n
[Date: 1800-1900; Origin: loggerhead 'stupid person, large head, type of heavy tool' (16-20 centuries), from logger 'block of wood' (16-18 centuries) (probably from LOG¹) + head]
be at loggerheads (with sb)
if two people are at loggerheads, they disagree very strongly
be at loggerheads (with somebody) over
　He is at loggerheads with many of his own party over the issue of taxation.