Ideas from 'Identity' by Harold Noonan [2009], by Theme Structure

[found in 'Stanford Online Encyclopaedia of Philosophy' (ed/tr Stanford University) [ ,-]].

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6. Mathematics / A. Nature of Mathematics / 3. Numbers / p. Counting
It is controversial whether only 'numerical identity' allows two things to be counted as one
9. Objects / E. Objects over Time / 4. Four-Dimensionalism
I could have died at five, but the summation of my adult stages could not
9. Objects / E. Objects over Time / 5. Temporal Parts
Stage theorists accept four-dimensionalism, but call each stage a whole object
9. Objects / F. Identity among Objects / 2. Defining Identity
Identity is usually defined as the equivalence relation satisfying Leibniz's Law
Problems about identity can't even be formulated without the concept of identity
Identity can only be characterised in a second-order language
Identity definitions (such as self-identity, or the smallest equivalence relation) are usually circular
9. Objects / F. Identity among Objects / 8. Leibniz's Law
Indiscernibility is basic to our understanding of identity and distinctness
Leibniz's Law must be kept separate from the substitutivity principle