Objectivity of the truth is separate, unnecessary, and non-existent
For various psychological, metaphysical, and quasi-religious reasons, many people find it insanely hard to understand an extremely simple fact – namely that quantum mechanics allows you to reason to pretty much the same extent (when it comes to the applicability) as classical physics did before the birth of quantum mechanics; but it fundamentally rejects the idea that there are statements about Nature that are objective in character.
I say it's simple and it really is. The point is that the laws of a quantum mechanical theory are tools to produce lots of statements of the form
"IF... THEN..."
These two words, "IF" and "THEN", basically cover everything that you need to understand the basic character of quantum mechanics. You don't need
43 pages of rubbish about Jesus Christ, John Wheeler, and random statements by 150 philosophers and physicists.
Quantum mechanics requires that you know some assumptions – the propositions behind the "IF". Those are the latest measurements that you, an observer, did in the past. And it allows you to derive or calculate some conclusions – the propositions behind the word "THEN". Because of this structure, "propositions are derived from others", we may say that the reasoning is
deductive.
Well, the conclusions sometimes include the word "probably" or "with the probability \(P\)" where \(P\) is a number. For this reason, it may sometimes be better to say that some of the quantum mechanical reasoning is
inductive or
abductive. But the differences between the adjectives inductive, abductive, and deductive are not what really matters.
What matters is that it's normal that there are some assumptions or inputs – the observations that have been made – and one shouldn't be surprised that there is no objective way to decide whether the assumptions are right. The truth value depends on the observer's perspective.