my car. Premise (1): My car is red[br]and it goes really fast. Premise (2): The muffler[br]is a part of my car. Conclusion: Therefore, my car's muffler is red and goes really fast. Okay, that was an easy one. Of course no one would make this argument, or assume that I own a car, but it demonstrates where[br]the style of argument fails. Clearly the muffler doesn't have the same properties as the car. So, let's try another[br]more familiar example. Suppose that your friend[br]made this argument: the computer is indestructible; the hard drive is a part of the computer; therefore, the hard[br]drive is indestructible. Now, suppose your friend's[br]premises are true. The conclusion could still be false. Maybe your friend was making this argument in order to transfer the hard drive of the indestructible computer[br]to a different computer. So, if would be unfortunate[br]for her to find out that the hard drive is only indestructible when it's connected to[br]the other components of the original computer. So, the hard drive itself[br]isn't indestructible like the whole computer. Your friend committed[br]the fallacy of division. That is, to be precise,[br]she hastily assumed that the hard drive, the[br]part, is indestructible like the whole computer. So, we just learned about[br]the fallacy of division, or the error in reasoning that comes about when a person infers that[br]what is true of something must also be true of its parts. It is important, however,[br]to note that this fallacious reasoning doesn't always lead to a false conclusion. I, for instance, might[br]argue the following. Premise (1): The house in pink. Premise (2): The front[br]door is part of the house. Conclusion: Therefore, the[br]front door is also pink. And in this case, my argument leads to a true conclusion. For I've, for whatever reason, painted every part of my house pink. Simply because there's[br]fallacious reasoning doesn't necessarily mean[br]that the conclusion will be false. It's interesting to note that this fallacy is also the converse of[br]the fallacy of composition, which says that it's fallacious to infer that what is true[br]of the parts of something is also true of the whole[br]those parts compose. These fallacies are quite similar, so you might want to check[br]out that video as well. Anyway, watch out for this fallacy. And remember that just[br]because water is wet, doesn't mean that you can conclude that water molecules are wet too. Subtitles by the Amara.org community