➘ #25 Source Article

◉ A plain English walkthrough of the Master Proof above.

1. We begin by saying that every hypothesis we might consider has a degree of belief, or credence, between 0 and 1. In other words, belief is not simply “yes” or “no” but a matter of degree.
2. Rationality requires that these credences behave like probabilities: they must add up correctly and remain coherent with one another.
3. When new evidence is encountered, rationality demands that we update our belief in a hypothesis proportionally using Bayes’ theorem. This ensures that the degree of belief reflects the strength of the evidence.
4. Another way of putting this is in terms of odds: the posterior odds equal the prior odds multiplied by the Bayes factor. This forces our belief revision to be proportionate to the evidential impact.
5. All hypotheses in a complete set must share the total credence, which sums to one. Assigning more belief to one automatically reduces what remains available for the others.
6. Not only must we consider known alternatives, but rational belief also requires allocating some probability to unknown or unimagined possibilities. This prevents us from prematurely treating the matter as settled.
7. If the evidence is incomplete, rationality does not force us to pick a single number. Instead, it allows us to hold an imprecise or interval-valued belief that captures the uncertainty honestly.
8. This means that a rational state of belief is often represented by an interval—somewhere between two bounds inside the range from 0 to 1—rather than by a sharp extreme.
9. By contrast, “faith” is defined as taking either complete certainty (1) or complete denial (0) regardless of the proportional strength of evidence. Faith thus ignores the norms of rational credence.
10. When someone defaults to faith, they effectively stop inquiry, adopt a dogmatic stance, and expose themselves to potential manipulation by authority or tradition.
11. Rationality, on the other hand, requires beliefs to track the proportional strength of the evidence. It is the opposite of the binary leap of faith.
12. When evidence is incomplete, rationality requires interval-valued or imprecise beliefs, while faith insists on extreme positions. The two are incompatible.
13. Therefore, under conditions of incomplete evidence, faith must be considered irrational.
14. The alternative is to embrace uncertainty. This means adopting imprecise but evidence-proportional credences while preserving an open attitude toward further inquiry.
15. Embracing uncertainty is therefore the rational posture, while defaulting to faith undermines rationality and inquiry.
16. The final conclusion is that whenever evidence is incomplete—which is precisely the case in existential questions—rationality requires graded, proportional belief (often imprecise), and faith is irrational. The most rational stance is the intellectual humility of being willing to say, “I don’t know.”

◉ Narrative Summary

The argument begins with the recognition that belief is not binary. For any hypothesis we consider, rationality requires assigning a degree of belief that falls somewhere between absolute certainty and absolute denial. This spectrum of confidence, called credence, must behave like probability: credences across all possibilities must add up coherently, and they must be updated in proportion to the evidence received. When new evidence emerges, Bayes’ theorem ensures that shifts in belief are not arbitrary but scaled according to how strongly the evidence favors one hypothesis over another.

Because the total probability must be distributed across all possible explanations, assigning more confidence to one hypothesis necessarily reduces the confidence available for others. Rationality also requires leaving room for unknown or unimagined alternatives, so that unexplored possibilities are not prematurely ruled out. This is especially important when evidence is incomplete, for in such cases rationality does not demand an exact number but allows us to represent our uncertainty with a range of values. In this way, imprecise or interval-valued beliefs honestly reflect the limitations of our knowledge.

Faith, by contrast, bypasses this proportional system. It locks belief into one of two extremes—total affirmation or total denial—without regard for how much evidence actually exists. To adopt faith in this way is to ignore the evidential landscape, halting inquiry and encouraging dogmatism. The result is an environment where beliefs become insulated from correction, and where individuals are more vulnerable to manipulation by external authorities.

The rational alternative is to embrace uncertainty. Rather than collapsing questions into premature closure, one acknowledges the incompleteness of evidence and maintains an openness to further discovery. This posture embodies epistemic humility, keeping belief proportionate to available support and preserving the freedom to adjust as new evidence arises.

The conclusion is clear: under conditions of incomplete evidence—which is the case in most existential and metaphysical questions—faith is irrational because it demands unwarranted certainty. Rationality requires a gradient of belief that tracks the strength of evidence, often through imprecise intervals rather than extremes. The virtue of saying “I don’t know” lies not in passivity but in the disciplined commitment to let belief rise and fall with evidence, leaving inquiry alive and possibility open.