#30-Formalization

|

➘ #30 Source Article

Symbolic Logic Formalization

\forall x\,\big(N(x)\rightarrow \lnot C(x)\big)
Annotation: If every person x is born with an inevitable tendency N(x), then that person cannot meet the control requirements C(x) needed for fair judgment.

\forall x\,\big(\lnot C(x)\rightarrow \lnot J\big)
Annotation: If someone lacks the right kind of control C(x), then punishing them eternally J cannot be fair.

\forall x\,N(x)
Annotation: In fact, every human x does have this built-in, unrequested tendency N(x).

\therefore \lnot J
Annotation: Putting these together, eternal punishment J is not fair or justified.

Severity(S)\,\propto\,Gravity(G)
Annotation: The seriousness of a punishment Severity(S) should match the seriousness of the wrongdoing Gravity(G).

\frac{Severity(ECT)}{Gravity(finite_T)}\;\longrightarrow\;\infty
Annotation: When a limited act finite_T is matched with eternal torment ECT, the punishment becomes infinitely out of proportion to the offense.

P(\text{no bark in }[0,T])\;\approx\;e^{-\lambda_{i}T}
Annotation: If each being has even a small chance \lambda_{i} of failing, then over time T the chance of never failing drops almost to zero.

\text{As }T\to \infty:\ P(\text{no bark})\to 0\ \text{ and }\ P(\text{at least one bark})\to 1
Annotation: In other words, given enough time, failure is guaranteed.

\frac{S(\text{eternal confinement})}{f(G(b))}\;\longrightarrow\;\infty
Annotation: Giving an eternal penalty for something as small as a single bark G(b) makes the punishment infinitely larger than the act.

I\;\rightarrow\;\forall x\,\big(B(x)\ \text{is inevitable}\big)\quad\text{(B1)}
Annotation: If inevitability I is true, then for everyone x the wrong act B(x) will eventually happen.

\forall x\,\big(Inevitable(B(x))\rightarrow \lnot A(x)\big)\quad\text{(B2)}
Annotation: If an act B(x) is unavoidable, then the person x cannot be held accountable A(x).

\forall x\,\big(\lnot A(x)\rightarrow \lnot P(x)\big)\quad\text{(B3)}
Annotation: And if someone is not accountable A(x), then eternal punishment P(x) is not fitting.

I\quad\text{(B4)}
Annotation: Inevitability I does apply to human nature.

\therefore\ \forall x\,\lnot P(x)\quad\text{(B5)}
Annotation: Therefore, no one x deserves eternal punishment P(x).

A Fitch-Style Proof.

1.\ \forall x\,(N(x)\rightarrow \lnot C(x))\quad\text{Premise}
Annotation: If a person x has the built-in, unrequested tendency N(x), then they lack the needed control C(x).

2.\ \forall x\,(\lnot C(x)\rightarrow \lnot J)\quad\text{Premise}
Annotation: If someone does not have that control C(x), then eternal punishment J is not justified.

3.\ \forall x\,N(x)\quad\text{Premise}
Annotation: Everyone x in fact has the unrequested tendency N(x).

4.\ \text{Let }a\ \text{be arbitrary}\quad\text{Arbitrary\ object\ (UI target)}
Annotation: We pick a generic individual a without assuming anything special about them.

5.\ N(a)\rightarrow \lnot C(a)\quad\text{from\ 1,\ UI}
Annotation: Instantiating line 1 at a: if N(a), then not-in-control \lnot C(a).

6.\ N(a)\quad\text{from\ 3,\ UI}
Annotation: From the universal claim, a has the tendency N(a).

7.\ \lnot C(a)\quad\text{from\ 5,6,\ MP}
Annotation: Putting 5 and 6 together, a lacks the needed control.

8.\ \lnot C(a)\rightarrow \lnot J\quad\text{from\ 2,\ UI}
Annotation: If someone like a lacks control, then \lnot J.

9.\ \lnot J\quad\text{from\ 7,8,\ MP}
Annotation: Therefore, eternal punishment J is not justified.

