The Logical Form
Argument 1: Bias in Standards for Ancient vs. Modern Miracle Claims
  1. Premise 1: If an event seems improbable, it’s rational to request further proof before believing it.
  2. Premise 2: Most people would maintain skepticism toward a modern miracle claim until presented with stronger evidence.
  3. Premise 3: Similar claims from ancient texts are often accepted without the same level of skepticism or requirement for evidence.
  4. Conclusion: It is inconsistent to apply lower standards of evidence to ancient miracle claims than to modern ones.
Argument 2: Influence of Ancient Mystique on Credulity
  1. Premise 1: Events set in the distant past often carry an allure that prompts people to suspend their usual standards of evidence.
  2. Premise 2: People may find miracle claims from ancient times more plausible simply because they are ancient, allowing for the suspension of disbelief.
  3. Conclusion: Ancient mystique can lead people to apply lower standards of evidence to miracle claims, even though these standards would not be applied to recent, similar events.
Argument 3: Universal Cognitive Bias Across Religions
  1. Premise 1: Believers in one religion may accept ancient miracles from their own religious texts while rejecting similar claims from other religions.
  2. Premise 2: This bias shows that believers often apply inconsistent standards of evidence to their own ancient miracle claims versus those of other religions.
  3. Conclusion: This cross-religious bias indicates that inconsistent standards are applied due to the religious or cultural origin of the miracle claims, rather than the quality of the evidence.
Argument 4: Consistency of Evidence Standards
  1. Premise 1: If one would question a modern miracle story from a newspaper today, then consistent standards should apply to ancient miracle claims as well.
  2. Premise 2: Asking critical questions (e.g., was the reporter credible, were there named witnesses, why wasn’t it documented immediately, etc.) is rational when assessing any extraordinary claim.
  3. Conclusion: Consistent standards require that ancient and modern miracle claims be assessed with the same level of scrutiny and skepticism.
Argument 5: Credibility of Anonymous or Unverified Sources
  1. Premise 1: Claims without named witnesses or verifiable sources are weaker and harder to cross-examine.
  2. Premise 2: Ancient miracle stories often come from anonymous sources or lack access to primary witnesses, which would normally reduce credibility.
  3. Conclusion: It is inconsistent to accept ancient miracle claims from anonymous or unverified sources when such claims would typically be dismissed in a modern context.
Argument 6: Rationality of Accepting Delayed Documentation
  1. Premise 1: If an event is genuinely amazing, it would likely be documented immediately by multiple sources, especially in a densely populated area.
  2. Premise 2: The lack of immediate documentation and corroboration in ancient miracle claims raises doubts about their occurrence.
  3. Conclusion: Given that amazing events today would require immediate and corroborated documentation, it is irrational to accept ancient miracle claims that lack these characteristics.
Argument 7: Rationality of Waiving Skepticism Based on Time Alone
  1. Premise 1: Skepticism toward an improbable claim is normally justified regardless of when it allegedly occurred.
  2. Premise 2: Ancient miracle claims should not automatically be accepted with less scrutiny solely because they happened long ago.
  3. Conclusion: Rational standards of evidence should be applied consistently to both ancient and modern miracle claims, as time alone does not validate a claim.


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A Dialogue
Standards of Evidence for Ancient vs. Modern Miracle Claims

CHRIS: I think we can agree that the Bible records extraordinary events, like miracles, that were meant to convey divine truth. These accounts have been preserved for centuries, which shows their value and reliability.

CLARUS: I understand the importance of these accounts to you, but shouldn’t we apply consistent standards of evidence to both ancient and modern miracle claims? If we wouldn’t accept a miracle claim today without strong evidence, why should we accept one just because it’s ancient?

CHRIS: But people in ancient times may have been more in touch with divine actions, and these accounts have been kept for a reason—they had significance. The people who witnessed these miracles felt so strongly about them that they passed them down through generations.

CLARUS: I get that, but consider this: just because a story has been preserved doesn’t make it true. If we heard of a miracle today in a densely populated city—say, people rising from graves in New York—we’d require robust proof like multiple witnesses, immediate documentation, and independent corroborations. Why should ancient stories of resurrection be treated differently?

CHRIS: Ancient people relied on oral tradition since they didn’t have our means of documentation. The fact that these stories endured shows their power and authenticity to those who experienced them.

