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As I know about the meaning of the verb acknowledge,
it presupposes the factive value of the complement.

ex. We acknowledged that he was wrong.
= That he was wrong is a fact.

But, some linguistic papers searched in the net says
acknowledge can be read as a sense of judging or
believing. That is, it can be factive or non-factive.

If this is really the case, the sentence above can be interpreted as 'We admit the strong assertion not the fact'.
Do you think this can be a possibility?
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cho7712ex. We acknowledged that he was wrong. = That he was wrong is a fact.
I don't see that at all. We acknowledged that he was wrong = We said that he was wrong.
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cho7712But I'm afraid that the truth-related factor is strongly implied in the meaning of acknowledge as you can see below;acknowledgeoxford; to accept that something is truecambridge;to accept, admit, or recognize something, or the truth or existence of something:Free Dictionary; a. To admit the existence, reality, or truth of. b. To recognize as being valid or having force or power.
Our acknowledgement/acceptance/recognition/admission of something does not mean that what we acknowledge/etc is a fact or true.
cho7712So let me get straight; the complement content followed by 'acknowledge' can be understood as the fact or the assertion depending on the context. Is it right thinking?
The arguments of the creationists have convinced me. I acknowledge that a divine being created the world in six days less than 10,000 years ago.

Does my acknowledgement make what I have acknowledged a fact?
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Thank you for the answer.
But I'm afraid that the truth-related factor is strongly implied in the meaning of acknowledge as you can see below;
acknowledge
oxford; to accept that something is true
cambridge;to accept, admit, or recognize something, or the truth or existence of something:
Free Dictionary; a. To admit the existence, reality, or truth of. b. To recognize as being valid or having force or power.

So let me get straight; the complement content followed by 'acknowledge' can be understood as the fact or
the assertion depending on the context. Is it right thinking?

For providing rich context of this matter, I'd better quote the following part.
"We find verbs which occur indifferently with factive and non-factive complements.
e.g. anticipate, acknowledge, suspect, report.... Such verbs have no specification in
the lexicon as to whether their complements are factive." (Kiparsky and Kiparsky 1971:360)
 fivejedjon's reply was promoted to an answer.
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Thank you for the answer.
I think the answer will be yes or no depending on whether one has the religious faith or not.
So to say, if one is on the side of the creationism he takes the content of that-clause as a fact.
And in the case of his belief being other than the creationism, then he merely recognizes this argument to exist.

So, context is everything to determine the factivity of the complement of 'acknowledge', I think.
What is your thinking??