Combining Texts

All the ideas for 'fragments/reports', 'works' and 'To be is to be the value of a variable..'

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16 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets

9565	Zermelo made 'set' and 'member' undefined axioms [Zermelo, by Chihara]

3339	For Zermelo's set theory the empty set is zero and the successor of each number is its unit set [Zermelo, by Blackburn]

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]

7. Existence / A. Nature of Existence / 3. Being / d. Non-being

18933

Not-Being obviously doesn't exist, and the five modes of Being are all impossible [Gorgias, by Diog. Laertius]

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]

19. Language / F. Communication / 1. Rhetoric

5864	Destroy seriousness with laughter, and laughter with seriousness [Gorgias]

9866	Gorgias says rhetoric is the best of arts, because it enslaves without using force [Gorgias, by Plato]