10.\ \therefore\ \lnot J\quad\text{Discharge\ of\ arbitrary\ }a
Annotation: Because \lnot J does not mention a, the result holds generally: eternal punishment is not justified.

Proportionality add-on (as a supporting mini-proof)

11.\ Severity(S)\propto Gravity(G)\quad\text{Proportionality\ principle}
Annotation: Punishment size Severity(S) should track offense seriousness Gravity(G).

12.\ Gravity(finite_T)<\infty\quad\text{Finite\ act}
Annotation: A human transgression finite_T is bounded in gravity.

13.\ Severity(ECT)=\infty\quad\text{Eternal\ sanction}
Annotation: Eternal torment has unbounded severity.

14.\ \frac{Severity(ECT)}{Gravity(finite_T)}\rightarrow \infty\quad\text{from\ 12,13}
Annotation: The punishment-to-offense ratio blows up to infinity.

15.\ \text{Hence proportionality fails for ECT on finite acts}\quad\text{from\ 11,14}
Annotation: An infinite penalty for a finite act breaks the stated matching rule, reinforcing \lnot J.

Bark-Nature reductio (Fitch-style)

1'.\ I\rightarrow \forall x\,(\text{Inevitable}(B(x)))\quad\text{Premise}
Annotation: If inevitability I holds for the kind, then everyone x will eventually do the act B(x).

2'.\ \forall x\,(\text{Inevitable}(B(x))\rightarrow \lnot A(x))\quad\text{Premise}
Annotation: If an act is unavoidable, accountability A(x) does not stick.

3'.\ \forall x\,(\lnot A(x)\rightarrow \lnot P(x))\quad\text{Premise}
Annotation: Without accountability, eternal punishment P(x) does not fit.

4'.\ I\quad\text{Premise}
Annotation: The inevitability condition I obtains.

5'.\ \forall x\,\text{Inevitable}(B(x))\quad\text{from\ 1',4',\ MP}
Annotation: So the act is inevitable for all x.

6'.\ \text{Let }a\ \text{be arbitrary}\quad\text{Arbitrary\ object}
Annotation: Consider any individual a.

7'.\ \text{Inevitable}(B(a))\quad\text{from\ 5',\ UI}
Annotation: For this a, the act is unavoidable.

8'.\ \lnot A(a)\quad\text{from\ 2',7',\ UI,\ MP}
Annotation: Then a is not accountable.

9'.\ \lnot P(a)\quad\text{from\ 3',8',\ UI,\ MP}
Annotation: And eternal punishment does not fittingly apply to a.

10'.\ \therefore\ \forall x\,\lnot P(x)\quad\text{UG\ on\ 9'}
Annotation: Since a was arbitrary, the result generalizes: for every x, \lnot P(x).

◉ A plain English walkthrough of the Master Proof above.

Control Argument Walkthrough
  1. Start with the idea: if someone is born with an inevitable tendency to commit a wrong, then they don’t really have the kind of control required to be held fully responsible.
  2. Next, we add: if a person doesn’t have the right control, then punishing them eternally cannot be fair.
  3. A third premise says: in fact, everyone has this unavoidable tendency.
  4. To test the logic, we consider a random person. They have this tendency. Because of that, they lack the control needed. And if they lack the control, eternal punishment isn’t fair.
  5. Since this holds for the random person, it must hold for everyone. The final conclusion is: eternal punishment is not justified for anyone.
Proportionality Add-On
  1. In justice, punishment should match the seriousness of the wrong done.
  2. Human wrongs are finite—bounded acts in time and impact.
  3. Eternal torment, however, is infinite in severity.
  4. When you compare the two, the punishment vastly outstrips the wrongdoing, blowing up the fairness ratio.
  5. That mismatch shows eternal torment is out of proportion and thus unfair.
Bark-Nature Reductio Walkthrough
  1. Suppose inevitability is built into human nature. That means everyone will eventually commit some wrong.
  2. If a wrong is unavoidable, then it can’t make someone truly accountable.
  3. And if someone isn’t accountable, eternal punishment cannot fairly apply to them.
  4. Since inevitability does hold for humans, it follows that everyone’s wrongs are unavoidable.
  5. Therefore, no one can rightly be subjected to eternal punishment.
Overall Picture

The argument works in three layers:
✓ First, inevitability undermines the very control conditions needed for responsibility.
✓ Second, even if a small slice of responsibility remains, eternal torment breaks proportionality.
✓ Third, the “barking puppy” analogy shows in another way that inevitability cancels accountability.

