  The long-term carbon cycle is vital for maintaining liquid water oceans on
rocky planets due to the negative climate feedbacks involved in silicate
weathering. Plate tectonics plays a crucial role in driving the long-term
carbon cycle because it is responsible for CO$_2$ degassing at ridges and arcs,
the return of CO$_2$ to the mantle through subduction, and supplying fresh,
weatherable rock to the surface via uplift and orogeny. However, the presence
of plate tectonics itself may depend on climate according to recent
geodynamical studies showing that cool surface temperatures are important for
maintaining vigorous plate tectonics. Using a simple carbon cycle model, I show
that the negative climate feedbacks inherent in the long-term carbon cycle are
uninhibited by climate's effect on plate tectonics. Furthermore, initial
atmospheric CO$_2$ conditions do not impact the final climate state reached
when the carbon cycle comes to equilibrium, as long as liquid water is present
and silicate weathering can occur. Thus an initially hot, CO$_2$ rich
atmosphere does not prevent the development of a temperate climate and plate
tectonics on a planet. However, globally supply-limited weathering does prevent
the development of temperate climates on planets with small subaerial land
areas and large total CO$_2$ budgets because supply-limited weathering lacks
stabilizing climate feedbacks. Planets in the supply-limited regime may become
inhospitable for life and could experience significant water loss.
Supply-limited weathering is less likely on plate tectonic planets, because
plate tectonics promotes high erosion rates and thus a greater supply of
bedrock to the surface.
