Final answer:
To 'stop' the regress means to provide a foundational element that doesn't require further explanation or cause. In cosmology, this refers to a first 'uncaused cause', while in epistemology, it pertains to foundational beliefs that are self-justified. The cosmological argument suggests a First Cause to halt infinite regress, but this is debated and not universally accepted as definitive proof.
Step-by-step explanation:
To "stop" the regress in both cosmology and epistemology means to provide a base or a grounding that does not require further explanation or cause. In the cosmological argument, proponents argue for the necessity of a first uncaused cause to halt the infinite regress of causes. This First Cause, which is typically referred to as God in classical theistic beliefs, is postulated to be necessary, uncaused, and atemporal, meaning it exists independently of time and therefore does not have a 'first' moment. The very nature of the First Cause is to exist without a prior cause.
Some have criticized this argument, suggesting that it is similarly difficult to conceive an infinite being as it is to conceive an infinite regress of causes. Relatedly, if a First Cause can be seen as uncaused and necessary, why couldn't the universe itself be seen as eternal and uncaused, thus negating the need for a First Cause? This parallels the foundationalist approach in epistemology, wherein some beliefs, termed foundational beliefs, are considered justified in themselves without inference from other beliefs, thus providing a stopping point for the regress of justification.
The cosmological argument, while aiming to prove the necessity of a First Cause, is not definitive. It leaves open questions about the nature of causality and the possibility of an eternal universe, as well as the problem of conceiving the existence of a necessary being that is infinite. Such debates remain central to the discussion in philosophical cosmology and metaphysics.