

- Vicious circularity leads to fallacies or uninformative conclusions, while virtuous circularity is used constructively in controlled systems, such as recursive functions or fixed-point theorems.
- The Transcendental Argument for God’s Existence (TAG) posits that the existence of the Christian God is the necessary precondition for the intelligibility of logic, morality, and science.
- Claiming that a text is true because it says it is true is a classic example of vicious circularity. It lacks external corroboration and does not provide an independent basis for validation.
- Presuppositionalists argue that an ultimate authority cannot be validated by any higher standard and must therefore be self-authenticating.
- According to Karl Popper, for a theory to be rational or scientific, it must be falsifiable; presuppositional apologetics fails this criterion, making it immune to disconfirmation.
Table of Contents: (Click any link below to navigate to that section.)
- Provide definitions of vicious and virtuous circularity, and discuss relevant attempts at delineation.
- Provide examples in which apparently vicious circularity is christened virtuous without adequate justification.
- Presuppositional religious apologists often claim circularity in their ideology is virtuous. Critique these claims.
- Provide the formal logical proof behind your claim that “circularity in presuppositional apologetics remains vicious.”
- Introduction
- Formal Logical Analysis of Presuppositional Apologetics
- Counter-Argument: Alternative Explanations for
- Conclusion
- References
- Quiz
- Provide 15 discussion questions relevant to the content above.

Provide definitions of vicious and virtuous circularity, and discuss relevant attempts at delineation.
Introduction
Circularity in logic refers to situations where a concept, definition, or argument relies on itself, either directly or indirectly. This self-referential nature can manifest in both problematic and acceptable forms. Academic logicians distinguish between vicious circularity, which leads to logical fallacies or paradoxes, and virtuous circularity, which can be a legitimate and even necessary aspect of certain logical systems. This distinction is crucial in formal logic, mathematics, and philosophy, where the integrity of definitions and arguments is paramount.
Definitions
- Vicious Circularity: Vicious circularity occurs when a definition, argument, or proof relies on itself in a way that renders it uninformative or invalid. It often leads to logical fallacies, paradoxes, or infinite regress. In essence, vicious circularity fails to provide a foundational basis for understanding because it presupposes the very thing it aims to establish.
- Virtuous Circularity: Virtuous circularity, on the other hand, refers to self-referential definitions or arguments that are coherent, informative, and logically sound. This type of circularity is often employed in recursive definitions, fixed-point theorems, and certain areas of semantics and mathematical logic where self-reference is handled in a controlled and meaningful way.
Examples
- Vicious Circularity: Defining a term by using the term itself without additional information. For instance, “Justice is the quality of being just.” This definition doesn’t advance understanding because it doesn’t break down the concept into more fundamental terms.
- Virtuous Circularity: The definition of natural numbers using the Peano axioms, where the successor function defines each natural number in terms of the previous one. This recursive definition is circular but provides a foundational structure for arithmetic.
Attempts at Delineation
Academic logicians have proposed various methods to distinguish between vicious and virtuous circularity:
- Foundational Approaches: Early logicians like Bertrand Russell tackled vicious circularity through the theory of types to resolve paradoxes like the Russell Paradox. By organizing sets into a hierarchy of types, self-referential sets that lead to paradoxes are avoided.
- Fixed-Point Theorems: Logicians such as Saul Kripke utilized fixed-point theorems to address semantic paradoxes like the Liar Paradox. In his seminal work on the theory of truth, Kripke demonstrated how a language could consistently contain its own truth predicate by allowing for partially defined truth values, thereby embracing a form of virtuous circularity.
- Well-Foundedness: The concept of well-founded sets avoids vicious circularity by ensuring there are no infinite descending membership chains. This approach is fundamental in set theory to prevent sets from containing themselves directly or indirectly in a problematic way.
- Acyclic Definitions: Logicians advocate for acyclic or non-circular definitions whenever possible. When circularity is necessary, they aim to construct definitions where the circularity does not prevent the assignment of meaning or truth. For example, in defining linguistic terms, mutual definitions can be acceptable if they form a finite, non-vicious circle.
- Stratification and Hierarchical Models: In formal semantics, stratified models are used to assign meanings at different levels, preventing vicious circularity by ensuring that a term at one level doesn’t depend on itself at the same level.
