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
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A definition need not capture the sense of an expression - just get the reference right [Dummett]
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4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / e. Axioms of PL
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Since every definition is an equation, one cannot define equality itself
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6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / e. Counting by correlation
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Counting rests on one-one correspondence, of numerals to objects
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9582
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Husserl rests sameness of number on one-one correlation, forgetting the correlation with numbers themselves
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6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
9586
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In a number-statement, something is predicated of a concept
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6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
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Our concepts recognise existing relations, they don't change them
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9589
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Numbers are not real like the sea, but (crucially) they are still objective
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6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
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The naïve view of number is that it is like a heap of things, or maybe a property of a heap
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7. Existence / C. Structure of Existence / 7. Abstract/Concrete / b. Levels of abstraction
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If objects are just presentation, we get increasing abstraction by ignoring their properties
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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
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18. Thought / E. Abstraction / 3. Abstracta by Ignoring
9579
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Disregarding properties of two cats still leaves different objects, but what is now the difference?
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9587
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How do you find the right level of inattention; you eliminate too many or too few characteristics
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18. Thought / E. Abstraction / 8. Abstractionism Critique
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Number-abstraction somehow makes things identical without changing them!
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19. Language / A. Nature of Meaning / 2. Meaning as Mental
9583
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Psychological logicians are concerned with sense of words, but mathematicians study the reference
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9584
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Identity baffles psychologists, since A and B must be presented differently to identify them
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