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Single Idea 13340

[filed under theme 5. Theory of Logic / I. Semantics of Logic / 4. Satisfaction ]

Full Idea

It has been found useful in defining semantical concepts to deal first with the concept of satisfaction; both because the definition of this concept presents relatively few difficulties, and because the other semantical concepts are easily reduced to it.

Gist of Idea

Satisfaction is the easiest semantical concept to define, and the others will reduce to it

Source

Alfred Tarski (The Establishment of Scientific Semantics [1936], p.406)

Book Ref

Tarski,Alfred: 'Logic, Semantics, Meta-mathematics' [Hackett 1956], p.406

A Reaction

See Idea 13339 for his explanation of satisfaction. We just say that a open sentence is 'acceptable' or 'assertible' (or even 'true') when particular values are assigned to the variables. Then sentence is then 'satisfied'.

Related Idea

Idea 13339 A sentence is satisfied when we can assert the sentence when the variables are assigned [Tarski]

The 12 ideas with the same theme [evaluating as True after all truth assignments are made]:

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]