Trees (Set Theory)

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Transcript of Trees (Set Theory)

  • Trees (set theory)From Wikipedia, the free encyclopedia

  • Contents

    1 Aronszajn tree 11.1 Existence of -Aronszajn trees . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Special Aronszajn trees . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.3 Construction of a special Aronszajn tree . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.4 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.5 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.6 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

    2 Cantor tree 32.1 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

    3 HalpernLuchli theorem 43.1 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

    4 Honest leftmost branch 64.1 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64.2 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

    5 JechKunen tree 75.1 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

    6 Kurepa tree 86.1 Specializing a Kurepa tree . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86.2 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86.3 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

    7 Laver tree 107.1 Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107.2 Denitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107.3 Amoeba forcing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107.4 Cohen forcing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107.5 Grigorie forcing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117.6 Hechler forcing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117.7 JockuschSoare forcing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117.8 Iterated forcing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

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  • ii CONTENTS

    7.9 Laver forcing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117.10 Levy collapsing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117.11 Magidor forcing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127.12 Mathias forcing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127.13 Namba forcing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127.14 Prikry forcing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127.15 Product forcing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137.16 Radin forcing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137.17 Random forcing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137.18 Sacks forcing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137.19 Shooting a fast club . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137.20 Shooting a club with countable conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137.21 Shooting a club with nite conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147.22 Silver forcing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147.23 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147.24 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

    8 Millikens tree theorem 158.1 Strong embedding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158.2 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

    9 Stemmatics 169.1 History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169.2 Basic notions and objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169.3 Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189.4 Eclecticism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

    9.4.1 External evidence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209.4.2 Internal evidence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209.4.3 Canons of textual criticism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209.4.4 Limitations of eclecticism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

    9.5 Stemmatics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219.5.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219.5.2 Limitations and criticism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

    9.6 Copy-text editing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239.6.1 McKerrows concept of copy-text . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249.6.2 W. W. Gregs rationale of copy-text . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249.6.3 GregBowersTanselle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

    9.7 Cladistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289.8 Application of textual criticism to religious documents . . . . . . . . . . . . . . . . . . . . . . . . 28

    9.8.1 Qur'an . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299.8.2 Book of Mormon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309.8.3 Hebrew Bible . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

  • CONTENTS iii

    9.8.4 New Testament . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329.8.5 Talmud . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

    9.9 Classical texts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359.10 Legal protection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359.11 Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359.12 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

    9.12.1 Topics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 369.12.2 Critical editions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379.12.3 Lists . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

    9.13 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 389.14 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 429.15 Further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 439.16 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

    9.16.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 449.16.2 Bible . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

    10 Suslin tree 4510.1 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4510.2 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

    11 Tree (descriptive set theory) 4611.1 Denitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

    11.1.1 Trees . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4611.1.2 Branches and bodies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4611.1.3 Terminal nodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

    11.2 Relation to other types of trees . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4611.3 Topology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4711.4 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4711.5 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

    12 Tree (set theory) 4812.1 Denition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4812.2 Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4812.3 Tree (automata theory) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

    12.3.1 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4912.4 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4912.5 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5012.6 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5012.7 Text and image sources, contributors, and licenses . . . . . . . . . . . . . . . . . . . . . . . . . . 51

    12.7.1 Text . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5112.7.2 Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5112.7.3 Content license . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

  • Chapter 1

    Aronszajn tree

    In set theory, an Aronszajn tree is an uncountable tree with no uncountable branches and no uncountable levels. Forexample, every Suslin tree is an Aronszajn tree. More generally, for a cardinal , a -Aronszajn tree is a tree ofheight such that all levels have size less than and all branches have height less than (so Aronszajn trees are thesame as @1 -Aronszajn trees). They are named for Nachman Aronszajn, who constructed an Aronszajn tree in 1934;his construction was described by Kurepa (1935).A cardinal for which no -Aronszajn trees exist is said to have the tree property. (sometimes the condition that is regular and uncountable is included.)

    1.1 Existence of -Aronszajn treesKnigs lemma states that @0 -Aronszajn trees do not exist.The existence of Aronszajn trees (= @1 -Aronszajn trees) was proven by Nachman Aronszajn, and implies that theanalogue of Knigs lemma does not hold for uncountable trees.The existence of @2 -Aronszajn trees is undecidable (assuming a certain large cardinal axiom): more precisely,the continuum hypothesis implies the existence of an @2 -Aronszajn tree, and Mitchell and Silver showed that it isconsistent (relative to the existence of a weakly compact cardinal) that no @2 -Aronszajn trees exist.Jensen proved that V=L implies that there is a -Aronszajn tree (in fact a -Suslin tree) for every innite successorcardinal .Cummings & Foreman (1998) showed (using a large cardinal axiom) that it is consistent that no @n -Aronszajn treesexist for any nite n other than 1.If is weakly compact then no -Aronszajn trees exist. Conversely if is inaccessible and no -Aronszajn trees existthen is weakly compact.

    1.2 Special Aronszajn treesAn Aronszajn tree is called special if there is a function f from the tree to the rationals so that f(x)

  • 2 CHAPTER 1. ARONSZAJN TREE

    The elements of the tree are certain well-ordered sets of rational numbers with supremum that is rational or . Ifx and y are two of these sets then we dene xy (in the tree order) to mean that x is an initial segment of the orderedset y. For each countable ordinal we write U for the elements of the tree of level , so that the elements of Uare certain sets of rationals with order type . The special Aronszajn tree is the union of the sets U for all countable.We construct U by transnite induction on as follows.

    If +1 is a successor then U consists of all extensions of a sequence x in U by a rational greater than supx.

    If is a limit then let T be the tree of all points of level less than . For each x in T and for each rationalnumber q greater than sup x, choose a level branch of T containing x with supremum q. Then U consistsof these branches.

    The function f(x) = sup x is rational or , and has the property that if x

  • Chapter 2

    Cantor tree

    For the surface, see Cantor tree surface.

    In mathematical set theory, theCantor tree is either the full binary tree of height + 1, or a topological space relatedto this by joining its points with intervals, that was introduced by Robert Lee Moore in the late 1920s as an exampleof a non-metrizable Moore space (Jones 1966).

    2.1 References Jones, F. Burton (1966), Remarks on the normal Moore space metrization problem, in Bing, R. H.; Bean,R. J., Topology Seminar, Wisconsin, 1965, Annals of Mathematics Studies 60, Princeton University Press, pp.115152, ISBN 978-0-691-08056-7, MR 0202100

    Nyikos, Peter (1989), The Cantor tree and the FrchetUrysohn property, Papers on general topology andrelated category theory and topological algebra (New York, 1985/1987), Ann. New York Acad. Sci. 552, NewYork: New York Acad. Sci., pp. 109123, doi:10.1111/j.1749-6632.1989.tb22391.x, ISBN 978-0-89766-516-2, MR 1020779

    Steen, Lynn Arthur; Seebach, J. Arthur Jr. (1995) [1978], Counterexamples in Topology (Dover reprint of1978 ed.), Berlin, New York: Springer-Verlag, ISBN 978-0-486-68735-3, MR 507446

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  • Chapter 3

    HalpernLuchli theorem

    In mathematics, theHalpernLuchli theorem is a partition result about nite products of innite trees. Its originalpurpose was to give a model for set theory in which the Boolean prime ideal theorem is true but the axiom of choiceis false. It is often called the HalpernLuchli theorem, but the proper attribution for the theorem as it is formulatedbelow is to HalpernLuchliLaverPincus or HLLP (named after James D. Halpern, Hans Luchli, Richard Laver,and David Pincus), following (Milliken 1979).Let d,r < , hTi : i 2 di be a sequence of nitely splitting trees of height . Let

    [n2!

    Yi

  • 3.1. REFERENCES 5

    3. Keith R. Milliken, A Partition Theorem for the Innite Subtrees of a Tree, Trans. Amer. Math. Soc. 263 No.1(1981), 137148

    4. J.D. Halpern and David Pincus, Partitions of Products, Trans. Amer. Math. Soc. 267, No.2 (1981), 549568.

  • Chapter 4

    Honest leftmost branch

    In set theory, an honest leftmost branch of a tree T on is a branch (maximal chain) [T] such that for eachbranch g [T], one has n : (n) g(n). Here, [T] denotes the set of branches of maximal length of T, is theordinal (represented by the natural numbers N) and is some other ordinal.

