If a plaintiff cannot prove that a respective defendant did not believe what they published was true, what is the state of the law on the basis of this?

Secondly, should the plaintiff be unable to prove that a respective defendant did not believe what he or she published was true, then the inquiry goes on to consider whether the untrue, defamatory material was published recklessly, without considering or caring whether it be true or not. Here the inquiry becomes most subtle as indifference to the truth (recklessness) of what he or she publishes is not to be equated with carelessness, impulsiveness or irrationality in arriving at a positive belief that it is true. Lord Diplock discusses this issue extensively. He reminds us that the law takes and accepts all manner of man or woman, be they rational or irrational by nature. He puts the nub of the analysis; “but despite the imperfection of the mental process by which a belief is arrived at, it must still be ‘honest’, i.e., a positive belief that the conclusions they have reached are true. The law demands no more”. ....what is required on the part of the defamer to entitle him to the protection of the privilege is positive belief in the truth of what he published or, as it is generally though tautologously termed, ‘honest belief’. If he publishes untrue defamatory matter recklessly, without considering or caring whether it be true or not, he is in this, as in other branches of the law, treated as if he knew it to be false. p. 699, Horrocks v. Lowe, supra