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The Phenomenology of Second-Level Inference: Perfumes in The Deductive Garden
Bulletin of the Section of Logic, Tome 49 (2020) no. 4, pp. 327-342.

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We comment on certain features that second-level inference rules commonly used in mathematical proof sometimes have, sometimes lack: suppositions, indirectness, goal-simplification, goal-preservation and premise-preservation. The emphasis is on the roles of these features, which we call 'perfumes', in mathematical practice rather than on the space of all formal possibilities, deployment in proof-theory, or conventions for display in systems of natural deduction.
Keywords: second-level inference, suppositions, indirect inference, goal simplification, goal preservation, wlog, premise preservation 
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Makinson, David. The Phenomenology of Second-Level Inference: Perfumes in The Deductive Garden. Bulletin of the Section of Logic, Tome 49 (2020) no. 4, pp. 327-342. http://geodesic.mathdoc.fr/item/BSL_2020_49_4_a0/

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