Combining Texts

All the ideas for 'fragments/reports', 'Preface to 'Principles of Philosophy'' and 'works'

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11 ideas

1. Philosophy / E. Nature of Metaphysics / 4. Metaphysics as Science

21962

Metaphysics is the roots of the tree of science [Descartes]

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 / F. Fallacies / 4. Circularity

3659	I know the truth that God exists and is the author of truth [Descartes]

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 / B. Certain Knowledge / 1. Certainty

3657	Understanding, not the senses, gives certainty [Descartes]

21. Aesthetics / C. Artistic Issues / 7. Art and Morality

468	Musical performance can reveal a range of virtues [Damon of Ath.]

28. God / C. Attitudes to God / 5. Atheism

3660	Atheism arises from empiricism, because God is intangible [Descartes]