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Full Idea
Validity (truth by virtue of logical form alone) and demonstrability (provability by virtue of logical form alone) have correlative notions of logical possibility, 'satisfiability' and 'consistency', which come apart in some logics.
Gist of Idea
Validity (for truth) and demonstrability (for proof) have correlates in satisfiability and consistency
Source
John P. Burgess (Philosophical Logic [2009], 3.3)
Book Ref
Burgess,John P.: 'Philosophical Logic' [Princeton 2009], p.47
Related Idea
Idea 15417 Logical necessity has two sides - validity and demonstrability - which coincide in classical logic [Burgess]
| 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] |