The issue of causality in f(T) gravity is investigated by examining the
possibility of existence of the closed timelike curves in the G\"{o}del-type
metric. By assuming a perfect fluid as the matter source, we find that the
fluid must have an equation of state parameter greater than minus one in order
to allow the G\"{o}del solutions to exist, and furthermore the critical radius
rc, beyond which the causality is broken down, is finite and it depends on
both matter and gravity. Remarkably, for certain f(T) models, the perfect
fluid that allows the G\"{o}del-type solutions can even be normal matter, such
as pressureless matter or radiation. However, if the matter source is a special
scalar field rather than a perfect fluid, then rc→∞ and the
causality violation is thus avoided.Comment: 18 pages, introduction revised, reference adde