Combining Texts

All the ideas for 'Through the Looking Glass', 'To be is to be the value of a variable..' and 'On the Infinite'

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22 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 / A. Nature of Mathematics / 1. Mathematics
12456 I aim to establish certainty for mathematical methods [Hilbert]
12461 We believe all mathematical problems are solvable [Hilbert]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
9633 No one shall drive us out of the paradise the Cantor has created for us [Hilbert]
12460 We extend finite statements with ideal ones, in order to preserve our logic [Hilbert]
12462 Only the finite can bring certainty to the infinite [Hilbert]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / d. Actual infinite
12455 The idea of an infinite totality is an illusion [Hilbert]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / j. Infinite divisibility
12457 There is no continuum in reality to realise the infinitely small [Hilbert]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
12459 The subject matter of mathematics is immediate and clear concrete symbols [Hilbert]
6. Mathematics / C. Sources of Mathematics / 8. Finitism
18112 Mathematics divides in two: meaningful finitary statements, and empty idealised statements [Hilbert]
7. Existence / A. Nature of Existence / 3. Being / e. Being and nothing
21982 I only wish I had such eyes as to see Nobody! It's as much as I can do to see real people. [Carroll,L]
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]
11. Knowledge Aims / B. Certain Knowledge / 1. Certainty
9636 My theory aims at the certitude of mathematical methods [Hilbert]