    4.1 See also scale (computing) Suslin set

    4.2 References Akihiro Kanamori, The higher innite, Perspectives in Mathematical Logic, Springer, Berlin, 1997. Yiannis N. Moschovakis, Descriptive set theory, North-Holland, Amsterdam, 1980.

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  • Chapter 5

    JechKunen tree

    In mathematics, a JechKunen tree is a tree of power 1 and height 1 in which the number of branches is greaterthan 1 and less than 21 . They are named after Thomas Jech (1971) who found the rst example, and KennethKunen (1975) who related them to the cardinalities of compact spaces.

    5.1 References Jech, Thomas J. (1971), Trees, J. Symbolic Logic 36: 114, doi:10.2307/2271510, MR 0284331 Kunen (1975), On the cardinality of compact spaces, Notices of the A. M. S. 22: 212

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  • Chapter 6

    Kurepa tree

    In set theory, a Kurepa tree is a tree (T,

  • 6.3. REFERENCES 9

    Kurepa, G. (1935), Ensembles ordonns et ramis, Publ. math. Univ. Belgrade 4: 1138, JFM 61.0980.01,Zbl 0014.39401

    Silver, Jack (1971), The independence of Kurepas conjecture and two-cardinal conjectures in model theory,Axiomatic Set Theory, Proc. Sympos. Pure Math. XIII, Providence, R.I.: Amer. Math. Soc., pp. 383390,MR 0277379, Zbl 0255.02068

  • Chapter 7

    Laver tree

    In mathematics, forcing is a method of constructing new modelsM[G] of set theory by adding a generic subset G ofa poset P to a model M. The poset P used will determine what statements hold in the new universe (the 'extension');to force a statement of interest thus requires construction of a suitable P. This article lists some of the posets P thathave been used in this construction.

    7.1 Notation P is a poset with order

  • 7.5. GRIGORIEFF FORCING 11

    7.5 Grigorie forcingGrigorie forcing (after Serge Grigorie) destroys a free ultralter on

    7.6 Hechler forcingHechler forcing (after Stephen Herman Hechler) is used to show that Martins axiom implies that every family of lessthan c functions from to is eventually dominated by some such function.P is the set of pairs (s,E) where s is a nite sequence of natural numbers (considered as functions from a nite ordinalto ) and E is a nite subset of some xed set G of functions from to . The element (s, E) is stronger than (t,F)if t is contained in s, F is contained in E, and if k is in the domain of s but not of t then s(k)>h(k) for all h in F.

    7.7 JockuschSoare forcingForcing with01 classes was invented by Robert Soare and Carl Jockusch to prove, among other results, the low basistheorem. Here P is the set of nonempty 01 subsets of 2! (meaning the sets of paths through innite, computablesubtrees of 27.8 Iterated forcingsee also iterated forcingIterated forcing with nite supports was introduced by Solovay and Tennenbaum to show the consistency of Suslinshypothesis. Easton introduced another type of iterated forcing to determine the possible values of the continuumfunction at regular cardinals. Iterated forcing with countable support was investigated by Laver in his proof of theconsistency of Borels conjecture, Baumgartner, who introducedAxiomA forcing, and Shelah, who introduced properforcing. Revised countable support iteration was introduced by Shelah to handle semi-proper forcings, such as Prikryforcing, and generalizations, notably including Namba forcing.

    7.9 Laver forcingLaver forcing was used by Laver to show that Borels conjecture, which says that all strong measure zero sets arecountable, is consistent with ZFC. (Borels conjecture is not consistent with the continuum hypothesis.)

    P is the set of Laver trees, ordered by inclusion.

    A Laver tree p is a subset of the nite sequences of natural numbers such that

    p is a tree: p contains any initial sequence of any element of p p has a stem: a maximal node s(p) = s 2 p such that s t or t s for all t in p, If t 2 p and s t then t has an innite number of immediate successors tn in p for n 2 .

    If G is generic for (P,), then the real {s(p) : p 2 G}, called a Laver-real, uniquely determines G.Laver forcing satises the Laver property.

    7.10 Levy collapsingMain article: collapsing algebra

  • 12 CHAPTER 7. LAVER TREE

    These posets will collapse various cardinals, in other words force them to be equal in size to smaller cardinals.

    Collapsing a cardinal to : P is the set of all nite sequences of ordinals less than a given cardinal . If isuncountable then forcing with this poset collapses to .

    Collapsing a cardinal to another: P is the set of all functions from a subset of of cardinality less than to (for xed cardinals and ). Forcing with this poset collapses down to .

    Levy collapsing: If is regular and is inaccessible, then P is the set of functions p on subsets of withdomain of size less than and p(,)Namba' forcing is the subset of P such that there is a node below which the ordering is linear and above which eachnode has @2 immediate successors.Magidor and Shelah proved that if CH holds then a generic object of Namba forcing does not exist in the genericextension by Namba', and vice versa.[1][2]

    7.14 Prikry forcingIn Prikry forcing (after Karel Prikr) P is the set of pairs (s,A) where s is a nite subset of a xed measurable cardinal, and A is an element of a xed normal measure D on . A condition (s,A) is stronger than (t, B) if t is an initialsegment of s, A is contained in B, and s is contained in t [ B. This forcing notion can be used to change to conalityof while preserving all cardinals.

  • 7.15. PRODUCT FORCING 13

    7.15 Product forcingTaking a product of forcing conditions is a way of simultaneously forcing all the conditions.

    Finite products: If P and Q are posets, the product poset P Q has the partial order dened by (p1, q1) (p2,q2) if p1 p2 and q1 q2.

    Innite products: The product of a set of posets Pi, i 2 I, each with a largest element 1 is the set of functionsp on I with p(i) 2 P(i) and such that p(i) = 1 for all but a nite number of i. The order is given by p q if p(i) q(i) for all i.

    The Easton product (after William Bigelow Easton) of a set of posets Pi, i 2 I, where I is a set of cardinalsis the set of functions p on I with p(i) 2 P(i) and such that for every regular cardinal the number of elements of with p() 1 is less than .

    7.16 Radin forcingRadin forcing (after Lon Berk Radin), a technically involved generalization of Magidor forcing, adds a closed, un-bounded subset to some regular cardinal .If is a suciently large cardinal, then the forcing keeps regular, measurable, supercompact, etc.

    7.17 Random forcingMain article: random algebra

    P is the set of Borel subsets of [0,1] of positive measure, where p is called stronger than q if it is contained inq. The generic set G then encodes a random real": the unique real xG in all rational intervals [r,s]V[G] suchthat [r,s]V is in G. This real is random in the sense that if X is any subset of [0,1]V of measure 1, lying in V,then xG X.

    7.18 Sacks forcing P is the set of all perfect trees contained in the set of nite {0,1} sequences. (A tree T is a set of nite sequencescontaining all initial segments of its members, and is called perfect if for any element t of T there is a tree scontaining it so that both s0 and s1 are in T.) A tree p is stronger than q if p is contained in q. Forcing withperfect trees was used by Gerald Enoch Sacks to produce a real a with minimal degree of constructibility.

    Sacks forcing has the Sacks property.

    7.19 Shooting a fast clubFor S a stationary subset of !1 we set P = fh;Ci : is a closed sequence from S and C is a closed unboundedsubset of !1g , ordered by h0; C 0i h;Ci i 0 end-extends and C 0 C and 0 [ C . In V [G] , wehave thatSf : (9C)(h;Ci 2 G)g is a closed unbounded subset of S almost contained in each club set in V. @1 ispreserved.

    7.20 Shooting a club with countable conditionsFor S a stationary subset of !1 we set P equal to the set of closed countable sequences from S. In V [G] , we have thatSG is a closed unbounded subset of S and @1 is preserved, and if CH holds then all cardinals are preserved.

  • 14 CHAPTER 7. LAVER TREE

    7.21 Shooting a club with nite conditionsFor S a stationary subset of !1 we set P equal to the set of nite sets of pairs of countable ordinals, such that ifp 2 P and h; i 2 p then and 2 S , and whenever h; i and h; i are distinct elements of p then either < or < . P is ordered by reverse inclusion. In V [G] , we have that f : (9)(h; i 2 SG)g is a closedunbounded subset of S and all cardinals are preserved.

    7.22 Silver forcingSilver forcing (after Jack Howard Silver) satises Fusion, the Sacks property, and is minimal with respect to reals(but not minimal).

