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In order to falsify a hypothesis, an observation must be compared to some statement of fact that would be true if the hypothesis were true. The unspoken assumption seems to be that the observation, the statement, or both represent an objective reality.

If the two contradict each other, it is impossible for both to be objectively real. Such a case would say that “A and not-A” is true, and would violate the principle that a thing cannot be and not be at the same time. Thus, something has been falsified; either the observation or the hypothesis is wrong.

Both contradictory statements could be false in relation to the real situation, but that possibility still assumes that some objective reality exists.

So does the idea of falsification assume the existence of an objective reality?

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    In positivist theories observation is "sense data", "protocol sentences" or something to this effect. Even Quine, who criticized the idea of independent observation language from holist perspective, had "observation sentences", which are admitted to be theory laden and culturally conditioned, but less so than outright theoretical claims. So no, one does not need any objective reality to use falsification, it is compatible with full anti-realism of appearances a la Kant or cultural relativism a la Feyerabend. Popper was a realist, but even to him observation reports are mere hypotheses. – Conifold Feb 15 '18 at 20:44
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    Every reasonable account of science must assume that science is "knowledge of something". – Mauro ALLEGRANZA Feb 16 '18 at 7:02
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    @Mauro ALLEGRANZA But there can be all kinds of views what knowledge is, and on the nature of things. In this example, it is crucial to recognise the limitations on our knowledge of objective reality. The greatest power of science has been not in finding knowledge, but in opening ourselves to recognition of how much we don't know. Through accepting knowledge is only ever tentative, models and descriptions always have limitations, we have been able to lift a corner of the curtain in front of the vast unknowns around. A shift in the nature of knowledge is the cornerstone of science – CriglCragl Feb 16 '18 at 19:20
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According to Julian Barbour Discovery of Dynamics, Aristotle disguised between an objective and 'potential' reality. I've put the latter in quotes as I don't recall the term for it.

In potential reality, contradictions are obtainable. In objective reality, not so, and the classical laws of logic obtain.

It seems to me that for hypotheses to be falsifiable they must be about objective reality where we can distinguish between p & not p objectively.

That there is something in this is shown in QM where it is possible for both p and not p to hold. For example, the spin of an electron can be potentially up and down. Yet in actuality, when we come to measure it, we only find it is either up or down and not both. We can only measure an objective reality, we can however infer a potential reality of which we cannot make direct hypotheses because we don't have direct access to it.

Heisenberg found these notions of Aristotle important enough to acknowledge it in writing, referring to potentia and actualite. It's important to note - as Barbour does - that Aristotle used these concepts in his theory of motion, which was developed in in an effort to solve Zenos paradox. And what is QM, but like every theory in physics, a theory of motion.

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I am not familiar with formulations of the non-existence of objective reality, but here's my stab at the question anyway:

Suppose you have the hypothesis "All apples are red", and you see a green apple. If objective reality exists, then the hypothesis has been falsified by the observation. If objective reality does not exist, then the hypothesis was false already, because it presupposes that apples can be red (and that apples exist), and seeing a green apple does not mean that the apple is green (or that the apple exists). If, instead, your hypothesis is that "I cannot remember at this moment seeing an apple which does not look red", then seeing an apple which looks green does falsify that for as long as you can remember seeing the apple, even if it never really happened.

Essentially, if you make a hypothesis about objective facts, then it assumes that there are such things and is false if there are not. And on the other hand, a hypothesis about subjective perceptions is still perfectly falsifiable because even if nothing objectively does or doesn't have some quality outside of your mind in any given instant, you can still reason about the ideas floating around in there, just so long as you don't make any assumptions about what if anything they reflect beyond what they are.

There are probably several conceptions of non-objectivity which would find some way to assert that you can't even know your own instantaneous thoughts and memories, but at that point you're simply beyond any useful definition of "know".

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All science implies the existence of a mind independent reality towards which science marches inexorably on (unless you are a social constructivist - god forbid !).

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