The Catholic Church holds the beliefs common to most churches, including the Trinity, and several that are unique to it. Each section below gives the belief in the Church's own words, its best case, the examination and, where relevant, what the Quran says.
The Trinity: the Catholic Church teaches the Trinity as the central mystery of the faith (CCC 234). Live
Divinity of Jesus, Original sin, Canon of scripture Coming next
The First Vatican Council, in Pastor Aeternus (18 July 1870), defined that when the pope speaks ex cathedra, defining "a doctrine concerning faith or morals to be held by the whole Church, he possesses ... that infallibility which the divine Redeemer willed his Church to enjoy", and that "such definitions of the Roman Pontiff are of themselves, and not by the consent of the Church, irreformable."
I also tell you that you are Peter, and on this rock I will build my assembly, and the gates of Hades will not prevail against it.Matthew 16:18, World English Bible
I will give to you the keys of the Kingdom of Heaven, and whatever you bind on earth will have been bound in heaven; and whatever you release on earth will have been released in heaven.”Matthew 16:19, World English Bible
Catholic teaching reads "this rock" as Peter himself; the New American Bible note explains that the Aramaic kepa means rock and is the name by which Paul calls Peter. The keys are read as authority passed to Peter's successors, the bishops of Rome.
Matthew 16:18 says nothing about successors, about Rome or about infallibility. Early Christian writers read "rock" in several ways: as Peter, as Peter's confession of faith in Matthew 16:16, or as Christ. The reading is disputed among Catholic, Orthodox and Protestant scholars. Elsewhere the New Testament calls Christ the only foundation (1 Corinthians 3:11) and builds the church on "the apostles and prophets" together (Ephesians 2:20). In Matthew 18:18 the same power to bind and loose is given to all the disciples.
Infallibility was defined as dogma in 1870, more than eighteen centuries after Peter. The Eastern Orthodox churches, which also trace their bishops to the apostles, have never accepted it.
For no one can lay any other foundation than that which has been laid, which is Jesus Christ.1 Corinthians 3:11, World English Bible
They have taken their scholars and monks as lords besides Allah, and [also] the Messiah, the son of Mary. And they were not commanded except to worship one God; there is no deity except Him. Exalted is He above whatever they associate with Him.Quran 9:31, Sahih International
The Quran's charge in 9:31 is that the People of the Book took their scholars and monks as lords besides God. In a report in Jami' at-Tirmidhi (3095), 'Adi ibn Hatim, a former Christian, heard the Prophet Muhammad (peace and blessings be upon him) recite this verse and explain: "As for them, they did not worship them, but when they made something lawful for them, they considered it lawful, and when they made something unlawful for them, they considered it unlawful." A definition that is "irreformable" of itself, and binding on every believer, places a human office in a position the Quran reserves for God's revelation.
Pope Pius IX defined the Immaculate Conception in Ineffabilis Deus (8 December 1854): Mary (peace be upon her), "in the first instance of her conception, by a singular grace and privilege granted by Almighty God, in view of the merits of Jesus Christ (peace be upon him) ... was preserved free from all stain of original sin."
Pope Pius XII defined the Assumption in Munificentissimus Deus (1 November 1950): "the Immaculate Mother of God, the ever Virgin Mary, having completed the course of her earthly life, was assumed body and soul into heavenly glory."
Having come in, the angel said to her, “Rejoice, you highly favored one! The Lord is with you. Blessed are you among women!”Luke 1:28, World English Bible
Catholic teaching reads "highly favored" (Latin gratia plena, "full of grace") as a sign of her unique holiness. Both dogmas are presented as developments of belief held by the faithful over many centuries, as both documents argue at length.
Neither dogma is stated in the Bible; both documents rest them on tradition and the developing belief of the Church. They were defined as binding in 1854 and 1950, 18 and 19 centuries after Mary. The Immaculate Conception was debated by major medieval theologians: Bernard of Clairvaux and Thomas Aquinas objected that a Mary free of original sin from conception would not need redemption, and Duns Scotus answered them. The history is documented; how much weight it carries is disputed.
The New Testament names brothers of Jesus (Mark 6:3; Galatians 1:19). Catholic teaching reads these as relatives or cousins to preserve Mary's perpetual virginity; that reading is disputed.
The Quran gives Mary a higher place than almost any other scripture: a whole surah carries her name, and the angels say God chose her above the women of the worlds (Quran 3:42). It also affirms the virgin birth (Quran 3:47). But it presents her as a servant of God, not one to be invoked alongside Him:
And [beware the Day] when Allah will say, "O Jesus, Son of Mary, did you say to the people, 'Take me and my mother as deities besides Allah?'" He will say, "Exalted are You! It was not for me to say that to which I have no right. If I had said it, You would have known it. You know what is within myself, and I do not know what is within Yourself. Indeed, it is You who is Knower of the unseen.Quran 5:116, Sahih International
I said not to them except what You commanded me - to worship Allah, my Lord and your Lord. And I was a witness over them as long as I was among them; but when You took me up, You were the Observer over them, and You are, over all things, Witness.Quran 5:117, Sahih International
In 5:116 to 117 Jesus disowns any call to take himself and his mother as gods besides God, and says he told people only to worship God, "my Lord and your Lord".
CCC 2132: "The Christian veneration of images is not contrary to the first commandment which proscribes idols. Indeed, 'the honor rendered to an image passes to its prototype,' and 'whoever venerates an image venerates the person portrayed in it.'" The Second Council of Nicaea (787) justified the veneration of icons of Christ, Mary (peace be upon her), the angels and the saints (CCC 2131). Catholics ask the saints to pray for them, and distinguish veneration (dulia) from the worship (latria) owed to God alone.
