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Circular reasoning

Circular reasoning, also known as begging the question or petitio principii, is a logical fallacy in which an argument's premises assume the truth of its conclusion, thereby providing no genuine evidence or justification for the claim being made.^[1] This fallacy occurs when the reasoning forms a closed loop, where the conclusion is restated or presupposed in the premises, rendering the argument epistemically circular and unpersuasive.^[2] For instance, the statement "The Bible is the word of God because God inspired it, and we know God inspired it because the Bible says so" exemplifies this by relying on the conclusion to support itself without independent verification.^[1] The concept originates in ancient Greek philosophy, particularly in Aristotle's Sophistical Refutations, where it is identified as a refutation that assumes the point at issue without proving it, often through subtle equivocation or direct restatement.^[1] Over time, logicians such as Richard Whately refined the term begging the question to emphasize its role in assuming a controversial proposition under a different guise, distinguishing simpler cases from more complex chains of circular inferences.^[1] Circular reasoning extends beyond direct restatements to multi-step arguments, as seen in René Descartes' epistemological demonstrations, where the reliability of clear and distinct ideas is justified by God's existence, which is in turn supported by the reliability of those ideas.^[1] In modern informal logic, circular reasoning is analyzed as a dialectical failure that hinders productive dialogue by evading scrutiny of foundational assumptions, often appearing in debates on religion, politics, and science.^[2] Philosophers like Douglas Walton have classified it among question-begging fallacies, highlighting its context-dependent nature in argumentation rather than strict formal invalidity.^[1] Detecting and avoiding this fallacy requires evaluating whether premises offer novel support or merely presuppose the conclusion, promoting more robust evidential reasoning.^[2]

Fundamentals

Definition

Circular reasoning, also known as circulus in probando (Latin for "circle in proving"), is an informal logical fallacy in which the conclusion of an argument is either explicitly or implicitly assumed in one or more of its premises, thereby rendering the reasoning non-independent and invalid.^[3] This fallacy occurs when the premises do not provide genuine support for the conclusion but instead restate or presuppose it, often in a disguised form that may appear persuasive at first glance.^[1] The reasoning fails logically because it creates a self-referential loop that lacks external or independent evidence to justify the claims, failing to advance any substantive justification or epistemic progress.^[1] In such arguments, the premises and conclusion mutually support each other without grounding in verifiable facts or separate reasoning, which violates the basic requirement for arguments to demonstrate their conclusions through non-circular means.^[4] This must be distinguished from valid forms of repetition or circularity, such as emphasizing a point for rhetorical clarity in non-argumentative contexts, where no claim of proof is being made; true circular reasoning, by contrast, attempts to establish a conclusion through fallacious self-reference.^[1] A basic structure of circular reasoning can be represented as assuming proposition P because of Q, while also assuming Q because of P, forming a closed loop without external validation.^[3]

Key Characteristics

Circular reasoning is characterized by premises that presuppose the truth of the conclusion, creating a self-referential loop without independent support. This core trait manifests as self-supporting premises where the argument relies on the very claim it seeks to establish, rendering the justification circular rather than linear. For instance, a premise might directly or indirectly affirm the conclusion, leading to a lack of genuine evidential grounding. Additionally, circular arguments often involve hidden assumptions that subtly embed the conclusion within the premises, obscuring the dependency and allowing the fallacy to evade immediate notice.^[5]^[6] The fallacy appears in two primary types: explicit and implicit circularity. Explicit circularity occurs through overt restatement, where the premise is essentially a verbatim or near-verbatim repetition of the conclusion, providing no new information. In contrast, implicit circularity is more subtle, disguised through synonyms, loaded terms, or equivalent propositions that paraphrase the conclusion without apparent duplication. This distinction highlights how implicit forms can masquerade as valid reasoning by avoiding direct repetition while still failing to offer external validation.^[6]^[3] Circular reasoning undermines sound argumentation by violating the principle of non-circular justification, essential to both deductive and inductive logic. In deductive reasoning, premises must entail the conclusion through independent truths, but circularity introduces premises equally in need of proof, collapsing the argument's validity. Similarly, in inductive reasoning, evidence should probabilistically support the conclusion without presupposing it, yet circular structures forfeit this by smuggling in the target claim. This pragmatic defect ensures the argument cannot establish its conclusion on firm grounds, as the reasoning doubles back without advancing justification.^[6]^[7] Detection of circular reasoning involves scrutinizing the argument's structure for premise-conclusion overlap, often by analyzing the role of repetition and grounding in agreed-upon facts. One method is to evaluate whether removing the circular premise leaves the conclusion unsupported, revealing the dependency. Rephrasing premises to check for equivalence with the conclusion can also expose hidden circularity, as equivalent statements indicate a lack of independent evidence. These techniques emphasize examining the argument's branching and informational flow to identify self-referential loops.^[6]

