Combining Texts
Ideas for
'On the Question of Absolute Undecidability', 'Principia Mathematica' and 'talk'
expand these ideas
|
start again
|
choose
another area for these texts
display all the ideas for this combination of texts
13 ideas
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / i. Reals from cuts
18248
|
A real number is the class of rationals less than the number [Russell/Whitehead, by Shapiro]
|
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity
17890
|
There are at least eleven types of large cardinal, of increasing logical strength [Koellner]
|
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
17887
|
PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner]
|
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
17891
|
Arithmetical undecidability is always settled at the next stage up [Koellner]
|
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / a. Defining numbers
18152
|
Russell takes numbers to be classes, but then reduces the classes to numerical quantifiers [Russell/Whitehead, by Bostock]
|
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
10025
|
Russell and Whitehead took arithmetic to be higher-order logic [Russell/Whitehead, by Hodes]
|
8683
|
Russell and Whitehead were not realists, but embraced nearly all of maths in logic [Russell/Whitehead, by Friend]
|
10037
|
'Principia' lacks a precise statement of the syntax [Gödel on Russell/Whitehead]
|
6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory
10093
|
The ramified theory of types used propositional functions, and covered bound variables [Russell/Whitehead, by George/Velleman]
|
8691
|
The Russell/Whitehead type theory was limited, and was not really logic [Friend on Russell/Whitehead]
|
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
10305
|
In 'Principia Mathematica', logic is exceeded in the axioms of infinity and reducibility, and in the domains [Bernays on Russell/Whitehead]
|
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism
8684
|
Russell and Whitehead consider the paradoxes to indicate that we create mathematical reality [Russell/Whitehead, by Friend]
|
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
8746
|
To avoid vicious circularity Russell produced ramified type theory, but Ramsey simplified it [Russell/Whitehead, by Shapiro]
|