Combining Texts

All the ideas for 'fragments/reports', 'To be is to be the value of a variable..' and 'Reference and Generality (3rd ed)'

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18 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 / 4. Using Numbers / d. Counting via concepts
12154 Are 'word token' and 'word type' different sorts of countable objects, or two ways of counting? [Geach, by Perry]
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 / A. Existence of Objects / 6. Nihilism about Objects
8969 We should abandon absolute identity, confining it to within some category [Geach, by Hawthorne]
9. Objects / F. Identity among Objects / 3. Relative Identity
16075 Denial of absolute identity has drastic implications for logic, semantics and set theory [Wasserman on Geach]
12152 Identity is relative. One must not say things are 'the same', but 'the same A as' [Geach]
9. Objects / F. Identity among Objects / 8. Leibniz's Law
16073 Leibniz's Law is incomplete, since it includes a non-relativized identity predicate [Geach, by Wasserman]
26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature
1748 Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius]
27. Natural Reality / G. Biology / 3. Evolution
5989 Archelaus said life began in a primeval slime [Archelaus, by Schofield]