Infinite regress in the context of "Foundationalism"

In mathematics, logic, philosophy, and formal systems, a primitive notion is a concept that is not defined in terms of previously defined concepts. It is often motivated informally, usually by an appeal to intuition or taken to be self-evident. In an axiomatic theory, relations between primitive notions are restricted by axioms. Some authors refer to the latter as "defining" primitive notions by one or more axioms, but this can be misleading. Formal theories cannot dispense with primitive notions, under pain of infinite regress (per the regress problem).

For example, in contemporary geometry, point, line, and contains are some primitive notions.

The Kalam cosmological argument is a modern formulation of the cosmological argument for the existence of God. It is named after the Kalam (medieval Islamic scholasticism) from which many of its key ideas originated. Philosopher and theologian William Lane Craig was principally responsible for revitalising these ideas for modern academic discourse through his book The Kalām Cosmological Argument (1979), as well as other publications.

The argument's central thesis is the metaphysical impossibility of a temporally past-infinite universe and of actual infinities existing in the real world, traced by Craig to 11th-century Persian Muslim scholastic philosopher Al-Ghazali. This feature distinguishes it from other cosmological arguments, such as Aquinas's Second Way, which rests on the impossibility of a causally ordered infinite regress, and those of Leibniz and Samuel Clarke, which refer to the principle of sufficient reason.

In epistemology, the regress argument is the argument that any proposition requires a justification. However, any justification itself requires support. This means that any proposition whatsoever can be endlessly (infinitely) questioned, resulting in infinite regress. It is a problem in epistemology and in any general situation where a statement has to be justified.

The argument is also known as diallelus (Latin) or diallelon, from Greek di' allelon "through or by means of one another" and as the epistemic regress problem. It is an element of the Münchhausen trilemma.

The principle of sufficient reason or PSR states that everything must have a sufficient reason. It is similar to the idea that everything must have a cause, a deterministic system of universal causation. A sufficient reason is sometimes described as the coincidence of every single thing that is needed for the occurrence of an effect. The principle is relevant to Munchausen's trilemma, as it seems to suppose an infinite regress, rather than a foundational brute fact. The principle was articulated and made prominent by Gottfried Wilhelm Leibniz. Arthur Schopenhauer wrote On the Fourfold Root of the Principle of Sufficient Reason.