Let's start with the problem of Judaism, before returning to Closest Continuers. Here is a family tree. Note that we will exclude the Samaritans, since they diverged even before 80 A.D., and Moslems, since my understanding is that they think that post- Genesis Jews, while not altogether wrong, were already diverging from the truth.
2 Christians (using Jesus's crucifixion to replace animal sacrifice)
2.B Christian. God gave the Jews and the World a new revelation in the New Testament,
which made much of the Old Testament obsolete. The Talmud was invented by men after 80
A.D. or at any rate codified traditions not inspired by God.
2.B.1 Roman Catholic. God also inspired many other traditions around the time that the
New Testament was written. These were made official doctrine at various times, even as
late as the 20th Century (e.g., Mary's being born without sin). Many of them were made
official in the Council of Trent in the 16th Century, in reaction to their official
denial by Protestants.
2.B.2 Protestant. God did not convey new doctrines to anyone after the New
Testament was written. Various false doctrines were proposed, and even accepted by
church officials, but The Church was officially purged of these in the 16th Century.
The Roman Catholics went the opposite way, making many of the false doctrines official
at that time in the Council of Trent and even introducing new ones later.
1 "Jews".
I'll try stating three important positions:
1.A Karaite (rejecting the Talmud)
1.B Rabbinic (using the Talmud and other traditions to replace animal sacrifice)
1.B.1 Orthodox (retaining the most traditions)
1.B.2 Conservative (retaining some traditions)
1.B.3 Reform (retaining the fewest traditions)
2.A Eastern Orthodox (lots of early tradition)
2.B Western
2.B.1 Roman Catholic (lots of tradition from all eras--early, 16th century, modern)
2.B.2 Protestant (rejecting tradition)
1.B.1 Rabbinic. The Talmud and other traditions are as old as the Bible and were simply
not written down until after 80 A.D. Christians invented new revelations from God and
abandoned both the Old Testament and existing tradition.
How do we go about saying what is the true continuation of pre-80 Judaism and of 1st
Century Christianity?
I see that I will not have time to really go into the question, but I will lay out some ideas that might be helpful. Philosophers have devoted quite a bit of attention to the question of "personal identity". I suppose existence and Is-ness is what Ontology is all about. My favorite example is the Ship of Theseus, which I read about in Robert Nozick's 1981 book, Philosophical Explanations.
The workman continues removing and replacing one plank each day, until eventually every
single plank has been changed. Is the ship still the same ship, or is it a different
one now? Probably we say that it is the same ship.
Now we discover that each day the workman took the old plank to his home town over
the mountain ridge, where he has been building another ship in the harbor there. By the
end of the project, the ship in the home harbor has all the old planks, and looks
exactly like the original Ship of Theseus. So which is the Ship of Theseus, the one
with the new planks in the old harbor or the one with the old planks in the new harbor?
The Ship of Theseus is under repair in a drydock. One day, a workman removed an old
plank and replaces it with a new plank of the same size. Is the ship still the same
ship, or is it a different one now? Probably we say that it is the same ship.
Another form of this puzzle, which I came across outside of philosophy, arises from
an old joke:
City Visitor: Wow! It sure looks in good repair for being so old.
Farmer: Well, of course since then the head's been replaced four times and the handle
nine times.
Farmer: This axe in my hand is the same one George Washington used 250 years ago,
which my family has been using ever since.
I think I'll stop here today. Nozick does address the puzzle with his Closest
Continuer idea, but I'd have to look it up in his book again to remember what it is.
Sorry for the cliffhanger!
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