Combining Texts

All the ideas for 'Precis of 'Limits of Abstraction'', 'On Multiplying Entities' and 'Review of Husserl's 'Phil of Arithmetic''

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23 ideas

2. Reason / B. Laws of Thought / 6. Ockham's Razor
8208 In arithmetic, ratios, negatives, irrationals and imaginaries were created in order to generalise [Quine]
8207 The quest for simplicity drove scientists to posit new entities, such as molecules in gases [Quine]
2. Reason / D. Definition / 2. Aims of Definition
9821 A definition need not capture the sense of an expression - just get the reference right [Frege, by Dummett]
10528 Definitions concern how we should speak, not how things are [Fine,K]
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 [Frege]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / e. Counting by correlation
17446 Counting rests on one-one correspondence, of numerals to objects [Frege]
9582 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
9586 In a number-statement, something is predicated of a concept [Frege]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / d. Hume's Principle
10529 If Hume's Principle can define numbers, we needn't worry about its truth [Fine,K]
10530 Hume's Principle is either adequate for number but fails to define properly, or vice versa [Fine,K]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
9580 Our concepts recognise existing relations, they don't change them [Frege]
9589 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
9577 The naïve view of number is that it is like a heap of things, or maybe a property of a heap [Frege]
7. Existence / B. Change in Existence / 4. Events / c. Reduction of events
8205 Explaining events just by bodies can't explain two events identical in space-time [Quine]
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 [Frege]
10. Modality / A. Necessity / 11. Denial of Necessity
8206 Necessity could be just generalisation over classes, or (maybe) quantifying over possibilia [Quine]
18. Thought / A. Modes of Thought / 1. Thought
9581 Many people have the same thought, which is the component, not the private presentation [Frege]
18. Thought / E. Abstraction / 3. Abstracta by Ignoring
9579 Disregarding properties of two cats still leaves different objects, but what is now the difference? [Frege]
9587 How do you find the right level of inattention; you eliminate too many or too few characteristics [Frege]
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
10527 An abstraction principle should not 'inflate', producing more abstractions than objects [Fine,K]
18. Thought / E. Abstraction / 8. Abstractionism Critique
9588 Number-abstraction somehow makes things identical without changing them! [Frege]
19. Language / A. Nature of Meaning / 2. Meaning as Mental
9583 Psychological logicians are concerned with sense of words, but mathematicians study the reference [Frege]
9584 Identity baffles psychologists, since A and B must be presented differently to identify them [Frege]