Logical argument, to have validity, must follow some basic rules that are broken by many letter writers. I am often concerned that some readers will allow themselves to be swayed by illogical connections and arguments (straw man fallacy, post hoc/false cause, false dichotomy, burden of proof reversal, etc.).
Telling the truth, your newspaper's founder is quoted as saying, is one of the aims of the paper. I believe that when you publish readers' letters that contain incorrect information presented as facts, you are entirely complicit in lying to your readers. In my opinion, to be true to your stated aim and to your obligation to your readers, you should -- at all times -- edit out any statements that you know to be untrue, or provide a disclaimer that you have elected not to fact-check the letter.
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Reflecting proportionality is important. If four out of five letters you receive express an opinion in favor of a position on a topic to each one letter opposing that position, then that 4-to-1 ratio should be clearly reflected in the number of letters published in print rather than giving the opposing views equal space. To the extent subscribers read letters to help themselves come to conclusions about issues, I believe they should be helped to understand what proportion of their neighbors holds each view.
While suggesting these responsibilities to the editor, I will urge my letter-writing neighbors to use logical arguments, present opinions as opinions, and present only facts that are verifiably true. They say you can't believe everything you read in the newspaper. Double that warning for readers of letters.