The difference between Arius and the modern heretics is that Arius was actually explicit in his teaching. The modern heretics are not. They inhabit our seminaries, our monasteries, our rectories and presbyteries. They are the modernist clergy who dominate the mainstream Protestant denominations and populate the Catholic Church as well.

Many of them don’t even know they are heretics. They have been poorly catechized from the start. Their beliefs about Jesus Christ have remained fuzzy and ill-formed. They hold their beliefs in a sentimental haze in which they vaguely feel that what they believe is “Christian” but would not want to pin it down too much. This is because they have been taught that dogma is “divisive”. They deliberately keep their beliefs vague, and focus on “pastoral concerns” in order to avoid the difficult questions. They have been taught that dogma is part of an earlier age in the church and that we have matured and moved on from such nit picky sort of questions. “After all” they say with a weaselly smile, “God is bigger than our definitions isn’t he? He can’t be put into a box…”

Their real dogma is indifferentism, and if they spin theories of Christology, revelation, or morality, those all exist to justify it: that is, to justify their belief that one's salvation doesn't depend on accepting divinely revealed doctrine or receiving the sacraments. This probably sets them apart from the Arians.

St. Thomas (II-II:11:1) defines heresy: "a species of infidelity in men who, having professed the faith of Christ, corrupt its dogmas". "The right Christian faith consists in giving one's voluntary assent to Christ in all that truly belongs to His teaching. There are, therefore, two ways of deviating from Christianity: the one by refusing to believe in Christ Himself, which is the way of infidelity, common to Pagans and Jews; the other by restricting belief to certain points of Christ's doctrine selected and fashioned at pleasure, which is the way of heretics. The subject-matter of both faith and heresy is, therefore, the deposit of the faith, that is, the sum total of truths revealed in Scripture and Tradition as proposed to our belief by the Church. The believer accepts the whole deposit as proposed by the Church; the heretic accepts only such parts of it as commend themselves to his own approval. The heretical tenets may be ignorance of the true creed, erroneous judgment, imperfect apprehension and comprehension of dogmas: in none of these does the will play an appreciable part, wherefore one of the necessary conditions of sinfulness--free choice--is wanting and such heresy is merely objective, or material. On the other hand the will may freely incline the intellect to adhere to tenets declared false by the Divine teaching authority of the Church. The impelling motives are many: intellectual pride or exaggerated reliance on one's own insight; the illusions of religious zeal; the allurements of political or ecclesiastical power; the ties of material interests and personal status; and perhaps others more dishonourable. Heresy thus willed is imputable to the subject and carries with it a varying degree of guilt; it is called formal, because to the material error it adds the informative element of "freely willed".

Pertinacity, that is, obstinate adhesion to a particular tenet is required to make heresy formal. For as long as one remains willing to submit to the Church's decision he remains a Catholic Christian at heart and his wrong beliefs are only transient errors and fleeting opinions. Considering that the human intellect can assent only to truth, real or apparent, studied pertinacity — as distinct from wanton opposition — supposes a firm subjective conviction which may be sufficient to inform the conscience and create "good faith". Such firm convictions result either from circumstances over which the heretic has no control or from intellectual delinquencies in themselves more or less voluntary and imputable. A man born and nurtured in heretical surroundings may live and die without ever having a doubt as to the truth of his creed. On the other hand a born Catholic may allow himself to drift into whirls of anti-Catholic thought from which no doctrinal authority can rescue him, and where his mind becomes incrusted with convictions, or considerations sufficiently powerful to overlay his Catholic conscience. It is not for man, but for Him who searcheth the mind and heart, to sit in judgment on the guilt which attaches to an heretical conscience.