CLARUS: But that raises a question: If these events were truly amazing and life-changing, wouldn’t they have been documented by multiple sources even in ancient times? Take your example of a resurrection; if that happened in a large, ancient city, wouldn’t we expect more than a single account?

CHRIS: Perhaps, but those closest to the events, like the disciples, were willing to risk their lives for these beliefs. Doesn’t that dedication suggest the truth of their experiences?

CLARUS: People in various religions have died for their beliefs, yet we don’t accept every religious claim as factual. People can believe fervently in something and still be mistaken or influenced by cultural expectations. Plus, we tend to be more skeptical of modern miracle claims, even if they’re backed by witnesses—we demand detailed evidence. Why do we make an exception for ancient, anonymous sources?

CHRIS: But the Bible is unique in its spiritual authority and its cultural context. Those accounts aren’t the same as today’s sensational stories; they come with a different weight.

CLARUS: Still, there’s a question of bias here. Other religious traditions also have miracle claims, which their followers believe without question. Christians tend to accept the Bible’s miracles while dismissing, say, the Quran’s miracles or the Book of Mormon’s. Doesn’t that suggest people often apply inconsistent standards of evidence based on their cultural and religious background?

CHRIS: That’s fair, but the context of faith makes these accounts meaningful. When something is grounded in faith, it has a unique truth that goes beyond ordinary evidence.

CLARUS: But if faith leads us to apply inconsistent standards, we should at least examine why we’re doing it. For instance, if a newspaper today reported a miraculous resurrection in New York, we’d have questions. Like, was the reporter credible, or did the story get exaggerated? We’d also want named witnesses and other sources confirming it. If a story doesn’t meet that standard, we’d likely dismiss it. Why lower the standard for ancient claims?

CHRIS: You’re saying that if we accept ancient miracles on weaker evidence, we’re using a double standard?

CLARUS: Exactly. Consistent standards would mean applying the same scrutiny to both ancient and modern miracle claims. If we wouldn’t trust a sensational story with only anonymous witnesses and no documentation today, why trust it from antiquity?

CHRIS: But ancient times were different; stories spread differently. And the people of the time accepted these stories, so perhaps they had reason to believe.

CLARUS: Or they might have been influenced by cultural pressures or shared biases. Think of how stories change over time. Even today, stories can be embellished as they’re retold. By the time a miracle story is written down—maybe ten years or more after the event—details can be heavily exaggerated. This tendency doesn’t disappear just because it’s ancient.

CHRIS: So you think embellishment could account for some biblical miracles?

CLARUS: It’s quite possible. And if the story only surfaced years later, there’s a strong chance that it wasn’t documented immediately. In today’s world, if an amazing event wasn’t reported right away, we’d question its authenticity. Wouldn’t you be suspicious if you heard a story that supposedly happened ten years ago but wasn’t reported until now?

CHRIS: Yes, I would question why it wasn’t immediately documented, especially if it’s extraordinary.

CLARUS: Exactly. And without early, multiple accounts, there’s no way to verify it, whether it’s a modern event or an ancient one. Applying consistent standards means holding both to the same level of scrutiny.

CHRIS: I see your point, but faith is about accepting things beyond ordinary reasoning.

CLARUS: That may be, but from a rational standpoint, accepting extraordinary claims without extraordinary evidence just because they’re ancient is questionable. Shouldn’t we at least require that ancient claims meet the same evidentiary standards as modern ones? After all, time doesn’t automatically make a claim true.


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Helpful Analogies

Imagine a group of people starts a rumor about an unusual event in a small town—say, a person who flew without any assistance. Over the years, as the story spreads, details change and new embellishments appear, making the story more fantastical. By the time it’s written down decades later, it’s nearly unrecognizable from the original account.

This is much like ancient miracle claims: stories can change as they are passed down, especially in oral traditions. Just because a story is old and has been preserved doesn’t necessarily mean it’s accurate. The passage of time doesn’t protect a claim from embellishment; in fact, it often makes it more likely.


Consider a court case where a major piece of evidence—the alleged eyewitness—can’t be identified or cross-examined, and there’s no documentation of the event in police records. If this happened in modern times, the court would likely dismiss the case due to insufficient evidence, especially if it’s an extraordinary claim.

