Hello Everyone:
The more fundamental question is being part of any system, which we are, what are the limits of understanding of the system being observed, i.e. what is knowable, and at what depth?
Causality is framed in repeatable environments being explained by a series of accepted axioms for the phenomena being observed. Since the observer is part of the system the question becomes to what extent if at all, does the experimenter's presence affect the outcomes?
The set of axioms has expanded over time beginning with classical, then quantum mechanics. For each there are a series of axioms that govern the constrained environment of observations. For macroscopic objects that can be observed with the eye, causation is synonymous with correlation. Into both enter the frameworks of heuristics.
Heuristic Overview
A series of axioms based on heuristics forms the foundation for further explorations. The assumptions are the experimental environment is stable, and repeatable is required for the correlation of causation.
The set of applicable axioms for the experiment is finite. In review of anomalies George Pólya's work is of utility.
George Pólya
How to Solve It
Since the set of finite axioms with which one is applying in an artificially constructed closed system a case can be made for the work of Kurt Gödel.
Kurt Gödel
Gödel's Incompleteness Theorems
From his Incompleteness Theorem:
1. Any consistent formal [axiomatic] system F within which a certain amount of elementary arithmetic can be carried out is incomplete; i.e. there are statements of the language of F which can neither be proved nor disproved in F.
2. For any consistent system F within which a certain amount of elementary arithmetic can be carried out, the consistency of F cannot be proved in F itself.
With a correlation of causation, and a set of finite axioms, a causation that is true may, or may not be provable. If it is false it has to be provable as false to be false.
As more phenomena has been explored fundamental axioms have been added to general cause and effect environments. The perimeter at which the environment is defined, and the extent of considered variable is relevant to expedient results. Our existence belies a complexity of which we are not normally aware. A baseball player is at bat in the series. When the player hits the pitch the observers, based on their past experiences, will instantly understand the ball is out of the park without any understanding of the underlying physiology, and biochemistry of the batter.
For each environment the granularity, boundaries of observation, and applicable axioms need to be defined.
Since we are part of the system, what is knowable, accessible, true, and provable about the area of experimental observations? From Gödel there are statements that are true, but not provable, and others which are true, and provable. If the statement is true, and provable is it provable in P time, or can it be shown to be an NP time problem? From Alan Turing, and the Halting Problem, can the experimenter devise a scenario to process the data such that the computer will halt in a reasonable amount of time?
Causation with axioms fits the Gödel requirements so that a causation may be true, but not provable, true and provable, or false.
When an inconsistent experimental result is obtained what other axioms are needed to rationalize the data? I do not have any answers to these questions. The preceding has application in other areas. When in a quandary I always fall back to writing the pertinent aspects with a real pencil, and real paper. At that juncture it is often more obvious what is missing, and what is unknown.
All the Best,
Volodymyr-----------------