Claim
The conciliarist side: the church should be governed by its councils, not controlled by one single person. ⚠ This was not a sudden idea — it came from Ockham's ecclesiology and was shaped by Marsilius of Padua (1275–1342) and other clergy. Olson notes that in the age of the Renaissance conciliarism became very popular, and its ideas helped prepare the church and society of Europe for the Protestant Reformation. ⭐ Olson adds that this movement also became a forerunner of modern democratic movements and laid some of their foundations.
⭐ The source does give this side's arguments, and we fill them in here (otherwise a reader who sees only this page might think they were simply seizing power while the popes fought among themselves). Ockham held, in Olson's summary, that only the most basic elements — believers, Scripture and the sacraments — exist in the structured church, and that the traditional hierarchical system of the church has no basis in Scripture at all for giving supreme authority to one bishop. He also denied, as Olson puts it, any so-called invisible essence of the church residing in the pope and in the bishops, patriarchs and cardinals the pope appoints, and instead saw the church as the individual believers who make it up — in Olson's summary of him, the church includes the whole body of believers, that is, the Christian community, and every believer is a member of that community.
⚠ That is to say: when the conciliarists demanded that the church be governed by its councils, this was not an administrative proposal; it followed from the question who is the church? If the church is the whole body of believers, then a council that represents the whole is closer to the church itself than any one person.
⭐ And the facts of the day gave this claim its strongest support: on the papal throne, as Olson puts it, first two men and then three at the same time declared themselves the true pope. ⚠ Without some body above the pope, no one could resolve this situation — which was exactly why the council was called.
Counterclaim
The papal side: ⚠ this side made no set argument at the council — its answer was not a speech but an act (see the decision and aftermath fields). We do not write arguments for it.
⚠ But this side's position has real substance of its own and should not be hidden behind that act, so we record it. The Western church had always held that, by apostolic succession, the bishop of Rome is Peter's successor. Jesus gave Peter the keys of the kingdom of heaven and promised, “on this rock I will build my assembly” (Matthew 16:18), and the Roman church interprets this rock as Peter himself. So, as Olson gives the claim, until the Lord comes again all the bishops of Rome hold first place over the whole church of Jesus Christ.
⭐ Given this premise, Martin V's refusal to sign was consistent: if the papal office was set up by Christ himself and handed down from Peter, then a council made up of men has no right to depose it — even if that council happens to be the very one that put him in the office. ⚠ We do not judge whether this reasoning is right; we only ask the reader to see that this was not one man going back on his word. It was two views of what the church is, colliding in the same room.