Similarly, if an ancient miracle claim lacks named witnesses, immediate documentation, or corroboration, we should view it with the same skepticism as a modern-day legal case with missing evidence. The fact that it’s ancient doesn’t change the basic need for strong evidence to support extraordinary claims.


Imagine hearing about a spectacular fireworks show that supposedly happened last night in a large, busy city. However, you can’t find a single video, photo, or witness who saw it. No media outlets reported it, and there’s no official record of the event. Most people would dismiss this story, especially if no one can provide tangible proof or explain why such a public event went unrecorded.

This is similar to ancient miracle accounts claiming public, extraordinary events. In a densely populated area, an amazing event would likely have multiple records. If it doesn’t, this absence is suspicious and suggests the story may not be reliable. Just like with the fireworks show, a lack of evidence in a populated setting raises doubts about whether the event actually occurred.


Addressing Theological Responses
1. The Limitations of Ancient Documentation

Theologians might argue that the lack of immediate documentation for ancient events doesn’t automatically discredit them. In ancient societies, many events, even important ones, weren’t documented due to limited resources, literacy levels, and the absence of widespread record-keeping practices. They might suggest that while we expect detailed evidence today, it’s unrealistic to apply modern documentation standards to ancient cultures. The focus should be on the preservation of the accounts and their impact rather than expecting immediate, multiple records from a different era.


2. Oral Tradition as Reliable Testimony

Oral traditions were highly valued in many ancient cultures, serving as the primary means of preserving history. Theologians could argue that oral transmission wasn’t merely a loose storytelling method but a carefully maintained practice, where communities placed great importance on accuracy. They might contend that, although oral traditions were eventually written down, they were sustained by collective memory and social structures that prioritized accuracy in transmission, thus providing a reasonable level of reliability.


3. Cultural and Religious Context as Verification

Theologians may argue that the cultural context of ancient religious beliefs supports the validity of miracle claims. They could point out that the claims were often tied to significant events in the life of the religious community, making them less likely to be invented or embellished. The willingness of early believers to endure persecution or even die for their beliefs could serve as indirect evidence of the authenticity of these miracles, as these events held deep meaning and were central to the community’s faith.


4. Miracles as Beyond Ordinary Evidence

Some theologians might contend that miracles are, by definition, extraordinary events meant to operate outside the bounds of ordinary experience and scientific verification. They might argue that requiring modern standards of proof for a miracle misunderstands the nature of a divine act. From this view, miracles aren’t subject to standard evidentiary criteria because they are inherently supernatural and thus inaccessible to typical means of verification.


5. The Consistency of Faith Across Religious Traditions

Theologians might address the bias argument by suggesting that the consistency of miracle claims across religious traditions actually supports the possibility of supernatural intervention. They could argue that the prevalence of similar miraculous accounts in different cultures and religions hints at a shared human experience of the divine. Instead of discrediting each other, these similar traditions might imply a broader spiritual reality that transcends individual religions.


6. Faith as Trust Beyond Rational Proof

Faith, for many theologians, is not merely belief without evidence but rather trust in a higher reality that surpasses ordinary reasoning. They might suggest that faith allows believers to embrace truths that can’t be fully proven but are meaningful within a spiritual framework. This approach acknowledges that faith involves a form of knowledge beyond empirical proof, allowing believers to accept ancient miracle claims as part of a spiritual reality, rather than dismissing them for lack of modern standards of evidence.


7. Resurrection and Unique Historical Impact

Theologians might argue that certain miracles, like the resurrection of Jesus, are unique in their historical and cultural impact. They might contend that the early Christian movement and its rapid growth lend credibility to the resurrection claim, as such transformative impact suggests something profound at its origin. Unlike a modern miracle that fades over time, these ancient claims fueled a lasting movement. Therefore, the historical endurance and influence of these miracle accounts serve as indirect evidence supporting their truth.

1. Standards of Evidence Should Apply Regardless of Era

While it’s true that ancient societies had limited means of documentation, this doesn’t negate the need for evidence when assessing extraordinary claims. Historians regularly evaluate ancient accounts using skeptical methods to determine their reliability, requiring corroboration, consistency, and proximity to the events described. An absence of documentation for an event that would have been groundbreaking even by ancient standards raises legitimate doubts. Simply being from a different era doesn’t justify lowering the bar for evidence; extraordinary claims still demand extraordinary evidence, regardless of the time period.


