If the intended structure M is apprehended through a conceptually prior informal understanding, invoking M is not question-begging but rather an appeal to the evidential basis that motivated the axioms in the first place.

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Conceptually prior(as used in epistemology): Something that is logically or mentally more basic or fundamental—you need to understand it before you can understand something else.
apprehended(as used in epistemology (the study of knowledge)): Understood or grasped mentally; basically, when you come to know or perceive something.
axioms(Stumpf, 1891): Propositions that we assume to be true and necessary, originating in the content of judgments.
evidential basis(as used in epistemology and logic): The collection of facts, observations, or reasons that support or justify a conclusion.
informal understanding(as used in epistemology): A loose, intuitive grasp of something based on common sense or rough experience, rather than a strict formal definition.
question-begging(Epistemology, anti-skeptical argumentation): A charge leveled against anti-skeptical arguments that assume what they set out to prove, particularly in Putnamian externalist arguments
structure M(as used in logic and formal philosophy): A formal system or logical framework being discussed; the 'M' is just a label (like calling something 'X' in algebra) that stands for some organized set of rules or relationships.

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