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 / 4. Using Numbers / c. Counting procedure

16014

It is controversial whether only 'numerical identity' allows two things to be counted as one

9. Objects / E. Objects over Time / 4. Four-Dimensionalism

16024

I could have died at five, but the summation of my adult stages could not

9. Objects / E. Objects over Time / 5. Temporal Parts

16023

Stage theorists accept four-dimensionalism, but call each stage a whole object

9. Objects / F. Identity among Objects / 2. Defining Identity

16015

Problems about identity can't even be formulated without the concept of identity

16017

Identity is usually defined as the equivalence relation satisfying Leibniz's Law

16016

Identity definitions (such as self-identity, or the smallest equivalence relation) are usually circular

16020

Identity can only be characterised in a second-order language

9. Objects / F. Identity among Objects / 8. Leibniz's Law

16018

Indiscernibility is basic to our understanding of identity and distinctness

16019

Leibniz's Law must be kept separate from the substitutivity principle