2. Oral Tradition Can Lead to Embellishment

Although oral traditions may have been structured, human psychology shows that memory is malleable and prone to embellishment, especially when retelling stories with high emotional or cultural significance. Studies on oral transmission reveal that details often change over time, influenced by the beliefs, needs, or biases of the community. This makes oral accounts particularly vulnerable to distortion. Thus, while oral traditions can preserve stories, they don’t guarantee the accuracy required to verify miracle claims.


3. Social Commitment Doesn’t Prove Truth

The dedication of believers or the significance of a religious event to a community doesn’t confirm the factual accuracy of the event. Throughout history, people have been deeply committed to causes, ideologies, and beliefs that were later shown to be false or exaggerated. The willingness to suffer or die for a belief might reflect faith but does not provide objective evidence for the events described. For example, followers of other religions are equally committed to their own miracles, yet most believers reject the miracles of other traditions. Commitment does not equate to historical validity.


4. Defining Miracles Outside Evidence Undermines Their Plausibility

By suggesting that miracles operate outside standard evidence and are beyond verification, theologians inadvertently make them unfalsifiable and indistinguishable from myth or fiction. If miracles are exempt from evidentiary scrutiny, then they lack a basis for rational acceptance and can be dismissed as easily as they are asserted. For a miracle to be plausible, it must at least meet basic standards of evidence; otherwise, it cannot be reasonably distinguished from imaginary events.


5. Similarity of Claims Across Religions Undermines, Rather Than Supports, Specific Claims

The prevalence of miracle claims across different religions actually challenges their validity rather than supporting a universal spiritual reality. This plurality suggests that such claims are influenced by human psychology and cultural contexts rather than pointing to an objective supernatural event. Furthermore, if miracles from one tradition are dismissed by followers of another, the inconsistency weakens the rational foundation for believing in any one set of miraculous claims. This indicates that miracle stories are likely a product of cultural biases and shared human tendencies, not evidence of actual events.


6. Faith as Trust Without Evidence Conflicts with Rational Standards

While faith can be personally meaningful, it does not provide objective justification for accepting miracle claims as true. Faith that bypasses evidence opens the door to believing in anything without scrutiny, which conflicts with rational inquiry. If we use faith as the standard for belief in ancient miracles, it equally justifies belief in other unverified or irrational claims. Trust without evidence may have spiritual value, but it does not offer the empirical basis needed to accept extraordinary claims as factual.


7. Historical Impact Does Not Validate Miraculous Events

While the impact of certain religious events, like the resurrection of Jesus, is undeniable, social or cultural influence does not confirm the truth of the underlying events. Major religions have arisen from events or figures whose historical accuracy is questionable, yet they had transformative effects on their followers. An event’s lasting influence is more reflective of the beliefs and needs of its adherents than of its factual accuracy. If impact were sufficient evidence, we would have to accept contradictory miracle claims from various religions as equally valid, which would be logically incoherent.

