Modern presidential debating only started with Richard Nixon and John F.Kennedy in 1960, although the proximity of that to the Lincoln-Douglas centennial is more than accidental. The reason is, I think, the medium. Abraham Lincoln and Stephen A. Douglas were talking, but the talking was in terms of logic, development, and reasoning. Television, as a medium, resists those qualities in speaking - it favors quick cuts, one-liners, and talking points. I think the modern debates are largely the prisoners of the televised medium
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