A few simple formulas which illustrate the mathematical impossibility of objectivity.
Believers in objectivity generally cite the following observations to support their belief: consensus, repeatability and the infallibility of instruments. Let us take a look how those hypotheses hold up mathematically.
Our first step is to define objectivity, and in this case, we are going to do so in relation to subjectivity. Objectivity implies that an observed phenomena appears to the observer as it would to any other observer, or even in the absence of observers. Subjectivity suggests that an observed phenomena is unique to the observer and observation. Given that we cannot directly experience any observation except for our own, we must default to subjectivity as the mode in which observation occurs. Objectivity is deduced from subjective observations in which consensus, repeatability and infallibility of instruments is also observed, but are those deductions mathematically justified?
Now let us assign a value of 0 (zero) to subjectivity and 1 (one) to objectivity.
The value of each observation independently is zero. Can we take multiple observations as proof of objectivity? What about ten people?
We cannot mathematically arrive at objectivity through consensus.
The value of each observation independently is zero. Can we take repeated observations as proof of objectivity? What about ten repetitions?
We cannot mathematically arrive at objectivity through repetition.
Infallibility of Instrument
This is not even a valid argument, since instruments are developed, used and observed by subjective individuals. They do not exist independent of human observers and their subjectivity. How could subjective beings build something which not only is objective itself, but can be observed objectively unlike absolutely everything else?
How much subjective information can be applied to a technology to cause it to transcend subjectivity?
We cannot mathematically arrive at objectivity through the infallibility of instruments.
Objectivity would require some kind of numerical magic, and that only seems to appear in songs for children.
Mathematics are not objective, either, they are axiomatic. They are a language of description, not the programming code which causes the phenomena described.