Infinite regress
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.
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.
[5] 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.
But it can also be used in a positive form to support a theory by showing that its alternative involves a vicious regress.
[5] 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.
[4][7] 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.
The easiest way to arrive at this result is by accepting the assumption that actual infinities are impossible, thereby directly leading to a contradiction.
[1] But it is open to defenders of the theory in question to deny this outright prohibition on actual infinities.
[1] For example, it seems implausible due to the limitations of the human mind that there are justified beliefs if this entails that the agent needs to have an infinite amount of them.
[4] Another reason for the implausibility of theories involving an infinite regress is due to the principle known as Ockham's razor, which posits that we should avoid ontological extravagance by not multiplying entities without necessity.
[1] For example, the cosmological argument for the existence of God promises to increase quantitative parsimony by positing that there is one first cause instead of allowing an infinite chain of events.
[4][7] Theories are often formulated with the goal of solving a specific problem, e.g. of answering the question why a certain type of entity exists.
One way how such an attempt can fail is if the answer to the question already assumes in disguised form what it was supposed to explain.
[4][1] Despite its shortcomings in clashing with modern physics and due to its ontological extravagance, this theory seems to be metaphysically possible assuming that space is infinite.
[1] So as a local explanation, the regress in the turtle theory is benign: it succeeds in explaining why the earth is not falling.
[1][4] It has been argued that infinite regresses can be benign under certain circumstances despite aiming at global explanation.
This line of thought rests on the idea of the transmission involved in the vicious cases:[9] it is explained that X is F because Y is F where this F was somehow transmitted from Y to X.
[12] So from any given position, the series can be traced back to elements on the most fundamental level, which the recursive principle fails to explain.
On such a view, an agent is inferentially justified to believe that it will rain tomorrow based on the belief that the weather forecast told so.
[1] It is based on a holistic explanation that usually sees the entities in question not as a linear series but as an interconnected network.
For example, coherentist theories of epistemic justification hold that beliefs are justified because of the way they hang together: they cohere well with each other.
The first school, assuming that there is no way of knowing other than by demonstration, maintain that an infinite regress is involved, on the ground that if behind the prior stands no primary, we could not know the posterior through the prior (wherein they are right, for one cannot traverse an infinite series): if on the other hand – they say – the series terminates and there are primary premises, yet these are unknowable because incapable of demonstration, which according to them is the only form of knowledge.
Such, then, is our doctrine, and in addition, we maintain that besides scientific knowledge there is its original source which enables us to recognize the definitions.
