Combining Texts
Ideas for
'To be is to be the value of a variable..', 'What is Logic?' and 'Ordinary Objects'
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16 ideas
5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
13845
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The various logics are abstractions made from terms like 'if...then' in English [Hacking]
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5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
13840
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First-order logic is the strongest complete compact theory with Löwenheim-Skolem [Hacking]
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13844
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A limitation of first-order logic is that it cannot handle branching quantifiers [Hacking]
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5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
13842
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Second-order completeness seems to need intensional entities and possible worlds [Hacking]
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10225
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Monadic second-order logic might be understood in terms of plural quantifiers [Boolos, by Shapiro]
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10736
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Boolos showed how plural quantifiers can interpret monadic second-order logic [Boolos, by Linnebo]
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10780
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Any sentence of monadic second-order logic can be translated into plural first-order logic [Boolos, by Linnebo]
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5. Theory of Logic / B. Logical Consequence / 6. Entailment
14471
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Analytical entailments arise from combinations of meanings and inference rules [Thomasson]
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5. Theory of Logic / D. Assumptions for Logic / 4. Identity in Logic
10697
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Identity is clearly a logical concept, and greatly enhances predicate calculus [Boolos]
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5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
13837
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With a pure notion of truth and consequence, the meanings of connectives are fixed syntactically [Hacking]
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5. Theory of Logic / E. Structures of Logic / 4. Variables in Logic
13839
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Perhaps variables could be dispensed with, by arrows joining places in the scope of quantifiers [Hacking]
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5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
13671
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Second-order quantifiers are just like plural quantifiers in ordinary language, with no extra ontology [Boolos, by Shapiro]
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5. Theory of Logic / G. Quantification / 6. Plural Quantification
10267
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We should understand second-order existential quantifiers as plural quantifiers [Boolos, by Shapiro]
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10698
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Plural forms have no more ontological commitment than to first-order objects [Boolos]
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5. Theory of Logic / G. Quantification / 7. Unorthodox Quantification
7806
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Boolos invented plural quantification [Boolos, by Benardete,JA]
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5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
13843
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If it is a logic, the Löwenheim-Skolem theorem holds for it [Hacking]
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