### Single Idea 13231

#### [catalogued under 14. Science / D. Explanation / 2. Types of Explanation / m. Explanation by proof]

Full Idea

My proposal is that an explanatory proof makes reference to the 'characterizing property' of an entity or structure mentioned in the theorem, where the proof depends on the property. If we substitute a different object, the theory collapses.

Gist of Idea

Explanatory proofs rest on 'characterizing properties' of entities or structure

Source

Mark Steiner (Mathematical Explanation [1978], p.34)

Book Reference

'Philosophy of Mathematics: anthology', ed/tr. Jacquette,Dale [Blackwell 2002], p.34

A Reaction

He prefers 'characterizing property' to 'essence', because he is not talking about necessary properties, since all properties are necessary in mathematics. He is, in fact, reverting to the older notion of an essence, as the core power of the thing.