CCC 2130 notes that God himself ordered images in the Old Testament, such as the bronze serpent and the cherubim on the Ark:
You shall make two cherubim of hammered gold. You shall make them at the two ends of the mercy seat.Exodus 25:18, World English Bible
Catholics also argue that since the Son became visible in the Incarnation, he can be depicted, and that asking a saint to pray is like asking a friend to pray.
“You shall not make for yourselves an idol, nor any image of anything that is in the heavens above, or that is in the earth beneath, or that is in the water under the earth:Exodus 20:4, World English Bible
you shall not bow yourself down to them, nor serve them, for I, Yahweh your God, am a jealous God, visiting the iniquity of the fathers on the children, on the third and on the fourth generation of those who hate me,Exodus 20:5, World English Bible
The commandment forbids not only making images but bowing down to them. Catholic practice includes bowing before, kneeling before and kissing images and relics. The distinction between veneration and worship is real in Catholic theology, but the commandment forbids the outward act of bowing, not only an inner intent.
A note on numbering: CCC 2066 says that "the division and numbering of the Commandments have varied in the course of history". The Catholic Church follows the division of Augustine, which is also that of the Lutheran confessions; in it, the ban on images belongs to the first commandment. The Orthodox and Reformed churches follow a division worked out by the Greek Fathers, in which the ban on images is a separate second commandment. Neither numbering removes the text; Catholic Bibles print Exodus 20:4 to 5 in full.
The New Testament names one mediator between God and humanity (1 Timothy 2:5) and contains no prayer addressed to a departed saint.
For there is one God, and one mediator between God and men, the man Christ Jesus,1 Timothy 2:5, World English Bible
And they worship other than Allah that which neither harms them nor benefits them, and they say, "These are our intercessors with Allah." Say, "Do you inform Allah of something He does not know in the heavens or on the earth?" Exalted is He and high above what they associate with Him.Quran 10:18, Sahih International
Unquestionably, for Allah is the pure religion. And those who take protectors besides Him [say], "We only worship them that they may bring us nearer to Allah in position." Indeed, Allah will judge between them concerning that over which they differ. Indeed, Allah does not guide he who is a liar and [confirmed] disbeliever.Quran 39:3, Sahih International
The Quran records those who say of the beings they call on, "We only worship them that they may bring us nearer to Allah" (Quran 39:3), and answers that intercession belongs to God, to grant to whom He wills (Quran 2:255). Catholic teaching rejects the comparison, since it says saints are not worshipped; the Quran's point is that calling on anyone besides God is the act it warns against. This is disputed between the two traditions.
The Council of Trent (Session XIII, 1551), building on the Fourth Lateran Council (1215), declared that "by the consecration of the bread and of the wine, a conversion is made of the whole substance of the bread into the substance of the body of Christ our Lord, and of the whole substance of the wine into the substance of his blood; which conversion is ... suitably and properly called Transubstantiation." CCC 1378 adds that Catholics express this faith "by genuflecting or bowing deeply as a sign of adoration of the Lord", and that the Church offers the Eucharist "the cult of adoration, not only during Mass, but also outside of it".
He took bread, and when he had given thanks, he broke, and gave it to them, saying, “This is my body which is given for you. Do this in memory of me.”Luke 22:19, World English Bible
Jesus therefore said to them, “Most certainly I tell you, unless you eat the flesh of the Son of Man and drink his blood, you don’t have life in yourselves.John 6:53, World English Bible
Catholics read "This is my body" literally, and point out that in John 6 many disciples left because of the hard saying and Jesus (peace be upon him) did not soften it.
It is the spirit who gives life. The flesh profits nothing. The words that I speak to you are spirit, and are life.John 6:63, World English Bible
In the same discourse Jesus says the flesh "profits nothing" and his words "are spirit", which many interpreters read as explaining the earlier saying spiritually. Jesus spoke many metaphors ("I am the door", "I am the vine"). In Luke 22:19 he adds "Do this in memory of me". The term "transubstantiation" relies on the Aristotelian distinction of substance and accidents and was defined in 1215; Orthodox and Protestant churches read the same verses differently. The meaning is disputed among Christians.
The practical consequence is that Catholics bow to and adore what all the senses perceive as bread.
The Quran does not speak of the Eucharist directly. Its principle is that worship belongs to God alone, and that the Messiah himself was a created servant who ate food (Quran 5:75).
The Council of Trent, on 8 April 1546, listed the books of the Bible and declared anathema anyone who did not accept them "entire with all their parts". The Catholic Old Testament has 46 books, including seven (Tobit, Judith, 1 and 2 Maccabees, Wisdom, Sirach and Baruch) that are not in the Hebrew Bible, giving 73 books in all.
Catholics note that these books were in the Greek Septuagint used by many early Christians, and that regional councils at Rome (382), Hippo (393) and Carthage (397 and 419) accepted them.
The Jewish canon, which Jesus (peace be upon him) and the apostles knew, does not contain these seven books. Jerome, who translated the Latin Vulgate, described in his prologues a canon that excluded these books, though he quoted some of them elsewhere as scripture. The list was made binding for the whole Church only in 1546, during the Reformation dispute. Eastern Orthodox churches accept a larger set and Protestants a smaller one, so Christians do not agree on what their scripture contains. See the Sects site for the full comparison.
The Quran says the earlier scriptures, the Torah and the Gospel, were revealed by God, and calls itself a criterion over them (Quran 5:48). It warns of those who write a book with their own hands and say, "This is from Allah" (Quran 2:79).