    7.23 References[1] Shelah, S., Proper and Improper Forcing (Claim XI.4.2), Springer, 1998

    [2] Schlindwein, C., Shelahs work on non-semiproper iterations, I, Archive for Mathematical Logic, vol. 47, no. 6, pp. 579-- 606 (2008)

    Kunen, Kenneth (2011), Set theory, Studies in Logic 34, London: College Publications, ISBN 978-1-84890-050-9, Zbl 1262.03001

    Jech, Thomas (2003), Set Theory: Millennium Edition, Springer Monographs in Mathematics, Berlin, NewYork: Springer-Verlag, ISBN 978-3-540-44085-7

    Kunen, Kenneth (1980), Set Theory: An Introduction to Independence Proofs, Elsevier, ISBN 978-0-444-86839-8

    Kunen, Kenneth (2011), Set theory, Studies in Logic 34, London: College Publications, ISBN 978-1-84890-050-9, Zbl 1262.03001

    7.24 External links A.Miller (2009), Forcing Tidbits.

  • Chapter 8

    Millikens tree theorem

    In mathematics,Millikens tree theorem in combinatorics is a partition theorem generalizing Ramseys theorem toinnite trees, objects with more structure than sets.Let T be a nitely splitting rooted tree of height , n a positive integer, and SnT the collection of all strongly embeddedsubtrees of T of height n. In one of its simple forms, Millikens tree theorem states that if SnT = C1 [ ::: [ Cr thenfor some strongly embedded innite subtree R of T, SnR Ci for some i r.This immediately implies Ramseys theorem; take the tree T to be a linear ordering on vertices.Dene Sn = ST SnT where T ranges over nitely splitting rooted trees of height . Millikens tree theorem says thatnot only is Sn partition regular for each n < , but that the homogeneous subtree R guaranteed by the theorem isstrongly embedded in T.

    8.1 Strong embeddingCall T an -tree if each branch of T has cardinality . Dene Succ(p, P)= fq 2 P : q pg , and IS(p; P ) to bethe set of immediate successors of p in P. Suppose S is an -tree and T is a -tree, with 0 . S is stronglyembedded in T if:

    S T , and the partial order on S is induced from T, if s 2 S is nonmaximal in S and t 2 IS(s; T ) , then jSucc(t; T ) \ IS(s; S)j = 1 , there exists a strictly increasing function from to , such that S(n) T (f(n)):

    Intuitively, for S to be strongly embedded in T,

    S must be a subset of T with the induced partial order S must preserve the branching structure of T; i.e., if a nonmaximal node in S has n immediate successors in T,then it has n immediate successors in S

    S preserves the level structure of T; all nodes on a common level of S must be on a common level in T.

    8.2 References1. Keith R. Milliken, A Ramsey Theorem for Trees J. Comb. Theory (Series A) 26 (1979), 215-237

    2. Keith R. Milliken, A Partition Theorem for the Innite Subtrees of a Tree, Trans. Amer. Math. Soc. 263 No.1(1981), 137-148.

    15

  • Chapter 9

    Stemmatics

    Critical edition redirects here. For critical editions of operatic scores, see Critical edition (opera).Textual criticism is a branch of textual scholarship, philology, and literary criticism that is concerned with the

    identication and removal of transcription errors in texts, both manuscripts and printed books. Ancient scribes madeerrors or alterations when copying manuscripts by hand.[1] Given a manuscript copy, several or many copies, but notthe original document, the textual critic seeks to reconstruct the original text (the archetype or autograph) as closelyas possible. The same processes can be used to attempt to reconstruct intermediate editions, or recensions, of adocuments transcription history.[2] The ultimate objective of the textual critics work is the production of a "criticaledition" containing a text most closely approximating the original.There are three fundamental approaches to textual criticism: eclecticism, stemmatics, and copy-text editing. Tech-niques from the biological discipline of cladistics are currently also being used to determine the relationships betweenmanuscripts.The phrase lower criticism is used to describe the contrast between textual criticism and "higher criticism", whichis the endeavor to establish the authorship, date, and place of composition of the original text.

    9.1 HistoryTextual criticism has been practiced for over two thousand years. Early textual criticsWho? were concerned withpreserving the works of antiquity, and this continued through the medieval period into early modern times until theinvention of the printing press.Many ancient works, such as the Bible and the Greek tragedies, survive in hundreds of copies, and the relationship ofeach copy to the original may be unclear. Textual scholars have debated for centuries which sources are most closelyderived from the original, hence which readings in those sources are correct. Although biblical books that are letters,like Greek plays, presumably had one original, the question of whether some biblical books, like the gospels, ever hadjust one original has been discussed.[3] Interest in applying textual criticism to the Qur'an has also developed afterthe discovery of the Sana'a manuscripts in 1972, which possibly date back to the 78th centuries.In the English language, the works of Shakespeare have been a particularly fertile ground for textual criticismbothbecause the texts, as transmitted, contain a considerable amount of variation, and because the eort and expenseof producing superior editions of his works have always been widely viewed as worthwhile.[4] The principles oftextual criticism, although originally developed and rened for works of antiquity, the Bible, and Shakespeare,[5]have been applied to many works, extending backwards from the present to the earliest known written documents,in Mesopotamia and Egypta period of about ve millennia. However, the application of textual criticism to non-religious works does not antedate the invention of printing. While Christianity has been relatively receptive to textualcriticism, application of it to the Jewish (Masoretic) Torah and the Qur'an is, to the devout, taboo.

    9.2 Basic notions and objectivesThe basic problem, as described by Paul Maas, is as follows:

    16

  • 9.2. BASIC NOTIONS AND OBJECTIVES 17

    Carmina Cantabrigiensia, Manuscript C, folio 436v, 11th century

  • 18 CHAPTER 9. STEMMATICS

    We have no autograph manuscripts of the Greek and Roman classical writers and no copies whichhave been collated with the originals; the manuscripts we possess derive from the originals through anunknown number of intermediate copies, and are consequently of questionable trustworthiness. Thebusiness of textual criticism is to produce a text as close as possible to the original (constitutio textus).[6]

    Maas comments further that A dictation revised by the author must be regarded as equivalent to an autographmanuscript. The lack of autograph manuscripts applies to many cultures other than Greek and Roman. In such asituation, a key objective becomes the identication of the rst exemplar before any split in the tradition. That exem-plar is known as the archetype. If we succeed in establishing the text of [the archetype], the constitutio (reconstructionof the original) is considerably advanced.[7]

    The textual critics ultimate objective is the production of a critical edition. This contains a text most closelyapproximating the original, which is accompanied by an apparatus criticus (or critical apparatus) that presents:

    the evidence that the editor considered (names of manuscripts, or abbreviations called sigla), the editors analysis of that evidence (sometimes a simple likelihood rating), and a record of rejected variants (often in order of preference).[8]

    9.3 ProcessBefore mechanical printing, literature was copied by hand, and many variations were introduced by copyists. Theage of printing made the scribal profession eectively redundant. Printed editions, while less susceptible to theproliferation of variations likely to arise during manual transmission, are nonetheless not immune to introducingvariations from an authors autograph. Instead of a scribe miscopying his source, a compositor or a printing shopmay read or typeset a work in a way that diers from the autograph.[9] Since each scribe or printer commits dierenterrors, reconstruction of the lost original is often aided by a selection of readings taken frommany sources. An editedtext that draws from multiple sources is said to be eclectic. In contrast to this approach, some textual critics prefer toidentify the single best surviving text, and not to combine readings from multiple sources.[10]

    When comparing dierent documents, or witnesses, of a single, original text, the observed dierences are calledvariant readings, or simply variants or readings. It is not always apparent which single variant represents the authorsoriginal work. The process of textual criticism seeks to explain how each variant may have entered the text, either byaccident (duplication or omission) or intention (harmonization or censorship), as scribes or supervisors transmittedthe original authors text by copying it. The textual critics task, therefore, is to sort through the variants, eliminatingthose most likely to be un-original, hence establishing a critical text, or critical edition, that is intended to bestapproximate the original. At the same time, the critical text should document variant readings, so the relation ofextant witnesses to the reconstructed original is apparent to a reader of the critical edition. In establishing the criticaltext, the textual critic considers both external evidence (the age, provenance, and aliation of each witness) andinternal or physical considerations (what the author and scribes, or printers, were likely to have done).[3]

    The collation of all known variants of a text is referred to as a variorum, namely a work of textual criticism wherebyall variations and emendations are set side by side so that a reader can track how textual decisions have been madein the preparation of a text for publication.[11] The Bible and the works of William Shakespeare have often been thesubjects of variorum editions, although the same techniques have been applied with less frequency to many otherworks, such as Walt Whitmans Leaves of Grass,[12] and the prose writings of Edward Fitzgerald.[13]

    9.4 EclecticismEclecticism refers to the practice of consulting a wide diversity of witnesses to a particular original. The practice isbased on the principle that the more independent transmission histories are, the less likely they will be to reproducethe same errors. What one omits, the others may retain; what one adds, the others are unlikely to add. Eclecticismallows inferences to be drawn regarding the original text, based on the evidence of contrasts between witnesses.Eclectic readings also normally give an impression of the number of witnesses to each available reading. Althougha reading supported by the majority of witnesses is frequently preferred, this does not follow automatically. For

  • 9.4. ECLECTICISM 19

    Folio from Papyrus 46, containing 2 Corinthians 11:3312:9

    example, a second edition of a Shakespeare play may include an addition alluding to an event known to have happenedbetween the two editions. Although nearly all subsequent manuscripts may have included the addition, textual criticsmay reconstruct the original without the addition.

