Possible Clues:

• Absurdity
• Neither up nor down, contrary Old Duke after a kiss? That's an absurd proposition
• Holding over detailed March vote shows inconsistency
• Statement seeming to be self-contradictory
• Logical contradiction ... or an aural hint to what are found in 20-, 25- and 45-Across
• Self-contradictory truth
• Logical statement that contradicts itself
• 'Less is more,' for one
• A contradictory statement
• It seems odd, releasing end of rope from show bull