Perhaps Leibniz was genuinely undecided between two interpretations of the pre-established harmony and two conceptions of the reality of body, sometimes being a committed idealism and sometimes a dualist.
These indicate the relative likelihood of a hypothesised difference/association (hypothesis 1) versus no difference/association (hypothesis 2); and allow one to distinguish between two interpretations of a null result: there is evidence for the null-hypothesis or the data are insensitive in distinguishing an effect.
Bistability is a powerful paradigm to investigate perception and its underlying neural mechanisms, a phenomenon during which perception alternates between two interpretations of a single, constant stimulus [1].
The main difference between the two interpretations of the term "set" consists in the fact that the membership relation is transitive under the mereological reading, but non-transitive under the distributive one.
What we are doing with the "as", therefore, is signalling that we are agnostic on the exact nature of the relationships between the two interpretations of the TOL.
To illustrate the gulf between the two interpretations, consider the social science example of 1971's now-famous Stanford Prison Experiment.
The kappa (k) values for resident radiologists (n = 6) ranged between 0.33 and 0.59 showing fair to moderate agreement in their interpretation of the repeated scans, while the p-value was ≤0.05, implying significant agreement between the two interpretations of the repeated scans.
For risk assessment, the distinction between the two interpretations is important for the following reason: In the deterministic interpretation, the animal dose response curve reflects the experimental variation and errors in the animal study, and therefore its shape (e.g., slope) would not be relevant information for predicting risks in humans.
The posterior probability of guilt and information gain plots do not allow us to distinguish between these two interpretations of the data: Both discrimination and response bias contribute to each curve.