  • 20 CHAPTER 9. STEMMATICS

    The result of the process is a text with readings drawn from many witnesses. It is not a copy of any particularmanuscript, and may deviate from the majority of existing manuscripts. In a purely eclectic approach, no singlewitness is theoretically favored. Instead, the critic forms opinions about individual witnesses, relying on both externaland internal evidence.[14]

    Since the mid-19th century, eclecticism, in which there is no a priori bias to a single manuscript, has been thedominant method of editing the Greek text of the New Testament (currently, the United Bible Society, 5th ed. andNestle-Aland, 28th ed.). Even so, the oldest manuscripts, being of the Alexandrian text-type, are the most favored,and the critical text has an Alexandrian disposition.[15]

    9.4.1 External evidenceExternal evidence is evidence of each physical witness, its date, source, and relationship to other known witnesses.Critics will often prefer the readings supported by the oldest witnesses. Since errors tend to accumulate, oldermanuscripts should have fewer errors. Readings supported by a majority of witnesses are also usually preferred,since these are less likely to reect accidents or individual biases. For the same reasons, the most geographicallydiverse witnesses are preferred. Some manuscripts show evidence that particular care was taken in their composition,for example, by including alternative readings in their margins, demonstrating that more than one prior copy (exem-plar) was consulted in producing the current one. Other factors being equal, these are the best witnesses. The role ofthe textual critic is necessary when these basic criteria are in conict. For instance, there will typically be fewer earlycopies, and a larger number of later copies. The textual critic will attempt to balance these criteria, to determine theoriginal text.There are many other more sophisticated considerations. For example, readings that depart from the known practiceof a scribe or a given period may be deemed more reliable, since a scribe is unlikely on his own initiative to havedeparted from the usual practice.[16]

    9.4.2 Internal evidenceInternal evidence is evidence that comes from the text itself, independent of the physical characteristics of the docu-ment. Various considerations can be used to decide which reading is the most likely to be original. Sometimes theseconsiderations can be in conict.[16]

    Two common considerations have the Latin names lectio brevior (shorter reading) and lectio dicilior (more dicultreading). The rst is the general observation that scribes tended to add words, for clarication or out of habit, moreoften than they removed them. The second, lectio dicilior potior (the harder reading is stronger), recognizes thetendency for harmonizationresolving apparent inconsistencies in the text. Applying this principle leads to takingthe more dicult (unharmonized) reading as being more likely to be the original. Such cases also include scribessimplifying and smoothing texts they did not fully understand.[17]

    Another scribal tendency is called homoioteleuton, meaning same endings. Homoioteleuton occurs when twowords/phrases/lines end with the same sequence of letters. The scribe, having nished copying the rst, skips to thesecond, omitting all intervening words. Homeoarchy refers to eye-skip when the beginnings of two lines are similar.[18]

    The critic may also examine the other writings of the author to decide what words and grammatical constructionsmatch his style. The evaluation of internal evidence also provides the critic with information that helps him evaluatethe reliability of individual manuscripts. Thus, the consideration of internal and external evidence is related.After considering all relevant factors, the textual critic seeks the reading that best explains how the other readingswould arise. That reading is then the most likely candidate to have been original.

    9.4.3 Canons of textual criticismVarious scholars have developed guidelines, or canons of textual criticism, to guide the exercise of the critics judg-ment in determining the best readings of a text. One of the earliest was Johann Albrecht Bengel (16871752), who in1734 produced an edition of the Greek New Testament. In his commentary, he established the rule Proclivi scriptionipraestat ardua, (the harder reading is to be preferred).[19]

    Johann Jakob Griesbach (17451812) published several editions of the New Testament. In his 1796 edition,[20] heestablished fteen critical rules. Among them was a variant of Bengels rule, Lectio dicilior potior, the harder

  • 9.5. STEMMATICS 21

    Luke 11:2 in Codex Sinaiticus

    reading is better. Another was Lectio brevior praeferenda, the shorter reading is better, based on the idea thatscribes were more likely to add than to delete.[21] This rule cannot be applied uncritically, as scribes may omit materialinadvertently.Brooke Foss Westcott (18251901) and Fenton J. A. Hort (18281892) published an edition of the New Testamentin Greek in 1881. They proposed nine critical rules, including a version of Bengels rule, The reading is less likelyto be original that shows a disposition to smooth away diculties. They also argued that Readings are approved orrejected by reason of the quality, and not the number, of their supporting witnesses, and that The reading is to bepreferred that most tly explains the existence of the others.[22]

    Many of these rules, although originally developed for biblical textual criticism, have wide applicability to any textsusceptible to errors of transmission.

    9.4.4 Limitations of eclecticism

    Since the canons of criticism are highly susceptible to interpretation, and at times even contradict each other, theymay be employed to justify a result that ts the textual critics aesthetic or theological agenda. Starting in the 19thcentury, scholars sought more rigorous methods to guide editorial judgment. Best-text editing (a complete rejectionof eclecticism) became one extreme. Stemmatics and copy-text editing while both eclectic, in that they permit theeditor to select readings from multiple sources sought to reduce subjectivity by establishing one or a few witnessespresumably as being favored by objective criteria. The citing of sources used, and alternate readings, and the useof original text and images helps readers and other critics determine to an extent the depth of research of the critic,and to independently verify their work.

    9.5 Stemmatics

    9.5.1 Overview

    Stemmatics, stemmology or stemmatology is a rigorous approach to textual criticism. Karl Lachmann (17931851) greatly contributed to making this method famous, even though he did not invent it.[23] The method takes itsname from the word stemma. The Ancient Greek word [24] and its loanword in classical Latin stemmata[24][25][26] may refer to "family trees". This specic meaning shows the relationships of the surviving witnesses (the

  • 22 CHAPTER 9. STEMMATICS

    rst known example of such a stemma, albeit with the name, dates from 1827).[27] The family tree is also referredto as a cladogram.[28] The method works from the principle that community of error implies community of origin.That is, if two witnesses have a number of errors in common, it may be presumed that they were derived from acommon intermediate source, called a hyparchetype. Relations between the lost intermediates are determined by thesame process, placing all extant manuscripts in a family tree or stemma codicum descended from a single archetype.The process of constructing the stemma is called recension, or the Latin recensio.[29]

    Having completed the stemma, the critic proceeds to the next step, called selection or selectio, where the text of thearchetype is determined by examining variants from the closest hyparchetypes to the archetype and selecting thebest ones. If one reading occurs more often than another at the same level of the tree, then the dominant readingis selected. If two competing readings occur equally often, then the editor uses his judgment to select the correctreading.[30]

    After selectio, the text may still contain errors, since there may be passages where no source preserves the correctreading. The step of examination, or examinatio is applied to nd corruptions. Where the editor concludes thatthe text is corrupt, it is corrected by a process called emendation, or emendatio (also sometimes called divinatio).Emendations not supported by any known source are sometimes called conjectural emendations.[31]

    The process of selectio resembles eclectic textual criticism, but applied to a restricted set of hypothetical hyparchetypes.The steps of examinatio and emendatio resemble copy-text editing. In fact, the other techniques can be seen as specialcases of stemmatics in which a rigorous family history of the text cannot be determined but only approximated. If itseems that one manuscript is by far the best text, then copy text editing is appropriate, and if it seems that a group ofmanuscripts are good, then eclecticism on that group would be proper.[32]

    The HodgesFarstad edition of the Greek New Testament attempts to use stemmatics for some portions.[33]

