Combining Texts

All the ideas for '67: Platonic Questions', 'works' and 'Mathematics, Science and Language'

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8 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 / 1. Mathematics

18119

Mathematics is a mental activity which does not use language [Brouwer, by Bostock]

6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / g. Applying mathematics

18118

Brouwer regards the application of mathematics to the world as somehow 'wicked' [Brouwer, by Bostock]

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]

15. Nature of Minds / A. Nature of Mind / 2. Psuche

5960	When the soul is intelligent and harmonious, it is part of god and derives from god [Plutarch]