Combining Texts
Ideas for
'Individuals without Sortals', 'works' and 'Principles of Arithmetic, by a new method'
expand these ideas
|
start again
|
choose
another area for these texts
display all the ideas for this combination of texts
7 ideas
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / d. Counting via concepts
17518
|
Counting 'coin in this box' may have coin as the unit, with 'in this box' merely as the scope [Ayers]
|
17516
|
If counting needs a sortal, what of things which fall under two sortals? [Ayers]
|
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
13949
|
All models of Peano axioms are isomorphic, so the models all seem equally good for natural numbers [Cartwright,R on Peano]
|
18113
|
PA concerns any entities which satisfy the axioms [Peano, by Bostock]
|
17634
|
Peano axioms not only support arithmetic, but are also fairly obvious [Peano, by Russell]
|
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
15653
|
We can add Reflexion Principles to Peano Arithmetic, which assert its consistency or soundness [Halbach on Peano]
|
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
17635
|
Arithmetic can have even simpler logical premises than the Peano Axioms [Russell on Peano]
|