    9.5.2 Limitations and criticismThe stemmatic method assumes that each witness is derived from one, and only one, predecessor. If a scribe refers tomore than one source when creating his copy, then the new copy will not clearly fall into a single branch of the familytree. In the stemmatic method, a manuscript that is derived from more than one source is said to be contaminated.The method also assumes that scribes only make new errors they do not attempt to correct the errors of theirpredecessors. When a text has been improved by the scribe, it is said to be sophisticated, but sophistication impairsthe method by obscuring a documents relationship to other witnesses, and making it more dicult to place themanuscript correctly in the stemma.The stemmatic method requires the textual critic to group manuscripts by commonality of error. It is required,therefore, that the critic can distinguish erroneous readings from correct ones. This assumption has often come underattack. W. W. Greg noted, That if a scribe makes a mistake he will inevitably produce nonsense is the tacit andwholly unwarranted assumption.[34]

    Franz Anton Knittel defended the traditional point of view in theology and was against the modern textual criticism.He defended an authenticity of the Pericopa Adulterae (John 7:538:11), Comma Johanneum (1 John 5:7), andTestimonium Flavianum. According to him Erasmus in his Novum Instrumentum omne did not incorporate theComma from Codex Montfortianus, because of grammar dierences, but used Complutensian Polyglotta. Accordingto him the Comma was known for Tertullian.[35]

    The critic Joseph Bdier (18641938) launched a particularly withering attack on stemmatics in 1928. He surveyededitions of medieval French texts that were produced with the stemmatic method, and found that textual critics tendedoverwhelmingly to produce trees divided into just two branches. He concluded that this outcome was unlikely to haveoccurred by chance, and that therefore, the method was tending to produce bipartite stemmas regardless of the actualhistory of the witnesses. He suspected that editors tended to favor trees with two branches, as this would maximizethe opportunities for editorial judgment (as there would be no third branch to break the tie whenever the witnessesdisagreed). He also noted that, for many works, more than one reasonable stemma could be postulated, suggestingthat the method was not as rigorous or as scientic as its proponents had claimed.The stemmatic methods nal step is emendatio, also sometimes referred to as conjectural emendation. But in fact,the critic employs conjecture at every step of the process. Some of the methods rules that are designed to reduce theexercise of editorial judgment do not necessarily produce the correct result. For example, where there are more thantwo witnesses at the same level of the tree, normally the critic will select the dominant reading. However, it may beno more than fortuitous that more witnesses have survived that present a particular reading. A plausible reading thatoccurs less often may, nevertheless, be the correct one.[36]

  • 9.6. COPY-TEXT EDITING 23

    Lastly, the stemmatic method assumes that every extant witness is derived, however remotely, from a single source.It does not account for the possibility that the original author may have revised his work, and that the text could haveexisted at dierent times in more than one authoritative version.

    9.6 Copy-text editing

    A page from Codex Vaticanus Graecus 1209 shows a medieval scribe (the marginal note between columns one and two) criticizinga predecessor for changing the text: Fool and knave, leave the old reading, don't change it!"[37]

    When copy-text editing, the scholar xes errors in a base text, often with the help of other witnesses. Often, the basetext is selected from the oldest manuscript of the text, but in the early days of printing, the copy text was often amanuscript that was at hand.Using the copy-text method, the critic examines the base text and makes corrections (called emendations) in placeswhere the base text appears wrong to the critic. This can be done by looking for places in the base text that do notmake sense or by looking at the text of other witnesses for a superior reading. Close-call decisions are usually resolvedin favor of the copy-text.The rst published, printed edition of the Greek New Testament was produced by this method. Erasmus, the editor,selected a manuscript from the local Dominican monastery in Basle and corrected its obvious errors by consulting

  • 24 CHAPTER 9. STEMMATICS

    other local manuscripts. The Westcott and Hort text, which was the basis for the Revised Version of the Englishbible, also used the copy-text method, using the Codex Vaticanus as the base manuscript.[38]

    9.6.1 McKerrows concept of copy-textThe bibliographer Ronald B. McKerrow introduced the term copy-text in his 1904 edition of the works of ThomasNashe, dening it as the text used in each particular case as the basis ofmine.McKerrowwas aware of the limitationsof the stemmatic method, and believed it was more prudent to choose one particular text that was thought to beparticularly reliable, and then to emend it only where the text was obviously corrupt. The French critic Joseph Bdierlikewise became disenchanted with the stemmatic method, and concluded that the editor should choose the bestavailable text, and emend it as little as possible.In McKerrows method as originally introduced, the copy-text was not necessarily the earliest text. In some cases,McKerrow would choose a later witness, noting that if an editor has reason to suppose that a certain text embodieslater corrections than any other, and at the same time has no ground for disbelieving that these corrections, or someof them at least, are the work of the author, he has no choice but to make that text the basis of his reprint.[39]

    By 1939, in his Prolegomena for the Oxford Shakespeare, McKerrow had changed his mind about this approach, ashe feared that a later edition even if it contained authorial corrections would deviate more widely than the earliestprint from the authors original manuscript. He therefore concluded that the correct procedure would be producedby using the earliest good print as copy-text and inserting into it, from the rst edition which contains them, suchcorrections as appear to us to be derived from the author. But, fearing the arbitrary exercise of editorial judgment,McKerrow stated that, having concluded that a later edition had substantive revisions attributable to the author, wemust accept all the alterations of that edition, saving any which seem obvious blunders or misprints.[40]

    9.6.2 W. W. Gregs rationale of copy-textAnglo-American textual criticism in the last half of the 20th century came to be dominated by a landmark 1950 essayby Sir Walter W. Greg, The Rationale of Copy-Text. Greg proposed:

    [A] distinction between the signicant, or as I shall call them 'substantive', readings of the text, thosenamely that aect the authors meaning or the essence of his expression, and others, such in general asspelling, punctuation, word-division, and the like, aecting mainly its formal presentation, which maybe regarded as the accidents, or as I shall call them 'accidentals, of the text.[41]

    Greg observed that compositors at printing shops tended to follow the substantive readings of their copy faithfully,except when they deviated unintentionally; but that as regards accidentals they will normally follow their own habitsor inclination, though they may, for various reasons and to varying degrees, be inuenced by their copy.[42]

    He concluded:

    The true theory is, I contend, that the copy-text should govern (generally) in the matter of accidentals,but that the choice between substantive readings belongs to the general theory of textual criticism andlies altogether beyond the narrow principle of the copy-text. Thus it may happen that in a critical editionthe text rightly chosen as copy may not by any means be the one that supplies most substantive readingsin cases of variation. The failure to make this distinction and to apply this principle has naturally ledto too close and too general a reliance upon the text chosen as basis for an edition, and there has arisenwhat may be called the tyranny of the copy-text, a tyranny that has, in my opinion, vitiated much of thebest editorial work of the past generation.[43]

    Gregs view, in short, was that the copy-text can be allowed no over-riding or even preponderant authority so far assubstantive readings are concerned. The choice between reasonable competing readings, he said:

    [W]ill be determined partly by the opinion the editor may form respecting the nature of the copyfrom which each substantive edition was printed, which is a matter of external authority; partly by theintrinsic authority of the several texts as judged by the relative frequency of manifest errors therein; and

  • 9.6. COPY-TEXT EDITING 25

    partly by the editors judgment of the intrinsic claims of individual readings to originality in otherwords their intrinsic merit, so long as by 'merit' we mean the likelihood of their being what the authorwrote rather than their appeal to the individual taste of the editor.[44]

    Although Greg argued that an editor should be free to use his judgment to choose between competing substantivereadings, he suggested that an editor should defer to the copy-text when the claims of two readings ... appear to beexactly balanced. ... In such a case, while there can be no logical reason for giving preference to the copy-text, inpractice, if there is no reason for altering its reading, the obvious thing seems to be to let it stand.[45] The exactlybalanced variants are said to be indierent.Editors who follow Gregs rationale produce eclectic editions, in that the authority for the accidentals is derivedfrom one particular source (usually the earliest one) that the editor considers to be authoritative, but the authority forthe substantives is determined in each individual case according to the editors judgment. The resulting text, exceptfor the accidentals, is constructed without relying predominantly on any one witness.

