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Looking at one deductive system, call it A, in the context of other deductive systems, can show how these extraneous systems motivates development of the system A. By being "in context" I mean that theorems in one system, which has presence in the logical, conceptual surrounding of the system A, hence providing context for it, are axioms or starting propositions for theorems in the system A. The systems need not to be mathematical only. What is important is that the systems are based on deductive reasoning, and that they are axiomatized as much as possible. I allow inductive reasoning, and definitely intuition as a method of discovery, but eventually, these both approaches will be morphed into a deductive structure and method. I wouldn't even differentiate inductive reasoning from deductive, but rather call it "dynamic deduction" or "deduction with self error correction".
This kind of deductive systems linking, where contextual nesting and inclusion can go infinitely (i.e. any system that provides context for system A can itself has its own context, etc), is a core of inventive, innovative thinking.
Looking at one deductive system, call it A, in the context of other deductive systems, can show how these extraneous systems motivates development of the system A. By being "in context" I mean that theorems in one system, which has presence in the logical, conceptual surrounding of the system A, hence providing context for it, are axioms or starting propositions for theorems in the system A. The systems need not to be mathematical only. What is important is that the systems are based on deductive reasoning, and that they are axiomatized as much as possible. I allow inductive reasoning, and definitely intuition as a method of discovery, but eventually, these both approaches will be morphed into a deductive structure and method. I wouldn't even differentiate inductive reasoning from deductive, but rather call it "dynamic deduction" or "deduction with self error correction".
This kind of deductive systems linking, where contextual nesting and inclusion can go infinitely (i.e. any system that provides context for system A can itself has its own context, etc), is a core of inventive, innovative thinking.
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