At the Edge of Miracles

David Hume argues that it is always more rational to disbelieve in miracles because the probability of human error is always greater than the probability of a violation of the laws of nature.
With sufficient and robust evidence that minimizes human error and deception, we would be justified in adjusting our epistemic stance toward accepting the possibility of miracles.
Advancements in technology can increase the reliability of evidence and decrease the likelihood of false testimony.
The cumulative effect of multiple independent accounts can significantly increase the probability of a miracle occurring.
Belief is not a binary switch but a continuum where confidence levels adjust incrementally with new evidence.
Each new piece of evidence should shift our degree of belief gradually rather than causing an abrupt acceptance.

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Hume suggests that the probability that human frailty, such as misremembering or mendacity, will always be greater than the probability of a single supernatural miracle claim being true…

… However, there could be a series of investigable miracle accounts that could legitimately alter the balance of these probabilities, right? Given the current objective tools of investigation and reduced dependence on subjective accounts, at some density of evidence for miracle accounts, we would be justified in moving the needle on the epistemic gradient toward the reality of miracles. Right? Rigorously elaborate on these dynamics and this possibility.

David Hume, in his essay “Of Miracles,” argues that it is always more rational to disbelieve in miracles because the probability of human error—such as misinterpretation, faulty memory, or intentional deceit—is always greater than the probability of a violation of the laws of nature. Hume’s skepticism is rooted in the principle that extraordinary claims require extraordinary evidence, and that human testimony is often unreliable.

However, the possibility arises that a sufficiently large and well-verified collection of miracle accounts could alter this balance of probabilities. With advances in investigative methodologies and technologies that reduce reliance on subjective human testimony, the cumulative weight of evidence might justify revisiting the skepticism toward miracles. To rigorously explore this dynamic, we can employ principles from probability theory and epistemology.

Hume’s Argument and the Weight of Testimony

Hume posits that when evaluating reports of miracles, we should weigh two probabilities:

The Probability of the Miracle Occurring ( $P(M)$ ): Given that a miracle is a violation of the laws of nature, which have been consistently observed, the prior probability is exceedingly low.
The Probability of the Testimony Being False ( $P(T_f)$ ): Human error, deception, or misunderstanding are relatively common, so this probability is comparatively higher.

Hume concludes that $P(T_f) > P(M)$ , and thus, it is more rational to assume that the testimony is false rather than the miracle having occurred.

Bayesian Framework for Updating Beliefs

To analyze how accumulating evidence might shift this balance, we can use Bayes’ Theorem, which provides a mathematical framework for updating probabilities based on new evidence:

$P(M|E) = \frac{P(E|M) \cdot P(M)}{P(E|M) \cdot P(M) + P(E|\neg M) \cdot P(\neg M)}$

Where:

$P(M|E)$ is the probability of the miracle given the evidence.
$P(E|M)$ is the probability of the evidence if the miracle occurred.
$P(M)$ is the prior probability of the miracle.
$P(E|\neg M)$ is the probability of the evidence if the miracle did not occur.
$P(\neg M)$ is the probability that the miracle did not occur.

Impact of Multiple Independent Accounts

Suppose we have multiple independent and reliable accounts ( $E_1, E_2, \ldots, E_n$ ) of a miracle. The cumulative effect can significantly impact $P(M|E)$ . Under the assumption of independence, the combined likelihood of all testimonies being false decreases exponentially with each additional independent account.

Modern Investigative Tools and Reduced Subjectivity

Advancements in technology—such as video recording, forensic analysis, and other scientific methods—can increase the reliability of evidence ( $P(E|M)$ ) and decrease the likelihood of false testimony ( $P(E|\neg M)$ ). This technological enhancement effectively reduces $P(T_f)$ , narrowing the gap between $P(T_f)$ and $P(M)$ .

Thresholds for Rational Belief

In epistemology, a belief becomes justified when the probability surpasses a certain threshold. As the evidence accumulates and $P(M|E)$ increases, there comes a point where it may surpass $P(T_f)$ , making belief in the miracle rational.

Rigorously Elaborated Dynamics

Reduction of $P(E|\neg M)$ : With objective evidence, the likelihood of observing the evidence if the miracle did not occur decreases.
Increase of $P(E|M)$ : If the miracle did occur, the likelihood of observing the collected evidence is high.
Updating $P(M)$ : While the prior probability of a miracle remains low, the posterior probability $P(M|E)$ increases with strong, consistent evidence.
Cumulative Effect: Each new piece of independent, objective evidence further increases $P(M|E)$ , potentially tipping the scales.

Addressing the Skeptic’s Objections

A skeptic might argue that no amount of testimony can establish a miracle due to its inherent improbability. However, if the cumulative evidence reduces the improbability of the testimony being false below that of the miracle occurring, the rational position would be to accept the miracle.

Conclusion

In light of these dynamics, it is theoretically possible for a series of investigable and objectively verified miracle accounts to alter the balance of probabilities posited by Hume. With sufficient and robust evidence that minimizes human error and deception, we would be justified in adjusting our epistemic stance toward accepting the possibility of miracles. This shift underscores the importance of evidence quality and quantity in rational belief formation.

You said, “…if the cumulative evidence reduces the improbability of the testimony being false below that of the miracle occurring, the rational position would be to accept the miracle.” However,…

…this treats the scenario as if it entailed a binary epistemic switch from off to on at the point of “acceptance” instead of a rational needle movement along the epistemic gradient. Rigorously address this.

You’re absolutely right, and I appreciate the clarification. Belief is not typically a binary switch from disbelief to belief but rather a continuum where confidence levels adjust incrementally with new evidence. In the context of evaluating miracles, each piece of evidence should shift our degree of belief gradually rather than causing an abrupt acceptance.

Degrees of Belief and Bayesian Updating

In Bayesian epistemology, beliefs are represented as probabilities on a continuous scale between 0 and 1. As new evidence is obtained, we update our prior beliefs to form new posterior beliefs using Bayes’ Theorem. This process reflects a gradual adjustment rather than a sudden change from disbelief to belief.

Revisiting the Earlier Statement

Instead of suggesting that we should “accept the miracle” once a certain threshold is crossed, it’s more accurate to say that our confidence in the occurrence of the miracle increases progressively with each new piece of credible evidence. This approach aligns with the concept of a “rational needle move,” where our belief adjusts in proportion to the strength and amount of evidence.

Mathematical Representation

Each new piece of evidence $E_i$ allows us to update our belief in the miracle $M$ :

$P(M|E_1, E_2, \ldots, E_n) = \frac{P(E_n|M) \cdot P(M|E_1, E_2, \ldots, E_{n-1})}{P(E_n)}$

Here:

$P(M|E_1, E_2, \ldots, E_n)$ is the updated probability of the miracle after considering all evidence up to $E_n$ .
$P(M|E_1, E_2, \ldots, E_{n-1})$ is the prior probability before considering the latest evidence $E_n$ .
$P(E_n|M)$ is the probability of observing the new evidence if the miracle occurred.
$P(E_n)$ is the overall probability of the new evidence.

This formula shows how our belief is updated incrementally with each new piece of evidence, reflecting a continuous adjustment rather than a binary shift.

The Continuum of Belief

Incremental Updates: Each new, reliable piece of evidence increases $P(M|E)$ by a certain amount, depending on its strength and reliability.
No Binary Threshold: There’s no specific point at which we must “accept” the miracle; instead, our confidence grows progressively.
Decision Thresholds: While belief itself is continuous, practical decisions might require setting thresholds (e.g., acting upon a belief when confidence exceeds 0.9). However, this threshold is subjective and varies by individual or context.

Implications for Evaluating Miracles

Evidence Quality: High-quality, objective evidence has a more significant impact on increasing our degree of belief than anecdotal or subjective reports.
Cumulative Effect: The accumulation of multiple independent pieces of strong evidence can collectively raise our degree of belief to a high level, even if each piece alone wouldn’t suffice.

Conclusion

Belief in miracles, or any extraordinary claim, should be viewed as a matter of degrees rather than an all-or-nothing stance. The rational approach involves continuously updating our beliefs in light of new evidence, allowing our confidence to adjust incrementally. This perspective acknowledges the nuanced nature of belief and aligns with a more accurate interpretation of Bayesian reasoning in epistemology.

Provide three scenarios of less subjective and more objective evidence for a series of miracle claims that would significantly “move the epistemic needle.”

Certainly! Below are three hypothetical scenarios where less subjective and more objective evidence for a series of miracle claims could significantly “move the epistemic needle” toward accepting the possibility of miracles. Each scenario is designed to minimize human error, bias, and deception, thereby strengthening the credibility of the miracle claims through objective verification.

Scenario 1: The Global Astronomical Anomaly

Event Description:

An unexpected celestial event occurs simultaneously across the globe. At precisely 12:00 PM GMT on a predetermined date, a new, brilliant light appears in the sky, visible from every point on Earth regardless of time zone or weather conditions. The light lasts exactly one hour and then disappears without a trace.

