Combining Texts

All the ideas for 'fragments/reports', 'On Propositions: What they are, and Meaning' and 'The Art of the Infinite'

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18 ideas

3. Truth / A. Truth Problems / 5. Truth Bearers
In its primary and formal sense, 'true' applies to propositions, not beliefs [Russell]
3. Truth / B. Truthmakers / 1. For Truthmakers
The truth or falsehood of a belief depends upon a fact to which the belief 'refers' [Russell]
3. Truth / C. Correspondence Truth / 1. Correspondence Truth
Propositions of existence, generalities, disjunctions and hypotheticals make correspondence tricky [Russell]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
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
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
The rationals are everywhere - the irrationals are everywhere else [Kaplan/Kaplan]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / f. Arithmetic
'Commutative' laws say order makes no difference; 'associative' laws say groupings make no difference [Kaplan/Kaplan]
'Distributive' laws say if you add then multiply, or multiply then add, you get the same result [Kaplan/Kaplan]
7. Existence / A. Nature of Existence / 3. Being / d. Non-being
Not-Being obviously doesn't exist, and the five modes of Being are all impossible [Gorgias, by Diog. Laertius]
11. Knowledge Aims / A. Knowledge / 4. Belief / b. Elements of beliefs
The three questions about belief are its contents, its success, and its character [Russell]
14. Science / C. Induction / 3. Limits of Induction
The first million numbers confirm that no number is greater than a million [Kaplan/Kaplan]
17. Mind and Body / B. Behaviourism / 4. Behaviourism Critique
If we object to all data which is 'introspective' we will cease to believe in toothaches [Russell]
17. Mind and Body / D. Property Dualism / 3. Property Dualism
There are distinct sets of psychological and physical causal laws [Russell]
19. Language / D. Propositions / 1. Propositions
Our important beliefs all, if put into words, take the form of propositions [Russell]
A proposition expressed in words is a 'word-proposition', and one of images an 'image-proposition' [Russell]
A proposition is what we believe when we believe truly or falsely [Russell]
19. Language / F. Communication / 1. Rhetoric
Gorgias says rhetoric is the best of arts, because it enslaves without using force [Gorgias, by Plato]
Destroy seriousness with laughter, and laughter with seriousness [Gorgias]