What Is An Infinite Regression

Infinite Regression

An Infinite regression is a loop of premises that continue on in ad infinitum. That is, since each premise is contingent on some reason, we then require another premise to justify that reason.

In philosophy, the infinite regression phenomenon frequently takes the form of an argument.

Infinite Regression In Philosophy

Infinite regression has been used in philosophy to justify and negate different arguments within philosophy, from greek to modern philosophy.

When used constructively, infinite regression arguments can create Epistemic Infinitism; which can either function as a framework to solve problems of infinite regression or create justified beliefs. When used destructively, infinite regression can demonstrate the falsehoods and fallacies of other epistemic frameworks.

And in philosophy, each infinite regress abides by the following:

• Infinite Regresses have to demonstrate, step-by-step, how each conclusion is derived and how each assumption leads to the regress.

Examples Of Infinite Regression:

Aristotle’s Highest Good:

Suppose anything is good only if we desire it for the sake of something else that is good. This yields a regress that is absurd. Hence: at least one thing is good and not desired for the sake of something else that is good, I.e., the highest good that is desired for the sake of itself.

Source: Nicomachen Ethics, 1094a

Aquinas’ Cosmological Argument:

Suppose that every finite and contingent being has a cause, and that every cause is a finite and contingent being. This yields a regress that is absurd. Hence: it is not the case that every cause is a finite and contingent being. There must be a first cause which is not finite or contingent, namely God.

Source: Summa Theologica, book 1, v. 2, Sect. 3

Hume’s Induction:

Suppose you want to justify an inductive inference. As a solution, you rely on the assumption that the future resembles the past. Yet, you cannot justify the initial inference unless you justify this assumption. As a solution, you again rely on the assumption that, in this case too, the future resembles the past. Regress. Hence: you will never justify any inductive inference.

Source: An Enquiry Concerning Human Understanding, Chap. 4.

The Two Types Of Infinite Regress Arguments

Constructive Infinite Regression

As seen in the example given to us by Aristotle, regress arguments can be constructive; that is, they are used as justifications for belief. For Aristotle, infinite regression presents as something absurd.

If we genuinely viewed something as good simply because it brought us something else, of which we presumed to be good, then we would have an infinite regression; more specifically, if apples are good because we want to be fit, then being fit is only good because we want to feel healthy, and feeling healthy is good because we want to live longer…ad infinitum.

Without a highest good, the regress has the potential to go on forever; and we have two ways of dealing with that. We can, like Aristotle, suppose that the highest good exists, so as to avoid the absurdity of regression. Or, we can suppose of a more immediate premise, perhaps premise one or two, that it is intrinsically good and desired for its own sake. Both stop the regress, if accepted.

But what we must takeaway from Aristotle is that the absurdity of regression can be used as a justification for various beliefs.

With Aquinas, we have an example of a constructive infinite regression that depends on vicious circularity. Since there cannot be a cause that caused its self, we either accept vicious circularity or some being that is infinite in nature. Similar to Aristotle, the argument depends on the absurd of fallacious nature that the infinite regression brings to our attention.

Destructive Infinite Regression

Hume’s example demonstrates the impossibility of inductive reasoning via an infinite regression. But he involves something more than aquinas does; that is, Hume incorporates justification not only for the inferences we make but also for the reasons which support that inference.

Sometimes known as an infinite regression of disputes, Hume reorients the skepticism to a justification for the evidence that supports our evidence. Doing so leads to something known as the münchhausen trilemma.

But now we have a problem, as Hume has thusly demonstrated through his argument: we can justify claims about the existence or non-existence of things, or conclude in favour or in disfavour of things, all while utilizing precisely the same argument structure.

For example:

Suppose anything is good only if we desire it for the sake of something else that is good. This yields a regress that is absurd. Hence: nothing is good.

Herein, we’ve simply adopted the same presupposition necessary for Aristotle to derive his infinite regression, except we’ve replaced the conclusion. And we have remained logically equivalent all while doing so; that is, we’ve not deviated from the schema of the argument.

So when are infinite regresses appropriately used? And why should we care about them?

Conclusion On Infinite Regression Arguments

As we have seen so far, infinite regressions can be used to justify precisely the same position that it advocates for, if only we switch the variable inside the argument to its opposite.

From that, it is clear that infinite regressions aren’t useful when it comes to justification. And in fact, much of the literature cannot come to any decisive agreement on the issue as well; that is, to what actually can be justified by an infinite regression argument, none seem to be clear on. (1)(2)

But the lack of consensus on the issue of infinite regression arguments need not make them necessarily useless or entirely unusable.

Infinite regressions can be used as a tool for skepticism, so as to doubt or negate those who claim to have some, albeit misguided, sense of certainty in their beliefs, such that they are unwilling to admit the possibility of a committed falsehood on their behalf.

And infinite regressions themselves can be used a demonstration of human nature; that is, since all arguments can be doubted, to point wherein which we reveal their unjustified nature, then it follows that “truth,” for humans must always be axiomatic. That we must suppose something to be the truth and proceed from there; all while being open to the possibility that a new axiom will in due time be required.

Infinite regressions don’t destroy philosophy, but instead demonstrate how much of a creative endeavour it truly is.

References

• Aquinas, T. 1952. Summa theologica. Trans. Fathers of the English Dominican Province. Chicago: Encyclopaedia Britannica.
• Aristotle. 1925. Nicomachean ethics. Trans. W.D. Ross. Oxford: Oxford University Press.
• Black, Oliver, 1996, “Infinite Regress Arguments and Infinite Regresses”, Acta Analytica, 16: 95–124.

• Hume, D. 1748. An enquiry concerning human understanding, eds. Selby-Bigge L.A. and Nidditch P.H. 3rd ed. 1975. Oxford: Clarendon.

• Klein, P. D. 2007. Human Knowledge and the Infinite Progress of Reasoning. Philosophical Studies 134: 1-17.
• Turri, John, and Peter D. Klein. Ad Infinitum: New Essays on Epistemological Infinitism. , 2014. Print.