Combining Texts

All the ideas for 'Particulars in Particular Clothing', 'Gentzen's Analysis of First-Order Proofs' and 'works'

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10 ideas

2. Reason / A. Nature of Reason / 1. On Reason

17892

For clear questions posed by reason, reason can also find clear answers [Gödel]

5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic

13831

Logic is based on transitions between sentences [Prawitz]

5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic

9188	Gödel proved that first-order logic is complete, and second-order logic incomplete [Gödel, by Dummett]

5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives

13825

Natural deduction introduction rules may represent 'definitions' of logical connectives [Prawitz]

5. Theory of Logic / H. Proof Systems / 4. Natural Deduction

13823

In natural deduction, inferences are atomic steps involving just one logical constant [Prawitz]

5. Theory of Logic / I. Semantics of Logic / 2. Formal Truth

10620

Originally truth was viewed with total suspicion, and only demonstrability was accepted [Gödel]

5. Theory of Logic / K. Features of Logics / 5. Incompleteness

17883

Gödel's Theorems did not refute the claim that all good mathematical questions have answers [Gödel, by Koellner]

6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic

17885

Gödel eventually hoped for a generalised completeness theorem leaving nothing undecidable [Gödel, by Koellner]

10614

The real reason for Incompleteness in arithmetic is inability to define truth in a language [Gödel]

8. Modes of Existence / B. Properties / 13. Tropes / a. Nature of tropes

18431

Internal relations combine some tropes into a nucleus, which bears the non-essential tropes [Simons, by Edwards]