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All the ideas for '', 'Review of Husserl's 'Phil of Arithmetic'' and 'To be is to be the value of a variable..'

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30 ideas

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]
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]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / a. Sets as existing
7785 The use of plurals doesn't commit us to sets; there do not exist individuals and collections [Boolos]
4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
10699 Does a bowl of Cheerios contain all its sets and subsets? [Boolos]
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
11211 If a sound conclusion comes from two errors that cancel out, the path of the argument must matter [Rumfitt]
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
10225 Monadic second-order logic might be understood in terms of plural quantifiers [Boolos, by Shapiro]
10736 Boolos showed how plural quantifiers can interpret monadic second-order logic [Boolos, by Linnebo]
10780 Any sentence of monadic second-order logic can be translated into plural first-order logic [Boolos, by Linnebo]
5. Theory of Logic / D. Assumptions for Logic / 4. Identity in Logic
10697 Identity is clearly a logical concept, and greatly enhances predicate calculus [Boolos]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
11212 The sense of a connective comes from primitively obvious rules of inference [Rumfitt]
11210 Standardly 'and' and 'but' are held to have the same sense by having the same truth table [Rumfitt]
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
13671 Second-order quantifiers are just like plural quantifiers in ordinary language, with no extra ontology [Boolos, by Shapiro]
5. Theory of Logic / G. Quantification / 6. Plural Quantification
10267 We should understand second-order existential quantifiers as plural quantifiers [Boolos, by Shapiro]
10698 Plural forms have no more ontological commitment than to first-order objects [Boolos]
5. Theory of Logic / G. Quantification / 7. Unorthodox Quantification
7806 Boolos invented plural quantification [Boolos, by Benardete,JA]
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 / 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 / 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]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / b. Commitment of quantifiers
10700 First- and second-order quantifiers are two ways of referring to the same things [Boolos]
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 / 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]
19. Language / F. Communication / 3. Denial
11214 We learn 'not' along with affirmation, by learning to either affirm or deny a sentence [Rumfitt]