    9.6.3 GregBowersTanselle

    W.W. Greg did not live long enough to apply his rationale of copy-text to any actual editions of works. His rationalewas adopted and signicantly expanded by Fredson Bowers (19051991). Starting in the 1970s, G. Thomas Tansellevigorously took up the methods defense and added signicant contributions of his own. Gregs rationale as practicedby Bowers and Tanselle has come to be known as the GregBowers or the GregBowersTanselle method.

    Application to works of all periods

    In his 1964 essay, Some Principles for Scholarly Editions of Nineteenth-Century American Authors, Bowers saidthat the theory of copy-text proposed by Sir Walter Greg rules supreme.[46] Bowerss assertion of supremacy wasin contrast to Gregs more modest claim that My desire is rather to provoke discussion than to lay down the law.[47]

    Whereas Greg had limited his illustrative examples to English Renaissance drama, where his expertise lay, Bowersargued that the rationale was the most workable editorial principle yet contrived to produce a critical text that is au-thoritative in the maximum of its details whether the author be Shakespeare, Dryden, Fielding, Nathaniel Hawthorne,or Stephen Crane. The principle is sound without regard for the literary period.[48] For works where an authorsmanuscript survived a case Greg had not considered Bowers concluded that the manuscript should generallyserve as copy-text. Citing the example of Nathaniel Hawthorne, he noted:

    When an authors manuscript is preserved, this has paramount authority, of course. Yet the fallacyis still maintained that since the rst edition was proofread by the author, it must represent his nalintentions and hence should be chosen as copy-text. Practical experience shows the contrary. When onecollates the manuscript of The House of the Seven Gables against the rst printed edition, one nds anaverage of ten to fteen dierences per page between the manuscript and the print, many of them con-sistent alterations from the manuscript system of punctuation, capitalization, spelling, and word-division.It would be ridiculous to argue that Hawthorne made approximately three to four thousand small changesin proof, and then wrote the manuscript of The Blithedale Romance according to the same system as themanuscript of the Seven Gables, a system that he had rejected in proof.[49]

    Following Greg, the editor would then replace any of the manuscript readings with substantives from printed editionsthat could be reliably attributed to the author: Obviously, an editor cannot simply reprint the manuscript, and hemust substitute for its readings any words that he believes Hawthorne changed in proof.[49]

    Uninuenced nal authorial intention

    McKerrow had articulated textual criticisms goal in terms of our ideal of an authors fair copy of his work in itsnal state.[50] Bowers asserted that editions founded on Gregs method would represent the nearest approximationin every respect of the authors nal intentions.[51] Bowers stated similarly that the editors task is to approximate as

  • 26 CHAPTER 9. STEMMATICS

    William Shakespeare, A Midsummer Nights Dream (First Folio)

    nearly as possible an inferential authorial fair copy.[52] Tanselle notes that, Textual criticism ... has generally beenundertaken with a view to reconstructing, as accurately as possible, the text nally intended by the author.[53]

    Bowers and Tanselle argue for rejecting textual variants that an author inserted at the suggestion of others. Bowerssaid that his edition of Stephen Crane's rst novel, Maggie, presented the authors nal and uninuenced artisticintentions.[54] In his writings, Tanselle refers to unconstrained authorial intention or an authors uninuencedintentions.[55] This marks a departure from Greg, who had merely suggested that the editor inquire whether a laterreading is one that the author can reasonably be supposed to have substituted for the former,[56] not implying anyfurther inquiry as to why the author had made the change.Tanselle discusses the example of Herman Melville's Typee. After the novels initial publication, Melvilles publisherasked him to soften the novels criticisms of missionaries in the South Seas. Although Melville pronounced thechanges an improvement, Tanselle rejected them in his edition, concluding that there is no evidence, internal orexternal, to suggest that they are the kinds of changes Melville would have made without pressure from someoneelse.[57]

    Bowers confronted a similar problem in his edition of Maggie. Crane originally printed the novel privately in 1893.To secure commercial publication in 1896, Crane agreed to remove profanity, but he also made stylistic revisions.Bowerss approach was to preserve the stylistic and literary changes of 1896, but to revert to the 1893 readings wherehe believed that Crane was fullling the publishers intention rather than his own. There were, however, intermediatecases that could reasonably have been attributed to either intention, and some of Bowerss choices came under re both as to his judgment, and as to the wisdom of conating readings from the two dierent versions of Maggie.[58]

  • 9.6. COPY-TEXT EDITING 27

    Hans Zeller argued that it is impossible to tease apart the changes Crane made for literary reasons and those made atthe publishers insistence:

    Firstly, in anticipation of the character of the expected censorship, Crane could be led to undertakealterations which also had literary value in the context of the new version. Secondly, because of thesystematic character of the work, purely censorial alterations sparked o further alterations, determinedat this stage by literary considerations. Again in consequence of the systemic character of the work, thecontamination of the two historical versions in the edited text gives rise to a third version. Though theeditor may indeed give a rational account of his decision at each point on the basis of the documents,nevertheless to aim to produce the ideal text which Crane would have produced in 1896 if the publisherhad left him complete freedom is to my mind just as unhistorical as the question of how the rst WorldWar or the history of the United States would have developed if Germany had not caused the USA toenter the war in 1917 by unlimited submarine combat. The nonspecic form of censorship describedabove is one of the historical conditions under which Crane wrote the second version of Maggie andmade it function. From the text which arose in this way it is not possible to subtract these forces andinuences, in order to obtain a text of the authors own. Indeed I regard the uninuenced artistic inten-tions of the author as something which exists only in terms of aesthetic abstraction. Between inuenceson the author and inuences on the text are all manner of transitions.[59]

    Bowers and Tanselle recognize that texts often exist in more than one authoritative version. Tanselle argues that:

    [T]wo types of revision must be distinguished: that which aims at altering the purpose, direction,or character of a work, thus attempting to make a dierent sort of work out of it; and that which aimsat intensifying, rening, or improving the work as then conceived (whether or not it succeeds in doingso), thus altering the work in degree but not in kind. If one may think of a work in terms of a spatialmetaphor, the rst might be labeled vertical revision, because it moves the work to a dierent plane,and the second horizontal revision, because it involves alterations within the same plane. Both producelocal changes in active intention; but revisions of the rst type appear to be in fulllment of an alteredprogrammatic intention or to reect an altered active intention in the work as a whole, whereas those ofthe second do not.[60]

    He suggests that where a revision is horizontal (i.e., aimed at improving the work as originally conceived), then theeditor should adopt the authors later version. But where a revision is vertical (i.e., fundamentally altering the worksintention as a whole), then the revision should be treated as a new work, and edited separately on its own terms.

    Format for apparatus

    Bowers was also inuential in dening the form of critical apparatus that should accompany a scholarly edition. Inaddition to the content of the apparatus, Bowers led a movement to relegate editorial matter to appendices, leavingthe critically established text in the clear, that is, free of any signs of editorial intervention. Tanselle explained therationale for this approach:

    In the rst place, an editors primary responsibility is to establish a text; whether his goal is to recon-struct that form of the text which represents the authors nal intention or some other form of the text,his essential task is to produce a reliable text according to some set of principles. Relegating all editorialmatter to an appendix and allowing the text to stand by itself serves to emphasize the primacy of thetext and permits the reader to confront the literary work without the distraction of editorial commentand to read the work with ease. A second advantage of a clear text is that it is easier to quote fromor to reprint. Although no device can insure accuracy of quotation, the insertion of symbols (or evenfootnote numbers) into a text places additional diculties in the way of the quoter. Furthermore, mostquotations appear in contexts where symbols are inappropriate; thus when it is necessary to quote froma text which has not been kept clear of apparatus, the burden of producing a clear text of the passageis placed on the quoter. Even footnotes at the bottom of the text pages are open to the same objection,when the question of a photographic reprint arises.[61]

  • 28 CHAPTER 9. STEMMATICS

    Some critics believe that a clear-text edition gives the edited text too great a prominence, relegating textual variantsto appendices that are dicult to use, and suggesting a greater sense of certainty about the established text than itdeserves. As Shillingsburg notes, English scholarly editions have tended to use notes at the foot of the text page,indicating, tacitly, a greater modesty about the established text and drawing attention more forcibly to at least someof the alternative forms of the text.[62]

    The MLAs CEAA and CSE

    In 1963, the Modern Language Association of America (MLA) established the Center for Editions of AmericanAuthors (CEAA). The CEAAs Statement of Editorial Principles and Procedures, rst published in 1967, adopted theGregBowers rationale in full. A CEAA examiner would inspect each edition, and only those meeting the require-ments would receive a seal denoting An Approved Text.Between 1966 and 1975, the Center allocated more than $1.5 million in funding from the National Endowmentfor the Humanities to various scholarly editing projects, which were required to follow the guidelines (including thestructure of editorial apparatus) as Bowers had dened them.[63] According to Davis, the funds coordinated by theCEAA over the same period were more than $6 million, counting funding from universities, university presses, andother bodies.[64]

