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Ideas for 'fragments/reports', 'Lysis' and 'Philosophy of Mathematics'

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13 ideas

5. Theory of Logic / B. Logical Consequence / 2. Types of Consequence
10259 The two standard explanations of consequence are semantic (in models) and deductive [Shapiro]
5. Theory of Logic / B. Logical Consequence / 5. Modus Ponens
10257 Intuitionism only sanctions modus ponens if all three components are proved [Shapiro]
5. Theory of Logic / C. Ontology of Logic / 1. Ontology of Logic
10253 Either logic determines objects, or objects determine logic, or they are separate [Shapiro]
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
10251 The law of excluded middle might be seen as a principle of omniscience [Shapiro]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
10212 Classical connectives differ from their ordinary language counterparts; '∧' is timeless, unlike 'and' [Shapiro]
5. Theory of Logic / E. Structures of Logic / 5. Functions in Logic
10209 A function is just an arbitrary correspondence between collections [Shapiro]
5. Theory of Logic / G. Quantification / 6. Plural Quantification
10268 Maybe plural quantifiers should be understood in terms of classes or sets [Shapiro]
5. Theory of Logic / I. Semantics of Logic / 4. Satisfaction
10235 A sentence is 'satisfiable' if it has a model [Shapiro]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
10240 Model theory deals with relations, reference and extensions [Shapiro]
10239 The central notion of model theory is the relation of 'satisfaction' [Shapiro]
5. Theory of Logic / J. Model Theory in Logic / 2. Isomorphisms
10214 Theory ontology is never complete, but is only determined 'up to isomorphism' [Shapiro]
10238 The set-theoretical hierarchy contains as many isomorphism types as possible [Shapiro]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
10234 Any theory with an infinite model has a model of every infinite cardinality [Shapiro]