Combining Texts

All the ideas for 'Leibniz: Guide for the Perplexed', 'Intros to Russell's 'Essays in Analysis'' and 'To be is to be the value of a variable..'

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14 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]

5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / b. Cantor's paradox

21554

Sets always exceed terms, so all the sets must exceed all the sets [Lackey]

5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / c. Burali-Forti's paradox

21553

It seems that the ordinal number of all the ordinals must be bigger than itself [Lackey]

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]

9. Objects / B. Unity of Objects / 2. Substance / d. Substance defined

19347

Substance needs independence, unity, and stability (for individuation); also it is a subject, for predicates [Perkins]