Acts 1:3 and the The Hapax Legomenon, "Infallible Proofs"

Acts 1:3-Greek (NA28): Οἷς καὶ παρέστησεν ἑαυτὸν ζῶντα μετὰ τὸ παθεῖν αὐτὸν ἐν πολλοῖς τεκμηρίοις, δι’ ἡμερῶν τεσσεράκοντα ὀπτανόμενος αὐτοῖς καὶ λέγων τὰ περὶ τῆς βασιλείας τοῦ θεοῦ·

Louw-Nida: " 'by many convincing proofs he showed himself alive after his death' Ac. 1:3. In a number of languages 'convincing proof' is rendered as 'that which causes one to know for sure' or 'with certainty' " (Semantic Domain 28.45).

BDAG Greek-English Lexicon: τεκμήριον, ου, τό ⟦tekmḗrion⟧ (Aeschyl., Hdt., Thu.+) that which causes someth. to be known in a convincing and decisive manner, proof (demonstrative proof: Aristot., An. Pr. 70b, 2; Rh. 1357b 4; 1402b 19; Diod S 17, 51, 3 τεκμήρια τῆς ἐκ τοῦ θεοῦ γενέσεως; SIG 867, 37 μέγιστον τεκμήριον w. ref. to Artemis; 685, 84; PGiss 39, 9) ἐν πολλοῖς τεκμηρίοις by many convincing proofs Ac 1:3 (DMealand, ZNW 80, ’89, 134f [Hell. reff.]; cp. Jos., Ant. 5, 39 διὰ πολλῶν τεκμηρίων.— τεκ. used w. παραστῆσαι Jos., Ant. 17, 128. Cp. Libanius, Or. 18, 13 τὸ τῆς φύσεως βασιλικὸν πολλοῖς καὶ μεγάλοις τεκμηρίοις ἐμηνύετο=his regal nature was attested by many exceptional signs).—DELG. M-M.

Herodotus writes:

[2.13.1] "This, too, that the priests told me about Egypt, is a strong proof : when Moeris was king, if the river rose as much as thirteen feet, it watered all of Egypt below Memphis. Moeris had not been dead nine hundred years when I heard this from the priests. But now, if the river does not rise at least twenty-six or twenty-five feet, the land is not flooded."

[The Histories, 2.13.1] ἔλεγον δὲ καὶ τόδε μοι μέγα τεκμήριον περὶ τῆς χώρης ταύτης οἱ ἱρέες, ὡς ἐπὶ Μοίριος βασιλέος, ὅκως ἔλθοι ὁ ποταμὸς ἐπὶ ὀκτὼ πήχεας τὸ ἐλάχιστον, ἄρδεσκε Αἴγυπτον τὴν ἔνερθε Μέμφιος: καὶ Μοίρι οὔκω ἦν ἔτεα εἰνακόσια τετελευτηκότι ὅτε τῶν ἱρέων ταῦτα ἐγὼ ἤκουον. νῦν δὲ εἰ μὴ ἐπ᾽ ἑκκαίδεκα ἢ πεντεκαίδεκα πήχεας ἀναβῇ τὸ ἐλάχιστον ὁ ποταμός, οὐκ ὑπερβαίνει ἐς τὴν χώρην.

Additionally, Sophocles pens these words in one of his plays:

Clytemnestra states:

"No, not in vain; how can you say 'in vain' when you have brought me sure proofs of his death?" (Soph. Electra 774)

Greek: οὔτοι μάτην γε: πῶς γὰρ ἂν μάτην λέγοις, εἴ μοι θανόντος πίστ᾽ ἔχων τεκμήρια
προσῆλθες

Ralph Earle (Word Meanings in the New Testament, page 97) commenting on Acts 1:3: "Infallible Proofs--This is one word in Greek, tekmeriois--a strong term (only here in the NT). J. R. Lumby says, 'A tekmerion is such an evidence as to remove all doubt.' "

In the final analysis, Earle cites "convincing proofs" (NASB, NIV) as a suitable rendering for tekmeriois.

The Amplified Bible prefers "unquestionable evidence" and another possibility is
"indubitable proof." The word's semantic range allow for this rendering. In the context of Acts 1:3, "unquestionable" or "indubitable" seems to be a good choice. The apostles are being shown signs that will make them suitable witnesses of Christ throughout the earth (Acts 1:8). Surely they would have needed strong proof to be convinced and to persuade others.

Another consideration here is the Classical usage of tekmerion. When consulting LSJ, I found that tekmerion was variously defined as "sure proof" or "strong proof" as well as "evidence." The word seems to have strong connotations of evidence that is undeniable. 

The Cambridge Greek Lexicon: τεκμήριον ου η.

1 sure sign or principle, criterion (for adopting a particular course of action) A.

2 piece of evidence seen or heard, sign, evidence, proof (of sthg.) Hdt. Trag. Men.

3 evidence from facts or logic, evidence, proof (of sthg.)

Hdt. Trag. Th. Ar. Att.orats. +

4 evidence which constitutes proof in a logical argument, necessary sign Arist.