Aquinas's cosmological argument is a posteriori argument based on the observation that the universe exists. Aquinas had 5 ways to prove God's existence but the main three ways are Motion, Cause and Contingency.
His first way is Motion. He explains that an object is either in a state of actuality or potentiality, the object cannot be in a state of both actuality and potentiality at the same time and the object can not move its-self- for example, a clay pot cannot become a pot until a potter causes it to become a pot.
. The only way an object can move is if something else of actuality moves it. Aquinas said that this chain of motion cannot go in to infinity so therefore there must be an unmoved mover to have started this chain, and he calls this 'God'.
Aquinas's second way is Cause. His argument on Cause is similar to his argument of Motion. He states that an event cannot be at potency and act at the same time, so there must be something else causing this event to happen- for example, oxygen is needed to make fire occur and also it is needed to sustain the flame. Aquinas goes on to explain, again, how this chain of cause cannot go in to infinity. He explains that there must be a first event which had no cause, he explains this as the final cause, and the final cause, he names as 'God'.
Aquinas's third way is Contingency. This is his idea that everything we see in the universe is contingent- for example volcanic rock depends upon the right minerals. He then said that it would then be reasonable to apply this theory to the universe as a whole. He indicates that he is trying to explain that the universe must have a beginning and it will have an end. He explains that if the universe had no beginning, and the universe has been here for infinity, there must have been a time when there was nothing, and nothing can come out of nothing, so therefore there must be something outside of time, to have brought something out of 'emptiness' and he calls this 'God'.