Forms and Variations

Begging the Question

Begging the question, also known as petitio principii, is a form of circular reasoning in which the premise of an argument assumes the truth of the conclusion without providing independent evidence to support it.^[1] In this fallacy, the conclusion is essentially restated in the premise, often in synonymous or equivalent terms, rendering the argument tautological and uninformative. For instance, the claim "Opium induces sleep because it possesses sleep-inducing properties" exemplifies this by defining the effect in the premise without justifying why opium has those properties.^[3] This direct assumption fails to advance the argument, as it begs the very point at issue rather than proving it.^[5] The term originates from the Latin petitio principii, meaning "assuming the initial point" or "requesting the first principle," which refers to illegitimately demanding that the disputed issue be conceded as a starting point in a debate.^[4] This phrase traces back to Aristotle's Sophistical Refutations, where he identified the fallacy as a sophistical tactic of presupposing what needs to be established.^[1] The English idiom "begging the question" emerged in the 16th century as a translation of the Latin, initially retaining the logical sense before later being misused to mean "raising the question."^[4] This form of circularity arises because the premise offers no new information beyond the conclusion, creating a self-reinforcing loop that evades genuine justification.^[3] As a result, the argument cannot persuade those who do not already accept the conclusion, since it relies on an unproven assumption equivalent to the claim itself.^[5] Begging the question often appears in subtle disguises that mask its circular nature. One variation involves equivocation, where ambiguous language allows the premise to imply the conclusion through shifting meanings of key terms.^[1] Another employs rhetorical questions that presuppose the answer, such as "Why wouldn't we trust the Bible when it's the word of God?" thereby assuming divine authority without evidence.^[1] Definitional tricks further conceal the fallacy by embedding the conclusion within a biased or loaded definition, for example, asserting that "celibacy is unnatural because it excludes sexual activity," which assumes unnaturalness is defined solely by that exclusion.^[5] These tactics exploit linguistic nuances to present the assumption as reasonable, though they ultimately provide no substantive support.^[3]

Vicious Circle Arguments

Vicious circle arguments represent a form of circular reasoning characterized by a chain of interdependent premises, where each premise supports the next in a sequence that loops back to the initial premise without independent external validation. In this structure, the justification for one claim relies on another, which in turn depends on subsequent claims, ultimately circling back to assume the truth of the first without providing novel evidence or grounding. For instance, an argument might posit that event A causes B, B causes C, and C causes A, creating a self-reinforcing loop that fails to establish any foundational support. This form is distinct from simpler circularities by involving multiple mediated steps rather than a direct assumption.^[3] Unlike begging the question, which involves an immediate restatement or direct presupposition of the conclusion within a single premise, vicious circle arguments unfold through a series of interconnected justifications that indirectly embed the conclusion across the chain. Begging the question typically manifests as a probative failure in a straightforward premise-conclusion relation, whereas vicious circles employ mediate reasoning, often spanning multiple propositions or even extended discourses, to obscure the circular dependency. This extended structure can make the fallacy less apparent, as each step appears provisionally valid until the loop is revealed.^[3]^[8] The logical consequences of vicious circle arguments include the risk of infinite regress in justification, where attempts to validate the chain require endlessly revisiting the premises without resolution, or unfounded bootstrapping, in which the argument illicitly elevates ungrounded assumptions to justified beliefs through mutual reinforcement. Such structures render the reasoning non-probative, as they do not advance understanding or provide evidential warrant beyond the initial assumptions, potentially leading to dialectical stalemates in debates. In formal terms, the cyclic dependence trivializes the proof, making it equivalent to tautological assertion without substantive inference.^[8] In applications to belief systems, vicious circle arguments often sustain dogmas by creating self-contained webs of mutual support that resist external empirical or rational scrutiny, thereby insulating core tenets from falsification or revision. For example, a doctrinal framework might justify sacred texts through divine inspiration, which is in turn validated by the texts themselves via interpretive chains, perpetuating the system without independent corroboration. This dynamic fosters coherence within the belief network but undermines its epistemic robustness, as challenges from outside the loop are dismissed as incompatible with the internal logic.^[8]

