From "The Letter to the Duke of Norfolk"

So we have sprung ahead but Matt or Anna and I will still be discussing Newman on Conscience and Authority on the Son Rise Morning Show today at 7:50 a.m. Eastern Daylight Savings Time/6:50 am.. Central Daylight Savings Time. We are not wasting daylight here!

In Chapter Five of Newman's Letter to the Duke of Norfolk, he explains both God's authority and its presence in "His rational creatures" as conscience:

I say, then, that the Supreme Being is of a certain character, which, expressed in human language, we call ethical. He has the attributes of justice, truth, wisdom, sanctity, benevolence and mercy, as eternal characteristics in His nature, the very Law of His being, identical with Himself; and next, when He became Creator, He implanted this Law, which is Himself, in the intelligence of all His rational creatures. The Divine Law, then, is the rule of ethical truth, the standard of right and wrong, a sovereign, irreversible, absolute authority in the presence of men and Angels. "The eternal law," says St. Augustine, "is the Divine Reason or Will of God, commanding {247} the observance, forbidding the disturbance, of the natural order of things." "The natural law," says St. Thomas, "is an impression of the Divine Light in us, a participation of the eternal law in the rational creature." (Gousset, Theol. Moral., t. i. pp. 24, &c.) This law, as apprehended in the minds of individual men, is called "conscience;" and though it may suffer refraction in passing into the intellectual medium of each, it is not therefore so affected as to lose its character of being the Divine Law, but still has, as such, the prerogative of commanding obedience. "The Divine Law," says Cardinal Gousset, "is the supreme rule of actions; our thoughts, desires, words, acts, all that man is, is subject to the domain of the law of God; and this law is the rule of our conduct by means of our conscience. Hence it is never lawful to go against our conscience; as the fourth Lateran Council says, 'Quidquid fit contra conscientiam, ædificat ad gehennam.'"

This view of conscience, I know, is very different from that ordinarily taken of it, both by the science and literature, and by the public opinion, of this day. It is founded on the doctrine that conscience is the voice of God, whereas it is fashionable on all hands now to consider it in one way or another a creation of man. Of course, there are great and broad exceptions to this statement. It is not true of many or most religious bodies of men; especially not of their teachers and ministers. When Anglicans, Wesleyans, the various Presbyterian sects in Scotland, and other denominations among us, speak of conscience, they mean what we mean, the voice of God in the nature and heart of man, as distinct from the voice of Revelation. They speak of a principle planted within us, before we have had any training, although training and experience are necessary for its strength, growth, and due formation. They consider it a constituent element of the mind, as our perception of other ideas may be, as our powers of reasoning, as our sense of order and the beautiful, and our other intellectual endowments. They consider it, as Catholics consider it, to be the internal witness of both the existence and the law of God. They think it holds of God, and not of man, as an Angel walking on the earth would be no citizen or dependent of the Civil Power. They would not allow, any more than we do, that it could be resolved into any combination of principles in our nature, more elementary than itself; nay, though it may be called, and is, a law of the mind, they would not grant that it was nothing more; I mean, that it was not a dictate, nor conveyed the notion of responsibility, of duty, of a threat and a promise, with a vividness which discriminated it from all other constituents of our nature.

This, at least, is how I read the doctrine of Protestants as well as of Catholics. The rule and measure of duty is not utility, nor expedience, nor the happiness of the greatest number, nor State convenience, nor fitness, order, and the pulchrum. Conscience is not a long-sighted selfishness, nor a desire to be consistent with oneself; but it is a messenger from Him, who, both in nature and in grace, speaks to us behind a veil, and teaches and rules us by His representatives. Conscience is the aboriginal Vicar of Christ, a prophet in its informations, a monarch in its peremptoriness, a priest in its blessings and anathemas, and, even though the eternal priesthood throughout the Church could cease to be, in it the sacerdotal principle would remain and would have a sway.

But as Newman concedes, most people in his day would not recognize that definition of conscience at all:

When men advocate the rights of conscience, they in no sense mean the rights of the Creator, nor the duty to Him, in thought and deed, of the creature; but the right of thinking, speaking, writing, and acting, according to their judgment or their humour, without any thought of God at all. They do not even pretend to go by any moral rule, but they demand, what they think is an Englishman's prerogative, for each to be his own master in all things, and to profess what he pleases, asking no one's leave, and accounting priest or preacher, speaker or writer, unutterably impertinent, who dares to say a word against his going to perdition, if he like it, in his own way. Conscience has rights because it has duties; but in this age, with a large portion of the public, it is the very right and freedom of conscience to dispense with conscience, to ignore a Lawgiver and Judge, to be independent of unseen obligations. It becomes a licence to take up any or no religion, to take up this or that and let it go again, to go to church, to go to chapel, to boast of being above all religions and to be an impartial critic of each of them. Conscience is a stern monitor, but in this century it has been superseded by a counterfeit, which the eighteen centuries prior to it never heard of, and could not have mistaken for it, if they had. It is the right of self-will.

What Newman is describing here is what he also calls "liberalism in religion" in his Biglietto Speech when he became a Cardinal: the idea that there is no truth and therefore there is neither any way to know the truth or any obligation to submit to the truth! So when William Gladstone protested that Catholics in England would have to deny their consciences in obedience to the infallibility of the Pope as defined at the First Vatican Council, he was really saying that Catholics would have to deny their "right of self-will." Since true conscience reflects the law of God, the Pope cannot make Catholics deny their conscience thus understood because he is only, when he speaks ex cathedra on matters of faith and morals, speaking the truth:

So indeed it is; did the Pope speak against Conscience in the true sense of the word, he would commit a suicidal act. He would be cutting the ground from under his feet. His very mission is to proclaim the moral law, and to protect and strengthen that "Light which enlighteneth every man that cometh into the world." On the law of conscience and its sacredness are founded both his authority in theory and his power in fact. Whether this or that particular Pope in this bad world always kept this great truth in view in all he did, it is for history to tell. I am considering here the Papacy in its office and its duties, and in reference to those who acknowledge its claims. They are not bound by the Pope's personal character or private acts, but by his formal teaching. Thus viewing his position, we shall find that it is by the universal sense of right and wrong, the consciousness of transgression, the pangs of guilt, and the dread of retribution, as first principles deeply lodged in the hearts of men, it is thus and only thus, that he has gained his footing in the world and achieved his success. It is his claim to come from the Divine Lawgiver, in order to elicit, protect, and enforce those truths which the Lawgiver has sown in our very nature, it is this and this only that is the explanation of his length of life more than antediluvian. The championship of the Moral Law and of conscience is his raison d'être. The fact of his mission is the answer to the complaints of those who feel the insufficiency of the natural light; and the insufficiency of that light is the justification of his mission.

Newman also discusses conscience in The Grammar of Assent in the context of belief in One God in chapter five.