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All the ideas for 'works', 'Review of Husserl's 'Phil of Arithmetic'' and 'Identity and Essence'

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29 ideas

2. Reason / D. Definition / 2. Aims of Definition
A definition need not capture the sense of an expression - just get the reference right [Frege, by 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 [Frege]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / e. Counting by correlation
Counting rests on one-one correspondence, of numerals to objects [Frege]
Husserl rests sameness of number on one-one correlation, forgetting the correlation with numbers themselves [Frege]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
In a number-statement, something is predicated of a concept [Frege]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
Our concepts recognise existing relations, they don't change them [Frege]
Numbers are not real like the sea, but (crucially) they are still objective [Frege]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
The naïve view of number is that it is like a heap of things, or maybe a property of a heap [Frege]
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 [Frege]
9. Objects / A. Existence of Objects / 5. Individuation / a. Individuation
Indiscernibility is a necessary and sufficient condition for identity [Brody]
9. Objects / A. Existence of Objects / 5. Individuation / e. Individuation by kind
Brody bases sortal essentialism on properties required throughout something's existence [Brody, by Mackie,P]
9. Objects / C. Structure of Objects / 2. Hylomorphism / a. Hylomorphism
Modern emphasis is on properties had essentially; traditional emphasis is on sort-defining properties [Brody]
9. Objects / D. Essence of Objects / 5. Essence as Kind
A sortal essence is a property which once possessed always possessed [Brody, by Mackie,P]
Maybe essential properties are those which determine a natural kind? [Brody]
9. Objects / D. Essence of Objects / 6. Essence as Unifier
De re essentialism standardly says all possible objects identical with a have a's essential properties [Brody]
9. Objects / D. Essence of Objects / 7. Essence and Necessity / a. Essence as necessary properties
Essentially, a has P, always had P, must have had P, and has never had a future without P [Brody]
An object having a property essentially is equivalent to its having it necessarily [Brody]
9. Objects / D. Essence of Objects / 8. Essence as Explanatory
Essentialism is justified if the essential properties of things explain their other properties [Brody]
9. Objects / D. Essence of Objects / 12. Essential Parts
Mereological essentialism says that every part that ensures the existence is essential [Brody]
9. Objects / E. Objects over Time / 12. Origin as Essential
Interrupted objects have two first moments of existence, which could be two beginnings [Brody]
9. Objects / F. Identity among Objects / 7. Indiscernible Objects
a and b share all properties; so they share being-identical-with-a; so a = b [Brody]
10. Modality / E. Possible worlds / 3. Transworld Objects / b. Rigid designation
Identity across possible worlds is prior to rigid designation [Brody]
18. Thought / A. Modes of Thought / 1. Thought
Many people have the same thought, which is the component, not the private presentation [Frege]
18. Thought / E. Abstraction / 3. Abstracta by Ignoring
Disregarding properties of two cats still leaves different objects, but what is now the difference? [Frege]
How do you find the right level of inattention; you eliminate too many or too few characteristics [Frege]
18. Thought / E. Abstraction / 8. Abstractionism Critique
Number-abstraction somehow makes things identical without changing them! [Frege]
19. Language / A. Nature of Meaning / 2. Meaning as Mental
Psychological logicians are concerned with sense of words, but mathematicians study the reference [Frege]
Identity baffles psychologists, since A and B must be presented differently to identify them [Frege]
19. Language / F. Communication / 4. Private Language
Dewey argued long before Wittgenstein that there could not seriously be a private language [Dewey, by Orenstein]