Combining Texts
Ideas for
'Axiomatic Theories of Truth (2005 ver)', 'A Pragmatic Conception of the A Priori' and 'Philosophies of Mathematics'
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12 ideas
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
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9358
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There are several logics, none of which will ever derive falsehoods from truth [Lewis,CI]
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5. Theory of Logic / C. Ontology of Logic / 1. Ontology of Logic
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15652
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We can use truth instead of ontologically loaded second-order comprehension assumptions about properties [Halbach]
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5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
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9357
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Excluded middle is just our preference for a simplified dichotomy in experience [Lewis,CI]
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10111
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Asserting Excluded Middle is a hallmark of realism about the natural world [George/Velleman]
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5. Theory of Logic / E. Structures of Logic / 7. Predicates in Logic
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15651
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Instead of saying x has a property, we can say a formula is true of x - as long as we have 'true' [Halbach]
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5. Theory of Logic / F. Referring in Logic / 1. Naming / a. Names
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9364
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Names represent a uniformity in experience, or they name nothing [Lewis,CI]
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5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
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10129
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A 'model' is a meaning-assignment which makes all the axioms true [George/Velleman]
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5. Theory of Logic / J. Model Theory in Logic / 2. Isomorphisms
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10105
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Differences between isomorphic structures seem unimportant [George/Velleman]
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5. Theory of Logic / K. Features of Logics / 2. Consistency
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10119
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Consistency is a purely syntactic property, unlike the semantic property of soundness [George/Velleman]
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10126
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A 'consistent' theory cannot contain both a sentence and its negation [George/Velleman]
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5. Theory of Logic / K. Features of Logics / 3. Soundness
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10120
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Soundness is a semantic property, unlike the purely syntactic property of consistency [George/Velleman]
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5. Theory of Logic / K. Features of Logics / 4. Completeness
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10127
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A 'complete' theory contains either any sentence or its negation [George/Velleman]
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