According to Aristotle’s demarcation, there are two kinds of science. There are the special sciences characterised by their determined study object. This embraces all traditional sciences including classical physics and axiomatic mathematics. Secondly, the science nowadays called metaphysics, is characterised by its study object having an undetermined genus. In this paper, I identify the quantum object as an instance of the fundamental study object of metaphysics.

Every science, to be tractable, requires first principles. For the special sciences, the first principles Ψ play the role as the foundational indemonstrables of the system, assumed true. The special sciences hence are based on rule-based ethics to apply deductive inference from the indemonstrables Ψ on the left to infer the consequents Θ on the right, as illustrated by the syllogism schematic F:

In the case of metaphysics, the reasoning is reversed. Starting from the right with the study-object Θ’ itself, the inference arrives at the indemonstrables Ψ’. This can be understood as what I call a co-syllogism G, illustrated by the schematic:

I refer to deductive inference #1 as expressing left-side rationality and non-deductive inference #2 as expressing right-side rationality.

In mathematics, naturality is colloquially regarded as avoiding ad hoc arbitrary constructs. Set theory is inadequate as a basis for formalising naturality. One must turn from the world of symbols to the “dyads” of Category Theory and the notion of natural transformations. A tractable starting point is to define naturality in terms of demanding First Classness (FC) defined as

In a world of undistinguished entities, one starts with entity X. This violates FC as X becomes a distinguished entity. Thus, FC theory must be starting point invariant. We are already on our way with our “logic of discovery,” and understanding the nature of the quantum object.

A key player in the solution is the role of category theoretic adjointness. Even #2 may be considered as the right adjoint of #1.

This approach involves reverse-engineering the Stoic synthesis of ethics, logic, and physics. Real physics results will be demonstrated using this physics-without-number methodology.

Keywords: Logic of discovery, ampliative reasoning, emergence, Stoicism, Category Theory

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