Clarifications
1. Historical Documentation
  • Is there any immediate documentation of the event from the time it allegedly occurred?
  • What sources documented this event, and how close were they to the event in time and place?
  • Were there any official records (e.g., government, military, or religious records) that corroborate the claim?
  • Is there any independent documentation of the event from sources that are not affiliated with the primary claimants?
  • How consistent are the accounts across different sources if there is more than one?
2. Named and Traceable Witnesses
  • Who were the witnesses of the event, and are they named in any sources?
  • Are there any recorded interviews with these witnesses that detail their observations?
  • Can these witnesses be traced or verified in any way, such as through other records of their lives or statements?
  • Do we know anything about the background of the witnesses that might influence their reliability or possible biases?
3. Independent Corroboration
  • Are there any sources independent of the main claimant that verify or refer to the same event?
  • Do any rival or neutral parties acknowledge or document the event?
  • Are there external confirmations from sources that had no affiliation with the community making the claim?
4. Physical Evidence
  • Is there any physical evidence from the site where the event allegedly took place?
  • Were any artifacts or remains recovered that can be analyzed to corroborate the claim?
  • Is there any photographic or video evidence if the event happened in modern times?
  • Does the physical evidence align with known historical or scientific records?
5. Consistency Over Time
  • How has the story changed over time in different retellings or documentations?
  • Are there significant variations in the accounts, and if so, do these differences affect the credibility?
  • Are there clear markers of embellishment or additions in later versions of the story?
  • How was the account preserved (e.g., through oral tradition, manuscript copying) and how might this affect its reliability?
6. Cultural and Psychological Context
  • What was the cultural climate around the time of the event? Were supernatural or miraculous beliefs common?
  • Was there any political or religious motivation to propagate the claim?
  • Could social or psychological factors (e.g., desire for communal identity, emotional needs) explain why people accepted or spread the story?
  • How do similar cultures handle miracle claims? Is there a pattern of acceptance in some societies and skepticism in others?
7. Motivation and Bias
  • Who benefits from the claim, and in what way (e.g., socially, politically, or financially)?
  • Is there a potential bias in the sources that could influence their account of the event?
  • Were there any incentives for witnesses to exaggerate, embellish, or fabricate the story?
8. Reputation and Reliability of the Sources
  • How credible is the source that originally documented the event?
  • What other types of events has the source recorded, and are these generally accepted or disputed by historians?
  • Does the source have a track record of reliable or unreliable reporting?
  • Is the source’s account supported by experts in relevant fields (e.g., historians, archaeologists, theologians)?
9. Probability and Prior Events
  • How likely is the event, based on what we know of natural laws or historical precedent?
  • Have similar events occurred elsewhere, and if so, were they documented with strong evidence?
  • Does this claim fit with known historical or scientific understanding, or does it contradict established knowledge?
10. Geographic and Environmental Details
  • Was the event in a location where it could be observed by multiple people?
  • Are there environmental factors that could have influenced the event or people’s perception of it?
  • If the event supposedly involved public phenomena (e.g., the opening of graves), why weren’t nearby people or authorities alarmed or involved?
11. Scientific Explanations and Skepticism
  • Is there a natural or scientific explanation that could account for the claims?
  • Have there been similar phenomena that were later explained by natural causes?
  • What does science say about the possibility of the event described, and are there precedents for debunking similar claims?
12. Comparative Religious and Historical Claims
  • Are there similar miraculous claims from other religious or historical traditions?
  • How do we evaluate this claim compared to other religious miracle claims?
  • If we accept this claim based on faith, should we also accept the miracle claims of other traditions?
13. Possibility of Fabrication or Distortion
  • Is there any evidence that the story was fabricated or influenced by later additions?
  • Could the claim have been exaggerated or transformed over time to enhance its appeal?
  • Were there any known motives for fabrication, such as attracting followers or gaining influence?
14. Role of Oral Tradition
  • Was the story transmitted orally before documentation, and if so, for how long?
  • How does oral tradition influence the accuracy and consistency of the details?
  • Have experts in oral history evaluated the reliability of the claim given its method of transmission?
15. Symbolic vs. Literal Interpretation
  • Is the claim meant to be understood literally, or could it be symbolic or metaphorical?
  • Does the context or language of the source suggest it may be a symbolic story rather than a factual account?
  • How have religious or cultural leaders interpreted the event, and do they view it as history or allegory?
16. Faith-Based Justification vs. Historical Evidence
  • Is faith being used as the primary basis for accepting the claim, or is there an attempt to provide evidence?
  • What reasons do proponents give for the truth of the claim if it lacks conventional evidence?
  • How does faith-based justification affect the claim’s credibility from a historical or rational perspective?
17. Implications of Accepting the Claim
  • If this claim is accepted as true, what are the implications for other similar claims?
  • Would accepting this claim require us to accept all unverified miracle claims based on faith alone?
  • Does accepting this claim undermine rational standards of evidence that we apply to other extraordinary events?
18. Expert Opinions and Peer Review
  • What do scholars and historians specializing in this period or culture say about the claim?
  • Has the claim been rigorously examined in academic literature or historical research?
  • Have experts from relevant fields, such as archaeology or theology, evaluated and critiqued the evidence?
19. Significance of the Event and Motivation for Immediate Documentation
  • Was the event remarkable enough that it would have prompted immediate recording by witnesses if it genuinely occurred?
  • Would ordinary people or authorities have seen the event as important or extraordinary enough to document promptly, or could it have been seen as insignificant or routine?
  • If the event was so astonishing and impactful, why might it only appear in records written decades later and in limited sources, instead of prompting immediate, widespread documentation by multiple individuals and groups?

