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This was written a few years after the First Vatican Council declared papal infallibility. It has the imprimatur and 2 theologians recommended this book for it's accuracy.

Familiar Explanation of Christian Doctrine
by Rev. Michael Müller, C.SS.R.
Adapted for the Family and More Advanced Students in Catholic Schools and Colleges. with the Approbation of the Sacred Congregation for the Propagation of the Faith

No. III.
Benziger Brothers: New York, 1876 Printers to the Holy Apostolic See

Nihil Obstat:
Joseph Helmpraecht, C.SS.R.
Baltimore, MD., 24 Sept., 1874

Imprimatur:
J. Roosevelt Bayley
Archiep. Baltimorensis
Baltimore, 24 Sept., 1874

copyright. M. Muller. 1876

Lesson IV.—Infallibility of the Pope
Q. Did our Blessed Saviour foresee that certain men would corrupt or misinterpret His holy Doctrine?
A. He did.

Q. When certain men either corrupted or misinterpreted Christ's holy Doctrine, what was necessary to remove all doubts about its true meaning, and preserve it always pure and uncorrupted?
A. That there should be one particularly priviledged by God to set forth and state plainly with divine certainty the true meaning of Christ's doctrine in all questions where His doctrine was concerned.

Q. What do we call such a priviledged person?
A. The supreme judge in all points of divine law, from whose sentences there is no appeal.

Q. Why is such a judge necessary?
A. To put an end to all disputes about points of divine law.

Q. How so?
A. If every man in the country were to take the laws of the State, and to explain them as he pleased, there would be nothing but confusion and disorder in society. In like manner, if every man were to take the sacred, eternal law of God, the doctrine of Jesus Christ, and to interpret it as he pleased, there would be nothing but confusion in religion.

Q. What safeguard has human wisdom adopted to prevent confusion and disorder in society?
A. It has found it necessary to appoint a supreme judge to decide ultimately in all disputed points of civil law.

Q. What is the plain inference from this?
A. That if even human wisdom sees the necessity of appointing a supreme judge to decide ultimately in all points of civil law, it cannot be supposed that God, who is InfiniteWisdom, should neglect to appoint a supreme judge to decide ultimately in all points of divine law, in order thus to prevent all confusion in religion.

Q. What safeguard has human wisdom adopted to prevent confusion and disorder in society?
A. It has found it necessary to appoint a supreme judge to decide ultimately in all disputed points of civil law.

Q. What is the plain inference from this?
A. That if even human wisdom sees the necessity of appointing a supreme judge to decide ultimately in all points of civil law, it cannot be supposed that God, who is Infinite Wisdom, should neglect to appoint a supreme judge to decide ultimately in all points of divine law, in order thus to prevent all confusion in religion.

Q. Was there ever a time when men were left to themselves, to fashion their own religion, to invent their own creed, their own form of worship, and to decide in matters of religion?
A. No; there always existed on earth a visible teaching authority, to which it was a bounden duty of every man to submit.

Q. Whom did God appoint to be this visible teaching authority before the coming of the Redeemer?
A. During the four thousand years that elapsed before the coming of the Redeemer, the doctrines that were to be believed, the feasts that were to be observed, the sacrifices, the ceremonies of worship, everything was regulated by the living, authoritative voice of the patriarchs, the priests, and the prophets.

Q. How do we know that God in the Old Law appointed a tribunal, presided over by the High-Priest, to judge in all controversies, both of doctrine and morals, and from whose decision there was no appeal?
A. The Jєωιѕн historian, Josephus, who was well aquainted with the laws and religion of his own nation, says: "The High-Priest offers sacrifice to God before the other priests; he guards the laws, judges controversies, punishes the guilty, and whoever disobeys him is punished as one that is impious towards God." Lib. 2, Contra Appium.

