The Fallacy of the Fallacy of Division

Lekhni wants to know what was wrong with Falstaff referring to the the Fallacy of Division in his post.  Thinking through the Boeing 747 example in the Wikipedia article should make the problem clear.  Yes, the fact that a jet plane can fly across the Atlantic does not mean that its individual parts can fly independently across the Atlantic.  That is because while a jet plane is composed of its individual parts,  a part of a plane is not the plane.  While we can have interesting philosophical debates about how many parts one has to remove from a plane for it to cease being a plane, the point is that an engine of an aeroplane is not an aeroplane.

Contrast this with the statement “People of Lucknow speak Hindi”.   Unlike the aeroplane example, one can divide the populace of Lucknow into two halves, four quarters, or ten tenths and to a large extent, any statement one made about Lucknowis will be applicable to those halves, quarters or tenths.

In fact, the statement “People of Lucknow speak Hindi” is a generalization whose truth or falsehood  one can verify only by looking at the level of individual Lucknowis. If I meet a sufficient number of Lucknowis and find that most of them speak Hindi fluently, I will feel sufficiently confident in stating that people from Lucknow, in general speak Hindi. If you hear from me that most Lucknowis speak Hindi, the statement will be useful to you only because the next time you meet an individual Lucknowi, you will know which language you can start off with. I don’t see how one claim that if you do just that, you will be committing any fallacy, let alone the fallacy of division.

Of course, it is a fallacy if you persist in trying to speak in Hindi to a Lucknowi even if it is abundantly clear that he does not know the language. It is also a fallacy to turn it into a moral issue (“Lucknowis speak Hindi. You are a Lucknowi. So, you must  know the language, or there is something wrong with you.)  But if you treat it as an example of the fallacy of division, it would mean that if you got off at Charbagh station and found a porter who does not speak a word of Hindi, you would be committing a fallacy if you so much as expressed surprise.

What applies to Lucknowis speaking Hindi applies just as much to women supporting women’s issues. If women in general are more likely to support women’s issues, you are not committing the fallacy of division if you expect an individual woman to be more sympathetic to women’s issues. As Falstaff rightly pointed out, it is an error to continue to expect the same even when you learn more about that individual woman. But this error has nothing to do with the fallacy of division.

22 thoughts on “The Fallacy of the Fallacy of Division

  1. Um, so if I say/expect that a particular sector of the economy has been doing well by just looking at the overall economy that is doing well, am I or am I not committing the fallacy of division?

  2. I agree with everything you say. My point – Falstaff’s analogy is still appropriate – if you replace “women in general” with “womankind”.

    You would expect womankind to be feminist by default.
    But a single woman (who is a part of womankind but does not represent all of womankind by herself) may or may not share that feminist view.

  3. Actually Lekhni, I have issues with the “you’d expect womankind to be feminist by default” point, but let that pass.

    Given that assumption, then yes, Falstaff’s point is valid. *But*, Falstaff’s point, valid as it is, has nothing to do with the fallacy of division.

    Ritwik, no… you are not committing the fallacy of division, though you are still committing a fallacy.

  4. I am surprised you don’t think womankind would be feminist by default. Perhaps it has to do with how you define “feminist”.
    I define a “feminist” as someone who thinks women are equal to men (as does Webster’s).
    How do you define a feminist?

  5. Ravikiran,

    If I am not committing the fallacy of division, then was Keynes wrong when he critiqued Say’s law as being a typical case of the fallacy of composition?

  6. Lekhni,

    Even going by your definition of ‘Feminism’, we can find some women who wouldn’t subscribe to your proposition. If you look at the practice of only males as capable of becoming catholic priests, then quite a many women in this world have agreed to the concept of ‘women not being equal to men’, even though it can’t be justified rationally.


    Though I initially felt that Ritwik was committing a fallacy of division, I’d like to give it a think after your comment. A Boeing 747 doesn’t fly because its parts can fly independently[In fact none can]. It flies because a unique combination of all of its parts enable it to. However, not even one single part of Boeing 747 would match the assertion ‘Since Boeing 747 flies, its part too should fly independently’.

    In Ritwik’s example, There definitely will be some sectors of economy that’ll be doing well. Otherwise, the economy couldn’t be doing well. So, If he says that ‘Since the overall economy is doing well, some sectors must be doing well’, He’d be absolutely correct. But if he wants to extend the assertion to any arbitrary sector of economy, this wouldn’t be valid. Hence, the fallacy of division wouldn’t apply, but yes, a fallacy would be committed by Ritwik. Am I correct?

    One small question. I can draw Ritwik’s assertion on a Venn-diagram to understand it better by Set theory. But going by your logic, ‘fallacy of division’ can’t be explained using set-theory, as it is the whole or none criteria you’re suggesting — which can’t be drawn on a Venn-diagram.

  7. Ravi,

    help me understand.

    In the lucknow example the conclusion/assertion is a result of an aggregation of many individual examples.

