Firstly, Catholics are not supposed to ask if something is infallible in order to determine if they will accept it. We are required to submit to all that the Church teaches, whether this be an infallibly defined dogma, or an act of the ordinary magisterium. Pope Pius XII discusses this point in Humani Generis.
The question is, since Vatican II defined no dogmas, and was therefore only infallible when it repeated what the Church has already defined (or at lest what the Church had always taught), is it theoretically possible that it taught error by deviating from what the Church has always taught? Is it possible that it taught, for example, what the Syllabus and a string of Popes formally condemned? Is it possible that God would permit such a thing for good and just reasons (such as for a punishment for sins). And lastly, is it possible that these erroneous points be stricken from the council at some point?
What no one can deny about Vatican II is that it has produce rotten fruits from the very beginning. If it does not in fact teach formally condemned errors, just about everyone who reads it concludes that it does; that is to say, just about everyone who reads Vatican II ends by believing what the Church has formally condemned.
And it is not just the laity who “interpret” it this way. The very Bishops who drew up the documents and who voted on them interpret them as teaching what was formally condemned.
And what’s more, after the council these same Bishops and peritus admitted that Vatican II taught what the Syllabus formally condemned. But for them it was not a problem since Liberals and Modernists believe in “evolution of doctrine” - another formally condemned error. They mistakenly believe, not only that dogmas should be reformulated in an “updated” manner, but that formally condemned errors can suddenly become true and good. Due to the destructive “intellectual cancer” of modernism, the have no problem in adhering to formally condemned error!
These same men went so far as to say that Vatican II was the French Revolution in the Church, as if this was a good thing! The French Revolution was a Masonic Revolution against the Church. It was the French Revolution that brought the separation of Church and state, or the “agnosticizing” of the State. It brought about a “new world order” in that it was a new ordering of the world. No longer was the State to be subordinate to the Church, and to reflect the laws of God as had always been taught, but rather completely separated from it. The “altar and throne” were desroyed and replaced with the illusion of “the will of the people”. The Christian state became the agnostic state, with all of its ill effects. The Syllabus was a formal condemnation of many of the error that came from the French Revolution.
Yet Cardinal Ratzinger himself taught that Vatican II was a “counter-syllabus”, in that it taught as true and good what the Syllabus condemned. He said it was a reconciliation between the Church and the “new world order” brought about by the French Revolution.
Cardinal Ratzinger:** "If one is looking for a global diagnosis of the text [of Gaudium et spes], one could say that it (along with the texts on religious liberty and world religions) is a revision of the Syllabus of Pius IX, a kind of counter-Syllabus **…
[F]irst in central Europe, conditioned by the situation, the unilateral dependence on the positions taken by the Church through** the initiatives of Pius IX and Pius X against the new period of History opened by the French Revolution was to a large extent corrected** via facti. But a fundamental new document regarding relations with the world as it had been since 1789 [the time of the Masonic French Revolution] was still lacking.
In reality, the mentality that preceded the revolution still reigned in the countries with strong Catholic majorities [thankfully]; today almost no one denies that the Spanish and Italian concordats [accords between Church and State] tried to conserve too many things from a conception of the world that for a long time had not corresponded to reality. Likewise, almost no one can deny that this dependence on an obsolete conception of relations between the Church and State was matched by similar anachronisms in the domain of education and the attitude taken toward the modern historical-critical method …
Let us content ourselves here with stating that the text [of Gaudium et spes] plays the role of a counter-Syllabus to the measure that it represents an attempt to officially reconcile the Church with the world as it had become after 1789. On one hand, this visualization alone clarifies the ghetto complex that we mentioned before. On the other hand, it permits us to understand the meaning of this new relationship between the Church and the Modern World. “World” is understood here, at depth, as the spirit of modern times. …
(Les Principes de la Theologie Catholique - Esquisse et Materiaux, Paris: Tequi, 1982, pp. 426-427).
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