Q. Is there still a greater authority than Josephus bearing witness to the fact?
A. Yes; the Word of God itself bears witness to the fact. "If thou perceive," says holy Scripture, "that there be among you a hard and doubtful matter in judgment between blood and blood, cause and cause, and thou seest that the words of the judges within the gates do vary, arise and go up to the place which the Lord thy God shall choose. And thou shalt come to the priests, and to the judge that shall be at that time, and thou shalt ask them, and they shall show thee the truth of the judgment. And thou shalt do whatsoever they shall say, and thou shalt follow their sentence. Neither shalt thou decline to the right hand nor to the left hand. Nut he that will be proud and refuse to obey the commandments of the priest, who ministereth at the time to the Lord thy God, and to the decree of the judge, that man shall die, and thou shalt take away the evil from Israel." Deut. xvii. 8-12.

Q. What do we see from this?
A. Here we see clearly a tribunal appointed by Almighty God Himself to decide in the last resort; a tribunal from whose sentence there is no appeal. There is no exception, the rule is for all, the terrible sentence is pronounced against every transgressor. Whosoever shall refuse to abide by the decision of the High-Priest shall die the death.

Q. How long did this tribunal remain intact?
A. Until the coming of the Saviour
.
Q. Who assures us of this?
A. Our Blessed Redeemer Himself, in these words: "The Scribes and Pharisees have sat in the chair of Moses. All things therefore whatsoever they shall say to you, observe and do." Matt. xxiii. 2.

Q. Now, did our Lord Jesus Christ establish a supreme tribunal; did He give to the world and infallible judge and teacher, to decide ultimately in all controversies, both of faith and morals, whose decision is final, and without appeal?
A. Our Blessed Saviour came not to destroy the Law, but to make it perfect. He therefore established in the New Law that which the Old Law was most necessary for the preservation of faith and morals. He gave to the whole world an infallible judge and teacher, to decide ultimately in all points of faith and morals.

Q. Whom did Jesus Christ appoint as the infallible judge and teacher in all points of faith and morals?
A. St. Peter, the Head of His Church.

Q. Were not all the successors of the Apostles to possess the gift of infallibility?
A. No; the successor of St. Peter, the Pope of Rome, only.

Q. How do we know that the successors of the other Apostles, the Catholic Bishops, were not endowed with the gift of infallibility?
A. Because Jesus Christ never promised it to them.

Q. How do we know that Jesus Christ never promised it to them?
A. Because no such promise is recorded either in Holy Scripture or tradition.

Q. Why did Christ not promise to the Bishops the gift of infallibility?
A. Because He does not multiply and dispense His gifts without necessity.

Q. Was not the gift of infallibility necessary to the Bishops?
A. By no means.

Q. Why not?
A. Because after the Apostles had preached the full doctrine of Christ, their successors had only to guard this doctrine, and deliver it uncorrupted to the faithful.

Q. What does the Apostle St. Paul write to the Bishop St. Timothy on this subject?
A. "Keep that which is committed to thy trust, avoiding the profane novelties of words, and oppositions of knowledge falsely so called." (1 Tim. vi. 20, and 2 Tim. i. 14.) "But evil men and seducers shall grow worse and worse, erring and driving into error. But continue thou in those things which thou hast learned, and which have been committed to thee." 2 Tim. iii. 13.

Q. But did not Christ promise the Apostles and their successors: "The Holy Ghost, the Spirit of Truth, shall be in you, and abide with you forever"? John xiv. 16.
A. He did so promise.

Q. If, then, according to this promise, the Spirit of Truth shall abide forever with the successors of the Apostles, are they not personally infallible?
A. By no means.

Q. Why not?
A. The Spirit of Truth may abide in a person, and yet that person may not be infallible. The Spirit of Truth may abide in a multitude, and yet not each individual of the multitude may possess it in its entirety.

Q. Give an example.
A. A million men may not know the road to a certain city to which they must go. A single guide suffices to set this million on the right road. Once on it, they have only to follow their guide and they cannot go astray. Once the way is pointed out, all know it to be right, but only one could point out the right road to be followed.