    The Center for Scholarly Editions (CSE) replaced the CEAA in 1976. The change of name indicated the shift to abroader agenda than just American authors. The Center also ceased its role in the allocation of funds. The Centerslatest guidelines (2003) no longer prescribe a particular editorial procedure.[65]

    9.7 Cladistics

    Cladistics is a technique borrowed from biology, where it was originally named phylogenetic systematics by WilliHennig. In biology, the technique is used to determine the evolutionary relationships between dierent species.[66]In its application in textual criticism, the text of a number of dierent manuscripts is entered into a computer, whichrecords all the dierences between them. The manuscripts are then grouped according to their shared characteristics.The dierence between cladistics and more traditional forms of statistical analysis is that, rather than simply arrangingthe manuscripts into rough groupings according to their overall similarity, cladistics assumes that they are part of abranching family tree and uses that assumption to derive relationships between them. This makes it more like anautomated approach to stemmatics. However, where there is a dierence, the computer does not attempt to decidewhich reading is closer to the original text, and so does not indicate which branch of the tree is the rootwhichmanuscript tradition is closest to the original. Other types of evidence must be used for that purpose.The major theoretical problem with applying cladistics to textual criticism is that cladistics assumes that, once abranching has occurred in the family tree, the two branches cannot rejoin; so all similarities can be taken as evidenceof common ancestry. While this assumption is applicable to the evolution of living creatures, it is not always true ofmanuscript traditions, since a scribe can work from two dierent manuscripts at once, producing a new copy withcharacteristics of both.Nonetheless, software developed for use in biology has been applied with some success to textual criticism; forexample, it is being used by the Canterbury Tales Project[67] to determine the relationship between the 84 survivingmanuscripts and four early printed editions of The Canterbury Tales.

    9.8 Application of textual criticism to religious documents

    All texts are subject to investigation and systematic criticism where the original veried rst document is not available.Believers in sacred texts and scriptures sometimes are reluctant to accept any form of challenge to what they believeto be divine revelation. Some opponents and polemicists may look for any way to nd fault with a particular religioustext. Legitimate textual criticism may be resisted by both believers and skeptics.

  • 9.8. APPLICATION OF TEXTUAL CRITICISM TO RELIGIOUS DOCUMENTS 29

    Canterbury Tales, Woodcut 1484

    9.8.1 Qur'an

    Main article: Textual Criticism and Qurn ManuscriptsSee also: Origin and development of the Qur'an

    Textual criticism of the Quran is a beginning area of study,[68][69] as Muslims have historically disapproved of highercriticism being applied to the Quran.[70] In some countries textual criticism can be seen as apostasy.[71]

    Muslims consider the original Arabic text to be the nal revelation, revealed to Muhammad from AD 610 to his deathin 632. In Islamic tradition, the Qur'an was memorised and written down by Muhammads companions and copiedas needed. However, it is well known to scholars that: written versions vary enormously in materials, format andaspect.[72][73]

    In the 1970s, 14,000 fragments of Qur'an were discovered in an old mosque in Sanaa, the Sana'a manuscripts. About12,000 fragments belonged to 926 copies of the Qur'an, the other 2,000 were loose fragments. The oldest knowncopy of the Qur'an so far belongs to this collection: it dates to the end of the 7th8th centuries. The important nduncovered many textual variants not known from the canonical 7 (or 10 or 14) texts.The examination of Gerd R. Puin who led the restoration project revealed, unconventional verse orderings, minortextual variations, and rare styles of orthography and artistic embellishment.[74] Recent authors have also proposedthat the Koran may have been written in ArabicSyriac.[75]

  • 30 CHAPTER 9. STEMMATICS

    9.8.2 Book of Mormon

    See also: Historicity of the Book of Mormon

    The Church of Jesus Christ of Latter-day Saints (LDS Church) includes the Book of Mormon as a foundationalreference. LDS members typically believe the book to be a literal historical record.Although some earlier unpublished studies had been prepared, not until the early 1970s was true textual criticismapplied to the Book of Mormon. At that time BYU Professor Ellis Rasmussen and his associates were asked by theLDS Church to begin preparation for a new edition of the Holy Scriptures. One aspect of that eort entailed digitizingthe text and preparing appropriate footnotes, another aspect required establishing the most dependable text. To thatlatter end, Stanley R. Larson (a Rasmussen graduate student) set about applying modern text critical standards to themanuscripts and early editions of the Book of Mormon as his thesis project which he completed in 1974. To thatend, Larson carefully examined the Original Manuscript (the one dictated by Joseph Smith to his scribes) and thePrinters Manuscript (the copy Oliver Cowdery prepared for the Printer in 18291830), and compared them withthe 1st, 2nd, and 3rd editions of the Book of Mormon to determine what sort of changes had occurred over timeand to make judgments as to which readings were the most original.[76] Larson proceeded to publish a useful setof well-argued articles on the phenomena which he had discovered.[77] Many of his observations were included asimprovements in the 1981 LDS edition of the Book of Mormon.By 1979, with the establishment of the Foundation for Ancient Research and Mormon Studies (FARMS) as a Cal-ifornia non-prot research institution, an eort led by Robert F. Smith began to take full account of Larsons workand to publish a Critical Text of the Book of Mormon. Thus was born the FARMS Critical Text Project which pub-lished the rst volume of the 3-volume Book of Mormon Critical Text in 1984. The third volume of that rst editionwas published in 1987, but was already being superseded by a second, revised edition of the entire work,[78] greatlyaided through the advice and assistance of then Yale doctoral candidate Grant Hardy, Dr. Gordon C. Thomasson,Professor JohnW.Welch (the head of FARMS), Professor Royal Skousen, and others too numerous to mention here.However, these were merely preliminary steps to a far more exacting and all-encompassing project.In 1988, with that preliminary phase of the project completed, Professor Skousen took over as editor and head ofthe FARMS Critical Text of the Book of Mormon Project and proceeded to gather still scattered fragments of theOriginal Manuscript of the Book of Mormon and to have advanced photographic techniques applied to obtain nereadings from otherwise unreadable pages and fragments. He also closely examined the Printers Manuscript (ownedby the Community of ChristRLDS Church in Independence, Missouri) for dierences in types of ink or pencil, inorder to determine when and by whom they were made. He also collated the various editions of the Book of Mormondown to the present to see what sorts of changes have been made through time.Thus far, Professor Skousen has published complete transcripts of the Original and Printers Manuscripts,[79] as wellas a six-volume analysis of textual variants.[80] Still in preparation are a history of the text, and a complete electroniccollation of editions and manuscripts (volumes 3 and 5 of the Project, respectively). Yale University has in themeantime published an edition of the Book of Mormon which incorporates all aspects of Skousens research.[81]

    9.8.3 Hebrew Bible

    Main article: Documentary hypothesisTextual criticism of the Hebrew Bible compares manuscript versions of the following sources (dates refer to theoldest extant manuscripts in each family):Given the sacred nature of the Hebrew Bible in Judaism, those unaware of the details dealt with in textual criticismmight think that there are no corruptions in the text, since these texts were meticulously transmitted and written. Andyet, as in the New Testament, in particular in the Masoretic texts, changes, corruptions, and erasures have been found.This is ascribed to the fact that early soferim (scribes) did not treat copy errors in the same manner later on.[82]

    There are three separate new editions of the Hebrew Bible currently in development: Biblia Hebraica Quinta, theHebrew University Bible, and the Oxford Hebrew Bible. Biblia Hebraica Quinta is a diplomatic edition based on theLeningrad Codex. The Hebrew University Bible is also diplomatic, but based on the Aleppo Codex. The OxfordHebrew Bible is an eclectic edition.[83]

  • 9.8. APPLICATION OF TEXTUAL CRITICISM TO RELIGIOUS DOCUMENTS 31

    11th-century manuscript of the Hebrew Bible with Targum

    Old Testament

    Shemaryahu Talmon, who summarized the amount of consensus and genetic relation to the original Urtext of theHebrew Bible, concluded that major divergences which intrinsically aect the sense are extremely rare. As far as theHebrew Bible referenced by Old Testament is concerned, almost all of the textual variants are fairly insignicant andhardly aect any doctrine. Professor Douglas Stuart states: It is fair to say that the verses, chapters, and books ofthe Bible would read largely the same, and would leave the same impression with the reader, even if one adoptedvirtually every possible alternative reading to those now serving as the basis for current English translations.[84]

  • 32 CHAPTER 9. STEMMATICS

    A page from the Aleppo Codex, Deuteronomy.

