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I'm sorry I wasn't clear. I understand what the objection states. What I don't understand is how it is an objection.

In other words, my understanding is that the objection is as follows:

Major: It is impossible that all the episcopal sees of the world be vacant simultaneously.
Minor: But sedevacantism says that all the episcopal sees are vacant simultaneously.
Conclusion: Therefore sedevacantism states something impossible, and is therefore false.

What I don't understand is where the Major comes from. Everyone who makes this argument asserts it as if it were Catholic dogma, but I have never seen anyone quote a dogmatic definition to that effect.

EDIT: typo correction.

In other words, my understanding is that the objection is as follows:

Major: It is impossible that all the episcopal sees of the world be vacant simultaneously.
Minor: But sedevacantism says that all the episcopal sees are vacant simultaneously.
Conclusion: Therefore sedevacantism states something impossible, and is therefore false.

Yes, that's right. That's the syllogism.

We agree I think that Straight or Simple Sedevacantism (hereafter SS) leads to EVism.

It remains for us to examine if the major is true. If it were true, the conclusion would follow.

There are perhaps 3 dogmatic statements that could be provided, before we look at texts of theologians. 

First, the statement of Vatican I, that there will always be Shepherds and Teachers in the Church, which seems to plainly refer to Bishops with Teaching Office and Ordinary Jurisdiction, "as he sent apostles, whom he chose out of the world [39], even as he had been sent by the Father [40], in like manner it was his will that in his Church there should be shepherds and teachers until the end of time." https://www.ewtn.com/catholicism/library/first-vatican-council-1505

Shepherds and Teachers, pastores et doctores in Latin, seems to describe Bishops who have Power of ruling i.e. jurisdiction, and of teaching, i.e. magisterial authority, doesn't it? Well, such would only come from appointment to an episcopal office/see/diocese.

Second, it follows from the Apostolicity of the Church. For the Church cannot cease to be Apostolic, and Apostolicity requires Bishops who have succeeded to episcopal sees, i.e. it requires ordinary jurisdiction not only valid orders. Another statement in Vatican I itself speaks of "that ordinary and immediate power of episcopal jurisdiction, by which bishops, who have succeeded to the place of the apostles by appointment of the Holy Spirit" from which the same conclusion would follow. So, what is requisite for apostolic succession? That Bishops have ordinary power of episcopal jurisdiction, and be appointed to an office/see to which it is attached.

There are various theological descriptions of this also in the manuals and one other dogmatic statement that we can look into later on.

Your thoughts on this, Yeti?

God bless.

I should be clear in this thread that I don't hold it as absolutely a fact that there are no Catholic bishops in the world today, just that as far as I know this appears to be the case, because if there we would know about it. Archbishop Lefebvre was a bishop with jurisdiction and he stood up for the Catholic Faith, and he was known worldwide for his stance. Is there anyone even remotely resembling that today? As far as I know, no. That is why I am inclined to think there are none, which logically implies that there is no dogma of the Faith that tells us such a thing is impossible. That is why I asked, to see if anyone could provide any solid proof that there is at least one bishop somewhere who publicly teachers the Catholic Faith as a successor of the Apostles, as Vatican I describes.

On the other hand, there are people much smarter than me who say it would imply a denial of Catholic teaching to say there are no Catholic bishops, despite the appearances of what is going on in the world today, so I hold the idea as plausible. I just need to see some proof that it's true. And it would sure help a lot if anyone had any idea who these bishops are. Presumably they're not hiding in a basement somewhere, but are publicly teaching the Faith and condemning heresy? Within the new church? Wouldn't that make them pretty easy to identify?