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Full Idea
No objective grounds are known to me which permit us to draw a sharp boundary between the two groups of terms, the logical and the non-logical.
Gist of Idea
There is no clear boundary between the logical and the non-logical
Source
Alfred Tarski (works [1936]), quoted by Alan Musgrave - Logicism Revisited §3
Book Ref
-: 'British Soc for the Philosophy of Science' [-], p.103
A Reaction
Musgrave is pointing out that this is bad news if you want to 'reduce' something like arithmetic to logic. 'Logic' is a vague object.
| 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] |