Mitchell, thank you for the clarification and the links. After reading them, I have a few questions about how the concepts of objectivity and physical reality you are using relate to one another.
This is where I am still not quite sure how these categories relate to one another.
Take a simple example: an ideal Euclidean circle.
No physically drawn circle is an ideal circle in the strict mathematical sense. Yet the properties of a circle do not seem to be merely a matter of personal experience or choice. Different people can independently verify the same mathematical relations and arrive at the same conclusions.
What exactly makes those relations objective in your sense, even though the ideal circle itself is not a physical object? The abstraction itself? The possibility of independent verification? Or something else?
But I am also interested in the converse kind of case.
There is, for example, the UNIVERSE+ research program on positive geometries in particle physics and cosmology. One well-known object associated with this line of research is the amplituhedron. In certain quantum field theories, scattering amplitudes can be given a geometric description in which familiar principles such as locality and unitarity are not built in as starting assumptions, but emerge from a deeper geometric structure.
The UNIVERSE+ program itself raises the broader question of a new mathematical foundation for fundamental physics that goes beyond the familiar formulations of quantum mechanics and spacetime.
What interests me here is the principle itself.
We can have a description that is objectively calculable, independently verifiable, and physically meaningful, while the question of whether the spacetime picture we use coincides with the fundamental structure of reality remains open.
This also made me wonder whether you are familiar with Donald Hoffmanâs work, particularly his interface theory of perception and the arguments he develops using evolutionary game theory.
As I understand his position, natural selection need not produce perception that truthfully represents the fundamental structure of reality. It may instead produce a useful interface sufficient for successful behavior. In the stronger version of his model, Hoffman treats spacetime and physical objects as such an interface, while conscious agents may belong to a more fundamental level of reality.
If we at least entertain that possibility, an interesting separation of categories appears.
A mathematical object that is not itself physical can be investigated objectively.
The physical world can be objectively investigated and intersubjectively verified, while this alone does not establish that its observable structure is the fundamental structure of reality.
And something accessible to us primarily through subjective participation could, at least logically, belong to a more fundamental level of reality than the observable physical world.
So it seems useful to distinguish at least three different questions:
How do we gain access to something?
To what extent can it be verified independently of an individual subject?
And to what extent does the representation obtained in this way correspond to reality itself?
This leads me to another question.
Am I understanding you correctly that, for you, âobjectiveâ refers primarily to a way of verifying or justifying knowledge, rather than to the ontological status of what is known?
If so, then where does the criterion of truth enter this picture?
What allows a person to move from:
âthis experience or belief is meaningful and compelling to meâ
to:
âthe spiritual reality to which I take this experience to refer actually existsâ?
And what allows us to distinguish such an experience from an equally subjectively compelling but mistaken belief?
It seems to me that this is where the distinction between our mode of access to reality, the objectivity of verification, and the ontological status of reality itself becomes especially important.