In economics or other fields, there's a concept trilemma. It means

A trilemma is a difficult choice from three options, each of which is (or appears) unacceptable or unfavourable. There are two logically equivalent ways in which to express a trilemma: it can be expressed as a choice among three unfavourable options, one of which must be chosen, or as a choice among three favourable options, only two of which are possible at the same time.

However, I have a new idea relevant to trilemma. Say there are three things A, B, C. If any two of them occur, the third must occur as well. That is to say:

A, B --> C
C, B --> A
A, C --> B

What I am going to ask is is there a concept in philosophy or logic to describe the relationship between A, B, and C I mentioned above?

  • Interesting proposal. Give the woman the attention she deserves ... so to speak, mate! Jul 15 at 11:37
  • Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking.
    – Community Bot
    Jul 15 at 14:13
  • 1
    It seems that it is a chain of interconnected events. Jul 15 at 14:37
  • 1
    Seems like ∧, the AND gate logical operator en.wikipedia.org/wiki/AND_gate
    – CriglCragl
    Jul 15 at 15:56

3 Answers 3


A slightly simpler way to write that in a single sentence is

(A ∨ B ∨ C) → (A ⊕ B ⊕ C)

where ∨ is inclusive OR, ⊕ is exclusive OR and → is the material conditional.

Whether this has any useful applications is another matter. One possibility might be a situation in which two people cannot be left together without a chaperone. So, for a given group of three people, any one person may be alone, or all three may be together, but two is not allowed.



This is just another type of dilemma. You have to choose one or choose all three. There are no other options.


Such a relationship is a 3-input logic gate that outputs 1 on (001, 010, 100, and 111) and 0 on (000, 011, 101, and 110), where 1 represents truth (or signal) and 0 represents falsehood (or lack of signal). I don't think it needs any more philosophizing than that.

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .