Combining Texts

All the ideas for 'The Architecture of Theories', 'works' and 'Ordinatio'

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10 ideas

5. Theory of Logic / A. Overview of Logic / 2. History of Logic
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
The inferential role of a logical constant constitutes its meaning [Gentzen, by Hanna]
The logical connectives are 'defined' by their introduction rules [Gentzen]
Each logical symbol has an 'introduction' rule to define it, and hence an 'elimination' rule [Gentzen]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
Gentzen proved the consistency of arithmetic from assumptions beyond arithmetic [Gentzen, by Musgrave]
8. Modes of Existence / E. Nominalism / 1. Nominalism / b. Nominalism about universals
A universal is not a real feature of objects, but only a thought-object in the mind [William of Ockham]
17. Mind and Body / A. Mind-Body Dualism / 1. Dualism
Physical and psychical laws of mind are either independent, or derived in one or other direction [Peirce]
18. Thought / E. Abstraction / 2. Abstracta by Selection
A universal is the result of abstraction, which is only a kind of mental picturing [William of Ockham]
26. Natural Theory / D. Laws of Nature / 1. Laws of Nature
The world is full of variety, but laws seem to produce uniformity [Peirce]
27. Natural Reality / G. Biology / 3. Evolution
Darwinian evolution is chance, with the destruction of bad results [Peirce]