The obvious answer is that individual popes are not concurrent with one another.
So, what is concurrent then if the heads are concurrent but the individual popes are not? The answer to this is not obvious and it is not all that easy to explain, but it is not impossible to understand either. Here is how it works.
The 7 heads are the 7 name of the popes that have been in office since 1798. The heads are not the individual popes in general, though there are a couple of places where the heads are used as a stand in for a particular pope in Revelation 13 and 17. Be very sure you understand that the heads are the names (see Daniel 2:38 where it says a head can be a name). Now, God, in looking down through human history and seeing the rise of the papacy with its attached history, would have seen the rise of the seven names after a date that we know as 1798. He decided that to represent this event, he would use the 7 heads of the beast. Had he wanted to represent the individual popes, he would have shown a beast with some 15 heads on it and used some method to indicate that each head represented an individual. But, he did not do that. Why, we don't know. Instead, he represented the names with heads.
Now, a name is an identifier, usually of an individual (either human or other nonhuman animal) or an entity of some sort, but in this case, it identifies a group - the 7 names of the popes in existence since 1798. The name of each group is something that exists as long as there are members who exist in the group or potentially can exist. Once a point in time is reached where no more members will be added to the group, the membership list of that group closes with the death of the last surviving member. But, some would argue that this should mean that the group name dies with the death of any one member of that group, for popes reign consecutively, not concurrently, and there are gaps where there are no living members of any one group. That is a human perspective because we look at time from our end of it. God sees time as one continuous whole from beginning to end. So, he can look at the group as one whole and group them as one whole for he sees all the members of the entire group as one. We can do that only after the fact. But, in looking at the group as a whole, he would know when it began and when it ended. So, he could look down history and see when the last member of the group died. He would be able to declare that at that time in history the membership list of the group is closed.
The idea here is that the membership list remains open until the last surviving member of that list of popes with the same name (such as Pope John) has died. At that time the membership list closes and we can know that there will be no more popes with that name ever again. The membership list remaining open corresponds to the continuous survival of the name, or in other words the head of the beast remains "up" (as contrasted to "...five are fallen, one is..." of Revelation 17:10), but once the membership list closes so that no more individuals will be added to that particular name list, then the head is said to be "fallen".
What this all boils down to is that the name line of any one of the 7 popes continues to exist as long as there are new members to join that list or name line. But, once the last member of that group has died, the membership list of that name line ceases, because there won't be any more individuals added to that list. It is the continuous existence of the open state of the membership list of any given papal name that makes it so that they are concurrent. Once closed, they are no longer in existence. The individual popes are not concurrent, but the group to which they belong has a membership list that remains open to add new members until the last member dies.
I hope this explanation makes sense. It is not particularly easy to explain this.
There are some who argue that the popes are neither consecutive nor sequential, but rather intertwine from one name to another after 1798. While this is literally true, the problem with that perspective is that the heads then become equated to individual popes. This is clearly not the case as the heads are equated in Revelation 17:9 to mountains, which based on cultural and religious history of Babylon, it can be demonstrated is representative of a group of individuals, not single individuals within the group. Further, history of the papacy itself since 1798 demonstrates this - there are 7 names, each of which has multiple individuals as members. Therefore, the intertwining of the individual popes is irrelevant. It is membership in a particular name line that is the defining event, not the order in which individual popes occur. The group name lines all continue to exist until the last member of each dies.
Some people have argued that this is an artificial construct not supported in scripture. If that is true, then how do you explain away the clear rules of Daniel 7 and 8? These rules clearly indicate that there are 7 kingdoms or rulers of some sort that come from the papacy AFTER 1798. Since they are also equated to mountains, that means multiple individuals are part of each group. The only thing that fits this is that the heads are the names of the popes existing since 1798. This would mean the group name, not the individual names, for it must be a name that is inclusive of all individuals within a group, such as the Pope John or the Pope John Paul series. Finally, the only way to be consistent is to conclude that since the heads are the group names and not the individual popes, it is the group names that are concurrent rather than the names of individual popes (the difference here is that Pope John would be a group name as it is inclusive of all Pope Johns, but Pope John X, say, would be a specific name of an individual pope within that group). If this is difficult to understand, think of the names as a membership list that is open until the last surviving member of each group dies, at which point the list closes to addition of any new members.
It is not all that unlike the American Presidency. There have been different American Presidents since about 1790, but we say that the presidency has been continuous. It is an intellectual construct, but it is true nonetheless. The office is continuously occupied, though by different individuals. The heads represent membership in a group name and is evidently considered to be continuous until it closes with the death of the last surviving member of each head or group name. This seems to be the only way to explain this in terms of the rules from Daniel 7 and 8.
In the one instance in which the time of a specific pope is mentioned in connection with a head in Revelation 17 (the other is in Revelation 13), it is plain to see that from the perspective of Pope Paul VI (1963-1978), 5 of the heads that started out with his group in 1798 had died out, so as the angel said "...five are fallen...". Their lists of membership was closed and therefore their corresponding heads were said to have fallen.
When Pope Paul VI died, the membership list for his group name, Pope Paul, was closed, so his corresponding head would be said to have "fallen" at that time. There was one more yet to come (meaning he had never existed before!) after the death of Pope Paul VI, which was John Paul, and who would remain only a short while, which has turned out to be true because if you add up the total years of reign for each of the papal names, the John Paul series is by far the shortest. Click here for information about that.
There are some who claim that the head that is wounded will have to return during the 8th king's time to be healed. But Revelation 17 indicates that once a head has fallen, it NEVER says it will rise again. Hence, once the head with the wound has fallen, it cannot arise again. Another reason this is false reasoning is that the body, heads, and horns represent successive periods of time (where multiple heads and multiple horns are present). Once the heads have completed their time, their time will not occur again because the horns succeed the heads. The bible does not provide any examples of the heads returning after horns have taken over. Therefore, the heads are done and gone and will not return again for ANY reason.
The 8th king is known to follow the time of the 7 heads so must be concurrent with the 10 horns. We are told that the construction of the Greek in Revelation 17:11 (And the beast that was, and is not, even he is the eighth, and is of the seven, and goeth into perdition) indicates that the 8th follows the last head (what is commonly called the 7th head). The English should indicate this as well because it says the 7 heads are 7 kings, and then says there is an 8th king. Does this indicate the 8th follows the 7th? I would think so. It is clear from the text that heads 6-7 are sequential, so this is telling us that kings 6-7 and 7-8 are in sequence. Hence, the 8th occurs after the 7 heads are done. Therefore, the wounded head will not arise during the time of the 8th king to be healed because the text itself indicates that the 8th occurs AFTER all previous 7 heads have passed from the scene. Any attempt to have the wounded head resurrect during the time of the 8th king is to insert text into the bible that is NOT THERE and is contradicted by the text itself! The healing must occur before the first 6 heads have all fallen, which must occur before the 7th head arises. The idea that the healing must occur before the first 6 heads have all fallen is true because the 7th head refers to the name of John Paul, while the wounded/healed head refers to the name of Pius. Remember it was Pius VI that was the individual pope who received the "wound", so the head that was wounded had the name Pius attached to it. The last Pius occurred before the first John Paul came along.
Hopefully this helps the reader understand the idea of concurrency of the heads. It is not easy to understand this, but not impossible either.
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