Objective Evidence:

Astronomical Observations:
Global Telescope Networks: Astronomers worldwide, using both ground-based telescopes and space observatories, record the event in real-time. The data collected includes high-resolution images, spectra, and other measurements.
Satellite Data: Satellites equipped with advanced sensors capture detailed information about the light’s properties, ruling out known astronomical phenomena like supernovae or solar flares.
Instrumental Verification:
Spectral Analysis: Independent laboratories analyze the light’s spectrum and find it does not match any known chemical emissions or physical processes.
Radiation Measurements: Geiger counters and other radiation detectors globally show anomalous readings corresponding precisely with the event’s duration.
Consistency Across Platforms:
Uninterrupted Documentation: The event is captured across various platforms—professional observatories, amateur astronomers, weather stations, and even smartphones equipped with astronomy apps.
Time-Stamped Data Logs: All recordings come with secure, time-stamped logs that are verified by international timekeeping agencies.

Impact on the Epistemic Needle:

Reduces Subjectivity: The sheer volume of consistent, high-quality data from independent sources minimizes the likelihood of mass deception or error.
Challenges Natural Explanations: The inability of current scientific models to explain the phenomenon increases the probability that the event is beyond natural laws.
Encourages Scientific Inquiry: The event prompts the scientific community to reconsider the limitations of current physical laws, potentially opening the door to accepting miraculous explanations.

Scenario 2: Verified Medical Miracles in Controlled Environments

Event Description:

A group of terminally ill patients with medically documented, incurable conditions experience spontaneous and complete recoveries within the same time frame. These patients are located in different, secure medical facilities around the world, all participating in a double-blind study unrelated to their miraculous recoveries.

Objective Evidence:

Medical Documentation:
Baseline Records: Comprehensive medical records before the event include diagnostics like MRI scans, blood tests, and genetic profiles confirming the severity and incurability of their conditions.
Post-Recovery Tests: After the spontaneous recoveries, new tests show no traces of the diseases, with biological markers indicating a state of health not achievable through known medical interventions.
Controlled Environment:
Double-Blind Study Conditions: The patients are part of studies where neither the participants nor the administrators know who is receiving treatment versus a placebo, eliminating the placebo effect as an explanation.
Independent Oversight: International medical boards and ethics committees oversee the studies, ensuring protocols are strictly followed.
Replication of Results:
Multiple Cases: The phenomenon occurs in multiple patients across different facilities, cultures, and demographics, reducing the likelihood of coordinated fraud.
Temporal Synchronization: The recoveries happen simultaneously, despite geographical separation and different treatment regimens.

Impact on the Epistemic Needle:

Eliminates Alternative Explanations: The controlled settings and rigorous protocols rule out misdiagnosis, experimental error, or fraud.
Demands Reassessment of Medical Knowledge: The medical impossibility of the recoveries under current science necessitates considering supernatural explanations.
Strengthens Credibility: The involvement of reputable institutions and professionals adds weight to the evidence.

Scenario 3: Predictive Miracles Confirmed by Advanced Technology

Event Description:

An ancient, previously undeciphered manuscript is found to contain detailed predictions of specific, improbable events that are to occur in the modern era. Linguists and historians authenticate the manuscript’s age and origin. Using advanced AI, researchers decode the text and discover predictions with precise dates, locations, and descriptions of events that subsequently occur exactly as described.

Objective Evidence:

Authentication of the Manuscript:
Carbon Dating: Scientific dating methods confirm the manuscript is several millennia old.
Material Analysis: The ink, paper, and writing style are consistent with the purported time period and region.
Decoding Process:
Advanced AI Algorithms: Machine learning models independently verify the decoding of the manuscript without human bias.
Peer Review: Cryptographers and linguists from around the world replicate the decoding process and reach the same conclusions.
Verification of Predictions:
Documented Occurrences: The predicted events are highly specific—such as rare natural phenomena or unexpected societal changes—and are recorded by modern technology (e.g., seismic sensors for earthquakes, live broadcasts for events).
Temporal Records: The timing of the predictions and their fulfillment is meticulously recorded and verified by international timekeeping agencies.

Impact on the Epistemic Needle:

Bridges Ancient and Modern Knowledge: The manuscript provides information that could not have been known by its authors through natural means.
Utilizes Objective Technology: The use of AI and machine learning reduces human error in decoding and interpretation.
Statistical Improbability: The precise fulfillment of multiple specific predictions greatly lowers the probability of chance or coincidence.

Collective Implications of the Scenarios

These scenarios share common features that enhance their credibility:

Independent Verification: Multiple, unrelated sources confirm the events, reducing the likelihood of collusion or mass hallucination.
Technological Support: Advanced technology objectively records and analyzes the events, minimizing subjective interpretation.
Scientific Anomalies: The inability of existing scientific frameworks to explain the phenomena forces a reconsideration of naturalistic assumptions.
Reproducibility and Consistency: The events are replicable or consistent across different contexts, strengthening the case for their authenticity.

