• 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.
  1. Provide definitions of vicious and virtuous circularity, and discuss relevant attempts at delineation.
    1. Introduction
    2. Definitions
    3. Examples
    4. Attempts at Delineation
    5. Notable Contributions
    6. Conclusion
  2. Provide examples in which apparently vicious circularity is christened virtuous without adequate justification.
    1. Introduction
    2. 1. Impredicative Definitions in Mathematics
      1. Explanation of Impredicative Definitions
      2. Why It Appears Viciously Circular
      3. Christening as Virtuous Without Adequate Justification
      4. Inadequate Justification
    3. 2. Kripke’s Fixed-Point Theory of Truth
      1. Overview of Kripke’s Theory
      2. Why It Appears Viciously Circular
      3. Christening as Virtuous Without Adequate Justification
      4. Inadequate Justification
    4. 3. Circular Definitions in Linguistics
      1. Circular Definitions in Lexicography
      2. Why It Appears Viciously Circular
      3. Christening as Virtuous Without Adequate Justification
      4. Inadequate Justification
    5. 4. Self-Reference in Computational Theory
      1. Recursive Function Definitions
      2. Why It Appears Viciously Circular
      3. Christening as Virtuous Without Adequate Justification
      4. Inadequate Justification
    6. Conclusion
  3. Presuppositional religious apologists often claim circularity in their ideology is virtuous. Critique these claims.
    1. Introduction
    2. Overview of Presuppositional Apologetics
      1. Key Figures and Their Claims
      2. Claim of Virtuous Circularity
    3. Logical Analysis of Circular Reasoning
      1. Definition of Circular Reasoning
      2. Vicious vs. Virtuous Circularity
    4. Critique of Presuppositionalist Claims
      1. Self-Authentication and Ultimate Authority
      2. The Transcendental Argument for God’s Existence (TAG)
      3. Comparison with Foundationalism and Coherentism
      4. The Problem of Arbitrariness
      5. Lack of Falsifiability
    5. Conclusion
    6. References
  4. Provide the formal logical proof behind your claim that “circularity in presuppositional apologetics remains vicious.”
    1. Introduction
    2. Formal Logical Analysis of Presuppositional Apologetics
      1. Definitions and Logical Framework
      2. The Transcendental Argument for God’s Existence (TAG)
      3. Formal Logical Proof Structure
      4. Analysis of the Argument
        1. Step 1: Identifying the Implicit Premise
        2. Step 2: Revealing the Circularity
        3. Step 3: Formal Proof of Circularity
      5. Demonstrating Vicious Circularity
        1. Formal Fallacy Identification
    3. Counter-Argument: Alternative Explanations for  M
    4. Conclusion
    5. References
  5. Quiz
  6. Provide 15 discussion questions relevant to the content above.

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.


Quiz


Provide 15 discussion questions relevant to the content above.


  1. Provide definitions of vicious and virtuous circularity, and discuss relevant attempts at delineation.
    1. Introduction
    2. Definitions
    3. Examples
    4. Attempts at Delineation
    5. Notable Contributions
    6. Conclusion
  2. Provide examples in which apparently vicious circularity is christened virtuous without adequate justification.
    1. Introduction
    2. 1. Impredicative Definitions in Mathematics
      1. Explanation of Impredicative Definitions
      2. Why It Appears Viciously Circular
      3. Christening as Virtuous Without Adequate Justification
      4. Inadequate Justification
    3. 2. Kripke’s Fixed-Point Theory of Truth
      1. Overview of Kripke’s Theory
      2. Why It Appears Viciously Circular
      3. Christening as Virtuous Without Adequate Justification
      4. Inadequate Justification
    4. 3. Circular Definitions in Linguistics
      1. Circular Definitions in Lexicography
      2. Why It Appears Viciously Circular
      3. Christening as Virtuous Without Adequate Justification
      4. Inadequate Justification
    5. 4. Self-Reference in Computational Theory
      1. Recursive Function Definitions
      2. Why It Appears Viciously Circular
      3. Christening as Virtuous Without Adequate Justification
      4. Inadequate Justification
    6. Conclusion
  3. Presuppositional religious apologists often claim circularity in their ideology is virtuous. Critique these claims.
    1. Introduction
    2. Overview of Presuppositional Apologetics
      1. Key Figures and Their Claims
      2. Claim of Virtuous Circularity
    3. Logical Analysis of Circular Reasoning
      1. Definition of Circular Reasoning
      2. Vicious vs. Virtuous Circularity
    4. Critique of Presuppositionalist Claims
      1. Self-Authentication and Ultimate Authority
      2. The Transcendental Argument for God’s Existence (TAG)
      3. Comparison with Foundationalism and Coherentism
      4. The Problem of Arbitrariness
      5. Lack of Falsifiability
    5. Conclusion
    6. References
  4. Provide the formal logical proof behind your claim that “circularity in presuppositional apologetics remains vicious.”
    1. Introduction
    2. Formal Logical Analysis of Presuppositional Apologetics
      1. Definitions and Logical Framework
      2. The Transcendental Argument for God’s Existence (TAG)
      3. Formal Logical Proof Structure
      4. Analysis of the Argument
        1. Step 1: Identifying the Implicit Premise
        2. Step 2: Revealing the Circularity
        3. Step 3: Formal Proof of Circularity
      5. Demonstrating Vicious Circularity
        1. Formal Fallacy Identification
    3. Counter-Argument: Alternative Explanations for  M
    4. Conclusion
    5. References
  5. Quiz
  6. Provide 15 discussion questions relevant to the content above.




Phil Stilwell

Phil picked up a BA in Philosophy a couple of decades ago. After his MA in Education, he took a 23-year break from reality in Tokyo. He occasionally teaches philosophy and critical thinking courses in university and industry. He is joined here by ChatGPT, GEMINI, CLAUDE, and occasionally Copilot, Perplexity, and Grok, his far more intelligent AI friends. The seven of them discuss and debate a wide variety of philosophical topics I think you’ll enjoy.

Phil curates the content and guides the discussion, primarily through questions. At times there are disagreements, and you may find the banter interesting.

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