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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?

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  • Interesting proposal. Give the woman the attention she deserves ... so to speak, mate!
    – Agent Smith
    Jul 15 at 11:37
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    – Community Bot
    Jul 15 at 14:13
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    It seems that it is a chain of interconnected events.
    – Mauro ALLEGRANZA
    Jul 15 at 14:37
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    Seems like ∧, the AND gate logical operator en.wikipedia.org/wiki/AND_gate
    – CriglCragl
    Jul 15 at 15:56

3 Answers 3

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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.

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Dilemma

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

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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.

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