Infinite regress

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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.

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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. 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, Bradley's regress and regress arguments in epistemology.

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. [1] 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. [1] [2] 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. [3] 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. [1] [4] 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. [5] 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. [1]

An infinite regress argument is an argument against a theory based on the fact that this theory leads to an infinite regress. [1] [5] 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. [1] [4] The mere existence of an infinite regress by itself is not a proof for anything. [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. [4] [5] 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). [1] [5] [3] [6] 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. [3] 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. [1] [4] [3]

Viciousness

For an infinite regress argument to be successful, it has to show that the involved regress is vicious. [3] A non-vicious regress is called virtuous or benign. [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. In most cases, it is not self-evident whether an infinite regress is vicious or not. [5] 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. [4] 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. [4]

There are different ways how a regress can be vicious. The most serious type of viciousness involves a contradiction in the form of metaphysical impossibility. [4] [1] [7] 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. [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. [1] In some cases, an infinite regress is not itself the source of the problem but merely indicates a different underlying problem. [1]

Impossibility

Infinite regresses that involve metaphysical impossibility are the most serious cases of viciousness. The easiest way to arrive at this result is by accepting the assumption that actual infinities are impossible, thereby directly leading to a contradiction. [5] This anti-infinitists position is opposed to infinity in general, not just specifically to infinite regresses. [1] But it is open to defenders of the theory in question to deny this outright prohibition on actual infinities. [5] For example, it has been argued that only certain types of infinities are problematic in this way, like infinite intensive magnitudes (e.g. infinite energy densities). [4] 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. [4] While there may be some instances of viciousness due to metaphysical impossibility, most vicious regresses are problematic because of other reasons. [4]

Implausibility

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. [4] This argument is weaker than the argument from impossibility since it allows that the regress in question is possible. It only denies that it is actual. [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. But this is not metaphysically impossible, e.g. if it is assumed that the infinite number of beliefs are only non-occurrent or dispositional while the limitation only applies to the number of beliefs one is actually thinking about at one moment. [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. [8] 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. [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. But it does so by decreasing qualitative parsimony: it posits God as a new type of entity. [4]

Failure to explain

Another form of viciousness applies not to the infinite regress by itself but to it in relation to the explanatory goals of a theory. [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] [7] This is akin to the informal fallacy of begging the question. [2] 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 turtles all the way down. [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. One way to assess the viciousness of this regress is to distinguish between local and global explanations. [1] A local 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 global explanation, on the other hand, tries to explain why there are any things with this property at all. [1] 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 than explain at each step that there is another thing that is not falling. It does not explain why nothing at all is 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. [1] 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. [1] This explanation is unsatisfying since ownership is presupposed at every step. In non-transmissive explanations, however, Y is still the reason for X being F and Y is also F but this is just seen as a contingent fact. [1] [9] This line of thought has been used to argue that the epistemic regress is not vicious. From a Bayesian point of view, for example, justification or evidence can be defined in terms of one belief raising the probability that another belief is true. [10] [11] The former belief may also be justified but this is not relevant for explaining why the latter belief is justified. [1]

Responses to infinite regress arguments

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. Infinitists, on the other hand, embrace the regress but deny that it is vicious. [6] Another response is to modify the theory in order to avoid the regress. This can be achieved in the form of foundationalism or of coherentism.

Foundationalism

Traditionally, the most common response is foundationalism. [1] 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. [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. This way an infinite regress is avoided. [1] [6] This position is well-known from its applications in the field of epistemology. [1] 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. [12] The non-inferentially justified beliefs constitute the foundation on which the superstructure consisting of all the inferentially justified beliefs rests. [13] 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. [12] So a different type of explanation (acquaintance) is used for the foundational elements.

Another example comes from the field of metaphysics concerning the problem of ontological hierarchy. 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. [14] Metaphysical foundationalism 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. [1] [15] This is sometimes expressed by stating that the grounding-relation responsible for this hierarchy is well-founded . [15]

Coherentism

Coherentism, mostly found in the field of epistemology, is another way to avoid infinite regresses. [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. [16] 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. [1] Laurence BonJour is a well-known contemporary defender of this position. [17] [18]

Examples

Aristotle

Aristotle argued that knowing does not necessitate an infinite regress because some knowledge does not depend on demonstration:

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 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. [19] [20]

— Aristotle, Posterior Analytics I.3 72b1–15

Philosophy of mind

Gilbert Ryle argues in the philosophy of mind that mind-body dualism is implausible because it produces an infinite regress of "inner observers" when trying to explain how mental states are able to influence physical states.

