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Full Idea
Tarski's definition of logical consequence (1936) is that in a fully interpreted formal language an argument is valid iff under any allowed interpretation of its nonlogical symbols, if the premises are true then so is the conclusion.
Gist of Idea
Logical consequence: true premises give true conclusions under all interpretations
Source
report of Alfred Tarski (works [1936]) by Wilfrid Hodges - Model Theory 3
Book Ref
'Stanford Online Encyclopaedia of Philosophy', ed/tr. Stanford University [plato.stanford.edu], p.9
A Reaction
The idea that you can only make these claims 'under an interpretation' seems to have had a huge influence on later philosophical thinking.
| 10153 | In everyday language, truth seems indefinable, inconsistent, and illogical [Tarski] |
| 19141 | Tarski thought axiomatic truth was too contingent, and in danger of inconsistencies [Tarski, by Davidson] |
| 10048 | There is no clear boundary between the logical and the non-logical [Tarski] |
| 10694 | Logical consequence is when in any model in which the premises are true, the conclusion is true [Tarski, by Beall/Restall] |
| 10479 | Logical consequence: true premises give true conclusions under all interpretations [Tarski, by Hodges,W] |
| 10157 | Tarski improved Hilbert's geometry axioms, and without set-theory [Tarski, by Feferman/Feferman] |