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Single Idea 12198

[from 'Logical Necessity' by Ian Rumfitt, in 5. Theory of Logic / H. Proof Systems / 2. Axiomatic Proof ]

Full Idea

The geometrical style of formalization of logic is now little more than a quaint anachronism, largely because it fails to show logical truths for what they are: simply by-products of rules of inference that are applicable to suppositions.

Gist of Idea

Geometrical axioms in logic are nowadays replaced by inference rules (which imply the logical truths)

Source

Ian Rumfitt (Logical Necessity [2010], §1)

Book Reference

'Modality', ed/tr. Hale,B/Hoffman,A [OUP 2010], p.41


A Reaction

This is the rejection of Russell-style axiom systems in favour of Gentzen-style natural deduction systems (starting from rules). Rumfitt quotes Dummett in support.