If no stable boundary exists between logical and non-logical simple ideas, then 'logical consequence' in Bolzano's sense collapses back into a context-sensitive, pragmatic notion rather than a formal one.
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logical consequence(WL II, 391–395; noted as similar to Tarski 1956, 419)
A proposition s is a logical consequence of a set of premises σ if and only if s follows from σ with respect to the sequence of all extra-logical simple ideas contained in σ or s.
logical vs. non-logical(as a distinction in formal logic)
Logical ideas are the basic rules and principles that make reasoning work (like 'and,' 'or,' 'if-then'), while non-logical ideas are the specific subjects we reason about (like 'dog,' 'red,' 'happy').
simple ideas(Empiricist epistemology as accepted by Price)
Ideas that cannot be invented or constructed but must be acquired through immediate intuition via a power of immediate perception in the human mind.