Q. Do you mean that Christ wished that in this same manner the Spirit of Truth should abide with the Catholic Bishops?
A. Precisely so; for Christ gave them and all the faithful, in the person of the Head of His Church, an infallible teacher of all the truths which He and His Apostles taught. By invariably following this teacher the Spirit of Truth will always abide with them.

Q. How do we know that the Pope as successor to St. Peter possesses the gift of infallibility?
A. Christ Himself assured St. Peter and his successors of this.

Q. On what occasion?
A. When He told St. Peter that by His prayer to His heavenly Father He had obtained this gift of infallibility for him and all his successors. "I have prayed for thee (Peter) that thy faith fail not, and thou being once converted, confirm thy brethren." Luke xxii. 31, 32.

Q. Why did Christ pray to His Father that St. Peter and his successors should be endowed with the gift of infallibility?
A. Because Christ wished that the never-failing faith of St. Peter and his successors should be forever the foundation-stone of His Church.

Q. On what occasion did Christ assure us of this?
A. When He asked the Apostles: "Whom do you say that I am?" Matt. xvi. 15.

Q.Which of the Apostles made answer to this question?
A. St. Peter.

Q. What was his answer?
A. "Thou art Christ, the Son of the living God."

Q. What answer did Christ make to this reply of St. Peter?
A. He said: "Blessed art thou, Simon Bar Jona: because flesh and blood hath not revealed it to thee, but my Father who is in heaven. And I say to thee: that thou art Peter, and upon this rock I will build my Church."

Q. What is the meaning of these words of our Lord?
A. Jesus Christ means to say that, as it is My Father who has made known to you, Peter, that I am His Son, I also make known to the whole world, that you and your successors will always know and understand who I am, and what I have taught.

Q. When did Christ build His Church upon Peter, that is, intrust him with the whole flock?
A. When He said to him: "Feed my lambs, feed my sheep." John xxi. 16.

Q. What is the meaning of this?
A. Christ says that His whole flock, teachers and hearers, priests and people, rulers and subjects, must believe and teach as Peter and his successors believe and teach.

Q. Why?
A. Because his faith, according to Christ's solemn words, shall not fail, since no power shall prevail against Peter or any of his successors so as to cause them to teach anything else than what Christ has taught. "The gates of hell shall not prevail against my Church," built upon Peter's faith. Matt. xvi. 18.

Q. What follows from this?
A. That where Peter, that is, the Pope, is, there is the Church of Christ, or in other words, that all those who believe and teach as the Pope does, form the true Church of Christ. St. Ambrose.

Q. Who, by his own motion, often condemned heresies, both before and after the first general council?
A. The Pope.

Q. To whom did the Catholic Bishops always have recourse in all controversies both of faith and morals?
A. To the Pope.

Q. If the obstinacy of the party condemned by the Pope made it advisable to have recourse to general councils, were these councils, then, after the most mature deliberation, ever found to do anything else than to confirm the sentence already passed by the Pope?
A. They were not. (See Q. and A. in Additional Questions and Answers)

Q. Did any Pope ever issue any decree concerning the truths of the faith or sound morality, which was not afterwards received by the great body of the Bishops, as containing the most solid and wholesome doctrine?
A. Such a thing never happened.

Q. Could the greatest enemies of the Catholic faith ever prove that any Pope taught any doctrine contrary to the sacred truths taught by Jesus Christ and His Apostles?
A. Never. (See Q. and A. in Additional Questions and Answers)

Q. What are we to understand from all this?
A. That it has always been the belief of the Catholic Church that the Pope, in his solemn decisions in matters of faith and morals, is infallible.

Q. If this be true, how then could it happen that some years ago a few Bishops and Priests were said not to have held this to be a doctrine of Catholic faith?
A. Because the divine tradition of this doctrine had not been as yet explicitly defined by the Holy Father.

