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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. And since thus one cannot know the primary premises, knowledge of the conclusions which follow from them is not pure scientific knowledge nor properly knowing at all, but rests on the mere supposition that the premises are true. The other party agrees with them as regards knowing, holding that it is only possible by demonstration, but they see no difficulty in holding that all truths are demonstrated, on the ground that demonstration may be circular and reciprocal. Our own doctrine is that not all knowledge is demonstrative: on the contrary, knowledge of the immediate premises is independent of demonstration. (The necessity of this is obvious; for since we must know the prior premises from which the demonstration is drawn, and since the regress must end in immediate truths, those truths must be indemonstrable.) 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.
455:. It 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. 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. This way an infinite regress is avoided. This position is well-known from its applications in the field of epistemology. Foundationalist theories of epistemic justification state that besides inferentially justified beliefs, which depend for their justification on other beliefs, there are also non-inferentially justified beliefs. The non-inferentially justified beliefs constitute the foundation on which the superstructure consisting of all the inferentially justified beliefs rests. Acquaintance theories, for example, explain the justification of non-inferential beliefs through acquaintance with the objects of the belief. 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. They are non-inferentially justified in believing that they are in pain because they are directly acquainted with the pain. So a different type of explanation (acquaintance) is used for the foundational elements.
488:, mostly found in the field of epistemology, is another way to avoid infinite regresses. 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. This view can be expressed by stating that justification is primarily a property of the system of beliefs as a whole. The justification of a single belief is derivative in the sense that it depends on the fact that this belief belongs to a coherent whole.
278:. 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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has been argued that only certain types of infinities are problematic in this way, like infinite intensive magnitudes (e.g. infinite energy densities). But other types of infinities, like infinite cardinality (e.g. infinitely many causes) or infinite extensive magnitude (e.g. the duration of the universe's history) are unproblematic from the point of view of metaphysical impossibility. While there may be some instances of viciousness due to metaphysical impossibility, most vicious regresses are problematic because of other reasons.
398:. The problem is that to transfer something, it first must be possessed, so the possession is presumed rather than explained. For example, in trying to explain why one's neighbor has the property of being the owner of a bag of sugar, it is revealed that this bag was first in someone else's possession before it was transferred to the neighbor and that the same is true for this and every other previous owner. This explanation is unsatisfying since ownership is presupposed at every step. In non-transmissive explanations, however,
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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
342:. From the perspective of a mythological world view, for example, one way to explain why the earth seems to be at rest instead of falling down is to hold that it rests on the back of a giant turtle. In order to explain why the turtle itself is not in free fall, another even bigger turtle is posited and so on, resulting in a world that is
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possible. It only denies that it is actual. 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. But this is not metaphysically impossible, e.g. if it is assumed that the infinite number of beliefs are only
313:, which posits that we should avoid ontological extravagance by not multiplying entities without necessity. Considerations of parsimony are complicated by the distinction between quantitative and qualitative parsimony: concerning how many entities are posited in contrast to how many kinds of entities are posited. For example, the
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Some hold that owing to the necessity of knowing the primary premises, there is no scientific knowledge. Others think there is, but that all truths are demonstrable. Neither doctrine is either true or a necessary deduction from the premises. The first school, assuming that there is no way of knowing
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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,
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are impossible, thereby directly leading to a contradiction. This anti-infinitists position is opposed to infinity in general, not just specifically to infinite regresses. But it is open to defenders of the theory in question to deny this outright prohibition on actual infinities. For example, it
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explanation, on the other hand, tries to explain why there are any things with this property at all. So as a local explanation, the regress in the turtle theory is benign: it succeeds in explaining why the earth is not falling. But as a global explanation, it fails because it has to assume rather
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Another form of viciousness applies not to the infinite regress by itself but to it in relation to the explanatory goals of a theory. 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
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A more common form of viciousness arises from the implausibility of the infinite regress in question. This category often applies to theories about human actions, states or capacities. This argument is weaker than the argument from impossibility since it allows that the regress in question is
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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
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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
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is the thesis that these dependence relations do not form an infinite regress: that there is a most fundamental level that grounds the existence of the entities from all other levels. This is sometimes expressed by stating that the grounding-relation responsible for this hierarchy is
213:. 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
250:. 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
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point of view, for example, justification or evidence can be defined in terms of one belief raising the probability that another belief is true. The former belief may also be justified but this is not relevant for explaining why the latter belief is justified.
346:. 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. One way to assess the viciousness of this regress is to distinguish between
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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
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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.