    The plane example or ‘fallacy of division’ is an ‘all or nothing’ case. where the conclusion/assertion only applies to the whole object and never (or mostly never) to the constituent parts.

    did I understand you correctly?

  8. so ritwick is not commiting the fallacy error because the final assertion is as a result of the contituent divisions doing well.

    more or less you are implying causality. if individual units being true to assertion causes the generalization to be true then it is not a ‘fallacy of division’ if you work your way back from ‘general’ to ‘specific’

    ( i know i am restating the obvious again and again. but its hard for me to get hold of this if I dont do it this way)

  9. Lekhni, it is a complicated point, which I will explain in a post later, when I have the time.

    Ritwik, regardless of what Keynes said, if you are thinking of the fallacy of division in terms of the opposite of the fallacy of composition, you are doing it wrong.

    Hawkeye, Himanshu, you guys are right.

  10. the more i think the more looped it gets.


    a corollary of the 747 example: if you ‘specifically’ know that engine, nuts bolts, alumnium cannot fly and so make a claim that the composition of these elements (a 747) cannot fly, wouldn’t you be making a ‘fallacy of composition’. So for every division fallacy – is there a compositional equalant.?

    ps1: (i know i am not thinking clearly but can’t get this off my head)

    ps2: thinking about this is a useful waste of time.

  11. Himanshu,

    I agree, I am sure we can find some women who may not subscribe to my proposition of feminism. But womankind as a whole cannot be taken to be anything other than feminist. To be otherwise would mean womankind as a whole does not think in its own self-interest. (It’s a different issue if womankind is powerless to act in its self-interest).


    I tend to be rather cynical about anyone who says “it’s too complicated, let me explain later” or words to that effect 😉 I asked you a simple question – how do you define a feminist? I don’t see how that’s so complicated to explain 🙁 If you’d rather not go into it, that’s fine with me.

  12. lekhni,

    it is actully to do with how you define womankind, isn’t it? only if womankind is defined as less than 40 yr old reasonably urban-brought up women would that default have a chance of being true.

    maybe im doing a fallacy thing here – but i’ve seen many many small-town girls who are infact proud to hold the view that women are subservient to men. they constantly dole out advise to would-be-brides to that effect.

  13. Hawkeye,

    I’m not sure – how many women out there know in their hearts that they are as good as any man, but just don’t say so? I am sure they are vast numbers of them, even in rural areas. That is why you have phenomena like the pink police, the women in AP who were waging war against drinking, and the success of micro-finance which depends on women.

    As for the advice to brides – it may be just a case of “stooping to conquer” 😉

  14. Hawkeye, the Wikipedia article on the fallacy of division says as much. But the fallacy of composition is a much broader fallacy than just the converse of the fallacy of division, which is why I said that it does not make sense to try to figure out the fallacy of division from the fallacy of composition.

    Lekhni, sigh..

    I thought that only we libertarians liked to present arguments of the form: “Do you agree with X principle? Yes? So you must also agree with the concrete form Y of principle X.”

    Yes, *individuals* think according to their self-interest. But when you move from thinking in terms of individuals to groups of individuals, and try to make the statement that groups of individuals think and act according to the the interest of their groups, lots of problems begin to crop up.

    For one thing, individuals typically belong to multiple groups. A person might be a woman, a Hindu, a software developer, a member of the upper class and a mother to a misogynist son who is in fighting a bitter divorce case. What view that person will take in any situation will be influenced by all her group identities.

    Even if we accept that a person’s gender is disproportionately important to the way that person thinks, there is no reason to expect a person belonging to the female gender will find that her interests will typically align with what a feminist thinks. This is not because of insufficient “class consciousness” – to use Falstaff’s awful Marxist jargon. This will be true in any world populated with normal people – in fact, the closer one gets to the world that feminists dream of, the more you will find women diverging from their “class interests”.

  15. Ravi, correct me if I am wrong here, but the way I understand your arguement is that the relation of airplane to its parts is unlike relation of group of people to individual in that the concerned attribute of the group is actually just an aggregate of attribute of individuals constituting the group, unlike plane the where it is the emergent behaviour arising out of interaction of its parts.
    Anyhow to be frank I can’t make any head or tail of what that dude Falstaff wrote, or why he wrote. Really it is all right not to right once in a while.

    Is feminist “today” really someone who believes males and females are equal. If one were to take this further since I supports women franchise must mean that I am a suffragist or since I oppose slavery I am a abolitionist.

    And do individuals really think according to their self-interest ?

  16. By the way does this FoD apply to both “can” and “is” statements. If it does, I don’t see how Ritwik is not committing that fallacy.

  17. lekhni,

    how many women out there know in their hearts that they are as good as any man, but just don’t say so?

    this takes it to a topic of ‘perception and reality’. And on whether ‘perception is reality’.

    The only and most common way of knowing whats really in their hearts is by asking them or monitoring their actions. If both reflect wilfull subservience (even if it is allegedly against what their heart/subconcious really believes ) then that is reality.

  18. BTW, how many angels can dance on the point of a needle without consequently commiting a fallacy of Division?

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