Historical Development

Ancient Philosophy

Circular reasoning, known in ancient Greek philosophy as a form of invalid argumentation, was first formally analyzed by Aristotle in the 4th century BCE. In his Prior Analytics (Book II, chapters 16–17), Aristotle identifies begging the question (petitio principii) as a paralogism where the premises assume the truth of the conclusion, resulting in a failure of proper demonstration because the argument circles back without independent support. He explains that such arguments appear to proceed from true premises but do not necessitate the conclusion due to their circular structure, distinguishing them from valid syllogisms.^[1] Aristotle further elaborates on this fallacy in Sophistical Refutations (chapter 5), classifying it among non-verbal fallacies and describing it as covertly requesting the admission of the point at issue, often through the use of synonymous terms or the illicit mixing of particular and universal propositions. For example, proving that "the Bible is true because God says it is, and we know God says it is because the Bible says so" exemplifies this by restating the conclusion in disguised form, yielding no genuine proof. This analysis underscored circular reasoning as a rhetorical trick rather than a logical advancement, particularly in eristic debates.^[1] Plato's dialogues, predating Aristotle's systematic treatment, critique self-referential arguments that devolve into circularity, especially those used by sophists in epistemological discussions. In works like the Euthydemus, Socrates exposes the sophists' eristic techniques—such as claiming contradictory statements are simultaneously true through verbal ambiguity—as self-referential loops that fail to yield knowledge, satirizing their reliance on circular assertions to win arguments without substantive reasoning. These portrayals highlight Plato's concern with how such fallacies undermine genuine inquiry into truth and virtue. Stoic logicians, building on earlier Greek traditions in the Hellenistic period, emphasized non-circular proofs to ensure the validity of inferences in their propositional logic system. They insisted on linear chains of deduction from kataleptic impressions (clear and distinct perceptions) to conclusions, rejecting circular arguments as invalid sophisms that violate the criteria for sound demonstration. This approach reinforced the need for arguments to progress without presupposing their endpoints, influencing later logical developments. In the broader cultural context of 4th-century BCE Greece, circular reasoning emerged as a key issue in debates on epistemology and rhetoric, where philosophers like Socrates sought to establish reliable knowledge amid sophistic challenges. The Socratic method, as illustrated in Plato's early dialogues, exemplified an approach to avoid circularity by employing elenchus—systematic questioning to reveal assumptions and contradictions—thereby fostering dialectical progress grounded in examined beliefs rather than unproven premises.

Modern Logical Analysis

In the 19th century, John Stuart Mill advanced the analysis of circular reasoning within the framework of inductive logic, emphasizing its pitfalls in empirical inquiry. In his seminal work A System of Logic (1843), Mill argued that deductive reasoning, such as syllogisms, appears circular because the conclusion merely restates information implicit in the premises, offering no genuine advancement in knowledge. He contended that true reasoning resides in induction, but warned against circularity in justifying inductive principles, such as the uniformity of nature, which must be grounded in experience rather than presupposed axioms to avoid petitio principii. For instance, Mill critiqued assumptions of universal causation as potentially self-reinforcing if derived solely from prior inductions without empirical verification, advocating methods like the Method of Difference to break such loops.^[9] Building on these foundations in the early 20th century, Bertrand Russell and Alfred North Whitehead provided a formal treatment of vicious circles in their collaborative Principia Mathematica (1910–1913), addressing paradoxes in set theory and logic. Motivated by Russell's paradox of 1901, which exposed self-referential contradictions in naive set theory (e.g., the set of all sets not containing themselves), they introduced the Vicious-Circle Principle: "Whatever involves all of a collection must not be one of the collection; and likewise of properties: whatever involves all of a class must not be one of the class." This principle, articulated in the introduction, ramified types to prevent impredicative definitions that lead to circular self-reference, ensuring a hierarchical structure where definitions avoid referencing the totality they define. Their approach resolved foundational crises in mathematics by eliminating vicious circles through type theory, influencing subsequent developments in formal logic. In analytic philosophy, Ludwig Wittgenstein further refined the understanding of circularity by examining its manifestations in ordinary language, particularly through his concept of language games in Philosophical Investigations (1953). Wittgenstein posited that philosophical confusions, including hidden circularities, arise when language is abstracted from its practical use, leading to self-referential traps in meaning and rule-following. For example, in the rule-following paradox (§§185–201), he illustrated how attempts to justify rule application regress into circularity—interpreting a rule requires another rule, ad infinitum—unless anchored in shared forms of life and communal agreement within language games. This view dissolved apparent vicious circles not by formal prohibition but by revealing them as grammatical illusions in everyday discourse, shifting focus from abstract logic to contextual practice.^[10] During the medieval period, scholastic philosophers like Thomas Aquinas addressed circular reasoning in theological and logical contexts, such as in the Summa Theologica, where arguments for God's existence avoid petitio principii by building on independent premises rather than presupposing the conclusion. This bridged ancient and modern analyses by integrating Aristotelian logic with Christian doctrine.^[11]

