You’re using two classes of argument but I can still get the gist of what you me

You’re using two classes of argument but I can still get the gist of what you mean. testimony (law, actions, real) vs probability (logic, words, abstract)

(a) eyewitness testimony requires trust. (I don’t believe you = I don’t trust that you’re correct) Unfortunate

(b) the eyewitness can be evidentially(externally by evidence) or logically(internally by inconsistency) falsified.

ie: the answer is ‘trust’.

ETYMOLOGY
The etymology of the word “believe” traces back through several languages and has an interesting history:

Modern English: “Believe” Used to express a mental conviction of the truth or reality of something, often without concrete evidence. (note migration of germanic harder f to english softer v.

Middle English: “Bileven” or “Believen”The word underwent various spellings and pronunciations during the Middle English period. (not migration of germanic ge, to englis be prefix.

The religious connotation of belief, as in faith or trust in a higher power, also has deep historical roots, reflecting the word’s original sense of trust, confidence, or faith in something.

Old English: “Gelēfan”In Old English, the term meant to trust, have faith in, or have confidence in someone or something. (Geh-LEE-fen) – note germanic ‘ge’ prefix.

Proto-Germanic: “*Ga-laubjan” The Proto-Germanic root is believed to have meant “to hold dear, valuable, or satisfactory.” The prefix “ga-” was an intensive prefix, and “laubjan” was related to love and desire. Note migration of protogermanic harder j to softer f.

Proto-Indo-European (PIE): “*Lēubh-“The PIE root “*lēubh-” is associated with love, care, and desire. It is also the root of words like “love” and “libido.”

Interesting:
The connection between belief and love or desire is an intriguing aspect of the word’s history. To believe in something or someone was to hold it dear or valuable, reflecting a connection between intellectual assent and emotional attachment.