Is Judas liable for his betrayal sin?
Absolutely!
We could actually let Our Lord speak for himself on the subject of Judas: "The Son of Man indeed goes, as it is written of him: but woe to that man by whom the Son of Man shall be betrayed. It were better for him, if that man had not been born."
The Saints, Fathers and Doctors of the Church say unanimously that Judas is in Hell.
Because of the fall of Judas, St. Peter led the Apostles in picking his replacement, who would be St. Matthias. While conducting the election, St. Peter had foreboding things to say about the traitorous Apostle. In Acts 1:16–20, St. Peter declares:
Men, brethren, the Scripture must needs be fulfilled, which the Holy Ghost spoke before by the mouth of David concerning Judas ... he indeed hath possessed a field of the reward of iniquity ... the same field was called ... the field of blood. For it is written in the book of Psalms: Let their habitation become desolate, and let there be none to dwell therein.
Saint Peter was referring to Psalm 108:6–8: "Set thou the sinner over him: and may the devil stand at his right hand. When he is judged, may he go out condemned; and may his prayer be turned to sin. May his days be few: and his bishopric let another take."
Three famous saints addressed Judas' final disposition:
St. Augustine: "For Judas, when he killed himself, killed a wicked man, and passed from this life chargeable not only with the death of Christ, but also with his own: for though he killed himself on account of his crime, his killing himself was another crime."
St. Thomas Aquinas: "In the case of Judas, the abuse of grace was the reason for his reprobation, since he was made reprobate because he died without grace."
Pope St. Leo the Great: "The godless betrayer, shutting his mind to all these things [offerings of God's Mercy], turned upon himself, not with a mind to repent, but in the madness of self-destruction; so that this man who had sold the Author of Life to the executioners of His death, even in the act of dying sinned unto the increase of his own eternal punishment."
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Erasmus believed that Judas was free to change his intention, but Martin Luther argued in rebuttal that Judas' will was immutable. John Calvin states that Judas was predestined to damnation, but writes on the question of Judas' guilt: "surely in Judas' betrayal, it will be no more right, because God himself willed that his son be delivered up and delivered him up to death, to ascribe the guilt of the crime to God than to transfer the credit for redemption to Judas." The Catholic Church has no view on his damnation. The Vatican only proclaims individuals' Eternal Salvation through the Canon of Saints. There is no 'Canon of the Damned', nor any official proclamation of the damnation of Judas, so Archbishop Vincenzo Paglia is wet behind his ears when he says: It’s heresy to say that Jesus is in Hell.