Alex: you say that because several scientists get the same value of a measurement, that it is not dependent on pattern comparisons of the scientists. No way!
Also, it is known as 'the reductive fallacy' to claim that a necessary condition for "A" (math of photon") is the same as "A". 'Math description of photon' AND photon both exist. Just as math description of "You take 1 apple from tabletop" (1-1=0) correctly depicts that event but is not the same as that event. Both exist (math-relationship and the event)
I wrote this proof for debate with Luis once:
1. Empiricism: Consider the claim: "...in order for a phenomenon to be labelled "objective", I'd venture to say at least two people would have to observe it. In fact this is the very nature of empiricism".
2. But what use is that, if the two scientists cannot communicate with each other or with others? So 'empiricism' depends on communication between people. But how do people communicate? By noticing similarities between their internal states. If you couldn't notice anything in common with another; you would have no language. All their sounds, signs, symbols would be a mystery.
3. So: empiricism requires communication; and communication requires similarities be noticed between the party's internal worlds. But to notice similarities between those internal worlds, requires each and every scientist to notice things about his/ her internal world.
4. And so, the very empiricism that scientists hold in such high regard; is totally dependent on individuals noticing their own internal worlds! Now, the common ground of 'similarities' that scientists notice in their internal worlds is represented by the 'net' in the following: Suppose you ran a storage warehouse for goods. And you had regular deliveries of fish from a fishing fleet,to be stored. And you knew that everything caught by the fishing fleet was delivered. But what if the nets used were a large-grid size, and many species sliped through the nets?
5. It would be a mistake to conclude that the contents of the sea were correctly depicted by the catch.
6. What if there are "nets" unknown to scientists that mean much of "reality" is not being caught; and what if scientists do not even notice that this filter is even there?
7.To improve the clarity of view of reality through this net; each scientist must notice as much as possible about his own internal world.
8. With more scientists doing this, more similarities with other scientists may become apparent. And the more similarities noticed, the better the communication among scientists and the better the testing of individual claims. So to improve the quality of scientific communication; each scientist would do well to "know thyself")
9. Why not take this further? Replace the scientists with machines, and make two machines so similar they are identical! The most accurate validation of a machine-X observation of event Y is another machine-X. Suppose machine-X observes Y and is tested by machine-Z.
10. If machine-Z had nothing in common with machine-X; then machine-Z wouldn't make any sense of machine-X, let alone verify X's observation.
11. The more that machine-Z is similar to machine-X; the more certain it can be that it is fairly testing X's observation report. The more that scientists can learn about themselves and increase the pool of common criteria to them all; the more empirical their science will be!
12. Suppose you say: Scientist A just has to use a little knowledge set K1 to observe an experiment; and scientist B just needs that same little knowledge set K1 to validate A's report. (Which is what scientists actually do).
But wait; what check does A use to be sure that his K1 criteria, for proper observing, is the same as the K1 of B"?
13. He must appeal to a further level of comparison; C1. And how does he know his C1 is the same as B's C1 criteria for assessing if they are using similar K1s (to judge the 'properly-comparable observation-method' question)?
14. He must appeal to yet another level of verification, V1. and how can he be sure that B's knowledge V1 is the same?
He has to appeal to a further level. Now we see empiricism breaking apart; because at some level the 'comparison criteria' of A and B may become increasingly different; and we find the comparison 'little knowledge sets' start to contain guesses and presumptions as to whether the other scientist is using the same "measuring stick', so to speak.
15. I could continue this description and show the closeness of this 'multi-level' comparison-verification process to the "Schrodinger's cat" question; to the probabilistic maths of the quantum; and to the way the brain works.
16. It appears that I have demonstrated that one's 'internal' world does have bearing on reality. It has been shown that internal investigation is both valid, and desirable, as a scientific enterprise. It has been shown that the whole of 'empiricist' science is utterly dependent on the comparisons scientists make between their 'taken for granted' internal-world awareness' and similarities with others' such awareness.
17. I have shown that having two or more observers of an event does not remove the subjective foundation of the 'empiricists' science.
18. So at some level scientists may be using non-identical 'knowledge sets', or non-identical measuring sticks, to compare other levels of measure sticks in verifying objectivity of an experiment. Their 'knowledge sets' might involve guesses. The more guesses made about another scientist's verification criteria; the more uncertain you might say the objectivity of the measurement is. This is comparable with the alleged uncertainty of the status of the cat in the Schrodinger's cat scenario. So the matrices and wave equations applied to that scenario, might apply to the scientist-scientist communication-verification scenario. Maybe scientists thus are seeing the uncertainty of the set: 'scientists'; reflected back at them in some way, when they depict the alleged uncertainty of quantum events.