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My friend (who is native German, we are both academics) wishes to include a sentence like this in his thesis:

"It is possible to design approximation algorithms which come conceivably close to exact algorithms."

The intended meaning here is that the algorithms of one type (approximation algorithms) are as close as one can imagine to the other type (exact algorithms).

My question is about the phrase "conceivably close". It did not sound right to me when reading the sentence, but my friend is quite convinced that such a formulation makes sense in English too. As an alternative, he would say the algorithms are "imaginably close" to each other.

Neither choice does sound correct to me, even the meaning eluded me at first, but I am not a native English speaker, either. Most of the time, I see the use with the adverb meaning a negative thing or a strange thing, things being "incredibly close" or "eerily close". I have used Google, but these phrases do come up -- interestingly, often by German authors or in English-language websites on Germany, but not exclusively so.

Can you help us figure out if the word choice is proper to use and the meaning comes across?

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    You are right that neither conceivably nor imaginably is adequate for the purpose. If it is not essential that the term be a single word, then the intended meaning can be conveyed by something like 'so close to exact algorithms as to be indistinguishable from them for all practical purposes'. What would be more interesting for the purposes of this site than just finding a substitute expression, is to explain why conceivably is a wrong word to use here; I suspect that it is due to its functioning as a negative polarity item of sorts.
    – jsw29
    Commented Oct 12, 2022 at 21:12
  • Indeed, a reformulation is possible. My question, as well as my difficulty, lies in proving or validating that the specific word choice is not right, as naive Google search does find the combination, however infrequent.
    – M. B.
    Commented Oct 12, 2022 at 22:06
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    Just go with very.
    – Jim
    Commented Oct 12, 2022 at 22:29
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    If you want a technical term for one thing coming as close to another as you like, you could probably go with "arbitrarily close" - that's what we use in maths, to mean you can make one thing as close to another as you like.
    – Showsni
    Commented Oct 12, 2022 at 23:10
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    It seems like the sentence is trying to suggest that an approximation is an approximation. The problem with "conceivably" is that it does not actually specify a metric. "Arbitrarily close" is useful because it suggests that it will be close based upon any arbitrary metric.
    – Yorik
    Commented Oct 13, 2022 at 19:49

3 Answers 3

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You could say conceivably close with your intended meaning.

Here's a snippet from a book that does it:

...it is this endogeneity coupled with the multiplicity of candidates, and hence the multiplicity of conceivably close races, that gives rise to the analytical complexity of the problem.

And here's a snippet from a journal that does it:

although a strict generalization of the results cannot be assured, considering the characteristics of the centers assessed the estimates are conceivably close to the overall situation of the HD patients in the country.

In the same vein, you could also say imaginably close.

Here's one example from a book:

I could have expected nothing imaginably close to this.

And here's an example from a journal:

I think this comes imaginably close to happening in the case of Schindler.

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    What exactly does "conceivably close" mean here? I'm not sure it means "as close as we can imagine"; it is more likely for "conceivably" to mean "possibly" or "imaginably".
    – Stuart F
    Commented Nov 7, 2022 at 22:12
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It is possible to design approximation algorithms which come exceptionally close to exact algorithms

is what I suggest.

'exceptionally' means - as close as makes no difference. Almost the real thing, in this case.

Indistinguishable.

https://dictionary.reverso.net/english-cobuild/an+exceptionally+close+view

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So far as the meaning of the word is concerned, something is conceivable if and only if it can be conceived. There would thus, at first sight, appear to be no obstacle to using its derivative, conceivably, in this way. The same goes for imaginably.

To understand why that would, nevertheless, be awkward, and possibly counterproductive, we need to consider the pragmatics. For what purposes are these words typically used in English? Obviously, saying that something is conceivable informs us that it is not inconceivable. A round square is inconceivable, unimaginable. That makes round squares altogether, completely, absolutely impossible. Saying that something is conceivable tells us that it is not like a round square: it is, in at least some way, possible. Pink elephants and winged horses, for example, are conceivable, imaginable. There are no such creatures, but there could be, and we understand what they would be like, if they existed. Now, the ordinary elephants that can be seen in the zoo, and the ordinary horses that can be seen on the racecourse, are also conceivable, but we do not normally say that. Why? Because there are stronger, more informative things that we can say about them. We can say, for example, that there are some elephants in the zoo. Or, if we are not certain about the matter, we can say that it is possible/probable/likely that there are some elephants in the zoo. We thus reserve the words conceivable and imaginable for the cases, like that of the pink elephants, in which we cannot say anything like that. As a matter of meaning these words convey the idea that the thing in question is possible, but as a matter conversational implicatures, they also convey the idea that it is not probable/likely/certain/actual; in other words they convey the idea that it is nothing more than barely possible.

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