Ideas from 'Review of Husserl's 'Phil of Arithmetic'' by Gottlob Frege [1894], by Theme Structure
[found in 'Mind' (ed/tr ) [ ,]].
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2. Reason / D. Definition / 2. Aims of Definition
9821

A definition need not capture the sense of an expression  just get the reference right [Dummett]

4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / e. Axioms of PL
9585

Since every definition is an equation, one cannot define equality itself

6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / e. Counting by correlation
17446

Counting rests on oneone correspondence, of numerals to objects

9582

Husserl rests sameness of number on oneone correlation, forgetting the correlation with numbers themselves

6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
9586

In a numberstatement, something is predicated of a concept

6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
9580

Our concepts recognise existing relations, they don't change them

9589

Numbers are not real like the sea, but (crucially) they are still objective

6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
9577

The naïve view of number is that it is like a heap of things, or maybe a property of a heap

7. Existence / C. Structure of Existence / 7. Abstract/Concrete / b. Levels of abstraction
9578

If objects are just presentation, we get increasing abstraction by ignoring their properties

18. Thought / A. Modes of Thought / 1. Thought
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Many people have the same thought, which is the component, not the private presentation

18. Thought / E. Abstraction / 3. Abstracta by Ignoring
9579

Disregarding properties of two cats still leaves different objects, but what is now the difference?

9587

How do you find the right level of inattention; you eliminate too many or too few characteristics

18. Thought / E. Abstraction / 8. Abstractionism Critique
9588

Numberabstraction somehow makes things identical without changing them!

19. Language / A. Nature of Meaning / 2. Meaning as Mental
9583

Psychological logicians are concerned with sense of words, but mathematicians study the reference

9584

Identity baffles psychologists, since A and B must be presented differently to identify them
