Combining Texts

All the ideas for 'Preface to 'Principles of Philosophy'', 'Commentary on 'Posterior Analytics'' and 'The Art of the Infinite'

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11 ideas

1. Philosophy / E. Nature of Metaphysics / 4. Metaphysics as Science

21962

Metaphysics is the roots of the tree of science [Descartes]

2. Reason / F. Fallacies / 4. Circularity

3659	I know the truth that God exists and is the author of truth [Descartes]

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]

9. Objects / B. Unity of Objects / 2. Substance / b. Need for substance

16629

By comparing qualities and features, reason can gradually infer the nature of substance [Grosseteste]

11. Knowledge Aims / B. Certain Knowledge / 1. Certainty

3657	Understanding, not the senses, gives certainty [Descartes]

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

15713

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

28. God / C. Attitudes to God / 5. Atheism

3660	Atheism arises from empiricism, because God is intangible [Descartes]