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Full Idea
An object satisfies an open sentence if and only if it possesses the property expressed by the predicate of the open sentence.
Gist of Idea
An open sentence is satisfied if the object possess that property
Source
Richard L. Kirkham (Theories of Truth: a Critical Introduction [1992], 5.4)
Book Ref
Kirkham,Richard L.: 'Theories of Truth: a Critical Introduction' [MIT 1995], p.153
A Reaction
This applies to atomic sentence, of the form Fx or Fa (that is, some variable is F, or some object is F). So strictly, only the world can decide whether some open sentence is satisfied. And it all depends on things called 'properties'.
| 13339 | A sentence is satisfied when we can assert the sentence when the variables are assigned [Tarski] |
| 13340 | Satisfaction is the easiest semantical concept to define, and the others will reduce to it [Tarski] |
| 19140 | 'Satisfaction' is a generalised form of reference [Davidson] |
| 9994 | A truth assignment to the components of a wff 'satisfy' it if the wff is then True [Enderton] |
| 10474 | |= should be read as 'is a model for' or 'satisfies' [Hodges,W] |
| 19317 | An open sentence is satisfied if the object possess that property [Kirkham] |
| 13633 | 'Satisfaction' is a function from models, assignments, and formulas to {true,false} [Shapiro] |
| 10235 | A sentence is 'satisfiable' if it has a model [Shapiro] |
| 15418 | Validity (for truth) and demonstrability (for proof) have correlates in satisfiability and consistency [Burgess] |
| 10894 | A sentence-set is 'satisfiable' if at least one truth-assignment makes them all true [Zalabardo] |
| 10901 | Some formulas are 'satisfiable' if there is a structure and interpretation that makes them true [Zalabardo] |
| 15366 | Satisfaction is a primitive notion, and very liable to semantical paradoxes [Horsten] |