See also

Related Research Articles

A cosmological argument, in natural theology, is an argument which claims that the existence of God can be inferred from facts concerning causation, explanation, change, motion, contingency, dependency, or finitude with respect to the universe or some totality of objects. A cosmological argument can also sometimes be referred to as an argument from universal causation, an argument from first cause, the causal argument, or the prime mover argument. Whichever term is employed, there are two basic variants of the argument, each with subtle yet important distinctions: in esse (essentiality), and in fieri (becoming).

Epistemology is the branch of philosophy concerned with knowledge. Epistemologists study the nature, origin, and scope of knowledge, epistemic justification, the rationality of belief, and various related issues. Debates in contemporary epistemology are generally clustered around four core areas:

Foundationalism concerns philosophical theories of knowledge resting upon non-inferential justified belief, or some secure foundation of certainty such as a conclusion inferred from a basis of sound premises. The main rival of the foundationalist theory of justification is the coherence theory of justification, whereby a body of knowledge, not requiring a secure foundation, can be established by the interlocking strength of its components, like a puzzle solved without prior certainty that each small region was solved correctly.

Justification is the property of belief that qualifies it as knowledge rather than mere opinion. Epistemology is the study of reasons that someone holds a rationally admissible belief. Epistemologists are concerned with various epistemic features of belief, which include the ideas of warrant, knowledge, rationality, and probability, among others.

<span class="mw-page-title-main">Regress argument (epistemology)</span> Problem in epistemology that any proposition can be endlessly questioned

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.

<span class="mw-page-title-main">Knowledge</span> Awareness of facts or being competent

Knowledge is an awareness of facts, a familiarity with individuals and situations, or a practical skill. Knowledge of facts, also called propositional knowledge, is often characterized as true belief that is distinct from opinion or guesswork by virtue of justification. While there is wide agreement among philosophers that propositional knowledge is a form of true belief, many controversies focus on justification. This includes questions like how to understand justification, whether it is needed at all, and whether something else besides it is needed. These controversies intensified in the latter half of the 20th century due to a series of thought experiments called Gettier cases that provoked alternative definitions.

In philosophical epistemology, there are two types of coherentism: the coherence theory of truth, and the coherence theory of justification.

Bertrand Russell makes a distinction between two different kinds of knowledge: knowledge by acquaintance and knowledge by description. Whereas knowledge by description is something like ordinary propositional knowledge, knowledge by acquaintance is familiarity with a person, place, or thing, typically obtained through perceptual experience. According to Bertrand Russell's classic account of acquaintance knowledge, acquaintance is a direct causal interaction between a person and some object that the person is perceiving.

Evidentialism is a thesis in epistemology which states that one is justified to believe something if and only if that person has evidence which supports said belief. Evidentialism is, therefore, a thesis about which beliefs are justified and which are not.

<span class="mw-page-title-main">Virtue epistemology</span> Philosophical approach

Virtue epistemology is a current philosophical approach to epistemology that stresses the importance of intellectual and specifically epistemic virtues. Virtue epistemology evaluates knowledge according to the properties of the persons who hold beliefs in addition to or instead of the properties of the propositions and beliefs. Some advocates of virtue epistemology also adhere to theories of virtue ethics, while others see only loose analogy between virtue in ethics and virtue in epistemology.

<span class="mw-page-title-main">Fallibilism</span> Philosophical principle

Originally, fallibilism is the philosophical principle that propositions can be accepted even though they cannot be conclusively proven or justified, or that neither knowledge nor belief is certain. The term was coined in the late nineteenth century by the American philosopher Charles Sanders Peirce, as a response to foundationalism. Theorists, following Austrian-British philosopher Karl Popper, may also refer to fallibilism as the notion that knowledge might turn out to be false. Furthermore, fallibilism is said to imply corrigibilism, the principle that propositions are open to revision. Fallibilism is often juxtaposed with infallibilism.

In epistemology, phenomenal conservatism (PC) holds that it is reasonable to assume that things are as they appear, except when there are positive grounds for doubting this.

<span class="mw-page-title-main">Münchhausen trilemma</span> A thought experiment used to demonstrate the impossibility of proving any truth

In epistemology, the Münchhausen trilemma is a thought experiment intended to demonstrate the theoretical impossibility of proving any truth, even in the fields of logic and mathematics, without appealing to accepted assumptions. If it is asked how any given proposition is known to be true, proof in support of that proposition may be provided. Yet that same question can be asked of that supporting proof, and any subsequent supporting proof. The Münchhausen trilemma is that there are only three ways of completing a proof:

Robert N. Audi is an American philosopher whose major work has focused on epistemology, ethics, rationality and the theory of action. He is O'Brien Professor of Philosophy at the University of Notre Dame, and previously held a chair in the business school there. His 2005 book, The Good in the Right, updates and strengthens Rossian intuitionism and develops the epistemology of ethics. He has also written important works of political philosophy, particularly on the relationship between church and state. He is a past president of the American Philosophical Association and the Society of Christian Philosophers.