These avenues of inquiry help a skeptic rigorously assess the validity of miracle claims, ensuring that extraordinary claims are supported by appropriate levels of evidence and critical examination.


◉ A Model to Assess Historical Claims

The following is a symbolic logic model followed by a plain-language decision framework

\textbf{Variables: } H\colon \mathrm{historical\ claim},; Cr(H)\in(0,1)\colon \mathrm{prior\ credence},; Extra(H)\colon \mathrm{extraordinary},; Mund(H)\equiv \neg Extra(H),; Pub(H)\colon \mathrm{public},; ER(H)\in{\mathrm{low},\mathrm{med},\mathrm{high}},; Scarce(H)\colon \mathrm{few\ surviving\ sources},; \mathcal{S}(H)={s_1,\dots,s_n},; Ind(s_i,s_j)\colon \mathrm{independence}
Annotation: Declares the core predicates and parameters used to score a claim and describe its evidential context.

\textbf{Source\ metrics: } Qual(s)\in(0,1],; Gap(s)\ge 0,; Bias(s)\in[0,1],; Anon(s)\in{0,1},; Tamper(s)\in[0,1],; LR(s)\colon \mathrm{base\ likelihood\ ratio}
Annotation: Defines per-source quality and risk measures plus the unadjusted likelihood ratio contributed by a source.

\textbf{Silence\ factor: } Sil(H)\colon \mathrm{silence\ of\ expected\ observers},\quad LR_{\mathrm{sil}}(H)=\frac{P(Sil(H)\mid H)}{P(Sil(H)\mid \neg H)}
Annotation: Encodes how damaging silence is for claims that should have generated reports if true.

\textbf{Adjusted\ LR\ per\ source: } LR_{\mathrm{eff}}(s)=LR(s)\cdot k_{\mathrm{gap}}(s)\cdot k_{\mathrm{bias}}(s)\cdot k_{\mathrm{anon}}(s)\cdot k_{\mathrm{tamper}}(s)\cdot k_{\mathrm{qual}}(s)\cdot k_{\mathrm{dep}}(s)
Annotation: Turns the base likelihood ratio into an effective one by multiplying penalty factors for weaknesses.

\textbf{Penalty\ definitions: } k_{\mathrm{gap}}(s)=e^{-\lambda, Gap(s)},\quad k_{\mathrm{bias}}(s)=\frac{1}{1+\beta, Bias(s)},\quad k_{\mathrm{anon}}(s)=\alpha\in(0,1]; \mathrm{if}; Anon(s)=1; \mathrm{else}; 1
Annotation: Longer time gaps, higher bias, and anonymity each reduce evidential weight via tunable parameters.

k_{\mathrm{tamper}}(s)=\frac{1}{1+\theta, Tamper(s)},\quad k_{\mathrm{qual}}(s)=Qual(s),\quad k_{\mathrm{dep}}(s)=\delta\in(0,1]; \mathrm{if\ not\ independent\ else}; 1
Annotation: Suspected tampering reduces weight, source quality scales weight, and dependence between sources applies a penalty.

\textbf{Overall\ evidence\ LR: } LR_{\mathrm{tot}}(H)=\left(\prod_{s\in \mathcal{S}(H)} LR_{\mathrm{eff}}(s)\right)\cdot LR_{\mathrm{sil}}(H)
Annotation: Combines all source evidence and the silence factor into a single likelihood ratio for the claim.

\textbf{Bayes\ update\ with\ LR: } Cr(H\mid E)=\frac{Cr(H)\cdot LR_{\mathrm{tot}}(H)}{Cr(H)\cdot LR_{\mathrm{tot}}(H)+\bigl(1-Cr(H)\bigr)}
Annotation: Updates prior credence to a posterior using the total likelihood ratio.

\textbf{High\ expected\ reportage\ rule: } \bigl(Pub(H)\wedge ER(H)=\mathrm{high}\bigr)\Rightarrow P(Sil(H)\mid H)\ll P(Sil(H)\mid \neg H)\Rightarrow LR_{\mathrm{sil}}(H)\ll 1
Annotation: For public, high-reportage claims, silence strongly counts against the claim.

\textbf{Scarcity\ rule: } Scarce(H)\wedge Extra(H)\wedge Pub(H)\wedge ER(H)=\mathrm{high}\Rightarrow Cr(H\mid E)\ \mathrm{decreases\ (ceteris\ paribus)}
Annotation: Scarcity of sources hurts extraordinary public claims that should have generated many accounts.

