Combining Texts

All the ideas for 'The Lagoon: how Aristotle invented science', 'The Art of the Infinite' and 'Stipulation, Meaning and Apriority'

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14 ideas

1. Philosophy / C. History of Philosophy / 2. Ancient Philosophy / b. Pre-Socratic philosophy

21355

The Pre-Socratics are not simple naturalists, because they do not always 'leave the gods out' [Leroi]

2. Reason / D. Definition / 13. Against Definition

9331	How do we determine which of the sentences containing a term comprise its definition? [Horwich]

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]

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]

12. Knowledge Sources / A. A Priori Knowledge / 1. Nature of the A Priori

9333	A priori belief is not necessarily a priori justification, or a priori knowledge [Horwich]

12. Knowledge Sources / A. A Priori Knowledge / 6. A Priori from Reason

9342	Understanding needs a priori commitment [Horwich]

12. Knowledge Sources / A. A Priori Knowledge / 8. A Priori as Analytic

9332	Meaning is generated by a priori commitment to truth, not the other way around [Horwich]

12. Knowledge Sources / A. A Priori Knowledge / 9. A Priori from Concepts

9341	Meanings and concepts cannot give a priori knowledge, because they may be unacceptable [Horwich]

9334	If we stipulate the meaning of 'number' to make Hume's Principle true, we first need Hume's Principle [Horwich]

12. Knowledge Sources / A. A Priori Knowledge / 10. A Priori as Subjective

9339	A priori knowledge (e.g. classical logic) may derive from the innate structure of our minds [Horwich]

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

15713

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