What is necessary is to rectify names. [...] If names be not correct, language is not in accordance with the truth of things. If language be not in accordance with the truth of things, affairs cannot be carried on to success. When affairs cannot be carried on to success, proprieties and music will not flourish. When proprieties and music do not flourish, punishments will not be properly awarded. When punishments are not properly awarded, the people do not know how to move hand or foot. Therefore a superior man considers it necessary that the names he uses may be spoken appropriately, and also that what he speaks may be carried out appropriately. What the superior man requires, is just that in his words there may be nothing incorrect.
[tr. Legge (1861)]

One thing of necessity, the rectification of terms. [...] If terms be incorrect, language will be incongruous; and if language be incongruous, deeds will be imperfect. -- So, again, when deeds are imperfect, propriety and harmony cannot prevail, and when this is the case laws relating to crime will fail in their aim; and if these last so fail, the people will not know where to set hand or foot. -- Hence, a man of superior mind, certain first of his terms, is fitted to speak; and being certain of what he says can proceed upon it. In the language of such a person there is nothing heedlessly irregular, -- and that is the sum of the matter.
[tr. Jennings (1895)]

I would begin by defining the names of things. [...] Now, if names of things are not properly defined, words will not correspond to facts. When words do not correspond to facts, it is impossible to perfect anything. Where it is impossible to perfect anything, the arts and institutions of civilisation cannot flourish. When the arts and institutions of civilisation cannot flourish, law and justice cannot attain their ends; and when law and justice do not attain their ends, the people will be at a loss to know what to do. Therefore a wise and good man can always specify whatever he names; whatever he can specify, he can carry out. A wise and good man makes it a point always to be exact in the words he uses.
[tr. Ku Hung-Ming (1898)]

Settle the names (determine a precise terminology). [...] If words (terminology) are not (is not) precise, they cannot be followed out, or completed in action according to specifications. When the services (actions) are not brought to true focus, the ceremonies and music will not prosper; where rites and music do not flourish punishments will be misapplied, not make bullseye, and the people won’t know how to move hand or foot (what to lay hand on, or stand on). Therefore the proper man must have terms that can be spoken, and when uttered be carried into effect; the proper man’s words must cohere to things, correspond to them (exactly) and no more fuss about it.
[tr. Pound (1933)]

It would certainly be to correct language. [...] If language is incorrect, then what is said does not concord with what was meant; and if what is said does not concord with what was meant, what is to be done cannot be effected. If what is to be done cannot be effected, then rites and music will not flourish. If rites and music do not flourish, then mutilations and lesser punishments will go astray. And if mutilations and lesser punishments go astray, then the people have nowhere to put hand or foot. Therefore the gentleman uses only such language as is proper for speech, and only speaks of what it would be proper to carry into effect. The gentleman, in what he says, leaves nothing to mere chance.
[tr. Waley (1938)]

The indispensable is to render designations correct. [...] If the designations are not correct, language will not be clear. If language is not clear, duties will not be carried out. If duties arc not carried out, rites and music will not flourish. If rites and music do not flourish, then punishments will not be specific. If punishments arc not specific, then the people will do nothing without getting into trouble, lienee when the perfect gentleman has given something a name it may with all certainty be expressed in language; when he expresses it, it may with certainty be set in operation. In regard to his language the perfect gentleman is never careless in any respect.
[tr. Ware (1950)]

If something has to be put first, it is, perhaps, the rectification (cheng) of names. [...] When names are not correct, what is said will not sound reasonable; when what is said does not sound reasonable, affairs will not culminate in success; when affairs do not culminate in success, rites and music will not flourish; when rites and music do not flourish, punishments will not fit the crimes; when punishments do not fit the crimes, the common people will not know where to put hand or foot. Thus when the gentleman names something, the name is sure to be usable in speech, and when he says something this is sure to be practicable. The thing about the gentleman is that his is anything but casual where speech is concerned.
[tr. Lau (1979)]

