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We axiomatize a theory when there are evident truths from which we can derive other truths by a previously defined set of rules of inference. Since Frege, though, a lot have changed and mathematics is not the only object of formal logic, and the reasoning style changes completely.

Is there a way to know if a conceptual system, i.e. a body of knowledge, is ready for axiomatization? Are there indicators of whether such an axiomatization would be fruitful?

I thought of some criteria, such as complete description of phenomena with few basic concepts.

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    Axiomatized not necessarily means formalized... Having said that, most physical theories have axioms; also in other fields, included some notable attempts in philosophy: Spinoza, can be considered as examples.
    – Mauro ALLEGRANZA
    Mar 9 at 11:58
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    The question is more or less "when will I know if my ideas can be logically expressed"? Just try it (in a written form, formalization implies written expression), and you will know.
    – RodolfoAP
    Mar 9 at 12:35
  • There is no need for fire to be sad. 😅
    – Agent Smith
    Mar 9 at 18:15
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    I think "ready for axiomatization" has in mind too narrow an idea of using axiomatizations, something like organizing an established mature theory. It can be quite the opposite, fostering emerging theories in a messy unsettled field. See, for example, What are axiomatizations good for? on need for axiomatizations and their fruitfulness in economic theory.
    – Conifold
    Mar 9 at 23:22

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