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... these problems Tarski began with a recursive definition of a near substitute of
sentence truth, namely satisfaction of sentential functions, and showed how we
could define sentence truth on the basis of this notion. A sentential function is an
...
2
Alfred Tarski: Life and Logic
The following is a recursive definition of what it means for F to be a sentential
function in general: Defn. 1: F is a sentential function if and only if either (i) F is a
basic sentential function, or (ii) F is of the form -,/" for some sentential function F', ...
Anita Burdman Feferman, Solomon Feferman, 2004
3
Logic, Semantics, Metamathematics: Papers from 1923 to 1938
DEFINITION 10. a; is a sentential function if and only if x is an expression which
satisfies one of the four following conditions: (a) there exist natural numbers k
and I such that x = ikl; (/2) there exists a sentential function y such that x — y; ...
Alfred Tarski, John Corcoran, 1983
4
Logic from Russell to Church
“Definition 22 The sequence f satisfies the sentential function x if and only if f is
an infinite sequence of classes and x is a sentential function and if f and x are
such that either (α) there exist natural numbers k and l such that x = ιk,l and fk ⊆ fl
; ...
Dov M. Gabbay, John Woods, 2009
Intuitively, the idea is that certain objects are said to satisfy a given sentential
function if the latter becomes a true sentence when its unbound variables are
replaced by the names of those objects. The sentential function 'x is taller thany'
is ...
Lawrence E. Johnson, 2006
6
Introduction to Logic: and to the Methodology of Deductive ...
A sentential function in which the variables “z”, “y”, “z”, - - - occur automatically
becomes a sentence as soon as one prefixes to it one or several operators
containing all those variables. If, however, some of the variables do not occur in
the ...
7
The World of Mathematics
In place of “sentential function" we shall sometimes simply say “sentence”—-but
only in cases where there is no danger of any misunderstanding. The role of the
variables in a sentential function has sometimes been compared very adequately
...
The advantage of the implicative notation lies in its replacing the individual signs
with a description carried out with the help of a free variable; that is, the sequence
of events (,v,-) is described with the help of another sentential function in which ...
Hans Reichenbach, M. Reichenbach, Robert S. Cohen, 1978
9
Logic: A History of its Central Concepts: LOGIC: HISTORY OF ...
Tarski writes: We can easily convince ourselves that every sentential function
which is constructed in such a way is a so-called TRUTH FUNCTION. This means
the following: if a sentence is obtained from that function by substituting whole ...
Dov M. Gabbay, Francis Jeffry Pelletier, John Woods, 2012
10
Dialogical Rhetoric: An Essay on Truth and Normativity After ...
Blood, being red, does not satisfy the sentential function 'x is white'. It is, as we
shall see, no coincidence that the sentence 'blood is white' is false, whereas the
sentence 'snow is white' is true. There is indeed an intimate connection between
...
