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

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

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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
Problems about identity can't even be formulated without the concept of identity
Identity is usually defined as the equivalence relation satisfying Leibniz's Law
Identity definitions (such as self-identity, or the smallest equivalence relation) are usually circular
Identity can only be characterised in a second-order language
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