Q. Did those Bishops, assembled in the Council of the Vatican, continue to oppose the dogma of the infallibility of the Pope, after it was defined?
A. No. All, without exception, freely and joyfully subscribed their names to the decrees of the council, and professed their faith in the infallibility of the Pope.

Q. If, then, in a general council, or assembly of all the Catholic Bishops, the meaning of a certain doctrine of Christ was to be set forth in precise language, and the majority of Bishops would explain it in one sense, and the minority in another, on which side would be the truth?
A. On that side, though it be the minority of Bishops, which agrees with the Pope.

Q. Why?
A. Simply because Christ bound Himself solemnly only to Peter and his successors that their faith should never fail; that is, that every one of them would always be so enlightened by the Holy Ghost as to understand the true meaning of His doctrine, and state and teach it plainly with divine certainty. "Where Peter is, there is the Church."

Q. Must we, then, believe that such decisions of the Pope in matters of faith and morals are infallibly true?
A. Yes; because this is an article of faith, which we must believe, as firmly as we believe that there is a God.

Q. If anyone should say, or even think otherwise, what would he be before God?
A. An apostate from the faith.

Q. Does the Pope then teach anything new, when in such misinterpretations of Christ's doctrine he declares what is to be believed?
A. No; he plainly states the truth in the sense in which Jesus Christ and the Apostles preached it.

Q. Can you now tell me whose office it is to guard the doctrine of Christ, as preached by the Apostles, and proclaim and apply it always and everywhere, one and the same, and to defend the rights of God on earth against every enemy, at all times, and in all places?
A. This is the Pope's office.

Q. Who is appointed by God Himself to declare and apply the invariable doctrine of Jesus Christ, and to govern all men and nations, kings and peoples, according to this invariable doctrine?
A. The Pope.

Q. Must the Pope as guardian and judge of the law of God, resist with all his might every passion or tendency of every age, nation, community, or individual, whenever it leaves the law of God?
A. He is bound in conscience to do so.

Q. When does the Pope speak "ex Cathedra," or infallibly?
A. He speaks infallibly whenever in the discharge of his office of pastor and teacher of all Christians, he defines (that is, finally determines), according to his supreme apostolic authority, a doctrine concerning faith or morals, to be held by the Universal Church, or anything else that is conducive to the preservation of faith and morals.

Q.When the Pope, in accordance with the duty of his apostolic ministry and his supreme apostolic authority, proceeds, in briefs, encyclical letters, consistorial allocutions, and other apostolic letters, to declare certain truths, to reprobate perverse doctrines, and condemn certain errors, must such declarations of truth, and condemnations of error, be considered as infallible, and as binding in conscience, and requiring our firm interior assent, although they do not express an anathema on those who disagree?
A. Such declarations of truth and condemnations of error are infallible, or ex cathedra acts of the Pope, and, therefore are binding in conscience, and requiring our firm interior assent; to refuse which would be for us a mortal sin, since such a refusal would be a virtual denial of the dogma of infallibility, and we should be heretics were we conscious of such a denial. St. Alphonsus Liguori. Theol. Mor., Lib I., 104.

Q. Are not such doctrinal utterances of the Pontiff of imperfect and incomplete authority until they are confirmed and accepted by the Bishops of the Church?
A. Nothing is ever farther from the thoughts of the bishops than that the papal declarations of truth, and condemnations of error, should need the confirmation and acceptance of the pastors of the Church to be true utterances of the Holy Ghost, and binding in conscience, because their confirmation and acceptance does not add certainty to that which is already infallible.

Q. What does the Vatican Council teach on this subject?
A. It teaches that "the definitions of the Roman Pontiff, concerning faith and morals, are irreformable of themselves, and not by force of the consent of the Church thereto." Sess. iv., c. iv.