\textbf{Mundane\ private\ rule: } Mund(H)\wedge \neg Pub(H)\Rightarrow Scarce(H)\ \mathrm{is\ weakly\ informative},\ LR_{\mathrm{sil}}(H)\approx 1
Annotation: For mundane and private claims, scarcity and silence carry little evidential force.

\textbf{Acceptance\ thresholds: } Extra(H)\Rightarrow T_{\mathrm{accept}}(H)=\tau_{\mathrm{extra}}>\tau_{\mathrm{mund}},\quad \mathrm{Accept}(H)\ \mathrm{iff}\ Cr(H\mid E)\ge T_{\mathrm{accept}}(H)
Annotation: Sets a higher posterior threshold for accepting extraordinary claims than for mundane ones.

\textbf{Reportage\ driver: } ER(H)=g\bigl(Pub(H),Mag(H),RecCap(H),CultRecNorm(H)\bigr),\quad \partial g/\partial _{Pub,Mag,RecCap,CultRecNorm}>0
Annotation: Expected reportage increases with publicity, magnitude, recording capacity, and cultural norms of record keeping.

\textbf{Extraordinary\ public\ silence\ corollary: } Extra(H)\wedge Pub(H)\wedge ER(H)=\mathrm{high}\Rightarrow LR_{\mathrm{sil}}(H)\ll 1\Rightarrow Cr(H\mid E)<\tau_{\mathrm{extra}}\ \mathrm{in\ typical\ cases}
Annotation: In typical extraordinary public scenarios, strong silence keeps the posterior below the acceptance threshold.


The logic above can be explained in simple steps:

  1. Start with a prior probability
    Every historical claim starts with some prior likelihood based on how it fits with what we already know about the world.
  2. Classify the claim
    Is it extraordinary (something rare, surprising, or contrary to established knowledge) or mundane? Extraordinary claims start with lower priors and require more evidence.
  3. Assess publicity
    Was this event public and dramatic enough that many people would have noticed it if it happened? The higher the publicity, the higher the “expected reportage.”
  4. Check the actual reportage
    • If you’d expect lots of reports but have only one or two, that’s a negative signal.
    • If the event is private or unremarkable, lack of reports isn’t a big deal.
  5. Evaluate the sources
    For each account, ask:
    • How long after the event was it recorded?
    • Does the author have bias?
    • Is the author anonymous?
    • Could the account have been tampered with?
    • Is it first-hand or dependent on others?
    • Is the writing quality high enough to trust?
      Each of these factors adjusts how much weight the source adds.
  6. Combine the source weights
    Multiply the adjusted credibility scores for all sources to get the overall strength of the evidence.
  7. Adjust for silence
    If many people could have reported it but didn’t, subtract from the credibility score.
  8. Compare to threshold
    Extraordinary claims must meet a higher bar for acceptance than mundane ones. If the evidence strength falls short, the claim remains unverified.

➘ Instantiating the Model with Dragons over Athens

Imagine that archaeologists, while excavating near the Acropolis, uncover an ornate, well-preserved manuscript. The text claims that during the height of the Greek empire, enormous dragons swooped over Athens, their wings casting shadows across the Parthenon as terrified citizens looked on. The handwriting is elegant, the language classical, and the imagery vivid—yet this is the first time any such account has surfaced in centuries of studying Greek history. No other known sources mention the event, and the claim runs counter to everything we understand about biology, physics, and ancient records. How should we go about weighing such a discovery? To avoid relying on gut feeling or the allure of the extraordinary, we can apply a structured evidential model that explicitly factors in prior plausibility, source quality, potential biases, and the deafening silence from other expected witnesses.

H\colon \mathrm{dragons\ flew\ over\ Athens\ during\ classical\ Greece}
Annotation: The historical claim under evaluation.

Extra(H)=\mathrm{true},\quad Pub(H)=\mathrm{true},\quad ER(H)=\mathrm{high},\quad Scarce(H)=\mathrm{true}
Annotation: Extraordinary, very public, high expected reportage, but few surviving sources.

\mathcal{S}(H)={s_1},\quad s_1=\mathrm{the\ discovered\ manuscript}
Annotation: Only one source exists.

Cr(H)=10^{-6}
Annotation: Extremely low prior due to conflict with biology and natural history.

