Truth via Satisfaction?
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One of Tarski's stated aims was to give an explication of the classical
conception of truth -- truth as `saying it how it is'.  Many subsequent
commentators have felt that he achieved this aim.  Tarski's core idea of
defining truth via satisfaction has now found its way into standard logic
textbooks.  This paper looks at such textbook definitions of truth in a
model for standard first-order languages and argues that they fail from the
point of view of explication of the classical notion of truth.  The paper
furthermore argues that a subtly different definition -- also to be found
in classic textbooks but much less prevalent than the kind of definition
that proceeds via satisfaction -- succeeds from this point of view.