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If someone has set up a dichotomy (an "either a, or b" exclusive disjunction kind of argument), how can we then refer back to the two parts being contrasted, such that one could form a sentence like, "if one grants the latter "dichotom", then xyz). "Dichotom," however does not appear to be a word. So what actual word would be a good substitute?

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5 Answers 5

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Alternative is a good word for that.

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    +1 I agree with this one.
    – GEdgar
    Dec 27, 2022 at 1:25
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As the question implies, there are two kinds of disjunction, the inclusive, in which, of the two statements (or terms), A and B, one or the other or both may be true. For example,

You can have sugar or milk in your tea.

This relationship is expressed using a symbol representing the Latin word vel, where "A vel B" means A or B or both A and B. The symbol used is the letter 'v' (the first letter of the Latin inclusive disjunction, vel.

In logic, we can say that (A v B) implies both (not-A implies B) and (not-B implies A). That is, if A is false, B is true and if B is false A is true. A and B cannot both be false but they can both be true.

We can speak of A and B as the terms of the disjunction.

The exclusive disjunction, as is said in the question, represents alternatives/a dichotomy. One of the terms must be true, but not both. In logic it is expressed by the Latin word aut, a word that conveys exclusive disjunction. The symbol used is a an upside down 'v', to suggest the 'A' for Aut without the crossbar (used also by a car manufacturer of a car model with and 'A' in its name). My lack of keyboard skill leaves me with '^', which I use with apology.

In logic, A ^ B is a way to say that the truth of the first term (A) implies that the second term (B) is false and vice versa. It is logically equivalent to

A -> -B, (or "A implies not-B"), which, mutatis mutandis implies B -> -A, or "B implies not-A". One or the other term but not both is true.

Historically, the German Frege in the late 19th century and finally Bertrand Russell in the early 20th century established the relatedness between logic and mathematics. So the word term came into use to express what stood one side or the other of a logical relationship. Logic, it turned out worked a bit like algebraic equations.

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  • So, term could be the word I'm looking for, then? The logic lesson was refreshing, so thank you. Logic was one of my favorite courses I took in college. Dec 27, 2022 at 12:41
  • @Jonathan Muse Yes. For example, in the Cambridge English Dictionary includes: "[ C ] MATHEMATICS specialized a number or symbol used in a mathematical series or calculation: We then use the same rule to compute the terms of the equation. The terms of a geometric series form a geometric progression, meaning that the ratio of successive terms in the series is constant."
    – Tuffy
    Dec 27, 2022 at 14:58
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A dichotomy produces parts, so I think you’ve answered your own question.

dichotomy, n.
1. a. Division into two sharply defined or contrasting parts; (Logic) division into two mutually exclusive categories or genera; binary classification. Also: an instance of such division.
Source: Oxford English Dictionary (login required)

If you can give the parts a more specific label, go for it. Your example sentence, with its use of grants (concedes), suggests that your two parts are arguments:

If one grants the latter argument, then xyz.

(Again, I think you’ve answered your own question.)

If one understands the latter possibility, then xyz.

If one chooses the latter alternative, then xyz.

And so on.

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The words dilemma and dichotomy are very closely related (see Wikipedia: false dilemma, also referred to as false dichotomy). The difference is the former more strongly alludes to the need to make a choice, where the latter stresses the fact of two things being mutually incompatible.

So here's a chart showing that when referring to the two "components" that constitute a dilemma, there's one particularly well-established term...

enter image description here

TL;DR: We don't say the horns of a dichotomy, but we do say the horns of a dilemma.

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    Dilemma means two (competing) truths, (lemmas are proofs). Dichotomy means two parts (same root as microtome, meaning 'cut'); the parts don't have to be opposite or competing, they just have to be separate. Feb 16, 2023 at 22:54
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    oic - obvious when you point it out. Well, the dilemma etymology was immediately recognizable to me 'cos I knew lemma, but I didn't get the -tome = 'cut' business until it dawned on me hysterectomy has "the same" roots. So if I'd learned vas deferens first, I wouldn't have needed to "learn" vasectomy at all, 'cos I could have worked it out whenever I needed to. I'm sure there are a whole bunch of other -ectomies I already know without needing to remember them. English is surely "complicated", but it's encouraging to see bits of it reflect regular patterns well worth knowing. Feb 17, 2023 at 0:10
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Option (if the dichotomy is a choice), case, possibility, eventuality.

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  • Your answer could be improved by citing some sources showing example usages, definitions etc. As it stands it has been flagged as being of low quality.
    – Jim
    Jan 2, 2023 at 19:53

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