Combining Texts

All the ideas for 'fragments/reports', 'Reals by Abstraction' and 'works'

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7 ideas

5. Theory of Logic / A. Overview of Logic / 2. History of Logic

11022

Gentzen introduced a natural deduction calculus (NK) in 1934 [Gentzen, by Read]

5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives

11065

The inferential role of a logical constant constitutes its meaning [Gentzen, by Hanna]

11023

The logical connectives are 'defined' by their introduction rules [Gentzen]

11213

Each logical symbol has an 'introduction' rule to define it, and hence an 'elimination' rule [Gentzen]

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers

10632

The real numbers may be introduced by abstraction as ratios of quantities [Hale, by Hale/Wright]

6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic

10067

Gentzen proved the consistency of arithmetic from assumptions beyond arithmetic [Gentzen, by Musgrave]

10. Modality / A. Necessity / 8. Transcendental Necessity

490	Everything happens by reason and necessity [Leucippus]