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