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Full Idea
If a designated conclusion follows from the premisses, but the argument involves two howlers which cancel each other out, then the moral is that the path an argument takes from premisses to conclusion does matter to its logical evaluation.
Gist of Idea
If a sound conclusion comes from two errors that cancel out, the path of the argument must matter
Source
Ian Rumfitt ("Yes" and "No" [2000], II)
Book Ref
-: 'Mind' [-], p.787
A Reaction
The drift of this is that our view of logic should be a little closer to the reasoning of ordinary language, and we should rely a little less on purely formal accounts.
11210 | Standardly 'and' and 'but' are held to have the same sense by having the same truth table [Rumfitt] |
11211 | If a sound conclusion comes from two errors that cancel out, the path of the argument must matter [Rumfitt] |
11212 | The sense of a connective comes from primitively obvious rules of inference [Rumfitt] |
11214 | We learn 'not' along with affirmation, by learning to either affirm or deny a sentence [Rumfitt] |