Combining Texts

All the ideas for 'To be is to be the value of a variable..', 'Structuralism and the Notion of Dependence' and 'The Value of Science'

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21 ideas

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 / 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 / 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 / B. Foundations for Mathematics / 7. Mathematical Structuralism / b. Varieties of structuralism
14085 'Deductivist' structuralism is just theories, with no commitment to objects, or modality [Linnebo]
14084 Non-eliminative structuralism treats mathematical objects as positions in real abstract structures [Linnebo]
14086 'Modal' structuralism studies all possible concrete models for various mathematical theories [Linnebo]
14087 'Set-theoretic' structuralism treats mathematics as various structures realised among the sets [Linnebo]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / d. Platonist structuralism
14089 Structuralism differs from traditional Platonism, because the objects depend ontologically on their structure [Linnebo]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
14083 Structuralism is right about algebra, but wrong about sets [Linnebo]
14090 In mathematical structuralism the small depends on the large, which is the opposite of physical structures [Linnebo]
7. Existence / C. Structure of Existence / 4. Ontological Dependence
14091 There may be a one-way direction of dependence among sets, and among natural numbers [Linnebo]
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]
8. Modes of Existence / B. Properties / 4. Intrinsic Properties
14088 An 'intrinsic' property is either found in every duplicate, or exists independent of all externals [Linnebo]
26. Natural Theory / D. Laws of Nature / 11. Against Laws of Nature
15877 The aim of science is just to create a comprehensive, elegant language to describe brute facts [Poincaré, by Harré]