Combining Texts
Ideas for
'fragments/reports', '03: Book of Leviticus' and 'Introduction to Mathematical Philosophy'
expand these ideas
|
start again
|
choose
another area for these texts
display all the ideas for this combination of texts
17 ideas
6. Mathematics / A. Nature of Mathematics / 2. Geometry
|
14442
|
If straight lines were like ratios they might intersect at a 'gap', and have no point in common [Russell]
|
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
|
14438
|
New numbers solve problems: negatives for subtraction, fractions for division, complex for equations [Russell]
|
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
|
13510
|
Could a number just be something which occurs in a progression? [Russell, by Hart,WD]
|
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / i. Reals from cuts
|
14436
|
A series can be 'Cut' in two, where the lower class has no maximum, the upper no minimum [Russell]
|
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / j. Complex numbers
|
14439
|
A complex number is simply an ordered couple of real numbers [Russell]
|
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / m. One
|
14421
|
Discovering that 1 is a number was difficult [Russell]
|
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
|
14424
|
Numbers are needed for counting, so they need a meaning, and not just formal properties [Russell]
|
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / f. Arithmetic
|
14441
|
The formal laws of arithmetic are the Commutative, the Associative and the Distributive [Russell]
|
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
|
14420
|
Infinity and continuity used to be philosophy, but are now mathematics [Russell]
|
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
|
14431
|
The definition of order needs a transitive relation, to leap over infinite intermediate terms [Russell]
|
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
|
14422
|
Any founded, non-repeating series all reachable in steps will satisfy Peano's axioms [Russell]
|
|
14423
|
'0', 'number' and 'successor' cannot be defined by Peano's axioms [Russell]
|
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / d. Hume's Principle
|
14425
|
A number is something which characterises collections of the same size [Russell]
|
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
|
14434
|
What matters is the logical interrelation of mathematical terms, not their intrinsic nature [Russell]
|
6. Mathematics / C. Sources of Mathematics / 5. Numbers as Adjectival
|
14465
|
Maybe numbers are adjectives, since 'ten men' grammatically resembles 'white men' [Russell]
|
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
|
13414
|
For Russell, numbers are sets of equivalent sets [Russell, by Benacerraf]
|
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / e. Psychologism
|
14449
|
There is always something psychological about inference [Russell]
|