Tarski and Grice on satisfaction, satisfactory, and satisfactoriness

Tarski, 1944, Philosophy and Phenomenological Research, online:

"To obtain a definition of satisfaction we have rather to apply again a recursive procedure."

"We indicate which objects satisfy the simplest sentential functions."

"Then we state the conditions under which given objects satisfy a compound function -- assuming that we know which objects satisfy the simpler functions from which the compound one has been constructed."

"For instance: we say that given numbers

satisfy

the logical disjunction "x is greater than y or x is equal to y" if they satisfy at least one of the functions "x is greater than y" or "x is equal to y."

"Once the general definition of satisfaction is obtained, we notice that it applies automatically also to those special sentential functions which contain no free variables, i. e., to sentences."

"It turns out that for a sentence only two cases are possible: a sentence is either satisfied by all objects, or by no objects."

----- "Hence we arrive at a definition of TRUTH ... simply by saying that a sentence is true if it is satisfied by all objects."