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Ideas for 'Tropes', 'Logical Necessity' and 'Mathematical logic and theory of types'

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6 ideas

5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence

12195

Soundness in argument varies with context, and may be achieved very informally indeed [Rumfitt]

12199

There is a modal element in consequence, in assessing reasoning from suppositions [Rumfitt]

12201

We reject deductions by bad consequence, so logical consequence can't be deduction [Rumfitt]

5. Theory of Logic / D. Assumptions for Logic / 3. Contradiction

12194

Contradictions include 'This is red and not coloured', as well as the formal 'B and not-B' [Rumfitt]

5. Theory of Logic / H. Proof Systems / 2. Axiomatic Proof

12198

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

5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / d. Russell's paradox

6407	The class of classes which lack self-membership leads to a contradiction [Russell, by Grayling]