Notable Contributions
- Alfred Tarski: Tarski’s undefinability theorem showed that truth in formal languages cannot be consistently defined within the same language, highlighting issues of self-reference and vicious circularity. His work led to the development of Tarski’s hierarchy of languages, separating object languages from their meta-languages to avoid paradoxes.
- Stephen Yablo: Yablo introduced paradoxes that are self-referential but do not rely on direct self-reference, challenging traditional notions of circularity and prompting further examination of what constitutes vicious circularity.
- Circular Proofs and Inductive Definitions: Some logicians have explored circular proofs in the context of inductive definitions, where circular reasoning is controlled and contributes to a constructive foundation rather than leading to inconsistency.
Conclusion
The distinction between vicious and virtuous circularity is a nuanced and critical area of study in logic. Vicious circularity undermines logical coherence and leads to paradoxes and fallacies, while virtuous circularity can be harnessed to construct robust logical systems and definitions. Academic logicians continue to refine the criteria that separate the two, employing strategies like hierarchical models, fixed-point theorems, and well-foundedness to navigate the complexities of self-reference. Understanding and delineating these forms of circularity is essential for advancing logical theory and its applications in mathematics, computer science, and philosophy.
Provide examples in which apparently vicious circularity is christened virtuous without adequate justification.
Introduction
In logic and mathematics, distinguishing between vicious and virtuous circularity is essential for maintaining the validity of definitions and arguments. However, there are instances where apparently vicious circularity is deemed virtuous without sufficient justification. Such cases often spark debate among logicians and philosophers regarding the soundness of the underlying reasoning. Below are examples where apparently vicious circularity is labeled as virtuous without adequate justification.
1. Impredicative Definitions in Mathematics
Explanation of Impredicative Definitions
An impredicative definition defines an entity in terms of a totality that includes the entity itself. This means a set or function is defined by quantifying over a domain that contains the very object being defined.
Why It Appears Viciously Circular
Impredicative definitions can seem viciously circular because they involve self-reference that presupposes the existence of the object being defined. Early logicians like Henri Poincaré and Bertrand Russell criticized such definitions, arguing they could lead to paradoxes akin to Russell’s Paradox in naive set theory.
Christening as Virtuous Without Adequate Justification
Despite these concerns, impredicative definitions are widely used in mathematics without thorough justification of their legitimacy. Examples include:
- Existence of Least Upper Bounds: In real analysis, the completeness property states that every non-empty set of real numbers bounded above has a least upper bound (supremum). The supremum is defined by quantifying over all upper bounds, including itself.
- Use in Type Theory: Modern type theories, like Girard’s System F, allow impredicative constructions without fully addressing foundational issues raised by earlier logicians.
Inadequate Justification
The acceptance of impredicative definitions often relies on the success and utility of the mathematical theories that use them rather than on rigorous foundational justification. This pragmatic approach overlooks potential inconsistencies, and justifications provided may be circular themselves, assuming the validity of the systems the definitions help construct.
2. Kripke’s Fixed-Point Theory of Truth
Overview of Kripke’s Theory
Saul Kripke developed a semantic theory of truth to address the Liar Paradox by allowing sentences to be neither true nor false (truth-value gaps). He constructs a “fixed point” where the assignment of truth values stabilizes.
Why It Appears Viciously Circular
Kripke’s approach involves self-referential sentences and builds the truth predicate in a way that seems to presuppose the very notion of truth it aims to define. Critics argue the theory does not fully escape vicious circularity because it relies on the concept of truth to define the truth predicate.
Christening as Virtuous Without Adequate Justification
Proponents consider the circularity virtuous, claiming that the fixed-point construction provides a consistent semantics for self-referential sentences. They argue the approach successfully navigates paradoxes by embracing a controlled form of circularity.
Inadequate Justification
The justification is sometimes seen as lacking because:
- Dependence on Intuitive Notions: The theory relies on intuitive concepts of truth and groundedness without fully formalizing them.
- Semantic Complexity: Using partially defined truth values complicates semantics without definitively resolving paradoxes.
- Criticism from Other Logicians: Some argue the theory shifts the problem rather than solves it, as it doesn’t provide a non-circular foundation for the truth predicate.
3. Circular Definitions in Linguistics
Circular Definitions in Lexicography
In dictionaries, terms are sometimes defined using other terms that, in turn, are defined using the original term, creating a definitional circle.
Why It Appears Viciously Circular
Such definitions can be uninformative and fail to decompose concepts into more fundamental terms, leading to ambiguity.
