Combining Texts

All the ideas for 'Isagoge ('Introduction')', 'Letters to Remond de Montmort' and 'works'

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11 ideas

2. Reason / A. Nature of Reason / 1. On Reason
For clear questions posed by reason, reason can also find clear answers [Gödel]
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
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
Originally truth was viewed with total suspicion, and only demonstrability was accepted [Gödel]
5. Theory of Logic / K. Features of Logics / 5. Incompleteness
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
Gödel eventually hoped for a generalised completeness theorem leaving nothing undecidable [Gödel, by Koellner]
The real reason for Incompleteness in arithmetic is inability to define truth in a language [Gödel]
8. Modes of Existence / D. Universals / 1. Universals
Are genera and species real or conceptual? bodies or incorporeal? in sensibles or separate from them? [Porphyry]
10. Modality / C. Sources of Modality / 2. Necessity as Primitive
Some necessary truths are brute, and others derive from final causes [Leibniz]
15. Nature of Minds / B. Features of Minds / 1. Consciousness / c. Parts of consciousness
Our large perceptions and appetites are made up tiny unconscious fragments [Leibniz]
18. Thought / A. Modes of Thought / 3. Emotions / c. Role of emotions
Passions reside in confused perceptions [Leibniz]
28. God / A. Divine Nature / 2. Divine Nature
God produces possibilities, and thus ideas [Leibniz]