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It calls for a formalization of all of mathematics in axiomatic form, together with a proof that this axiomatization of mathematics is consistent.
The intuitionistic calculus aims at presenting in axiomatic form those and only those principles of propositional logic that are accepted as sound in intuitionist mathematics.
The interest in axiomatic systems at the turn of the century led to axiom systems for the known algebraic structures, that for the theory of fields, for example, being developed by the German mathematician Ernst Steinitz in 1910.
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The groundwork was a study of the four foundational problems in axiomatic formulations of pure logic.
A new mathematical concept, which is introduced in axiomatic approach in general, is discussed.
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In our axiomatic formulation, such normal in-vivo dynamics clearly violates assumption A4, and indeed we cannot expect that any one-dimensional model will adequately describe this interaction.
Arithmetic and analysis are completely conceptual and logical in their axiomatic sources and in their deductive development.
Despite his initial conjecture that the ground-consequence relation might be simple and thus undefinable, at the end of his investigation, he conjectures that grounding might well be a formal relation definable in terms of deducibility in an axiomatic system.
Nevertheless, Weyl seems to have been initially attracted to set theory at least in the axiomatic formulation Zermelo provided for it in 1908.
Thus the paradox can be handled in the frame of fuzzy logic in an axiomatic way, not enforcing any unique semantics.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com