Christening as Virtuous Without Adequate Justification
Lexicographers may defend these circular definitions by arguing they reflect the interconnected nature of language and that understanding emerges from the holistic network of definitions.
Inadequate Justification
Accepting these definitions as virtuous is sometimes inadequately justified because:
- Lack of Foundational Clarity: They do not provide the foundational explanations necessary for learners or precise linguistic analysis.
- Potential for Misinterpretation: Without clear, non-circular definitions, the risk of misunderstanding increases.
4. Self-Reference in Computational Theory
Recursive Function Definitions
In computer science, recursive functions are defined in terms of themselves. While recursion is a powerful tool, it can introduce circularity that is not always adequately addressed.
Why It Appears Viciously Circular
If the base case of a recursive function is not properly defined, or if recursion doesn’t progress towards the base case, the function can become infinitely recursive, leading to runtime errors or undefined behavior.
Christening as Virtuous Without Adequate Justification
Developers may accept these recursive definitions as virtuous by assuming the recursion will terminate or by relying on recursion’s power without fully ensuring its correctness.
Inadequate Justification
The justification may be insufficient because:
- Assumption of Termination: There’s sometimes an unwarranted assumption that recursion will naturally reach a base case without rigorous proof.
- Overlooking Edge Cases: Potential issues arising from certain inputs aren’t thoroughly analyzed, leading to software vulnerabilities or failures.
Conclusion
Labeling apparently vicious circularity as virtuous without adequate justification presents challenges in logic, mathematics, linguistics, and computer science. While certain circular constructs offer utility and elegance, critically assessing and rigorously justifying their validity is essential to avoid foundational inconsistencies and practical pitfalls. Clear definitions and sound reasoning are paramount to maintain the coherence of theoretical frameworks.
Presuppositional religious apologists often claim circularity in their ideology is virtuous. Critique these claims.
Introduction
Presuppositional apologetics is a school of Christian thought prominently developed by theologians such as Cornelius Van Til and later expounded by his student Greg Bahnsen. This approach asserts that the Christian worldview is the necessary precondition for intelligibility, rational thought, and moral reasoning. Presuppositionalists claim that their reasoning, though circular, is virtuous because it starts from the ultimate authority of God and Scripture, which they argue cannot be validated by any higher standard. This response provides a logically rigorous critique of these claims, analyzing whether the circularity in presuppositional apologetics is indeed virtuous or remains viciously circular from a logical and philosophical standpoint.
Overview of Presuppositional Apologetics
Key Figures and Their Claims
- Cornelius Van Til: Van Til argued that all reasoning is grounded in presuppositions, and the Christian worldview is the only one that can account for logic, science, and morality. He asserted that non-Christian worldviews are internally inconsistent and cannot provide a basis for rational thought.
- Greg Bahnsen: Bahnsen expanded on Van Til’s ideas, emphasizing the Transcendental Argument for God’s existence (TAG), which posits that the existence of God is the necessary precondition for the possibility of logic, science, and ethics.
Claim of Virtuous Circularity
Presuppositionalists acknowledge that their argument is circular but contend that it is a “virtuous” circularity because:
- Ultimate Authority: An ultimate authority cannot be validated by any higher standard; thus, it must be self-authenticating.
- Transcendental Necessity: They argue that without presupposing the Christian God, one cannot make sense of the laws of logic, uniformity of nature, or objective moral values.
Logical Analysis of Circular Reasoning
Definition of Circular Reasoning
In formal logic, circular reasoning (also known as begging the question or petitio principii) occurs when an argument’s conclusion is assumed in its premises without independent support. This form of reasoning is generally considered fallacious because it fails to provide a substantive justification for the conclusion.
Vicious vs. Virtuous Circularity
- Vicious Circularity: A logical fallacy where the conclusion is no more certain than the premises because the premises depend on the conclusion. It provides no external validation and thus is unpersuasive to those who do not already accept the conclusion.
- Virtuous Circularity: In specific contexts, such as certain mathematical proofs or definitions (e.g., recursive functions), circularity is acceptable when it is part of a well-founded system that leads to meaningful and non-contradictory results.
Critique of Presuppositionalist Claims
Self-Authentication and Ultimate Authority
Presuppositionalists argue that the Bible is the ultimate authority and must authenticate itself. However, from a logical standpoint:
- Self-Referential Justification: Claiming that a text is true because it says it is true is a classic example of vicious circularity. It lacks external corroboration and does not provide an independent basis for validation.