Together, these threads converge on the same result: eternal punishment for inevitable failings cannot be justified.

◉ Narrative Summary

The argument begins by focusing on control. If people inherit an inevitable tendency to commit wrong actions, then by definition they lack the control needed to fairly be held responsible for them. And if a person lacks that sort of control, then eternal punishment cannot be a just response. The theological claim is that all humans do in fact possess this unrequested and unavoidable tendency. Taken together, these points lead directly to the conclusion that eternal condemnation is not justified for anyone.

The case is reinforced by proportionality. Punishments are meant to scale with the seriousness of the act. Human acts are finite, bounded in scope and severity. Eternal conscious torment, however, is infinite. Pairing a limited offense with an unlimited penalty produces a ratio that explodes toward infinity, showing that proportionality breaks down completely. Even if one grants some residual responsibility, the scale of sanction is wildly mismatched to the gravity of the act.

The Bark-Nature reductio makes the point vivid by analogy. If a behavior is structurally inevitable—like a puppy’s first bark—then the subject cannot fairly be blamed. Without accountability, punishment is misplaced. Since inevitability holds for the entire species, it follows that eternal punishment does not fittingly apply to anyone.

In sum, the argument shows that inevitability undercuts control, proportionality collapses when finite acts are matched with infinite penalties, and accountability fails when wrong actions cannot be avoided. The three strands converge on the same conclusion: eternal punishment for inevitable transgressions cannot be justified.

Leave a comment

Recent posts

  • ✓ The Semantic Creep of Faith

    Hebrews 11:1 is often misquoted as a clear definition of faith, but its Greek origins reveal ambiguity. Different interpretations exist, leading to confusion in Christian discourse. Faith is described both as assurance and as evidence, contributing to semantic sloppiness. Consequently, discussions about faith lack clarity and rigor, oscillating between certitude…

  • ✓ AI for Christian Apologists

    This post emphasizes the importance of using AI as a tool for Christian apologetics rather than a replacement for personal discernment. It addresses common concerns among Christians about AI, advocating for its responsible application in improving reasoning, clarity, and theological accuracy. The article outlines various use cases for AI, such…

  • ✓ Deductive Closure on Inductive Contingencies

    This post argues that if deductive proofs demonstrate the logical incoherence of Christianity’s core teachings, then inductive arguments supporting it lose their evidential strength. Inductive reasoning relies on hypotheses that are logically possible; if a claim-set collapses into contradiction, evidence cannot confirm it. Instead, it may prompt revisions to attain…

  • ✓ A Typical Christian Post

    This post addresses common excuses for rejecting Christianity, arguing that they stem from the human heart’s resistance to surrendering pride and sin. The piece critiques various objections, such as the existence of multiple religions and perceived hypocrisy within Christianity. It emphasizes the uniqueness of Christianity, the importance of faith in…

  • ✓ Mistaking Structural Failure for Moral Fact

    The Outrage Trap discusses the frequent confusion between justice and morality in ethical discourse. It argues that feelings of moral outrage at injustice stem not from belief in objective moral facts but from a violation of social contracts that ensure safety and cooperation. The distinction between justice as a human…

  • ✓ Age of Accountability Calculus

    Isn’t the killing of infants always best under Christian theology? This post demonstrates that the theological premises used to defend biblical violence collapse into absurdity when applied consistently. If your theology implies that a school shooter is a more effective savior than a missionary, the error lies in the theology.

