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Full Idea
Logical sentences are often assigned preliminary conditions under which they are true or false (often given as truth tables). However, these are outside the system of logic, and should not be regarded as definitions of the terms involved.
Gist of Idea
Truth tables give prior conditions for logic, but are outside the system, and not definitions
Source
Alfred Tarski (The Semantic Conception of Truth [1944], 15)
Book Ref
'Semantics and the Philosophy of Language', ed/tr. Linsky,Leonard [University of Illinois 1972], p.29
A Reaction
Hence, presumably, the connectives are primitives (with no nature or meaning), and the truth tables are axioms for their use? This opinion of Tarski's may have helped shift the preference towards natural deduction introduction and elimination rules.
19195 | Truth tables give prior conditions for logic, but are outside the system, and not definitions [Tarski] |
9537 | Truth-tables are good for showing invalidity [Lemmon] |
9538 | A truth-table test is entirely mechanical, but this won't work for more complex logic [Lemmon] |
19060 | Truth-tables are dubious in some cases, and may be a bad way to explain connective meaning [Dummett] |
9724 | Until the 1960s the only semantics was truth-tables [Enderton] |
9738 | Each line of a truth table is a model [Fitting/Mendelsohn] |
13705 | Truth tables assume truth functionality, and are just pictures of truth functions [Sider] |
8713 | In classical/realist logic the connectives are defined by truth-tables [Friend] |
17764 | Boolean connectives are interpreted as functions on the set {1,0} [Walicki] |