- Comparison with Other Ultimate Authorities: Any religious or philosophical system could claim ultimate authority using the same reasoning (e.g., the Qur’an in Islam, the Vedas in Hinduism), leading to a plurality of mutually exclusive “ultimate authorities.”
The Transcendental Argument for God’s Existence (TAG)
Structure of TAG:
- Premise 1: Logical absolutes (laws of logic), uniformity of nature, and moral laws exist.
- Premise 2: These phenomena require a transcendent, unchanging source.
- Conclusion: Therefore, the Christian God exists as that necessary source.
Logical Analysis:
- Question-Begging: TAG assumes that only the Christian God can account for these preconditions, which is the point under contention. This is an instance of begging the question.
- False Dilemma: The argument often presents a choice between Christianity and atheism, ignoring other theistic and non-theistic worldviews that may offer alternative explanations.
- Non-Sequitur: Even if the premises were accepted, the conclusion does not necessarily follow exclusively. The existence of logical absolutes does not inherently prove the Christian God’s existence over other possible explanations.
Comparison with Foundationalism and Coherentism
- Foundationalism: Epistemological view that certain basic beliefs (foundations) justify other beliefs but are themselves self-justified or infallible. Presuppositionalists attempt to align with this by positing God as the ultimate foundation.
- Critique: Foundational beliefs in foundationalism are typically self-evident or incorrigible, such as “I exist.” The existence of God is not self-evident in the same way and requires justification.
- Coherentism: Beliefs are justified if they cohere with a system of interconnected beliefs.
- Critique: Presuppositionalists reject coherentism, but their reliance on a self-contained system of beliefs that justify each other resembles a coherentist approach, yet without addressing potential inconsistencies or alternative coherent systems.
The Problem of Arbitrariness
- Arbitrary Presuppositions: By accepting any presupposed ultimate authority without independent justification, the selection becomes arbitrary.
- Equivalence to Other Circular Claims: Other religions or ideologies could claim their sacred texts or foundational principles as ultimate authorities using the same circular reasoning, leading to relativism rather than objective truth.
Lack of Falsifiability
- Immunization Against Criticism: Presuppositionalism’s circular reasoning makes it unfalsifiable, as any counter-argument is dismissed on the grounds that it does not accept the presupposed authority.
- Popper’s Criterion: According to philosopher Karl Popper, for a theory to be scientific or rational, it must be falsifiable. Presuppositionalism fails this criterion, undermining its claim to provide a rational foundation for knowledge.
Conclusion
While presuppositional apologists like Cornelius Van Til and Greg Bahnsen argue that their circular reasoning is virtuous due to the necessity of an ultimate authority, this claim faces significant logical challenges:
- Vicious Circularity: The self-authenticating nature of their argument is an instance of vicious circularity, as it fails to provide independent justification and is unconvincing to those who do not already accept its premises.
- Logical Fallacies: The use of begging the question, false dilemmas, and non-sequiturs undermines the logical validity of their arguments.
- Arbitrariness and Relativism: Without independent criteria for selecting an ultimate authority, any belief system could claim validity, leading to arbitrariness and conflicting truth claims.
- Lack of Rigorous Justification: The presuppositionalist approach does not meet the standards of rigorous logical reasoning required to transform apparent vicious circularity into virtuous circularity.
From a logical and philosophical standpoint, the circularity in presuppositional apologetics remains vicious. For circular reasoning to be considered virtuous in academic logic, it must be part of a well-defined system that provides new insights or resolves contradictions, which presuppositional apologetics does not sufficiently achieve.
References
- Van Til, Cornelius. The Defense of the Faith. P&R Publishing, 1955.
- Bahnsen, Greg L. Presuppositional Apologetics: Stated and Defended. American Vision, 2008.
- Popper, Karl R. Conjectures and Refutations: The Growth of Scientific Knowledge. Routledge, 1963.
- Audi, Robert, ed. The Cambridge Dictionary of Philosophy. Cambridge University Press, 1999.
Provide the formal logical proof behind your claim that “circularity in presuppositional apologetics remains vicious.“
Introduction
To substantiate the claim that the circularity in presuppositional apologetics remains vicious, we will present a formal logical analysis of the core arguments used by presuppositional apologists like Cornelius Van Til and Greg Bahnsen. By structuring their arguments into formal logical proofs, we can examine whether they commit the logical fallacy of begging the question (petitio principii), which characterizes vicious circularity. The analysis will demonstrate that presuppositional apologetics assumes its conclusion within its premises, rendering the argument circular in a way that is logically invalid.
