Infinite regress is a philosophical concept to describe a series of entities. Each entity in the series depends on its predecessor, following a recursive principle. For example, the epistemic regress is a series of beliefs in which the justification of each belief depends on the justification of the belief that comes before it. An infinite regress argument is an argument against a theory based on the fact that this theory leads to an infinite regress. For such an argument to be successful, it must demonstrate not just that the theory in question entails an infinite regress but also that this regress is vicious. There are different ways in which a regress can be vicious. The most serious form of viciousness involves a contradiction in the form of metaphysical impossibility. Other forms occur when the infinite regress is responsible for the theory in question being implausible or for its failure to solve the problem it was formulated to solve. Traditionally, it was often assumed without much argument that each infinite regress is vicious but this assumption has been put into question in contemporary philosophy. While some philosophers have explicitly defended theories with infinite regresses, the more common strategy has been to reformulate the theory in question in a way that avoids the regress. One such strategy is foundationalism, which posits that there is a first element in the series from which all the other elements arise but which is not itself explained this way. Another way is coherentism, which is based on a holistic explanation that usually sees the entities in question not as a linear series but as an interconnected network. Infinite regress arguments have been made in various areas of philosophy. Famous examples include the cosmological argument and Bradley's regress.
Definition
An infinite regress is an infinite series of entities governed by a recursive principle that determines how each entity in the series depends on or is produced by its predecessor. This principle can often be expressed in the following form: X is F because X stands in R to Y and Y is F. X and Y stand for objects, R stands for a relation and F stands for a property in the widest sense. In the epistemic regress, for example, a belief is justified because it is based on another belief that is justified. But this other belief is itself in need of one more justified belief for itself to be justified and so on. Or in the cosmological argument, an event occurred because it was caused by another event that occurred before it, which was itself caused by a previous event, and so on. This principle by itself is not sufficient: it does not lead to a regress if there is no X that is F. This is why an additional triggering condition has to be fulfilled: there has to be an X that is F for the regress to get started. So the regress starts with the fact that X is F. According to the recursive principle, this is only possible if there is a distinct Y that is also F. But in order to account for the fact that Y is F, we need to posit a Z that is F and so on. Once the regress has started, there is no way of stopping it since a new entity has to be introduced at each step in order to make the previous step possible. An infinite regress argument is an argument against a theory based on the fact that this theory leads to an infinite regress. For such an argument to be successful, it has to demonstrate not just that the theory in question entails an infinite regress but also that this regress is vicious. The mere existence of an infinite regress by itself is not a proof for anything. So in addition to connecting the theory to a recursive principle paired with a triggering condition, the argument has to show in which way the resulting regress is vicious. For example, one form of evidentialism in epistemology holds that a belief is only justified if it is based on another belief that is justified. An opponent of this theory could use an infinite regress argument by demonstrating (1) that this theory leads to an infinite regress (e.g. by pointing out the recursive principle and the triggering condition) and (2) that this infinite regress is vicious (e.g. by showing that it is implausible given the limitations of the human mind). In this example, the argument has a negative form since it only denies that another theory is true. But it can also be used in a positive form to support a theory by showing that its alternative involves a vicious regress. This is how the cosmological argument for the existence of God works: it claims that positing God's existence is necessary in order to avoid an infinite regress of causes.
Viciousness For an infinite regress argument to be successful, it has to show that the involved regress is vicious. A non-vicious regress is called virtuous or benign. Traditionally, it was often assumed without much argument that each infinite regress is vicious but this assumption has been put into question in contemporary philosophy. In most cases, it is not self-evident whether an infinite regress is vicious or not. The truth regress constitutes an example of an infinite regress that is not vicious: if the proposition "P" is true, then the proposition that "It is true that P" is also true and so on. Infinite regresses pose a problem mostly if the regress concerns concrete objects. Abstract objects, on the other hand, are often considered to be unproblematic in this respect. For example, the truth-regress leads to an infinite number of true propositions or the Peano axioms entail the existence of infinitely many natural numbers. But these regresses are usually not held against the theories that entail them. There are different ways in which a regress can be vicious. The most serious type of viciousness involves a contradiction in the form of metaphysical impossibility. Other types occur when the infinite regress is responsible for the theory in question being implausible or for its failure to solve the problem it was formulated to solve. The vice of an infinite regress can be local if it causes problems only for certain theories when combined with other assumptions, or global otherwise. For example, an otherwise virtuous regress is locally vicious for a theory that posits a finite domain. In some cases, an infinite regress is not itself the source of the problem but merely indicates a different underlying problem.
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