Conclusion

By significantly reducing the elements of human error, deception, and subjective interpretation, these scenarios provide strong, objective evidence that could compel rational individuals to adjust their beliefs about the possibility of miracles. The cumulative weight of such evidence would move the epistemic needle by increasing the posterior probability that miracles can and do occur, thus challenging Hume’s assertion that it is always more rational to disbelieve in miracles.

Was Hume’s depth of skepticism perhaps justified given the unavailability of the objective tools of scrutiny at his time?

David Hume’s skepticism regarding miracles, as articulated in his 1748 essay “Of Miracles,” was profoundly influenced by the epistemological and technological limitations of his time. Hume argued that miracles are violations of the laws of nature, and as such, the probability of their occurrence is exceedingly low. He maintained that human testimony, which is prone to error, deception, and bias, is insufficient to establish the authenticity of miraculous events.

Justification of Hume’s Skepticism in His Historical Context

Limited Investigative Tools: In the 18th century, the scientific method was still in its developmental stages, and the instruments available for empirical investigation were rudimentary. There were no advanced technologies like spectroscopy, radiometric dating, or electron microscopy to analyze phenomena with precision. This lack of sophisticated tools made it difficult to objectively verify extraordinary claims.
Reliance on Human Testimony: Without technological means to record or measure events, people had to rely heavily on eyewitness accounts and personal testimonies. Hume recognized that such accounts are susceptible to errors arising from misperception, faulty memory, exaggeration, or intentional deceit. The absence of objective recording devices like cameras or audio recorders meant that there was no way to cross-verify individual claims independently.
Prevalence of Superstition and Lack of Scientific Literacy: The general population during Hume’s time had limited access to scientific education. Superstitions and unfounded beliefs were widespread, often filling gaps in understanding natural phenomena. This environment fostered a readiness to accept miraculous explanations without demanding rigorous evidence.
Challenges in Communication and Verification: Information dissemination was slow, and cross-cultural or international verification of events was cumbersome. News of miracles could spread without being subjected to scrutiny by experts from different regions or disciplines, allowing unverified claims to gain credibility.

Contrast with Modern Tools of Scrutiny

Today, we have access to a plethora of advanced technologies and methodologies that enhance our ability to investigate and verify claims:

Scientific Instrumentation: Devices like high-powered telescopes, particle accelerators, and genomic sequencers allow us to explore and understand phenomena at cosmic and microscopic levels.
Digital Recording and Surveillance: Cameras, smartphones, and other recording devices can capture events in real-time, providing objective evidence that can be analyzed and authenticated.
Data Analysis and Computational Power: Advanced software and algorithms enable us to detect patterns, analyze large datasets, and simulate complex systems, reducing reliance on subjective interpretation.
Global Communication Networks: The internet and satellite communications allow for instant sharing of information, enabling peer review and collaborative verification across the world.

Implications for Hume’s Argument

Given the limitations of his era, Hume’s insistence on skepticism was a rational stance. He advocated for a high evidentiary standard, which was appropriate considering that most miracle claims could not be substantiated beyond anecdotal reports. His approach encouraged critical thinking and demanded that claims be proportionate to the evidence available.

In modern times, while we have better tools to investigate and potentially verify extraordinary events, Hume’s underlying principles remain relevant:

Extraordinary Claims Require Extraordinary Evidence: Even with advanced technology, the burden of proof lies heavily on demonstrating that an event genuinely violates natural laws.
Fallibility of Human Perception: Despite technological aids, human interpretation of data can still be influenced by cognitive biases and errors.
Necessity of Peer Review and Replication: Objective scrutiny by the scientific community is essential to validate any claim, miraculous or otherwise.

Conclusion

Hume’s depth of skepticism was justified within the context of his time due to the unavailability of objective and reliable tools for scrutiny. His arguments highlighted the need for critical examination and empirical evidence when assessing extraordinary claims. While modern technology provides us with better means to investigate such claims, the foundational principles of skepticism and rigorous inquiry that Hume championed continue to be essential in distinguishing between credible evidence and unfounded assertions. His work laid important groundwork for the development of scientific methodology and the emphasis on evidence-based reasoning that persists in contemporary discourse.

Quiz

#1: What is the main reason David Hume argues that it is more rational to disbelieve in miracles?

Answer:

Because the probability of human error—such as misinterpretation, faulty memory, or intentional deceit—is always greater than the probability of a violation of the laws of nature.

#2: What principle is Hume’s skepticism about miracles rooted in?

