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All the ideas for 'Reportatio', 'Philosophy of Arithmetic' and 'Identity'

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18 ideas

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / l. Zero
0 is not a number, as it answers 'how many?' negatively [Husserl, by Dummett]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / a. Units
Multiplicity in general is just one and one and one, etc. [Husserl]
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 / A. Nature of Mathematics / 4. Using Numbers / e. Counting by correlation
Husserl said counting is more basic than Frege's one-one correspondence [Husserl, by Heck]
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]
15. Nature of Minds / C. Capacities of Minds / 3. Abstraction by mind
Husserl identifies a positive mental act of unification, and a negative mental act for differences [Husserl, by Frege]
18. Thought / D. Concepts / 4. Structure of Concepts / b. Analysis of concepts
We clarify concepts (e.g. numbers) by determining their psychological origin [Husserl, by Velarde-Mayol]
18. Thought / E. Abstraction / 8. Abstractionism Critique
Psychologism blunders in focusing on concept-formation instead of delineating the concepts [Dummett on Husserl]
Husserl wanted to keep a shadowy remnant of abstracted objects, to correlate them [Dummett on Husserl]
28. God / A. Divine Nature / 3. Divine Perfections
God is not wise, but more-than-wise; God is not good, but more-than-good [William of Ockham]
28. God / C. Attitudes to God / 4. God Reflects Humanity
We could never form a concept of God's wisdom if we couldn't abstract it from creatures [William of Ockham]