Combining Texts

All the ideas for 'works', 'Phenomenalism' and 'An Outline of Empiricism'

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9 ideas

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

17892

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

2. Reason / A. Nature of Reason / 7. Status of Reason

23248

Early empiricists said reason was just a useless concept introduced by philosophers [Galen, by Frede,M]

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 / 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]

11. Knowledge Aims / C. Knowing Reality / 2. Phenomenalism

2614	Modern phenomenalism holds that objects are logical constructions out of sense-data [Ayer]

12. Knowledge Sources / B. Perception / 4. Sense Data / a. Sense-data theory

2615	The concept of sense-data allows us to discuss appearances without worrying about reality [Ayer]