Answer:

The principle that extraordinary claims require extraordinary evidence, and that human testimony is often unreliable.

#3: Which mathematical framework is used to analyze how accumulating evidence might shift the balance of probabilities regarding miracles?

Answer:

Bayes’ Theorem.

#4: In evaluating reports of miracles, what two probabilities does Hume suggest we should weigh?

Answer:

The probability of the miracle occurring ( $P(M)$ ) and the probability of the testimony being false ( $P(T_f)$ ).

#5: How can modern investigative tools impact the evaluation of miracle claims?

Answer:

They can increase the reliability of evidence and decrease the likelihood of false testimony, effectively reducing the probability of human error.

#6: What happens to the posterior probability $P(M|E)$ as we gather multiple independent and reliable accounts of a miracle?

Answer:

The cumulative effect can significantly increase $P(M|E)$ , potentially making belief in the miracle rational.

#7: What does “moving the epistemic needle” mean in this context?

Answer:

Adjusting our degree of belief in the occurrence of a miracle based on new, credible evidence.

#8: Why is belief in miracles considered a matter of degrees rather than a binary stance?

Answer:

Because beliefs are represented as probabilities on a continuous scale between 0 and 1, and confidence levels adjust incrementally with new evidence.

#9: Name two features shared by the hypothetical scenarios that enhance their credibility.

Answer:

Independent verification and technological support (others include scientific anomalies and reproducibility and consistency).

#10: In Scenario 1, what global event occurs that challenges natural explanations?

Answer:

An unexpected celestial light appears simultaneously across the globe, visible from every point on Earth, and cannot be explained by known astronomical phenomena.

#11: How are the spontaneous recoveries of terminally ill patients verified in Scenario 2?

Answer:

Through comprehensive medical documentation, controlled environments, and independent oversight ensuring protocols are strictly followed.

#12: What role does advanced AI play in verifying miracle claims in Scenario 3?

Answer:

AI is used to decode an ancient manuscript containing detailed predictions, reducing human error in decoding and interpretation.

#13: According to Bayesian reasoning, what is the impact of objective evidence on the posterior probability of miracles?

Answer:

It increases the posterior probability $P(M|E)$ , moving our belief incrementally toward accepting the possibility of miracles.

#14: How does modern technology contribute to the verification of miracle claims in the scenarios?

Answer:

By providing objective recordings and analyses of events, minimizing subjective interpretation and human error.

#15: What is the overall conclusion about adjusting our epistemic stance toward accepting miracles?

Answer:

With sufficient and robust evidence that minimizes human error and deception, we would be justified in adjusting our epistemic stance toward accepting the possibility of miracles.

Provide 20 discussion questions relevant to the content above.

How does Hume’s principle that “extraordinary claims require extraordinary evidence” apply in the context of modern technology and investigative tools?
In what ways can Bayesian reasoning help us evaluate the probability of miracles occurring, and what are its limitations in this context?
Can the accumulation of objective, independent evidence ever fully overcome Hume’s skepticism about miracles? Why or why not?
How does treating belief as a continuum rather than a binary switch affect our evaluation of miracle claims?
What role do prior probabilities play in assessing the likelihood of miracles, and how might they be updated with new evidence?
Discuss the impact of cognitive biases on the interpretation of evidence for and against miracles.
How might the concept of “moving the epistemic needle” be applied in other areas of epistemology beyond miracles?
In Scenario 1, what are some potential natural explanations for the global astronomical anomaly, and how might they be systematically ruled out?
How does independent verification across multiple disciplines strengthen the credibility of the miracle claims in the scenarios provided?
What ethical considerations arise when accepting miracles based on evidence that challenges current scientific understanding?
Can accepting the possibility of miracles coexist with a commitment to scientific naturalism, or does it necessitate a paradigm shift?
How do advancements in technology reduce the probability of human error ( $P(T_f)$ ) in evaluating miracle claims?
In what ways could widespread acceptance of miracles impact scientific progress and inquiry?
How does the use of advanced AI in Scenario 3 address potential issues of human interpretation and bias in decoding ancient manuscripts?
What are the implications of the “cumulative effect” of evidence on our rational belief system, particularly concerning rare or unprecedented events?
Discuss how cultural and societal factors might influence the collective movement of the epistemic needle regarding miracles.
How might a skeptic respond to the scenarios provided, and what counterarguments could they offer?
What is the significance of reproducibility and consistency in the verification of miracle claims?
How do the concepts of prior probability and posterior probability differ, and why are they important in the context of evaluating miracles?
Is it possible for miracles to be scientifically investigated without bias, and what methodologies would be necessary to achieve this?

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