Combining Texts
Ideas for
'A Résumé of Metaphysics', 'A Tour through Mathematical Logic' and 'What Does It Take to Refer?'
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16 ideas
5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
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13534
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In first-order logic syntactic and semantic consequence (|- and |=) nicely coincide [Wolf,RS]
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13535
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First-order logic is weakly complete (valid sentences are provable); we can't prove every sentence or its negation [Wolf,RS]
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5. Theory of Logic / C. Ontology of Logic / 1. Ontology of Logic
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10454
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In first-order we can't just assert existence, and it is very hard to deny something's existence [Bach]
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5. Theory of Logic / E. Structures of Logic / 3. Constants in Logic
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10453
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In logic constants play the role of proper names [Bach]
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5. Theory of Logic / F. Referring in Logic / 1. Naming / b. Names as descriptive
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10452
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Proper names can be non-referential - even predicate as well as attributive uses [Bach]
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5. Theory of Logic / F. Referring in Logic / 1. Naming / c. Names as referential
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10456
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Millian names struggle with existence, empty names, identities and attitude ascription [Bach]
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5. Theory of Logic / F. Referring in Logic / 2. Descriptions / a. Descriptions
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10440
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An object can be described without being referred to [Bach]
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5. Theory of Logic / F. Referring in Logic / 2. Descriptions / b. Definite descriptions
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10444
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Definite descriptions can be used to refer, but are not semantically referential [Bach]
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5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
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13519
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Model theory uses sets to show that mathematical deduction fits mathematical truth [Wolf,RS]
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13533
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First-order model theory rests on completeness, compactness, and the Löwenheim-Skolem-Tarski theorem [Wolf,RS]
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13532
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Model theory 'structures' have a 'universe', some 'relations', some 'functions', and some 'constants' [Wolf,RS]
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13531
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Model theory reveals the structures of mathematics [Wolf,RS]
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5. Theory of Logic / J. Model Theory in Logic / 2. Isomorphisms
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13537
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An 'isomorphism' is a bijection that preserves all structural components [Wolf,RS]
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5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
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13539
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The LST Theorem is a serious limitation of first-order logic [Wolf,RS]
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5. Theory of Logic / K. Features of Logics / 4. Completeness
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13538
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If a theory is complete, only a more powerful language can strengthen it [Wolf,RS]
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5. Theory of Logic / K. Features of Logics / 10. Monotonicity
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13525
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Most deductive logic (unlike ordinary reasoning) is 'monotonic' - we don't retract after new givens [Wolf,RS]
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