Combining Texts

All the ideas for 'Laches', 'Introduction to 'Absolute Generality'' and 'Gentzen's Analysis of First-Order Proofs'

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11 ideas

1. Philosophy / A. Wisdom / 3. Wisdom Deflated

291	Don't assume that wisdom is the automatic consequence of old age [Plato]

4. Formal Logic / F. Set Theory ST / 1. Set Theory

13451

The two best understood conceptions of set are the Iterative and the Limitation of Size [Rayo/Uzquiano]

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / m. Axiom of Separation

13452

Some set theories give up Separation in exchange for a universal set [Rayo/Uzquiano]

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 / 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 / G. Quantification / 2. Domain of Quantification

13449

We could have unrestricted quantification without having an all-inclusive domain [Rayo/Uzquiano]

13450

Absolute generality is impossible, if there are indefinitely extensible concepts like sets and ordinals [Rayo/Uzquiano]

5. Theory of Logic / G. Quantification / 5. Second-Order Quantification

13453

Perhaps second-order quantifications cover concepts of objects, rather than plain objects [Rayo/Uzquiano]

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

13823

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

19. Language / F. Communication / 5. Pragmatics / a. Contextual meaning

13448

The domain of an assertion is restricted by context, either semantically or pragmatically [Rayo/Uzquiano]

23. Ethics / C. Virtue Theory / 3. Virtues / d. Courage

293	Being unafraid (perhaps through ignorance) and being brave are two different things [Plato]