We investigate mechanisms for language change within a framework where an unconventional signal for a meaning is first innovated, and then subsequently propagated through a speech community to replace the existing convention. We appeal to the notion of universality as it applies to complex interacting systems in the physical sciences and which establishes a link between generic (universal) patterns at the macroscopic scale and relates them to symmetries at the microscopic scale. By relating the presence and absence of specific symmetries to fundamentally distinct mechanisms for language change at the level of individual speakers and speech acts, we are able to draw conclusions about which of these underlying mechanisms are most likely to be responsible for the changes that actually occur. Since these mechanisms are typically believed to be common to all speakers in all speech communities, this provides a means to relate universals in individual behaviour to language universals.