Full Idea
A 'natural' system of deduction does not posit any axioms, but looks instead for its formulae to the practices of ordinary rationality.
Gist of Idea
'Natural' systems of deduction are based on normal rational practice, rather than on axioms
Source
J Baggini / PS Fosl (The Philosopher's Toolkit [2003], §1.09)
Book Reference
Baggini,J and Fosl,P.S.: 'The Philosopher's Toolkit' [Blackwells 2003], p.26
A Reaction
Presumably there is some middle ground, where we attempt to infer the axioms of normal practice, and then build a strict system on them. We must be allowed to criticise 'normal' rationality, I hope.