What is necessary is to rectify names, is it not? [...] If names are not rectified, then words are not appropriate. If words are not appropriate, then deeds are not accomplished. If deeds are not accomplished, then the rites and music do not flourish. If the rites and music do not flourish, then punishments do not hit the mark. If punishments do not hit the mark, then the people have nowhere to put hand or foot. So when a gentleman names something, the name can definitely be used in speech; and when he says something, it can definitely be put into practice. In his utterances the gentleman is definitely not casual about anything.
[tr. Dawson (1993)]

It would certainly be to rectify the names. [...] If the names are not correct, language is without an object. When language is without an object, no affair can be effected. When no affair can be effected, rites and music wither. When rites and music wither, punishments and penalties miss their target. When punishments and penalties miss their target, the people do not know where they stand. Therefore whatever a gentleman conceives of, he must be able to say; and whatever he says, he must be able to do. In the matter of language, a gentleman leaves nothing to chance.
[tr. Leys (1997)]

It must be the rectification of character. [...] For if characters are not correct, speech will not be relevant; if speech is not relevant, affairs will not be accomplished; if affairs are not accomplished, the rituals and music will not prevail; if the rituals and music do not prevail, tortures and penalties will not be just right; if tortures and penalties are not just right, the people will not know where to put their hands and feet. Therefore, when the gentleman adopts a character, he surely can used it to say things; when he says something, it surely can be put into practice. The gentleman, in regard to his speech, is never negligent, that is all.
[tr. Huang (1997)]

I must define the intention of names! [...] If the intention of names is not defined, the word will not be exact; if the word is not exact, the thing will not be done; if the thing is not done, the rituals and music will not be practiced; if the rituals and music are not practiced, the penalty will not be appropriate; if the penalty is not appropriate, people will not know where to go and how to do. So a gentleman must can word out its intention when he names a thing, and must can practice it after he words out the intention. So a gentleman is never unserious to his words.
[tr. Cai/Yu (1998), #313]

Without question it would be to insure that names are used properly (zhengming). [...] When names are not used properly, language will not be used effectively; when language is not used effectively, matters will not be taken care of; when matters are not taken care of, the observance of ritual propriety (li) and the playing of music (yue) will not flourish; when the observance of ritual propriety and the playing of music do not flourish, the application of laws and punishments will not be on the mark. When the application of laws and punishments is not on the mark, the people will not know what to do with themselves. Thus, when the exemplary person puts a name to something, it can certainly be spoken, and when spoken it can certainly be acted upon. There is nothing careless in the attitude of the exemplary person toward what is said.
[tr. Ames/Rosemont (1998)]

It would certainly be to rectify names, would it not? [...] If names are not rectified, speech will not be representative. If speech is not representative, things will not get done. If things do not get done, rites and music will not flourish. If rites and music do not flourish, punishments and penalties will not be just. And if punishments and penalties are not just, the people will have nowhere to put hand or foot. Therefore, as to the gentleman: if he names something, it must be sayable, and if he says something, it must be doable. The gentleman's relation to words is to leave nothing whatever to chance.
[tr. Brooks/Brooks (1998)]

The rectification of names. Without a doubt. [...] Listen. If names aren't rectified, speech doesn't follow from reality. If speech doesn't follow from reality, endeavors never come to fruition. If endeavors never come to fruition, then Ritual and music cannot flourish. If Ritual and music cannot flourish, punishments don't fit the crime. If punishments don't fit the crime, people can't put their hands and feet anywhere without fear of losing them. Naming enables the noble-minded to speak, and speech enables the noble-minded to act. Therefore, the noble-minded are anything but careless in speech.
[tr. Hinton (1998)]

It would, of course, be the rectification of names. [...] If names are not rectified, speech will not accord with reality; when speech does not accord with reality, things will not be successfully accomplished. When things are not successfully accomplished, ritual practice and music will fail to flourish; when ritual and music fail to flourish, punishments and penalties will miss the mark. And when punishments and penalties miss the mark, the common people will be at a loss as to what to do with themselves. This is why the gentleman only applies names that can be properly spoken and assures that what he says can be properly put into action. The gentleman simply guards against arbitrariness in his speech. That is all there is to it.
[tr. Slingerland (2003)]

