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According to Webster's dictionary, a dichotomy is "a splitting of two mutually exclusive groups or entities".

However, does this imply that the two events must be collectively exhaustive (i.e. that at least one of them must occur)? For example, does the phrase "a dichotomy of people who love alcohol and people who hate alcohol" make sense (since there are other choices, including being indifferent towards alcohol), or does it strictly have to be a partition (both events are mutually exclusive and cover all possibilities)?

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    What does Collins (sense 1) say? Always go further than a single dictionary. Note also the conflicting usages (sense 2).
    – Edwin Ashworth
    Commented Feb 5, 2017 at 23:28
  • I'm not sure whether the "sense 2" definition you're referring to is the astronomy one or the logic one. In either case, how does it conflict with sense 1?
    – Steve Smith
    Commented Feb 6, 2017 at 0:44
  • According to the OED, the origin of the term in English is from Latin "dichotomia" meaning division into two parts. I can't give you a link through their subscription checker.
    – Al Maki
    Commented Feb 6, 2017 at 3:43
  • I'm using Collins' (you might be confusing the AHD entry) numberings; I don't understand why you say you don't follow. Their sense 2 (logic register) is far more tightly defined (the division of a class into two mutually exclusive subclasses) than their sense 1, which doesn't make this stipulation. So "a splitting [into] two mutually exclusive groups or entities" is itself not even binding. // I can't find your Webster's definition; please link so it is clear you are quoting accurately.
    – Edwin Ashworth
    Commented Feb 6, 2017 at 11:02
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    The ODO definition given first<< dichotomy NOUN 1 A division or contrast between two things that are or are represented as being opposed or entirely different: ‘a rigid dichotomy between science and mysticism’ >> certainly doesn't demand that there are not other concepts etc that may be involved (eg fundamentalist religion in their example). Other dictionaries more strongly suggest that the two contrasted things together exhaust all possibilities.
    – Edwin Ashworth
    Commented Feb 6, 2017 at 23:17

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A false dichotomy is the logical fallacy of presenting two options as exhaustive when in fact a third option (or more) exists. This wouldn't be “false” if “dichotomy” did not imply that the two options are jointly exhaustive.

So yes, I would say that a “dichotomy” between A and B means that A xor B is true. Not both, and not neither.

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    There are contrasting definitions for 'dichotomy' and 'false dichotomy' selects one of them. This invalidates this argument.
    – Edwin Ashworth
    Commented Feb 5, 2017 at 23:37
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    @EdwinAshworth Contrasting definitions like what? And how does this invalidate "the argument" (whatever that argument is)?
    – Steve Smith
    Commented Feb 6, 2017 at 0:46
  • @Steve Smith M-W, Collins etc don't demand mutual exclusivity: <<dichotomy: a division into two especially mutually exclusive or contradictory groups or entities >> (bolding mine). Collins adds a stricter definition used in the logic domain, but this is not the complete picture.
    – Edwin Ashworth
    Commented Feb 6, 2017 at 11:14
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    @EdwinAshworth The question is whether the dichotomy must be exhaustive, not whether they're mutually exclusive. That definition implies that they're exhaustive, since it says that you take the original group and split it.
    – Barmar
    Commented Feb 6, 2017 at 22:31
  • @Barmar '... does this imply ...' is falsely predicated.
    – Edwin Ashworth
    Commented Feb 6, 2017 at 23:01
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You have set up a false dichotomy. Love and hate do not form a dichotomy; love and not love, and hate and not hate are the dichotomies. No middle ground with these. You either love or do not love alcohol, there is nothing in the middle, therefore they are mutually exclusive and are the propositions in a true dichotomy

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