LR(s_1)=3
Annotation: Generous base likelihood ratio for a seemingly formal manuscript before penalties.

\lambda=0.1\ \mathrm{per\ century},\quad \beta=1,\quad \theta=1,\quad \alpha=0.5,\quad \delta=0.6
Annotation: Penalty hyperparameters for time gap, bias, tamper, anonymity, and dependence.

Gap(s_1)=23\ \mathrm{centuries}\ \Rightarrow\ k_{\mathrm{gap}}(s_1)=e^{-\lambda\cdot Gap}=e^{-2.3}\approx 0.100
Annotation: Long transmission gap severely weakens the source.

Bias(s_1)=0.3\ \Rightarrow\ k_{\mathrm{bias}}(s_1)=\frac{1}{1+\beta\cdot Bias}=\frac{1}{1+0.3}\approx 0.769
Annotation: Moderate suspected motive or genre inflation.

Anon(s_1)=0\ \Rightarrow\ k_{\mathrm{anon}}(s_1)=1
Annotation: Assume the writer is named; no anonymity penalty. If anonymous, multiply by \alpha.

Tamper(s_1)=0.3\ \Rightarrow\ k_{\mathrm{tamper}}(s_1)=\frac{1}{1+\theta\cdot Tamper}=\frac{1}{1+0.3}\approx 0.769
Annotation: Nontrivial interpolation or corruption risk over centuries.

Qual(s_1)=0.6\ \Rightarrow\ k_{\mathrm{qual}}(s_1)=0.6
Annotation: Decent but not superb manuscript quality and probity.

k_{\mathrm{dep}}(s_1)=1
Annotation: No dependence penalty with a single source.

LR_{\mathrm{eff}}(s_1)=LR(s_1)\cdot k_{\mathrm{gap}}\cdot k_{\mathrm{bias}}\cdot k_{\mathrm{anon}}\cdot k_{\mathrm{tamper}}\cdot k_{\mathrm{qual}}\cdot k_{\mathrm{dep}}
\phantom{LR_{\mathrm{eff}}(s_1)}=3\cdot 0.100\cdot 0.769\cdot 1\cdot 0.769\cdot 0.6\cdot 1\approx 0.107
Annotation: After adjustments, the manuscript favors \neg H because the value drops below 1.

P(Sil(H)\mid H)=0.001,\quad P(Sil(H)\mid \neg H)=0.99
Annotation: If dragons really flew, broad silence is very unlikely; silence is very likely if nothing happened.

LR_{\mathrm{sil}}(H)=\frac{P(Sil(H)\mid H)}{P(Sil(H)\mid \neg H)}=\frac{0.001}{0.99}\approx 0.00101
Annotation: The silence factor alone strongly pushes against H.

LR_{\mathrm{tot}}(H)=\left(\prod_{s\in \mathcal{S}(H)} LR_{\mathrm{eff}}(s)\right)\cdot LR_{\mathrm{sil}}(H)=0.107\cdot 0.00101\approx 1.08\times 10^{-4}
Annotation: Total likelihood ratio after combining source weight and silence.

Cr(H\mid E)=\frac{Cr(H)\cdot LR_{\mathrm{tot}}(H)}{Cr(H)\cdot LR_{\mathrm{tot}}(H)+\bigl(1-Cr(H)\bigr)}\approx \frac{10^{-6}\cdot 1.08\times 10^{-4}}{10^{-6}\cdot 1.08\times 10^{-4}+1}\approx 1.08\times 10^{-10}
Annotation: Posterior credence collapses to essentially zero.

\tau_{\mathrm{extra}}=0.5
Annotation: Illustrative acceptance threshold for extraordinary claims.

Cr(H\mid E)\ll \tau_{\mathrm{extra}}\ \Rightarrow\ \mathrm{Reject}(H)\ \mathrm{under\ the\ model}
Annotation: The claim fails the acceptance criterion by many orders of magnitude.

Sensitivity sketch
Even if you raise the manuscript’s base LR a lot or add a few more late, middling sources, the silence term keeps LR_{\mathrm{tot}} tiny. To move the posterior into credible territory you’d need multiple independent, near-contemporary, high-quality accounts plus corroborating physical evidence that also lifts the prior. Without that, the model says the manuscript is net evidence against dragons over Athens.



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