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### 5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic

#### [logic when interpreted, rather than mere formal systems]

21 ideas
 13335 Semantics is the concepts of connections of language to reality, such as denotation, definition and truth [Tarski]
 13336 A language containing its own semantics is inconsistent - but we can use a second language [Tarski]
 18756 Tarski built a compositional semantics for predicate logic, from dependent satisfactions [Tarski, by McGee]
 19313 Tarksi invented the first semantics for predicate logic, using this conception of truth [Tarski, by Kirkham]
 19059 In standard views you could replace 'true' and 'false' with mere 0 and 1 [Dummett]
 19062 Classical two-valued semantics implies that meaning is grasped through truth-conditions [Dummett]
 19063 Beth trees show semantics for intuitionistic logic, in terms of how truth has been established [Dummett]
 3810 In real reasoning semantics gives validity, not syntax [Searle]
 13364 Interpretation by assigning objects to names, or assigning them to variables first [Bostock, by PG]
 10284 There are three different standard presentations of semantics [Hodges,W]
 10283 A formula needs an 'interpretation' of its constants, and a 'valuation' of its variables [Hodges,W]
 10285 I |= φ means that the formula φ is true in the interpretation I [Hodges,W]
 10016 When an 'interpretation' creates a model based on truth, this doesn't include Fregean 'sense' [Hodes]
 10570 Assigning an entity to each predicate in semantics is largely a technical convenience [Fine,K]
 6653 Syntactical methods of proof need only structure, where semantic methods (truth-tables) need truth [Lowe]
 10898 The semantics shows how truth values depend on instantiations of properties and relations [Zalabardo]
 10902 We can do semantics by looking at given propositions, or by building new ones [Zalabardo]
 13697 Valuations in PC assign truth values to formulas relative to variable assignments [Sider]
 18792 Situation semantics for logics: not possible worlds, but information in situations [Mares]
 18753 An ontologically secure semantics for predicate calculus relies on sets [McGee]
 15349 It is easier to imagine truth-value gaps (for the Liar, say) than for truth-value gluts (both T and F) [Horsten]