Philosophical Implications

Connection to the Problem of Induction

Circular reasoning plays a central role in David Hume's formulation of the problem of induction, where inductive inferences rely on the unproven assumption that the future will resemble the past. In his Enquiry Concerning Human Understanding (1748), Hume argues that all inductive reasoning presupposes the uniformity of nature—the principle that observed patterns will continue unchanged—but this principle itself can only be justified through inductive inference, resulting in a circular justification.^[12]^[13] This circularity manifests as begging the question because the uniformity premise is invoked to validate predictions based on past experiences, yet its own validity depends on the success of those same inductive methods it seeks to support. Hume contends that no empirical observation can establish this principle a priori, as it concerns unobserved future events, nor can deductive logic demonstrate it without assuming what it aims to prove.^[13]^[12] Epistemologically, this challenge undermines the foundations of empiricism by revealing that inductive knowledge, central to scientific and everyday reasoning, lacks a non-circular rational basis, though Hume maintains it remains psychologically compelling through habit.^[13]^[14] Subsequent attempts to resolve this issue without vicious circularity include probabilistic approaches, such as Bayesian confirmation theory, which reframe induction as degree-of-belief updates rather than strict uniformity assumptions, though these are explored in greater detail in broader discussions of inductive logic.^[13]^[15]

Critiques and Responses

Critiques of circular reasoning often center on its potential to undermine genuine justification, yet philosophers have defended certain forms of circularity as benign or even virtuous in specific contexts, particularly within coherentist theories of epistemic justification. In coherentism, justification arises holistically from the mutual support among beliefs in a comprehensive system, forming what some describe as a "virtuous circle" where the coherence of the entire web provides legitimacy without requiring independent foundations.^[16] This contrasts with vicious circularity, where a belief is justified solely by another belief that itself depends on the first, offering no external grounding and thus failing to advance knowledge.^[17] The distinction between benign and vicious circularity hinges on whether the loop contributes to overall epistemic reliability; benign forms, as in coherentism, allow for systemic mutual reinforcement that tracks truth through interconnected evidence, whereas vicious ones merely beg the question without adding justificatory power.^[16] Philosophical debates highlight tensions between foundationalism and coherentism regarding circularity's role. Foundationalists critique coherentism for inevitably entailing circular justification, arguing that without self-evident basic beliefs, all knowledge risks regressing into loops that cannot be rationally defended.^[18] Coherentists respond by embracing holism, as articulated in Quine's "web of belief," where beliefs form an interdependent network revised collectively in light of experience, rendering some degree of circularity not only inevitable but epistemically productive.^[19] This view posits that no belief stands in complete isolation, and adjustments to the web—often at its periphery—mitigate potential viciousness by incorporating empirical constraints.^[19] In addressing inductive circularity, Karl Popper's falsificationism offers a prominent alternative, rejecting inductive confirmation altogether in favor of deductive testing that seeks to disprove hypotheses through empirical observation.^[20] By emphasizing falsifiability over verification, Popper's approach avoids circular appeals to past successes to justify future predictions, instead grounding scientific progress in the potential refutation of bold conjectures.^[20] Strategies for avoiding or mitigating circular reasoning include pursuing axiomatic foundations, rigorous empirical testing, and probabilistic updating methods. Foundationalism seeks to break loops by positing a set of basic, non-inferentially justified beliefs—such as immediate perceptual experiences—that serve as secure starting points for further inferences.^[18] Empirical testing, as in Popper's framework, prioritizes falsification to ensure arguments remain tethered to observable reality rather than self-referential claims.^[20] Bayesian epistemology provides another response through conditionalization, where degrees of belief are updated via Bayes' theorem in response to new evidence, incorporating prior probabilities and likelihoods to incrementally refine justifications without relying on circular bootstrapping.^[21]