  • ✓ The Repellent Effect in Apologetics

    This article discusses the counterproductive nature of hostile Christian apologetics, which can inadvertently serve the skepticism community. When apologists exhibit traits like hostility and arrogance, they undermine their persuasive efforts and authenticity. This phenomenon, termed the Repellent Effect, suggests that such behavior diminishes the credibility of their arguments. As a…

  • ✓ Mental Irreductionism?

    The post argues against the irreducibility of conscious experiences to neural realizations by clarifying distinctions between experiences, their neural correlates, and descriptions of these relationships. It critiques the regression argument that infers E cannot equal N by demonstrating that distinguishing between representations and their references is trivial. The author emphasizes…

  • ✓ The Digital Berean

    The article highlights the value of AI tools, like Large Language Models, to “Red Team” apologetic arguments, ensuring intellectual integrity. It explains how AI can identify logical fallacies such as circular reasoning, strawman arguments, and tone issues, urging apologists to embrace critique for improved discourse. The author advocates for rigorous…

  • ✓ Differentiating Effects of the Spirit?

    The concept of the Holy Spirit’s indwelling is central to Christian belief, promising transformative experiences and divine insights. However, this article highlights that the claimed supernatural benefits, such as unique knowledge, innovation, accurate disaster predictions, and improved health outcomes, do not manifest in believers. Instead, evidence shows that Christians demonstrate…

  • ✓ The Source of Human Rights

    This post examines the widespread claim that human rights come from the God of the Bible. By comparing what universal rights would require with what biblical narratives actually depict, it shows that Scripture offers conditional privileges, not enduring rights. The article explains how universal rights emerged from human reason, shared…

  • ✓ The Evasion of 1 Samuel 15:3

    This post exposes how Christian apologists attempt to escape the moral weight of 1 Samuel 15:3, where God commands Saul to kill infants among the Amalekites. It argues that the “hyperbole defense” is self-refuting because softening the command proves its literal reading is indefensible and implies divine deception if exaggerated.…

  • ✓ Atrocity Blunders on Both Sides

    This post challenges both skeptics and Christians for abusing biblical atrocity texts by failing to distinguish between descriptive and prescriptive passages. Skeptics often cite descriptive narratives like Nahum 3:10 or Psalm 137:9 as if they were divine commands, committing a genre error that weakens their critique. Christians, on the other…

  • ✓ The Irrelevance of the Messenger

    In rational inquiry, the source of a message does not influence its validity; truth depends on logical structure and evidence. Human bias towards accepting or rejecting ideas based on origin—known as the genetic fallacy—hinders clear thinking. The merit of arguments lies in coherence and evidential strength, not in the messenger’s…

  • ✓ When Inerrancy Becomes Moot

    The defense of biblical inerrancy overlooks a critical flaw: internal contradictions within its concepts render the notion incoherent, regardless of textual accuracy. Examples include the contradiction between divine love and commanded genocide, free will versus foreordination, and the clash between faith and evidence. These logical inconsistencies negate the divine origin…

  • ✓ Apologists’ Favorite Arguments

    The referenced video outlines various arguments for the existence of God, categorized based on insights from over 100 Christian apologists. The arguments range from existential experiences and unique, less-cited claims, to evidence about Jesus, moral reasoning, and creation-related arguments. Key apologists emphasize different perspectives, with some arguing against a single…

  1. Phil Stilwell's avatar

    Ryan, your response attempts to bridge the gap between ancient text and modern rationality, but it relies on several logical…

  2. Ryan Stohldrier's avatar
  3. Ryan Stohldrier's avatar

    [Biblical faith, as presented in the New Testament, is primarily concerned with conviction in divine authority, rather than rational belief…

  4. Phil Stilwell's avatar
  5. J's avatar
  6. J's avatar
  7. J's avatar
  8. Phil Stilwell's avatar
  9. Ryan Stohldrier's avatar
  10. J.'s avatar

Phil Stilwell

A Deep Dive into Common Faith-Based Concepts & Claims

Free of Faith