Combining Texts

All the ideas for 'Frege's Theory of Numbers', 'Identity' and 'Precis of 'Limits of Abstraction''

expand these ideas     |    start again     |     specify just one area for these texts


14 ideas

2. Reason / D. Definition / 2. Aims of Definition
Definitions concern how we should speak, not how things are [Fine,K]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
Parsons says counting is tagging as first, second, third..., and converting the last to a cardinal [Parsons,C, by Heck]
It is controversial whether only 'numerical identity' allows two things to be counted as one [Noonan]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / d. Hume's Principle
If Hume's Principle can define numbers, we needn't worry about its truth [Fine,K]
Hume's Principle is either adequate for number but fails to define properly, or vice versa [Fine,K]
9. Objects / E. Objects over Time / 4. Four-Dimensionalism
I could have died at five, but the summation of my adult stages could not [Noonan]
9. Objects / E. Objects over Time / 5. Temporal Parts
Stage theorists accept four-dimensionalism, but call each stage a whole object [Noonan]
9. Objects / F. Identity among Objects / 2. Defining Identity
Identity definitions (such as self-identity, or the smallest equivalence relation) are usually circular [Noonan]
Identity is usually defined as the equivalence relation satisfying Leibniz's Law [Noonan]
Problems about identity can't even be formulated without the concept of identity [Noonan]
Identity can only be characterised in a second-order language [Noonan]
9. Objects / F. Identity among Objects / 8. Leibniz's Law
Leibniz's Law must be kept separate from the substitutivity principle [Noonan]
Indiscernibility is basic to our understanding of identity and distinctness [Noonan]
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
An abstraction principle should not 'inflate', producing more abstractions than objects [Fine,K]