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'fragments/reports', 'Logical Properties' and 'Philosophy of Mathematics'
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20 ideas
5. Theory of Logic / B. Logical Consequence / 2. Types of Consequence
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10259
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The two standard explanations of consequence are semantic (in models) and deductive [Shapiro]
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5. Theory of Logic / B. Logical Consequence / 5. Modus Ponens
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10257
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Intuitionism only sanctions modus ponens if all three components are proved [Shapiro]
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5. Theory of Logic / C. Ontology of Logic / 1. Ontology of Logic
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10253
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Either logic determines objects, or objects determine logic, or they are separate [Shapiro]
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5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
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10251
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The law of excluded middle might be seen as a principle of omniscience [Shapiro]
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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 / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
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10212
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Classical connectives differ from their ordinary language counterparts; '∧' is timeless, unlike 'and' [Shapiro]
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5. Theory of Logic / E. Structures of Logic / 5. Functions in Logic
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10209
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A function is just an arbitrary correspondence between collections [Shapiro]
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5. Theory of Logic / G. Quantification / 1. Quantification
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6042
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The quantifier is overrated as an analytical tool [McGinn]
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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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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 / 6. Plural Quantification
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10268
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Maybe plural quantifiers should be understood in terms of classes or sets [Shapiro]
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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 / I. Semantics of Logic / 4. Satisfaction
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10235
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A sentence is 'satisfiable' if it has a model [Shapiro]
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5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
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10240
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Model theory deals with relations, reference and extensions [Shapiro]
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10239
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The central notion of model theory is the relation of 'satisfaction' [Shapiro]
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5. Theory of Logic / J. Model Theory in Logic / 2. Isomorphisms
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10214
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Theory ontology is never complete, but is only determined 'up to isomorphism' [Shapiro]
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10238
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The set-theoretical hierarchy contains as many isomorphism types as possible [Shapiro]
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5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
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10234
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Any theory with an infinite model has a model of every infinite cardinality [Shapiro]
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