Combining Texts

All the ideas for 'To be is to be the value of a variable..', 'Speaking of Objects' and 'Models and Reality'

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22 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / o. Axiom of Constructibility V = L
13655 The Löwenheim-Skolem theorems show that whether all sets are constructible is indeterminate [Putnam, by Shapiro]
9915 V = L just says all sets are constructible [Putnam]
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 / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
9913 The Löwenheim-Skolem Theorem is close to an antinomy in philosophy of language [Putnam]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
9914 It is unfashionable, but most mathematical intuitions come from nature [Putnam]
7. Existence / C. Structure of Existence / 7. Abstract/Concrete / a. Abstract/concrete
1630 We can only see an alien language in terms of our own thought structures (e.g. physical/abstract) [Quine]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / b. Commitment of quantifiers
5747 "No entity without identity" - our ontology must contain items with settled identity conditions [Quine, by Melia]
10700 First- and second-order quantifiers are two ways of referring to the same things [Boolos]
8. Modes of Existence / B. Properties / 12. Denial of Properties
7925 There is no proper identity concept for properties, and it is hard to distinguish one from two [Quine]
9. Objects / A. Existence of Objects / 2. Abstract Objects / b. Need for abstracta
13387 Our conceptual scheme becomes more powerful when we posit abstract objects [Quine]
9. Objects / A. Existence of Objects / 5. Individuation / a. Individuation
8277 I prefer 'no object without identity' to Quine's 'no entity without identity' [Lowe on Quine]
19. Language / F. Communication / 6. Interpreting Language / b. Indeterminate translation
1631 You could know the complete behavioural conditions for a foreign language, and still not know their beliefs [Quine]
1632 Translation of our remote past or language could be as problematic as alien languages [Quine]