Infinitism is the view that knowledge may be justified by an infinite chain of reasons. It belongs to epistemology, the branch of philosophy that considers the possibility, nature, and means of knowledge.

The following outline is provided as an overview of and topical guide to epistemology:

Epistemology or theory of knowledge is the branch of philosophy concerned with the nature and scope (limitations) of knowledge. It addresses the questions "What is knowledge?", "How is knowledge acquired?", "What do people know?", "How do we know what we know?", and "Why do we know what we know?". Much of the debate in this field has focused on analyzing the nature of knowledge and how it relates to similar notions such as truth, belief, and justification. It also deals with the means of production of knowledge, as well as skepticism about different knowledge claims.

Richard Anthony Fumerton is a Canadian American philosopher and professor of philosophy at the University of Iowa with research interests in epistemology, metaphysics, philosophy of mind and value theory. He has been cited as an influential expert on the position of "metaepistemological scepticism". He received his B.A. in philosophy from the University of Toronto in 1971 and his M.A. and PhD from Brown University in 1973 and 1974, respectively. He has been the F. Wendell Miller Professor of Philosophy at the University of Iowa since 2003.

Definitions of knowledge try to determine the essential features of knowledge. Closely related terms are conception of knowledge, theory of knowledge, and analysis of knowledge. Some general features of knowledge are widely accepted among philosophers, for example, that it constitutes a cognitive success or an epistemic contact with reality and that propositional knowledge involves true belief. Most definitions of knowledge in analytic philosophy focus on propositional knowledge or knowledge-that, as in knowing that Dave is at home, in contrast to knowledge-how (know-how) expressing practical competence. However, despite the intense study of knowledge in epistemology, the disagreements about its precise nature are still both numerous and deep. Some of those disagreements arise from the fact that different theorists have different goals in mind: some try to provide a practically useful definition by delineating its most salient feature or features, while others aim at a theoretically precise definition of its necessary and sufficient conditions. Further disputes are caused by methodological differences: some theorists start from abstract and general intuitions or hypotheses, others from concrete and specific cases, and still others from linguistic usage. Additional disagreements arise concerning the standards of knowledge: whether knowledge is something rare that demands very high standards, like infallibility, or whether it is something common that requires only the possession of some evidence.

References

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  8. ↑ Schaffer, Jonathan (2015). "What Not to Multiply Without Necessity" (PDF). Australasian Journal of Philosophy. 93 (4): 644–664. doi:10.1080/00048402.2014.992447. S2CID   16923735.
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  11. ↑ Hájek, Alan; Lin, Hanti (2017). "A Tale of Two Epistemologies?". Res Philosophica. 94 (2): 207–232. doi:10.11612/resphil.1540. S2CID   160029122.
  12. 1 2 3 Hasan, Ali; Fumerton, Richard (2018). "Foundationalist Theories of Epistemic Justification". The Stanford Encyclopedia of Philosophy. Metaphysics Research Lab, Stanford University. Retrieved 9 March 2021.
  13. ↑ Audi, Robert (2001). The Architecture of Reason: The Structure and Substance of Rationality. Oxford University Press. pp. 13, 29–31.
  14. ↑ Bliss, Ricki; Trogdon, Kelly (2016). "Metaphysical Grounding". The Stanford Encyclopedia of Philosophy. Metaphysics Research Lab, Stanford University. Retrieved 10 March 2021.
  15. 1 2 Cameron, Ross. "Infinite Regress Arguments > Metaphysical Foundationalism and the Well-Foundedness of Grounding (Stanford Encyclopedia of Philosophy)". plato.stanford.edu. Retrieved 10 March 2021.
  16. ↑ Olsson, Erik (2017). "Coherentist Theories of Epistemic Justification". The Stanford Encyclopedia of Philosophy. Metaphysics Research Lab, Stanford University. Retrieved 9 March 2021.
  17. ↑ BonJour, Laurence (1985). The Structure of Empirical Knowledge. Harvard University Press.
  18. ↑ Goldman, Alan H. (1989). "BonJour's Coherentism". The Current State of the Coherence Theory: Critical Essays on the Epistemic Theories of Keith Lehrer and Laurence BonJour, with Replies. Springer Netherlands: 125–133. doi:10.1007/978-94-009-2360-7_11. ISBN   978-94-010-7563-3.
  19. ↑ Byrne, Patrick Hugh (1997). Analysis & Science in Aristotle. SUNY Series in Ancient Greek Philosophy. State University of New York Press. p. 83. ISBN   9780791433218. LCCN   96037783.
  20. ↑ Aristotle (1901). Posterior Analytics. B.H. Blackwell. p. 7.

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