Combining Texts

All the ideas for 'To be is to be the value of a variable..', 'Laughter' and 'Proof that every set can be well-ordered'

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17 ideas

1. Philosophy / D. Nature of Philosophy / 8. Humour

12170

Amusement rests on superiority, or relief, or incongruity [Scruton]

12173

The central object of amusement is the human [Scruton]

12169

Since only men laugh, it seems to be an attribute of reason [Scruton]

12172

Objects of amusement do not have to be real [Scruton]

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 / 5. The Infinite / e. Countable infinity

15897

Zermelo realised that Choice would facilitate the sort of 'counting' Cantor needed [Zermelo, by Lavine]

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 / 5. Rationality / a. Rationality

12174

Only rational beings are attentive without motive or concern [Scruton]