Q. What have the Fathers of the Church styled the Pope?
A. The mouth of the Church, ever living and open to teach the whole world;
The centre of Christian faith and unity, and the light of truth for the universe;
The Father of souls, the guide of consciences, and the sovereign judge of the religious interests of mankind; The Prince of priests—a greater Patriarch than Abraham—greater than Melchisedech in priesthood—than Moses in authority—than Samuel in jurisdiction; a Peter in power, Christ by unction, pastor of pastors, guide of guides, the cardinal joint of all churches, the impregnable citadel of the communion of the children of God, the immovable corner-stone upon which the Church of God reposes.

Q. Why have the Fathers given these titles to the Pope?
A. Because the Pope is the infallible teacher of the Church of Christ.

Q. What sentiments, then, should every Catholic express concerning the Pope?
A. I acknowledge in the Pope an authority before which my soul bows, and yet suffers no humiliation.

Wallflower, in case you got lost sometime between when you replied to me and now (which I think is very likely) I answered your question on page forty of this thread: http://www.cathinfo.com/catholic.php?a=topic&t=31535&min=195&num=5

I would also like to add (since it's too late) a relevant quote from McHugh and Callan on moral certainty, and it's much too late to edit my reply:

Quote from: Moral Theology A Complete Course Based on St. Thomas Aquinas and the Best Modern Authorities

 

643. Kinds of Certitude.--Judgments may be certain in a greater or less
degree.

(a) They are metaphysically certain, when error is absolutely
impossible, the opposite of what is held by the mind being a
contradiction in terms which omnipotence itself could not make true.
Example: The judgments that the same, identical act cannot be both good
and bad, that good is to be done and evil to be avoided, that God is to
be honored, are metaphysically certain, since they result immediately
from the very concepts of being, of goodness, and of God.

(b) Judgments are physically certain, when error is impossible
according to the laws of nature, the opposite of what is held by the
mind being unrealizable except through intervention of another cause.
Example: The judgments that he who takes poison will destroy life, that
he who applies fire to a house will destroy property, are physically
certain. because natural agencies, like poison and fire, act infallibly
when applied to suitable matters and under suitable conditions and left
to their course, unless they are overruled by superior power.

(c) Judgments are morally certain, when error is impossible according
to what is customary among mankind, the opposite of what is held by the
mind being so unlikely that it would be imprudent to be moved by it.
Examples: One is morally certain that what a reputedly truthful and
competent person relates to one is true. A person is morally certain
that a conclusion he has drawn about his duty in a particular instance
is correct, if he believes that he has overlooked no means of reaching
the truth. Testimony and inference, since they come from free and
fallible agencies, may lead into error; but, when they appear to have
the requisite qualities indicative of truth, they are for the most part
reliable and in practical life have to be considered as such.

...

644. As to the certainty that is required in the judgment of
conscience, the following points must be noted:

(a) Metaphysical certainty is not required, since conscience does not
deal with primary propositions, but with deductions about particular
acts. The first moral principles, which are the object of synderesis,
and at least some of the general conclusions, which are the object of
moral science, are metaphysically certain (see above 145, 300), as they
are based on necessary relations; but the particular conclusions, which
are the object of conscience, are concerned with the contingent and the
individual.

(b) Physical certainty is not required for the judgment of conscience,
since conscience is not concerned with the activities of natural
agents, but with the activities of moral agents that act with freedom
and responsibility.

(c) Moral certitude, therefore, is sufficient for the conclusions drawn
by conscience. That a higher kind of certitude is not necessary should
not surprise us, for it would be unreasonable to expect that the same
degree of assent be given to judgments that are concerned with
particular and contingent cases as to those that are concerned with
universal and necessary principles.

...

646. Moral certitude in the wide sense is sufficient for a safe
conscience, even in matters of great importance, since it is frequently
the only kind of certitude one can have, and he who would strive to be
free from every slight and baseless suspicion would be soon involved in
a maze of scruples and perplexities.

Source: McHugh and Callan