Objection 1. It would seem that Christ should not have demonstrated the truth of His Resurrection by proofs. For Ambrose says (De Fide, ad Gratian. i): "Let there be no proofs where faith is required." But faith is required regarding the Resurrection. Therefore proofs are out of place there.
Objection 2. Further, Gregory says (Hom. xxvi): "Faith has no merit where human reason supplies the test." But it was no part of Christ's office to void the merit of faith. Consequently, it was not for Him to confirm the Resurrection by proofs.
Objection 3. Further, Christ came into the world in order that men might attain beatitude through Him, according to John 10:10: "I am come that they may have life, and may have it more abundantly." But supplying proofs seems to be a hindrance in the way of man's beatitude; because our Lord Himself said (John 20:29): "Blessed are they that have not seen, and have believed." Consequently, it seems that Christ ought not to manifest His Resurrection by any proofs.
On the contrary, It is related in Acts 1:3, that Christ appeared to His disciples "for forty days by many proofs, speaking of the Kingdom of God."
I answer that, The word "proof" is susceptible of a twofold meaning: sometimes it is employed to designate any sort "of reason in confirmation of what is a matter of doubt" [Tully, Topic. ii]: and sometimes it means a sensible sign employed to manifest the truth; thus also Aristotle occasionally uses the term in his works [Cf. Prior. Anal. ii; Rhetor. i]. Taking "proof" in the first sense, Christ did not demonstrate His Resurrection to the disciples by proofs, because such argumentative proof would have to be grounded on some principles: and if these were not known to the disciples, nothing would thereby be demonstrated to them, because nothing can be known from the unknown. And if such principles were known to them, they would not go beyond human reason, and consequently would not be efficacious for establishing faith in the Resurrection, which is beyond human reason, since principles must be assumed which are of the same order, according to 1 Poster. But it was from the authority of the Sacred Scriptures that He proved to them the truth of His Resurrection, which authority is the basis of faith, when He said: "All things must needs be fulfilled which are written in the Law, and in the prophets, and in the Psalms, concerning Me": as is set forth Luke 24:44.
But if the term "proof" be taken in the second sense, then Christ is said to have demonstrated His Resurrection by proofs, inasmuch as by most evident signs He showed that He was truly risen. Hence where our version has "by many proofs," the Greek text, instead of proof has tekmerion, i.e. "an evident sign affording positive proof" [Cf. Prior. Anal. ii]. Now Christ showed these signs of the Resurrection to His disciples, for two reasons. First, because their hearts were not disposed so as to accept readily the faith in the Resurrection. Hence He says Himself (Luke 24:25): "O foolish and slow of heart to believe": and (Mark 16:14): "He upbraided them with their incredulity and hardness of heart." Secondly, that their testimony might be rendered more efficacious through the signs shown them, according to 1 John 1:1-3: "That which we have seen, and have heard, and our hands have handled... we declare."
Reply to Objection 1. Ambrose is speaking there of proofs drawn from human reason, which are useless for demonstrating things of faith, as was shown above.
Reply to Objection 2. The merit of faith arises from this, that at God's bidding man believes what he does not see. Accordingly, only that reason debars merit of faith which enables one to see by knowledge what is proposed for belief: and this is demonstrative argument. But Christ did not make use of any such argument for demonstrating His Resurrection.
Reply to Objection 3. As stated already (ad 2), the merit of beatitude, which comes of faith, is not entirely excluded except a man refuse to believe only such things as he can see. But for a man to believe from visible signs the things he does not see, does not entirely deprive him of faith nor of the merit of faith: just as Thomas, to whom it was said (John 20:29): "'Because thou hast seen Me, Thomas, thou hast believed,' saw one thing and believed another" [Gregory, Hom. xxvi]: the wounds were what he saw, God was the object of His belief. But his is the more perfect faith who does not require such helps for belief. Hence, to put to shame the faith of some men, our Lord said (John 4:48): "Unless you see signs and wonders, you believe not." From this one can learn how they who are so ready to believe God, even without beholding signs, are blessed in comparison with them who do not believe except they see the like.
Source: Summa Theologica (New Advent)