Practical Examples

Everyday and Rhetorical Uses

In everyday discourse, circular reasoning frequently appears in advertising, where slogans assert a product's superiority by restating its popularity or quality without independent evidence. For instance, a shampoo advertisement might claim, "This is the best shampoo because it's superior," relying on the conclusion to justify itself rather than providing comparative data or user testimonials.^[22] Such tactics exploit consumer trust in repetition, making the argument persuasive despite its logical flaw.^[23] Political rhetoric often employs circular reasoning to reinforce assumptions about loyalty or competence. A politician might argue that voters should support the incumbent because "they are the proven leader," using the status of leadership to prove its own validity without citing policy achievements or public metrics. In another case, claims during election debates, such as "Our party's policies work because they align with American values, which our party uniquely represents," create a self-reinforcing loop that assumes partisan alignment as both premise and conclusion. Common conversations reveal circular reasoning in parental or familial exchanges, where authority is invoked to justify itself. A parent might tell a child, "You need to go to bed now because it's bedtime," responding to the child's "why" with a restatement that offers no external rationale like health benefits or routine importance.^[24] Similarly, in intimate discussions, one partner may insist, "I love this job despite the toxic environment because it's the right fit for me," dismissing evidence of dissatisfaction by circling back to the unproven affection.^[25] Conspiracy theories thrive on circular reasoning through self-reinforcing claims that resist external scrutiny. Proponents might assert, "The government hides the truth because official denials prove the cover-up," where denial serves as evidence for the very conspiracy it supposedly conceals. This structure, often involving repetition of unproven premises, strengthens belief by framing counter-evidence as part of the plot. These uses contribute to social impacts by perpetuating biases and echo chambers in media and group discussions. In online forums or news cycles, repeated circular claims, such as "This source is reliable because it confirms what we already know," isolate communities from diverse viewpoints, reinforcing preconceptions without validation. Over time, this fosters polarization, as individuals dismiss opposing information as biased while accepting aligned narratives on faith alone.^[26] Detecting circular reasoning in debates involves scrutinizing arguments for repetition of the core claim as "evidence." Ask whether the premise and conclusion are essentially identical, lacking independent support like data or examples; for instance, probe unstated assumptions by requesting specifics beyond the assertion itself.^[24] Challenging with counterexamples or external facts can break the loop, promoting clearer reasoning.^[6]

Philosophical and Scientific Cases

In philosophy, Anselm of Canterbury's ontological argument, presented in his Proslogion (circa 1078), exemplifies circular reasoning by embedding the existence of God within the very definition of God as "that than which nothing greater can be conceived." Anselm argues that if God exists only in the understanding, a greater being—one existing in reality—could be conceived, leading to a contradiction; thus, God must exist in reality. This structure assumes existence as inherent to the concept, begging the question of God's actual existence. Immanuel Kant critiqued this argument in his Critique of Pure Reason (1781/1787), asserting that existence is not a predicate or property that adds to a concept's content, rendering the inference invalid and exposing its circularity.^[27] Kant's analysis influenced subsequent philosophy by shifting focus from definitional proofs to empirical and synthetic judgments, diminishing the argument's persuasive power in theological debates.^[27] Another philosophical instance appears in René Descartes' Meditations on First Philosophy (1641), where the cogito ergo sum ("I think, therefore I am") seeks to establish indubitable certainty of the self's existence through the act of doubting.^[28] Critics identify circularity in Descartes' broader epistemology, known as the Cartesian circle: clear and distinct perceptions (including the cogito) are guaranteed true by God's non-deceptive nature, yet God's existence is proven via those same perceptions.^[29] In science, circular reasoning manifests in certain formulations of evolutionary theory, particularly the phrase "survival of the fittest," coined by Herbert Spencer in 1864 and adopted by Charles Darwin in later editions of On the Origin of Species (first published 1859).^[30] This expression can become tautological when "fitness" is defined retrospectively as survival itself, implying that those who survive are fittest because they survived, without independent criteria for fitness.^[31] Such circularity in 19th-century Darwin-era debates prompted critiques that natural selection explanations risked reducing to non-explanatory restatements, as fitness appears post-hoc rather than predictive.^[31] Modern evolutionary biology addresses this by defining fitness through heritable traits and reproductive success in advance, allowing testable predictions and mitigating the tautology.^[31] These cases highlight circular reasoning's potential to undermine foundational arguments, spurring refinements in both philosophical proofs and scientific methodologies.

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