Combining Texts

All the ideas for 'The Architecture of Theories', 'Rechnungsmethoden (dissertation)' and 'works'

expand these ideas     |    start again     |     specify just one area for these texts

---

10 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 / c. Priority of numbers

18256

Quantity is inconceivable without the idea of addition [Frege]

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]

6. Mathematics / C. Sources of Mathematics / 2. Intuition of Mathematics

9831	Geometry appeals to intuition as the source of its axioms [Frege]

17. Mind and Body / A. Mind-Body Dualism / 1. Dualism

14802

Physical and psychical laws of mind are either independent, or derived in one or other direction [Peirce]

26. Natural Theory / D. Laws of Nature / 1. Laws of Nature

14800

The world is full of variety, but laws seem to produce uniformity [Peirce]

27. Natural Reality / G. Biology / 3. Evolution

14801

Darwinian evolution is chance, with the destruction of bad results [Peirce]