Formal Logical Analysis of Presuppositional Apologetics
Definitions and Logical Framework
- Logical Validity: An argument is valid if, assuming the premises are true, the conclusion must be true.
- Begging the Question: A logical fallacy where the conclusion is assumed in one of the premises.
- Vicious Circularity: Circular reasoning that provides no independent support for the conclusion, making the argument unpersuasive to those who do not already accept the premises.
The Transcendental Argument for God’s Existence (TAG)
The TAG is central to presuppositional apologetics. It can be formalized as follows:
- Premise 1: Logic, reasoning, morality, and science require the existence of the Christian God to be meaningful or intelligible.
- Premise 2: Logic, reasoning, morality, and science are meaningful and intelligible.
- Conclusion: Therefore, the Christian God exists.
Formal Logical Proof Structure
Let:
represent “The Christian God exists.”
represent “Logic, reasoning, morality, and science are meaningful and intelligible.”
represent “The Christian God is required for
.”
The argument can be structured as:
(Premise: If the Christian God exists, then
is true.)
(Premise:
is true.)
- Therefore,
(Conclusion: The Christian God exists.)
Analysis of the Argument
Step 1: Identifying the Implicit Premise
The argument assumes that is the only possible explanation for
. This is an implicit premise:
(Implicit Premise: If
is true, then the Christian God exists.)
This premise effectively states that can only be the case if
is true.
Step 2: Revealing the Circularity
By combining and
, the argument becomes:
(The Christian God’s existence is both necessary and sufficient for
.)
(Premise:
is true.)
- Therefore,
(Conclusion: The Christian God exists.)
However, this means that the conclusion is assumed in the premises because
being true is predicated on
being true.
Step 3: Formal Proof of Circularity
Let’s formalize the argument using propositional logic.
Given:
(Premise 1)
(Premise 2)
- Implicitly,
(Assumed or required for the argument to work)
From these, the argument proceeds:
(Implicit Premise)
(Premise 2)
- Therefore,
(Modus Ponens on 4 and 5)
But:
- The implicit premise
assumes that the only possible explanation for
is
, which is the conclusion we are trying to prove.
- This makes the argument circular, as the truth of
is presupposed in the premises.
Demonstrating Vicious Circularity
- Begging the Question: The argument assumes
in order to prove
. The premise
is only valid if
is already accepted as true.
- Lack of Independent Support: No external evidence or reasoning is provided to support
without already assuming
.
- Invalid Argument Form: The argument’s validity depends on an implicit premise that is equivalent to the conclusion.
Formal Fallacy Identification
The argument commits the fallacy of affirming the consequent if is taken alone:
- Therefore,
This is invalid because could be true for reasons other than
.
However, presuppositionalists introduce to make the argument valid, but this premise is unjustified without already accepting
, resulting in circular reasoning.
Counter-Argument: Alternative Explanations for 
To further illustrate the vicious circularity, consider that there could be alternative explanations for :
- Let
represent “A non-Christian worldview (e.g., humanism, another religion) explains
.”
- It is possible to assert
without contradiction.
- Therefore,
does not necessarily imply
.
This demonstrates that assuming is unwarranted without additional proof, and relying on it is circular.
Conclusion
The formal logical analysis shows that presuppositional apologetics:
- Assumes the Conclusion: The existence of the Christian God (
) is presupposed in the premises.
- Commits Logical Fallacies: Specifically, it commits begging the question by assuming what it seeks to prove.
- Demonstrates Vicious Circularity: The argument lacks independent support for its conclusion and is unpersuasive to those who do not already accept its premises.
Therefore, the circularity in presuppositional apologetics remains vicious because it fails to provide a logically valid and non-circular proof of its conclusion.
References
- Van Til, Cornelius. The Defense of the Faith. P&R Publishing, 1955.
- Bahnsen, Greg L. Van Til’s Apologetic: Readings and Analysis. P&R Publishing, 1998.
- Copi, Irving M., and Carl Cohen. Introduction to Logic. 14th ed., Routledge, 2011.
- Audi, Robert, ed. The Cambridge Dictionary of Philosophy. Cambridge University Press, 1999.
Quiz
#1: What is the central claim of presuppositional apologetics regarding the foundation of rational thought and logic?
