Categorical proof is proof so strong, so definite, so compelling as to defy any alternative explanation. Corroborated proof with verifiable transparency coupled with no way of contradicting the evidence and no alternative explanation––such would represent a good first step in these instances. Seeking to convince others––there are gradations, from the obvious to the extraordinary. The obvious. These facts are taken for granted, and are readily accepted by others. The extraordinary. These fall outside the bounds of normal patterns and require significantly higher levels of proof before others will even begin to consider their validity.
Let’s take a unique example. In 2013, a meteor known as the “Chelyabinsk meteor” struck Russia. “The Chelyabinsk meteor was a superbolide that entered Earth’s atmosphere over the southern Ural region in Russia on 15 February 2013 at about 09:20 YEKT (03:20 UTC). It was caused by an approximately 20 m (66 ft) near-Earth asteroid that entered the atmosphere at a shallow 18.3 ± 0.4 degree angle with a speed relative to Earth of 19.16 ± 0.15 kilometres per second (69,000 km/h or 42,690 mph). The light from the meteor was briefly brighter than the Sun, visible up to 100 km (62 mi) away…” Wikipedia/Chelyabinsk meteor/https:/en.wikipedia.org/wiki/Chelyabinsk_meteor
Let’s assume your persuasive task is to convince a panel that this was not a meteor, but in fact a spacecraft from another planet. Here, the proof required would have to be unassailable, utterly incapable of being contradicted. If there were any alternative explanation, however slight, the conclusion would fail. The fantastic, the extraordinary, the unknown––these are not inferences we’re prepared to draw without first being convinced by absolute, categorical proof. “We found technology that’s not found on earth”––not enough since, within the realm of possibility, such could be mechanically fabricated. “We found DNA not found on any living life-form on earth”––not enough since, within the realm of possibility, such could be biologically fabricated. Etc. In the face of the unknown, our minds are poised to postulate explanations to rationalize our existing beliefs.
Categorical proof of those facts which exist outside our normal patterns implicate far more stringent levels and layers of proof. Also, one may soon arrive at this rather harsh realization––any newly presented fact, or set of facts, shares certain similarities with this phenomenon. So with any newly presented case––you’re having to prove something others have not previously encountered. But what do most proceed to do? Ignore this entire area, and treat ordinary proof and categorical proof in much the same way.
“In our reasonings concerning matter of fact, there are all imaginable degrees of assurance, from the highest certainty to the lowest species of moral evidence. A wise man, therefore, proportions his belief to the evidence.” ― David Hume
Having a sensitivity to the spectrum of required proof depending on the remoteness and novelty of the conclusion sought––no one emphasizes this. But in any contested proceeding some sensitivity to this area is required. A common mistake is to assume that one person’s testimony alone is categorical. A good rule of thumb: one’s person testimony, rarely if ever, can provide a categorical answer to any seriously contested question. And so the maxim “Proof of the extraordinary requires extraordinary proof” becomes a question of combining both step-by-step process and layer-by-layer substance where an effort is made to move beyond the fixed and formulaic.
And finally there’s this: “All the interests of my reason, speculative as well as practical, combine in the three following questions: 1. What can I know? 2. What ought I to do? 3. What may I hope?”– Immanuel Kant. Those three questions actually have some relevance in this context since they can provide a text, or subtext, against which to assess the terrain about to be crossed. It may be that level of abstractness is what’s needed to at last achieve some degree of framework and focus.