Combining Texts

All the ideas for 'fragments/reports', 'The Laws of Thought' and 'The Art of the Infinite'

expand these ideas     |    start again     |     specify just one area for these texts

---

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 / j. Axiom of Choice IX

15717

Using Choice, you can cut up a small ball and make an enormous one from the pieces [Kaplan/Kaplan]

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 / H. Proof Systems / 2. Axiomatic Proof

22277

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

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number

15712

1 and 0, then add for naturals, subtract for negatives, divide for rationals, take roots for irrationals [Kaplan/Kaplan]

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers

15711

The rationals are everywhere - the irrationals are everywhere else [Kaplan/Kaplan]

6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / f. Arithmetic

15714

'Commutative' laws say order makes no difference; 'associative' laws say groupings make no difference [Kaplan/Kaplan]

15715

'Distributive' laws say if you add then multiply, or multiply then add, you get the same result [Kaplan/Kaplan]

13. Knowledge Criteria / E. Relativism / 2. Knowledge as Convention

1556	By nature people are close to one another, but culture drives them apart [Hippias]

14. Science / C. Induction / 3. Limits of Induction

15713

The first million numbers confirm that no number is greater than a million [Kaplan/Kaplan]