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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
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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:
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while the limitation only applies to the number of beliefs one is actually thinking about at one moment. Another reason for the implausibility of theories involving an infinite regress is due to the principle known as
49:, 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. An
466:. One position in this debate claims that some entities exist on a more fundamental level than other entities and that the latter entities depend on or are grounded in the former entities.
435:, on the other hand, embrace the regress but deny that it is vicious. Another response is to modify the theory in order to avoid the regress. This can be achieved in the form of
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Philosophers have responded to infinite regress arguments in various ways. The criticized theory can be defended, for example, by denying that an infinite regress is involved.
68:. 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.
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explanation is only interested in explaining why one thing has a certain property through reference to another thing without trying to explain this other thing as well. A
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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.
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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
259:, 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
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is implausible because it produces an infinite regress of "inner observers" when trying to explain how mental states are able to influence physical states.
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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
84:, which is based on a holistic explanation that usually sees the entities in question not as a linear series but as an interconnected network.
1203:"Infinite Regress Arguments > Metaphysical Foundationalism and the Well-Foundedness of Grounding (Stanford Encyclopedia of Philosophy)"
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but this is just seen as a contingent fact. This line of thought has been used to argue that the epistemic regress is not vicious. From a
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attempt can fail is if the answer to the question already assumes in disguised form what it was supposed to explain. This is akin to the
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for the existence of God works: it claims that positing God's existence is necessary in order to avoid an infinite regress of causes.
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parsimony by positing that there is one first cause instead of allowing an infinite chain of events. But it does so by decreasing
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than explain at each step that there is another thing that is not falling. It does not explain why nothing at all is falling.
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are the most serious cases of viciousness. The easiest way to arrive at this result is by accepting the assumption that
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argued that knowing does not necessitate an infinite regress because some knowledge does not depend on demonstration:
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There are different ways how a regress can be vicious. The most serious type of viciousness involves a
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Infinite regress arguments have been made in various areas of philosophy. Famous examples include the
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principle that determines how each entity in the series depends on or is produced by its predecessor.
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is an argument against a theory based on the fact that this theory leads to an infinite regress.
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reformulate the theory in question in a way that avoids the regress. One such strategy is
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for the regress to get started. So the regress starts with the fact that
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The
Architecture of Reason: The Structure and Substance of Rationality
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Huemer, Michael (2016). "13. Assessing
Infinite Regress Arguments".
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Maurin, Anna-Sofia (2007). "Infinite
Regress - Virtue or Vice?".
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The
Unreality of Time § The contradiction of the A-series
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to be successful, it has to show that the involved regress is
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is a well-known contemporary defender of this position.
1129:"Foundationalist Theories of Epistemic Justification"
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involved in the vicious cases: it is explained that
325:parsimony: it posits God as a new type of entity.
1229:"Coherentist Theories of Epistemic Justification"
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724:. Metaphysics Research Lab, Stanford University.
38:is an infinite series of entities governed by a
1235:. Metaphysics Research Lab, Stanford University
1179:. Metaphysics Research Lab, Stanford University
1135:. Metaphysics Research Lab, Stanford University
1064:. Metaphysics Research Lab, Stanford University
1160:. Oxford University Press. pp. 13, 29–31.
556:Action (philosophy) § Basic and non-basic
317:for the existence of God promises to increase
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892:. Department of Philosophy, Lund University.
185:. But in order to account for the fact that
451:Traditionally, the most common response is
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1083:Hájek, Alan; Lin, Hanti (2017).
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1085:"A Tale of Two Epistemologies?"
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1369:. B.H. Blackwell. p. 7.
1328:Byrne, Patrick Hugh (1997).
1285:10.1007/978-94-009-2360-7_11
1001:10.1080/00048402.2014.992447
943:"Infinite Regress Arguments"
941:Wieland, Jan Willem (2013).
910:"Infinitism in Epistemology"
788:"Infinite Regress Arguments"
786:Day, Timothy Joseph (1987).
718:"Infinite Regress Arguments"
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468:Metaphysical foundationalism
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1260:. Harvard University Press.
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148:stands for a relation and
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1271:Goldman, Alan H. (1989).
1056:Talbott, William (2016).
1027:"The Source Of Necessity"
959:10.1007/s12136-012-0165-1
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232:infinite regress argument
206:infinite regress argument
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1173:"Metaphysical Grounding"
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1058:"Bayesian Epistemology"
738:Clark, Romane (1988).
716:Cameron, Ross (2018).
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1391:at Wikimedia Commons
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1154:Audi, Robert (2001).
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521:Posterior Analytics
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1363:Aristotle (1901).
1207:plato.stanford.edu
1025:Hale, Bob (2002).
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