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
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
Since every definition is an equation, one cannot define equality itself
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / e. Counting by correlation
Counting rests on one-one correspondence, of numerals to objects
Husserl rests sameness of number on one-one correlation, forgetting the correlation with numbers themselves
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
In a number-statement, something is predicated of a concept
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
Our concepts recognise existing relations, they don't change them
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
The na´ve 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
If objects are just presentation, we get increasing abstraction by ignoring their properties
18. Thought / A. Modes of Thought / 1. Thought
Many people have the same thought, which is the component, not the private presentation
18. Thought / E. Abstraction / 3. Abstracta by Ignoring
Disregarding properties of two cats still leaves different objects, but what is now the difference?
How do you find the right level of inattention; you eliminate too many or too few characteristics
18. Thought / E. Abstraction / 8. Abstractionism Critique
Number-abstraction somehow makes things identical without changing them!
19. Language / A. Nature of Meaning / 2. Meaning as Mental
Psychological logicians are concerned with sense of words, but mathematicians study the reference
Identity baffles psychologists, since A and B must be presented differently to identify them