Difference between 証【あかし】 and 証拠【しょうこ】 (proof)

Question

証明｛しょうめい｝means proof, but in the sense "certification"

But 証｛あかし｝ and 証拠｛しょうこ｝look very similar, meaning "proof, evidence".

Would the difference be that 証拠 requires something physical (object), while 証 can be intangible, eg mathematical proof?

Answer 1

• 証【あかし】: An object (mainly tangible) that symbolizes/proves the existence of something (often intangible, such as love, safety and friendship). Dictionaries just say 証【あかし】 is 証拠, but I feel this word is somewhat closer to "symbol" in modern Japanese. This is a bit literary expression, and is not frequently seen in scientific contexts.
• 証拠【しょうこ】: An object or observational result that proves not only the existence of something but also the correctness of any theory/hypothesis/idea in general. Sounds more technical/scientific than 証【あかし】. This I think is closest to English "evidence".
• 証明【しょうめい】: This mainly refers to the "process" of proof rather than the object itself (ie. We do 証明 using 証拠). Mathematical proof is almost always 証明. Additionally, it can mean "certificate" or "proving something is genuine", as in 証明書.
• 認証【にんしょう】: Certification/authorization/verification/license, typically issued by a certain organization.
• ～証【しょう】: A suffix that means "certificate/license". 「運転【うんてん】免許【めんきょ】証【しょう】 (driving license)」

• 恐竜が生きていた証拠: OK
• 恐竜が生きていた証: Uncommon in scientific articles, but OK in TV shows
• 愛の証拠として指輪を贈る: OK but sounds less romantic
• 愛の証として指輪を贈る: OK
• 彼が犯人であるという証拠: OK (Refers to a physical entity, like a fingerprint)
• 彼が犯人であるという証: Weird
• 彼が犯人であるという証明: OK (Refers to the logic and reasoning)
• ピタゴラスの定理の証明: OK
• ピタゴラスの定理の証拠／証: Incorrect (Pythagorean theorem can be proved purely by logic)