Combining Texts

All the ideas for 'Why coherence is not enough', 'On the General Idea of Proof Theory' and 'works'

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9 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 / B. Logical Consequence / 1. Logical Consequence

13827

Logical consequence isn't a black box (Tarski's approach); we should explain how arguments work [Prawitz]

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]

5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models

13826

Model theory looks at valid sentences and consequence, but not how we know these things [Prawitz]

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]

13. Knowledge Criteria / A. Justification Problems / 2. Justification Challenges / a. Agrippa's trilemma

8840	There are five possible responses to the problem of infinite regress in justification [Cleve]

13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / a. Foundationalism

8841	Modern foundationalists say basic beliefs are fallible, and coherence is relevant [Cleve]