Combining Texts

All the ideas for 'fragments/reports', 'Criterion of Validity in Reasoning' and 'works'

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11 ideas

2. Reason / A. Nature of Reason / 4. Aims of Reason
I reason in order to avoid disappointment and surprise [Peirce]
3. Truth / H. Deflationary Truth / 1. Redundant Truth
That a judgement is true and that we judge it true are quite different things [Peirce]
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 / A. Overview of Logic / 3. Value of Logic
Only study logic if you think your own reasoning is deficient [Peirce]
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]
7. Existence / D. Theories of Reality / 8. Facts / a. Facts
Facts are hard unmoved things, unaffected by what people may think of them [Peirce]
9. Objects / E. Objects over Time / 8. Continuity of Rivers
Cratylus said you couldn't even step into the same river once [Cratylus, by Aristotle]
13. Knowledge Criteria / D. Scepticism / 1. Scepticism
Cratylus decided speech was hopeless, and his only expression was the movement of a finger [Cratylus, by Aristotle]