Combining Texts

All the ideas for 'The Laws of Thought', 'On Fate ('De fato')' and 'Models and Reality'

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11 ideas

4. Formal Logic / B. Propositional Logic PL / 1. Propositional Logic

8083	Boole applied normal algebra to logic, aiming at an algebra of thought [Boole, by Devlin]

7727	Boole's notation can represent syllogisms and propositional arguments, but not both at once [Boole, by Weiner]

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / o. Axiom of Constructibility V = L

13655

The Löwenheim-Skolem theorems show that whether all sets are constructible is indeterminate [Putnam, by Shapiro]

9915	V = L just says all sets are constructible [Putnam]

5. Theory of Logic / A. Overview of Logic / 2. History of Logic

8686	Boole made logic more mathematical, with algebra, quantifiers and probability [Boole, by Friend]

5. Theory of Logic / D. Assumptions for Logic / 1. Bivalence

21677

How can the not-true fail to be false, or the not-false fail to be true? [Cicero]

5. Theory of Logic / H. Proof Systems / 2. Axiomatic Proof

22277

Boole's method was axiomatic, achieving economy, plus multiple interpretations [Boole, by Potter]

5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems

9913	The Löwenheim-Skolem Theorem is close to an antinomy in philosophy of language [Putnam]

6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism

9914	It is unfashionable, but most mathematical intuitions come from nature [Putnam]

19. Language / F. Communication / 1. Rhetoric

21667

Oratory and philosophy are closely allied; orators borrow from philosophy, and ornament it [Cicero]

22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / g. Moral responsibility

21678

If desire is not in our power then neither are choices, so we should not be praised or punished [Cicero]