Combining Texts
Ideas for
'The Evolution of Modern Metaphysics', 'Introduction to the Theory of Logic' and 'On What There Is'
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16 ideas
5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
10897
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A first-order 'sentence' is a formula with no free variables [Zalabardo]
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5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=
10893
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Γ |= φ for sentences if φ is true when all of Γ is true [Zalabardo]
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10899
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Γ |= φ if φ is true when all of Γ is true, for all structures and interpretations [Zalabardo]
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5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / b. Basic connectives
10896
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Propositional logic just needs ¬, and one of ∧, ∨ and → [Zalabardo]
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5. Theory of Logic / E. Structures of Logic / 4. Variables in Logic
1618
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We study bound variables not to know reality, but to know what reality language asserts [Quine]
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5. Theory of Logic / F. Referring in Logic / 1. Naming / f. Names eliminated
8455
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Canonical notation needs quantification, variables and predicates, but not names [Quine, by Orenstein]
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8456
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Quine extended Russell's defining away of definite descriptions, to also define away names [Quine, by Orenstein]
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5. Theory of Logic / F. Referring in Logic / 2. Descriptions / c. Theory of definite descriptions
1611
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Names can be converted to descriptions, and Russell showed how to eliminate those [Quine]
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5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
10898
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The semantics shows how truth values depend on instantiations of properties and relations [Zalabardo]
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10902
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We can do semantics by looking at given propositions, or by building new ones [Zalabardo]
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5. Theory of Logic / I. Semantics of Logic / 2. Formal Truth
10892
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We make a truth assignment to T and F, which may be true and false, but merely differ from one another [Zalabardo]
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5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
10895
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'Logically true' (|= φ) is true for every truth-assignment [Zalabardo]
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10900
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Logically true sentences are true in all structures [Zalabardo]
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5. Theory of Logic / I. Semantics of Logic / 4. Satisfaction
10901
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Some formulas are 'satisfiable' if there is a structure and interpretation that makes them true [Zalabardo]
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10894
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A sentence-set is 'satisfiable' if at least one truth-assignment makes them all true [Zalabardo]
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5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
10903
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A structure models a sentence if it is true in the model, and a set of sentences if they are all true in the model [Zalabardo]
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