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Encountered this word for the first and only time at an Anglican church, from a rector. I suspect that it is a word from Christian liturgy.

I had pointed out that two of the beliefs he had been promoting were completely contradictory - i.e. if one held one of them it was not possible to hold the other at the same time. He took this in stride, smiled easily, and used the word I am looking for.

In reply to the replies below:

Thanks all for the input.

"Antinomy", from philosophy, might be close, and "koan" might be another word for what the rector was describing!

Uh oh ... I'll admit that I am now wondering whether memory serves me well enough to recognize the word when I see it! Could antinomy be it? Koan is too short.

I'm guessing that the best bet for a definitive answer will come from a student of this level and form of Christianity. (Anyone care to call up their well-schooled rector? Orthodox Anglican as mentioned below.)

To answer questions posed to me here:

Unfortunately I do not recall the beliefs promoted.

It was in Canada and, when pressed, the rector - who did have a high-level affiliation with the Church of England - said that this flavour of Anglican would be "orthodox".

More as of April 13 2017:

I don't understand how this board works. Seems 5 users have claimed that my question is a duplicate. I am asked to explain why this is not the case. But I don't see where those 5 users have provided the "duplicate" question and answers ...

Also, there is a 2nd claim that this question has already been asked and answered - which includes a question which is clearly not the same as mine ...

Anyway, I've seen evidence neither of my question having been asked before nor its answer (though koan and antinomy are closest and on the right track). Thanks.

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It sounds like you're describing a paradox, with the word used in the following sense:

paradox noun A seemingly absurd or contradictory statement or proposition which when investigated may prove to be well founded or true. ‘the uncertainty principle leads to all sorts of paradoxes, like the particles being in two places at once’ - ODO

Here's an example in which the term is used in a setting close to your term 'Christian liturgy':

The Christian faith seems rife with paradoxes—an all-powerful God who allows suffering; a God who is distant and yet present at the same time. What if it’s in the difficult parts of the Bible that God is most clearly revealed? - Jonathan Petersen, Living with Biblical Paradox: An Interview with Krish Kandiah

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I'd think of a duality, in this case of mutually conflicting beliefs.

duality noun (djuːˈælɪtɪ) n, pl -ties 1. the state or quality of being two or in two parts; dichotomy - TFD

The general case might be a "plurality" which does not indicate a quantity, where duality would be exactly two beliefs.

An example of mutually incompatible concepts might be a strict belief that the planet Earth is ~4000 years old, and a simultaneous belief that fossils are millions of years old.

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