If I had to name my first action, I would rectify names. [...] If names are not rectified, then speech will not function properly, and if speech does not function properly, then undertakings will not succeed. If undertakings do not succeed, then rites and music will not flourish. If rites and music do not flourish, then punishments and penalties will not be justly administered. And if punishments and penalties are not justly administered, then the common people will not know where to place their hands and feet. Therefore, when the gentleman names a thing, that naming can be conveyed in speech, and if it is conveyed in speech, then it can surely be put into action. When the gentleman speaks, there is nothing arbitrary in the way he does so.
[tr. Watson (2007)]

It would have to be rectifying names. [...] If names are not rectified, what is said will not seem reasonable. When what is said does not seem reasonable, nothing will be accomplished. When nothing gets accomplished, rites and music will not flourish. When rites and music do not flourish, punishment and penalties [will take their place, and they] will fail to be just when put into use. And when punishments and penalties fail to be just in practice, people will not know where to put their hands and feet. Thus when a gentleman names something, the name can surely hold up in speech. When he says something, his words can surely be carried out in action. When a gentleman speaks, there is nothing casual or careless about what he says.
[tr. Chin (2014)]

For the man of education will seek exactness so far in each subject as the nature of the thing admits, it being plainly much the same absurdity to put up with a mathematician who tries to persuade instead of proving, and to demand strict demonstrative reasoning of a Rhetorician.
[tr. Chase (1847), ch. 1]

It is the mark of an instructed mind to rest satisfied with the degree of precision which the nature of the subject admits and not to seek exactness where only an approximation is possible.
[Source (1852) - earliest version of this frequent translation I found.]

A man who has been well trained will not in any case look for more accuracy than the nature of the matter allows; for to expect exact demonstration from a rhetorician is as absurd as to accept from a mathematician a statement only probable.
[tr. Williams (1869)]

For an educated person will expect accuracy in each subject only so far as the nature of the subject allows; he might as well accept probable reasoning from a mathematician as require demonstrative proofs from a rhetorician.
[tr. Welldon (1892), ch. 2]

For it is the mark of an educated man to require, in each kind of inquiry, just so much exactness as the subject admits of: it is equally absurd to accept probable reasoning from a mathematician, and to demand scientific proof from an orator.
[tr. Peters (1893)]

For it is the mark of an educated mind to expect that amount of exactness in each kind which the nature of the particular subject admits. It is equally unreasonable to accept merely probable conclusions from a mathematician and to demand strict demonstration from an orator.
[tr. Rackham (1934)]

For it is characteristic of a well-educated person to look for the degree of exactness in each kind of investigation that the nature of the subject itself allows. For it is evident that accepting persuasive arguments from a mathematician is like demanding demonstrations from a rhetorician.
[tr. Reeve (1948)]

For a well-schooled man is one who searches for that degree of precision in each kind of study which the nature of the subject at hand admits: it is obviously just as foolish to accept arguments of probability from a mathematician as to demand strict demonstrations from an orator.
[tr. Ostwald (1962)]

For it is the mark of an educated man to seek as much precision in things of a given genus as their nature allows, for to accept persuasive arguments from a mathematician appears to be [as improper as] to demand demonstrations from a rhetorician.
[tr. Apostle (1975)]

For it is the mark of the trained mind never to expect more precision in the treatment of any subject than the nature of that subject permits; for demanding logical demonstrates from a teacher of rhetoric is clearly about as reasonable as accepting mere plausibility from a mathematician.
[tr. Thomson/Tredennick (1976)]

Since it is the mark of an educated person to look in each area for only that degree of accuracy that the nature of the subject permits. Accepting persuasive arguments from a mathematician is like demanding demonstrations from a rhetorician.
[tr. Crisp (2000)]

For it is the mark of an educated person to search for the same kind of clarity in each topic to the extent that the nature of the matter accepts it. For it is similar to expect a mathematician to speak persuasively or for an orator to furnish clear proofs!
[tr. @sentantiq (2018)]

For it belongs to an educated person to seek out precision in each genus to the extent that the nature of the matter allows: to accept persuasive speech from a skilled mathematician appears comparable to demanding demonstrations from a skilled rhetorician.
[tr. Bartlett/Collins (2011)]