Purgatory

Defined as "The place and state in which souls suffer for a while and are purged after death, before they go to Heaven, on account of their sins. Venial sins, which have never in life been remitted by an act of repentance or love or by good deeds, and grave sins, the guilt of which with its eternal punishment has indeed been removed by God after an act of repentance but for which there is still left a debt of temporal punishment due ot his justice on account of the imperfection of that repentance, must be purged away after death by the pain of intense longing for God, whose blissful vision is delayed, and also, as is commonly taught, by some pain of sense inflicted probably by material fire." (Definition from A Catholic Dictionary, 1951)
 

References in Scripture:

• And making a gathering, he twelve thousand drachms of silver to Jerusalem for sacrifice to be offered for the sins of the dead, thinking well and religiously concerning the resurrection, And because he considered that the who had fallen asleep with godliness, had great grace laid up for them. It is therefore a holy and wholesome thought to pray for the dead, that they may be loosed from sins. 2 Machabees 12:43,45,46
• "Every man's work shall be manifest; for the day of the Lord shall declare it, because it shall be revealed in fire; and the fire shall try every man's work, of what sort it is. If any man's work abide, which he hath built thereupon, he shall receive a reward. If any man's work burn, he shall suffer loss; but he himself shall be saved, yet so as by fire." 1 Corinthians 3:13-15
• "But I say unto you, that every idle word that men shall speak, they shall render an account for it in the day of judgment." Matthew 12:36
   

Church Teaching:

• "Even as in the same fire gold glistens and straw smokes, so in the same fire the sinner burns and the elect is cleansed." Pope St. Gregory I, 6th century, quoted from St. Augustine (De Civ. Dei i, 8)
• "If they have died repentant for their sins and having love of God, but have not made satisfaction for things they have done or omitted by fruits worthy of penance, then their souls, after death, are cleansed by the punishment of Purgatory; also . . . the suffrages of the faithful still living are efficacious in bringing them relief from such punishment, namely the Sacrifice of the Mass, prayers and almsgiving and other works of piety which, in accordance with the designation of the Church, are customarily offered by the faithful for each other." Council of Florence (1438-1443)
• "Among them is also the fire of purgatory, in which the souls of just men are cleansed by a temporary punishment, in order to be admitted into their eternal country, into which nothing defiled entereth. The truth of this doctrine, founded, as holy Councils declare,' on Scripture, and confirmed by Apostolic tradition, demands exposition from the pastor, all the more diligent and frequent, because we live in times when men endure not sound doctrine." Catechism of Council of Trent, The Creed - Article V, Different Abodes Called Hell
• "Prayers for the dead, that they may be liberated from the fire of purgatory, are derived from Apostolic teaching" Catechism of Council of Trent, Prayer
• "We also beg of God that we be not cut off by a sudden death; that we provoke not His anger against us; that we be not condemned to suffer the punishments reserved for the wicked; that we be not sentenced to endure the fire of purgatory, from which we piously and devoutly implore that others may be liberated." Catechism of Council of Trent, The Lord's Prayer, Seventh Petition
• "I answer that, From the conclusions we have drawn above (III, 86, 4-5; Supplement, 12, 1) it is sufficiently clear that there is a Purgatory after this life. For if the debt of punishment is not paid in full after the stain of sin has been washed away by contrition, nor again are venial sins always removed when mortal sins are remitted, and if justice demands that sin be set in order by due punishment, it follows that one who after contrition for his fault and after being absolved, dies before making due satisfaction, is punished after this life. Wherefore those who deny Purgatory speak against the justice of God: for which reason such a statement is erroneous and contrary to faith. Hence Gregory of Nyssa, after the words quoted above, adds: "This we preach, holding to the teaching of truth, and this is our belief; this the universal Church holds, by praying for the dead that they may be loosed from sins." This cannot be understood except as referring to Purgatory: and whosoever resists the authority of the Church, incurs the note of heresy." Summa Theologica, St. Thomas Aquinas, Is There a Purgatory After This Life?
• "The faithful must be fully aware that sin and its eternal punishment are remitted by the Sacrament of Penance if one makes proper use of it; however the entire temporal punishment is very seldom taken away. This must be removed either by satisfactory works in this life or by the fire of Purgatory after death. The holy Council of Trent in session 6, chap. 4, and canon 30 of the same session teaches this under the heading de Justificatione."
  Encyclical of Pope Benedict XIV in Preparation for the Holy Year, 1749
• "Therefore, since it is certain by the doctrine of the Catholic Church, that the souls detained in purgatory are benefited by the prayers of the faithful, and especially by the august Sacrifice of the Altar, We think we can give them no more useful and desirable pledge of Our love than by everywhere increasing the offering of the pure oblation of the Most Holy Sacrifice of Our Divine Mediator, for the extinction of their pain.......As to the faithful, We strenuously exhort them after Sacramental confession devoutly to partake of the Bread of Angels for the benefit of the souls in purgatory" Encyclical On His Sacerdotal Jubilee by Pope Leo XIII, 1888
• "You must also discuss carefully how much efficacy there is in indulgences; how great is the fruit of remission, not only of the canonical but also of the temporal punishment due for sins; and finally, how much aid from the treasure of merits from Christ and the saints may be applied to those who died truly penitent before they had made adequate satisfaction for their sins. Their souls must be purified in the fires of purgatory so that entry into the eternal fatherland may open to them" Encyclical On Proclaiming a Universal Jubilee by Pope Leo XII, 1824
• "Moreover they should fast once within the same period and give some alms to the poor. This indulgence can also be applied to the souls in purgatory." Encyclical on Urging Prayers for Peace by Pope Pius IX, 1854
• "Finally, she extends to the souls in purgatory, who implore her intercession and her prayers, the helping hand which may lead them happily at last to eternal blessedness in heaven." Encyclical on the Sacred Liturgy by Pope Pius XII, 1947
   

Summary

It is clear that Scripture speaks of Purgatory, and it is a dogma of the Catholic Church that Purgatory exists. One cannot call themselves Catholic who deny it.