Combining Texts
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'Logical Properties', 'On Formally Undecidable Propositions' and 'Identity and Necessity'
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14 ideas
5. Theory of Logic / D. Assumptions for Logic / 4. Identity in Logic
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6051
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In 'x is F and x is G' we must assume the identity of x in the two statements [McGinn]
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6055
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Both non-contradiction and excluded middle need identity in their formulation [McGinn]
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6059
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Identity is unitary, indefinable, fundamental and a genuine relation [McGinn]
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5. Theory of Logic / F. Referring in Logic / 1. Naming / b. Names as descriptive
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9175
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We may fix the reference of 'Cicero' by a description, but thereafter the name is rigid [Kripke]
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5. Theory of Logic / F. Referring in Logic / 1. Naming / c. Names as referential
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9171
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The function of names is simply to refer [Kripke]
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5. Theory of Logic / G. Quantification / 1. Quantification
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6067
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Existential quantifiers just express the quantity of things, leaving existence to the predicate 'exists' [McGinn]
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6042
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The quantifier is overrated as an analytical tool [McGinn]
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5. Theory of Logic / G. Quantification / 3. Objectual Quantification
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6069
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'Partial quantifier' would be a better name than 'existential quantifier', as no existence would be implied [McGinn]
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5. Theory of Logic / G. Quantification / 7. Unorthodox Quantification
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6068
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We need an Intentional Quantifier ("some of the things we talk about.."), so existence goes into the proposition [McGinn]
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5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
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17886
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The limitations of axiomatisation were revealed by the incompleteness theorems [Gödel, by Koellner]
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5. Theory of Logic / K. Features of Logics / 2. Consistency
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10071
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Second Incompleteness: nice theories can't prove their own consistency [Gödel, by Smith,P]
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5. Theory of Logic / K. Features of Logics / 3. Soundness
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19123
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If soundness can't be proved internally, 'reflection principles' can be added to assert soundness [Gödel, by Halbach/Leigh]
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5. Theory of Logic / K. Features of Logics / 5. Incompleteness
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10621
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Gödel's First Theorem sabotages logicism, and the Second sabotages Hilbert's Programme [Smith,P on Gödel]
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17888
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The undecidable sentence can be decided at a 'higher' level in the system [Gödel]
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