In Ido, the constructed language he helped to build, Louis Couturat attempted to introduce vel, a conjunction that would express inclusive disjunction—so that, in logical sentences, the conjunction o(d) would express exclusive disjunction.

Louis Couturat was a logician who corresponded with Bertrand Russell. For some time, the conjuction vel was adopted by the Ido Academy and people started using it. However, in Progreso, the official Ido magazine, Couturat argued that Idists were using vel incorrectly. For instance, somewhere one could read: "We offer gratis [vel] not gratis books". He argued that the use of vel in that sentence is wrong, since a book cannot be gratis and not gratis at the same time. Similarly, he said that "in the daytime [vel] in the nighttime" is illogical, since day and night cannot exist at the same time. However, he gave this sentence as a "good" example: "We are looking for someone who speaks German [vel] Ido", saying that German and Ido can coexist at the same time.

So my question is: was Louis Couturat right when he implied that the inclusive disjunction must be valid for each element of a group considered individually (i.e. a single book cannot be gratis and not gratis), and not only for all elements considered as a whole (i.e. some books can be gratis while the others are not)?

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    Surely what is called for in the first example would simply be conjunction? "We offer free and not free books." Mar 5, 2017 at 13:54
  • Yes, all instances where I wrote [vel] can be translated to a conjunction that expresses inclusive disjunction. As far as I know, in English it is “or” (not “and” nor the popular “and/or”), and in French it is “ou” (not “et” nor “et/ou”). So when someone asks “Do you speak French or English?”, the respondent can answer “Both”. In the case of “Do you speak French and English”, the answer would be “Yes”. In the case of an exclusive “or”—which would sound absurd in that context—the answer would be “No”. Did I answer your question?
    – maliktunga
    Mar 5, 2017 at 14:17
  • My question is about the fact that Couturat said that the inclusive disjunction is inappropriate in the first and second examples. I would like to know whether he was right and why.
    – maliktunga
    Mar 5, 2017 at 14:21
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    What I meant was, conjunction without any type of disjunction. Presumably both types of books are on offer. Inclusive disjunction seems like it would mean either one type, or the other type, or both types are on offer. I guess it could be a "free choice" disjunction, though, like "Do you want sugar or tea in your coffee?" Mar 5, 2017 at 14:25
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    This has nothing to do with correctness in Ido, if there is any such thing. Couturat introduced the word, after all. He gets to say if it's right or not. The logical use of exclusive OR (Truth Table FTTF) instead of inclusive OR (Truth Table TTTF) differs only in the first line of the truth table. If both P and Q are True, then inclusive P OR Q is True, while exclusive P OR Q is False. Vel is another matter entirely, as are Couturat's motives.
    – jlawler
    Mar 5, 2017 at 14:33

1 Answer 1


If Ido coordinating conjunctions have ambiguous scope like English conjunctions, then it will be possible for logically coherent sentences to include sequences like "gratis vel not gratis" or "in the daytime vel in the nighttime."

Let's consider the example "gratis [vel] not gratis books". In the corresponding English phrase "free or not free books", "free" and "not free" do not refer to the same things. There is an ellipsis; this really means "gratis books vel not gratis books." And this is a reasonable thing to offer, if you mean to emphasize that a customer can make either a selection composed entirely of free books, or a selection composed entirely of not-free books, or a selection composed of both free and not-free books. In other words, the idea expressed is "either [free books], or [not-free books], or both," which is not logically incorrect and which is a disjunction. (I actually do think it sounds better to just use simple conjunction, though. I don't quite understand the logical underpinnings of how free-choice disjunctives work, and it seems simpler to me to just talk about what is offered in general and say that it includes "(both) free and non-free books.")

"In the daytime, or in the nighttime, or both" is a very unlikely thing to want to express, so I agree that it is likely that someone using "vel" in this context is making an error. But again, in English at least it might make sense if the conjunction is really operating on a wider scope, for example "If [you like hiking in the daytime] vel [(you like hiking) in the nightime], you will find it helpful to have a map."

  • Thank you for the interpretation! You mentioned ellipsis, and I think it is the central explanation to Couturat's comments: he considered the first example without acknowledging the ellipsis. I think that's odd, since he did acknowledge the ellipsis in other features of Ido, such as ka ne. The latter expresses the same idea as isn't it and others at the end of sentences in English, e.g. You like chocolate, don't you (like chocolate)?. So ellipses do exist in Ido and are not generally seen as erroneous.
    – maliktunga
    Mar 5, 2017 at 16:37
  • I guess he saw vel differently, since in ka ne the ellipsis is outside the main sentence (so it's as if they were two isolated propositions). Otherwise I think your explanation is clear and shows "free or not free books" is correct, at least from the point of view of English.
    – maliktunga
    Mar 5, 2017 at 16:37

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