Combining Texts

All the ideas for 'Reply to 'Rorarius' 2nd ed', 'Our Knowledge of Mathematical Objects' and 'Identity'

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13 ideas

6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
It is controversial whether only 'numerical identity' allows two things to be counted as one [Noonan]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism
Proceduralism offers a version of logicism with no axioms, or objects, or ontological commitment [Fine,K]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism
The objects and truths of mathematics are imperative procedures for their construction [Fine,K]
My Proceduralism has one simple rule, and four complex rules [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
Problems about identity can't even be formulated without the concept of identity [Noonan]
Identity is usually defined as the equivalence relation satisfying Leibniz's Law [Noonan]
Identity definitions (such as self-identity, or the smallest equivalence relation) are usually circular [Noonan]
Identity can only be characterised in a second-order language [Noonan]
9. Objects / F. Identity among Objects / 8. Leibniz's Law
Indiscernibility is basic to our understanding of identity and distinctness [Noonan]
Leibniz's Law must be kept separate from the substitutivity principle [Noonan]
27. Natural Reality / D. Time / 1. Nature of Time / b. Relative time
Space and time are the order of all possibilities, and don't just relate to what is actual [Leibniz]