Answer:
Presuppositional apologetics claims that the Christian worldview, including belief in God and Scripture, is the necessary foundation for rational thought, logic, morality, and science.#2: Who are two prominent figures associated with the development and promotion of presuppositional apologetics?
Answer:
Cornelius Van Til and Greg Bahnsen.#3: What is the main difference between vicious and virtuous circularity in logic?
Answer:
Vicious circularity leads to fallacies or uninformative conclusions, while virtuous circularity is used constructively in controlled systems, such as recursive functions or fixed-point theorems.#4: What logical fallacy is committed when the conclusion of an argument is assumed within its premises?
Answer:
Begging the question (petitio principii).#5: How does the Transcendental Argument for God’s Existence (TAG) attempt to prove the Christian God’s existence?
Answer:
TAG argues that the existence of the Christian God is the necessary precondition for the intelligibility of logic, morality, and science.#6: What implicit assumption in presuppositional apologetics renders the circularity of its argument vicious?
Answer:
The assumption that logic, morality, and science are only possible through the Christian God, which presupposes the conclusion it aims to prove.#7: What logical form does the presuppositional argument take when the fallacy of affirming the consequent is committed?
Answer:
If#8: How does presuppositional apologetics respond to the criticism that it relies on circular reasoning?
Answer:
It claims that the circularity is “virtuous” because an ultimate authority, such as God, must authenticate itself since appealing to anything external would contradict its ultimacy.#9: Why does the presuppositional argument fail to satisfy Karl Popper’s criterion for falsifiability?
Answer:
It is unfalsifiable because any counter-argument is dismissed as invalid for not accepting the presupposed authority of God, making it immune to empirical or rational disconfirmation.#10: What alternative explanation could challenge the presuppositionalist claim that logic and morality require the Christian God?
Answer:
Other worldviews, such as humanism or other religions, could provide alternative foundations for logic and morality, showing thatProvide 15 discussion questions relevant to the content above.
#1: How does presuppositional apologetics differ from other forms of Christian apologetics in its approach to proving God’s existence?
#2: Is it possible to justify an ultimate authority without falling into circular reasoning? If so, how?
#3: In what ways does presuppositional apologetics rely on the Transcendental Argument for God’s Existence (TAG), and how effective is TAG as an argument?
#4: Why is the distinction between vicious and virtuous circularity important in logic and philosophy? How do they differ in impact on arguments?
#5: Are there situations where self-referential reasoning might be unavoidable? If so, does that make such reasoning logically acceptable?
#6: How do Van Til and Bahnsen address the critique that their reasoning commits the fallacy of begging the question? Are their responses satisfactory?
#7: Could another religion, such as Islam, construct a similarly circular argument using its holy text as the ultimate authority? If so, how would presuppositional apologetics respond?
#8: What are the consequences of allowing circular reasoning in religious discourse? Does it undermine or strengthen faith-based arguments?
#9: How might a secular worldview, such as humanism, account for logic, morality, and science without appealing to a divine being?
#10: In what ways does the presuppositionalist use of TAG rely on the assumption that other worldviews are incoherent? Is this assumption justified?
#11: How does the logical fallacy of affirming the consequent weaken the presuppositionalist argument? Can this flaw be resolved?
#12: Is it possible to argue for the existence of an ultimate authority (like God) without committing any logical fallacies? If so, what would such an argument look like?
#13: Should logical arguments in religious discourse be held to the same standards as those in science and philosophy? Why or why not?
#14: What role does falsifiability play in determining whether presuppositional apologetics is a sound argument? How does it relate to Karl Popper’s criterion for scientific theories?
#15: How would a presuppositional apologist respond to the critique that their argument fails to persuade those outside their worldview? Is persuasion necessary for an argument to be valid?
Table of Contents: (Click any link below to navigate to that section.)
- Provide definitions of vicious and virtuous circularity, and discuss relevant attempts at delineation.
- Provide examples in which apparently vicious circularity is christened virtuous without adequate justification.
- Presuppositional religious apologists often claim circularity in their ideology is virtuous. Critique these claims.
- Provide the formal logical proof behind your claim that “circularity in presuppositional apologetics remains vicious.”
- Introduction
- Formal Logical Analysis of Presuppositional Apologetics
- Counter-Argument: Alternative Explanations for
- Conclusion
- References
- Quiz
- Provide 15 discussion questions relevant to the content above.







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