Wednesday, December 7, 2011

Testing the soundness of an argument

Formal propositional logic can make your head hurt. It’s higher mathematics applied to language use, and many people are scared of higher mathematics of any kind. In running through every inference, it often has the appearance of belaboring the obvious. Not only is it accessible only to the trained, because of that limited accessibility it’s off-putting to the untrained, as if though the subject in question belonged only to specialists and therefore the unwashed masses mustn’t even hope to participate.

Why go through such a megillah, then?

The rigor. It belabors the obvious precisely because it doesn’t take the “obvious” for granted; not everything that’s obvious to you and me is obvious to everyone else. By forcing the reader through the supposedly unnecessary steps, it demonstrates irrefutably the internal consistency of an argument. Informal logic tests the soundness of an argument by walking the floors and pounding the walls; formal logic supervises the welding of the steel beams and the pouring of the reinforced concrete.

Over on The Impractical Catholic I posted a formal argument demonstrating the infallible reliability of the Church. Reliability, after all, is the crux of the infallibility question: Can the Church be trusted not only to teach the evangelium correctly but also to teach dogmatic propositions that aren’t explicit or obviously implicit in Scripture?


The argument as posted there is relatively simple even in its extended form because the heart of the question — the guidance of the Holy Spirit — is relatively simple. Nevertheless, in reconsidering it, it appears I took some things for granted that a truly rigorous argument wouldn’t … opening it up to objections. *sigh*

Objection: The Holy Spirit may guide the Church, but that doesn’t mean the Church follows the Holy Spirit.

Answer: Nonsense. To follow is to suffer to be guided or led. A leads B if and only if B follows A. A guides B if and only if B is guided by A. The logical relationship is not only implied, it’s baked in — lead and follow are antonyms of each other. Therefore, “The Church follows the Holy Spirit” is tautologous to “The Holy Spirit leads/guides the Church”.

Objection: The Holy Spirit may have guided the Church in the beginning (Ac 2:1-4), but Scripture tells us that people would eventually abandon sound doctrine (1 Tim 4:1-4; 2 Tim 4:3-4). Does it not follow that the Church abandoned sound doctrine?

Answer: No. It merely follows that people apostatized from the True Faith as individuals; we can’t logically infer from that that the Church itself as a corporate whole or in its institutional aspect stopped following the Holy Spirit. Informally, the objection constitutes a composition fallacy; the parts do not distribute to the whole. Put formally, the objection proposes that if some of the people have abandoned sound doctrine, then the whole Church has abandoned sound doctrine. The Church’s doctrine is sound only if the Holy Spirit is guided by the Church; if the Church has abandoned sound doctrine, then the Holy Spirit stopped guiding the Church.

Scripture tells us that God is faithful (2 Tim 2:13), and that Jesus as God the Son (“I and the Father are one” [Jn 10:30]) promised to be with his Church’s leaders “until the end of the age [world]” (Mt 28:20). If the Holy Spirit left the Church at any time prior to Jesus’ return (the end of the age), then it would follow that: 1) Jesus has abandoned his Church, and 2) God has reneged on the promise made in his name and with his authority by Jesus. Therefore, if God is faithful, and Jesus is with us until the end of the age, then (since the Holy Spirit leads only if the Church follows) the Holy Spirit still guides the Church today: “My sheep hear my voice, and I know them, and they follow me; and I give them eternal life, and they shall never perish, and no one shall snatch them out of my hand. My Father, who has given them to me, is greater than all, and no one is able to snatch them out of the Father's hand” (Jn 10:27-29). Therefore, the Church has not abandoned sound doctrine, which falsifies the objection; some of the people can abandon sound doctrine and the Church as a whole still maintain sound doctrine.

Objection: The Catholic Church of today is not the Church of Scripture, but rather the creation of heretics who came into the Church after the Edict of Milan in 313.

Answer: Strictly speaking, this is an historical objection which doesn’t pertain to the logic of the Scriptural argument; in fact, it almost tacitly grants the logic. However, there’s no empirical evidence to support such a charge: wishing doesn’t make it so. The Christian Church has been known as “Catholic” (Gr. katholikos = “universal”) since before 110 AD (Ignatius of Antioch, Letter to the Smyrnaeans 8); none of the Protestant communions can trace their lineage back to the first Christians except through the medium of the Catholic Church. But more to the point, to say that the “Christian” Church was hijacked by post-Milan “Catholics” is still to say that the Church stopped following the Holy Spirit, which by our two previous answers we know could not have happened given the reliability of Scriptures (“Scripture cannot be broken” [Jn 10:35]).

Objection: The Catholic Church’s interpretation of Scripture cannot be relied on because there are obvious contradictions between the literal word and the Church’s teachings. Therefore the Church cannot be guided by the Holy Spirit.

Answer: The apparent contradictions created by the Church’s interpretation of Scripture through its tradition are true contradictions only if the objector’s interpretation of Scripture is reliable: the objector’s interpretation is reliable only if the promise of guidance is given to non-leaders of the Church. But the promise, which was given in the context of the Last Supper, was not given to all Christ’s followers but only to the apostles. Since the promise is not extensible by implication to non-leaders, the reliability of the objector cannot be inferred, and therefore the apparent contradictions cannot be inferred to be true contradictions.

The objection posits, “If the apparent contradictions are true contradictions, then the Church’s interpretation is not reliable; if the Church’s interpretation is not reliable, then the Church is not guided by the Holy Spirit”. Assuming the argument is true, then we have a case where Scripture makes a promise that the conclusion contradicts. Not only does this falsify the argument, this bolsters the reliability of the Church by reinforcing the reliability of its interpretation. This has given us a second direction from which to deny the non-leader’s reliability, weakening his position further than if he’d never made the argument.

So what have we learned today?

Obviously, the formal proof still needs work to be impeccable. First, to fend off the objections we have to anticipate the “HS no longer guides Church” proposition by demonstrating that, if the Holy Spirit’s guidance stopped working at any point between AD 30 and  AD 2011, then God’s faithfulness would be impeached and Scripture broken. Second, by incorporating the latter three objections into the framework of the argument, then we can infer from the reliability of the Holy Spirit not only the reliability of Church leadership but also the reliability of her doctrines and Scriptural interpretation.

However, at its heart, the engine of the argument is the disjunction created by asserting that the Church’s leadership is not reliable: at some point, you contradict Scripture. If “Scripture cannot be broken” (Jn 10:30), then sola scriptura breaks on that rock: if Scripture is reliable, then so is the Church.

Why? Because her authority is derived from the same source as Scripture: God