The deductive structure of a general system S in Theorem 1 can be proved inductively.
It is notorious that Aristotle's syllogistic logic cannot capture the logic of relations, and so is inadequate to the task of presenting the deductive structure of mathematics.
Kilwardby is also responsible for propagating, if not developing, the distinction between material and formal logic, where the former treats of propositions and its parts (namely the categories), while the latter treats the deductive structure of argumentation.
This analysis is most plausible in the beginning of Book I, and the initially structured presentation degenerates to a mere list of points made, often with little evident deductive structure, in the discussion of the latter part of Book I and in Book II.
As noted above, unless the hidden structure argument is accepted, this conclusion is strongly suggested by examples like (2.4.1) ("The impact of my knee caused the tipping over of the inkwell") which appear to involve explanation without the explicit citing of a law or a deductive structure.
In short order, McCrea, Walker and Robertson succumbed to Milne's methodological recommendations: first, to carry out an operationalist paring of non-observational concepts, then, secondly, to embed the resulting minimalist concept set in an axiomatic hypothetical-deductive structure.
Even so, this work did much to convince later scholars, including many of the Pragmatic View, of certain weaknesses in understanding theories as deductive axiomatic structures.
This brings us back to the deductive, geometrical structure of the Ethics.
McCrea's overall view is that theories are set up to be hypothetico-deductive in structure.
