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Throughout history, there has been a long-standing debate on the [[ontological]] and [[epistemological]] aspects of causality and emergence.

Throughout history, there has been a long-standing debate on the [[ontological]] and [[epistemological]] aspects of causality and emergence.

For example, Yurchenko pointed out in literature <ref>Yurchenko, S. B. (2023). Can there be a synergistic core emerging in the brain hierarchy to control neural activity by downward causation?. Authorea Preprints.</ref> that the concept of "causation" is often vague and should be distinguished into two different concepts, cause and reason, which conform to the ontological and epistemological causation respectively. Among them, cause refers to the real cause that fully leads to the result, while reason is only the observer's explanation of the result. Reason may not be as strict as a real cause, but it does provide a certain degree of [[predictability]]. Similarly, there is also a debate about the nature of causal emergence.

For example, Yurchenko pointed out in literature <ref>Yurchenko, S. B. (2023). Can there be a synergistic core emerging in the brain hierarchy to control neural activity by downward causation?. Authorea Preprints.</ref> that the concept of "causation" is often vague and should be distinguished into two different concepts, cause and reason, which conform to the ontological and epistemological causation respectively. Among them, cause refers to the real cause that fully leads to the effect, while reason is only the observer's explanation of the result. Reason may not be as strict as a real cause, but it does provide a certain degree of [[predictability]]. Similarly, there is also a debate about the nature of causal emergence.

Is causal emergence a real phenomenon that exists independently of a specific observer? Here it should be emphasized that for Hoel's theory, different coarse-graining strategies can lead to different macroscopic dynamical mechanisms and different measures of the strength of causal effects (<math>EI</math>). Essentially, different coarse-graining strategies can represent different observers. Hoel's theory links emergence with causality through intervention and introduces the concept of causal emergence in a quantitative way. Hoel's theory proposes a scheme to eliminate the influence of different coarse-graining strategy, that is, maximizing <math>EI</math>. The coarse-graining strategy that maximizes EI is the only objective scheme. Therefore, for a given set of [[Markov dynamics]], only the coarse-graining strategy and corresponding macroscopic dynamics that maximize <math>EI</math> can be considered objective results. If multiple coarse-graining strategies maximize <math>EI</math> is not unique, that is, there are multiple coarse-graining strategies that can maximize <math>EI</math>, it introduces theoretical difficulties and unavoidable subjectivity.

Is causal emergence a real phenomenon that exists independently of a specific observer? Here it should be emphasized that for Hoel's theory, different coarse-graining strategies can lead to different macroscopic dynamical mechanisms and different measures of the strength of causal effects (<math>EI</math>). Essentially, different coarse-graining strategies can represent different observers. Hoel's theory links emergence with causality through intervention and introduces the concept of causal emergence in a quantitative way. Hoel's theory proposes a scheme to eliminate the influence of different coarse-graining strategy, that is, maximizing <math>EI</math>. The coarse-graining strategy that maximizes EI is the only objective scheme. Therefore, for a given set of [[Markov dynamics]], only the coarse-graining strategy and corresponding macroscopic dynamics that maximize <math>EI</math> can be considered objective results. If multiple coarse-graining strategies maximize <math>EI</math> is not unique, that is, there are multiple coarse-graining strategies that can maximize <math>EI</math>, it introduces theoretical difficulties and unavoidable subjectivity.