Combining Texts

All the ideas for 'Elements of Mathematical Logic', 'Mathematics and the Metaphysicians' and 'To be is to be the value of a variable..'

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16 ideas

4. Formal Logic / E. Nonclassical Logics / 3. Many-Valued Logic
8942 Lukasiewicz's L3 logic has three truth-values, T, F and I (for 'indeterminate') [Lukasiewicz, by Fisher]
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 / 4. Paradoxes in Logic / a. Achilles paradox
7557 To solve Zeno's paradox, reject the axiom that the whole has more terms than the parts [Russell]
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
10059 In mathematic we are ignorant of both subject-matter and truth [Russell]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / b. Mark of the infinite
7556 A collection is infinite if you can remove some terms without diminishing its number [Russell]
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]
12. Knowledge Sources / A. A Priori Knowledge / 2. Self-Evidence
7554 Self-evidence is often a mere will-o'-the-wisp [Russell]