    9.8.4 New Testament

    See also: Novum Testamentum Graece

    The New Testament has been preserved in more than 5,800 Greek manuscripts, 10,000 Latin manuscripts and 9,300manuscripts in various other ancient languages including Syriac, Slavic, Ethiopic and Armenian. There are approx-imately 300,000 textual variants among the manuscripts, most of them being the changes of word order and othercomparative trivialities.[85][86] Nonetheless, for over 250 years, New Testament scholars have argued that no textualvariant aects any doctrine.[85]

    The sheer number of witnesses presents unique diculties, chiey in that it makes stemmatics in many cases im-

  • 9.8. APPLICATION OF TEXTUAL CRITICISM TO RELIGIOUS DOCUMENTS 33

    possible, because many writers used two or more dierent manuscripts as sources. Consequently, New Testamenttextual critics have adopted eclecticism after sorting the witnesses into three major groups, called text-types. Themost common division today is as follows:

    Alexandrian text versus Byzantine text

    See also: List of major textual variants in the New TestamentThe New Testament portion of the English translation known as the King James Version was based on the TextusReceptus, a Greek text prepared by Erasmus based on a few late medieval Greek manuscripts of the Byzantine text-type (1, 1rK, 2e, 2ap, 4, 7, 817).[87] For some books of the Bible, Erasmus used just single manuscripts, and for smallsections made his own translations into Greek from the Vulgate.[88] However, following Westcott and Hort, mostmodern New Testament textual critics have concluded that the Byzantine text-type was formalised at a later date thanthe Alexandrian andWestern text-types. Among the other types, the Alexandrian text-type is viewed by some as morepure than the Western and Byzantine text-types, however, this view is held by the minority of scholars, and so one ofthe central tenets in the current practice ofNewTestament textual criticism is that one should follow the readings of theAlexandrian texts unless those of the other types are clearly superior. Most modern New Testament translations nowuse an Eclectic Greek text (UBS5 and NA 28) that is closest to the Alexandrian text-type. TheUnited Bible SocietiessGreek New Testament (UBS5) and Nestle Aland (NA 28) are accepted by most of the academic community as thebest attempt at reconstructing the original texts of the Greek NT.[89]

    A minority position represented by The Greek New Testament According to the Majority Text edition by Zane C.Hodges and Arthur L. Farstad argues that the Byzantine text-type represents an earlier text-type than the survivingAlexandrian texts. This position is also held by Maurice A. Robinson and William G. Pierpont in their The NewTestament in the Original Greek: Byzantine Textform, and the King James Only Movement. The argument states thatthe far greater number of surviving late Byzantine manuscripts implies an equivalent preponderance of Byzantinetexts amongst lost earlier manuscripts. Hence, a critical reconstruction of the predominant text of the Byzantinetradition would have a superior claim to being closest to the autographs.Another position is that of the Neo-Byzantine School. The Neo-Byzantines (or new Byzantines) of the 16th and17th centuries rst formally compiled the New Testament Received Text under such textual analysts as Erasmus,Stephanus (Robert Estienne), Beza, and Elzevir. The early 21st century saw the rise of the rst textual analyst of thisschool in over three centuries with Gavin McGrath (b. 1960). A religiously conservative Protestant from Australia,his Neo-Byzantine School principles maintain that the representative or majority Byzantine text, such as compiledby Hodges & Farstad (1985) or Robinson & Pierpont (2005), is to be upheld unless there is a clear and obvioustextual problem with it. When this occurs, he adopts either a minority Byzantine reading, a reading from the ancientVulgate, or a reading attested to in the writings of an ancient Church Father (in either Greek or Latin) by way ofquotation. The Neo-Byzantine School considers that the doctrine of the Divine Preservation of Scripture means thatGod preserved the Byzantine Greek manuscripts, Latin manuscripts, and Greek and Latin church writers citationsof Scripture over time and through time. These are regarded as a closed class of sources i.e., non-Byzantine Greekmanuscripts such as the Alexandrian texts, or manuscripts in other languages such as Armenian, Syriac, or Ethiopian,are regarded as outside the closed class of sources providentially protected over time, and so not used to composethe New Testament text.[90] Other scholars have criticized the current categorization of manuscripts into text-typesand prefer either to subdivide the manuscripts in other ways or to discard the text-type taxonomy.Textual criticism is also used by those who assert that the New Testament was written in Aramaic (see Aramaicprimacy).[91]

    Interpolations

    In attempting to determine the original text of the New Testament books, some modern textual critics have identiedsections as interpolations. In modern translations of the Bible such as the New International Version, the results oftextual criticism have led to certain verses, words and phrases being left out or marked as not original. Previously,translations of the New Testament such as the King James Version had mostly been based on Erasmus's redaction ofthe New Testament in Greek, the Textus Receptus from the 16th century based on later manuscripts.According to Bart D. Ehrman, These scribal additions are often found in late medieval manuscripts of the NewTestament, but not in the manuscripts of the earlier centuries, he adds. And because the King James Bible is basedon later manuscripts, such verses became part of the Bible tradition in English-speaking lands.[92]

    Most modern Bibles have footnotes to indicate passages that have disputed source documents. Bible Commentaries

  • 34 CHAPTER 9. STEMMATICS

    Byzantine illuminated manuscript, 1020

    also discuss these, sometimes in great detail.

  • 9.9. CLASSICAL TEXTS 35

    These possible later additions include the following:[93][94]

    the longer ending of Mark, see Mark 16 (Mark 16:920). Jesus sweating blood in Luke, Christs agony at Gethsemane (Luke 22:4344). the story in John of the woman taken in adultery, the Pericope Adulterae (John 7:538:11). an explicit reference to the Trinity in 1 John, the Comma Johanneum (1 John 5:78).

    Other disputed NT passages Opinions are divided on whether Jesus is referred to as unique [or only-begotten:Gk. monogenes] Son or unique [monogenes] God, in John 1:18[94]

    1 Corinthians 14:3335. Gordon Fee[95] regards the instruction for women to be silent in churches as a later, non-Pauline addition to the Letter, more in keeping with the viewpoint of the Pastoral Epistles (see 1 Tim 2.1112; Titus2.5) than of the certainly Pauline Epistles. A few manuscripts place these verses after 40[96]

    Various groups of highly conservative Christians believe that when Ps.12:67 speaks of the preservation of the wordsof God, that this nullies the need for textual criticism, lower, and higher. Such people include Gail Riplinger,Peter Ruckman, and others. Many theological organisations, societies, newsletters, and churches also hold to thisbelief, including AV Publications, Sword of The LORD Newsletter, The Antioch Bible Society [97] and others. Onthe other hand, Reformation biblical scholars such as Martin Luther saw the academic analysis of biblical texts andtheir provenance as entirely in line with orthodox Christian faith. Many of these men called themselves Christianhumanists, precisely because textual criticism (usually of biblical texts) lay at the heart of their work.

    9.8.5 TalmudMain article: Textual criticism of the Talmud

    Textual criticism of the Talmud has a long pre-history but has become a separate discipline from Talmudic studyonly recently.[98] Much of the research is in Hebrew and German language periodicals.[99]

    9.9 Classical textsWhile textual criticism developed into a discipline of thorough analysis of the Bible both the Hebrew Bible and theNew Testament scholars also use it to determine the original content of classic texts, such as Plato's Republic.[100]There are far fewer witnesses to classical texts than to the Bible, so scholars can use stemmatics and, in some cases,copy text editing. However, unlike theNewTestament where the earliest witnesses are within 200 years of the original,the earliest existingmanuscripts of most classical texts were written about a millennium after their composition. Otherthings being equal, textual scholars expect that a larger time gap between an original and a manuscript means morechanges in the text.

    9.10 Legal protectionScientic and critical editions can be protected by copyright as works of authorship if enough creativity/originalityis provided. The mere addition of a word, or substitution of a term with another one believed to be more correct,usually does not achieve such level of originality/creativity. All the notes accounting for the analysis and why and howsuch changes have been made represent a dierent work autonomously copyrightable if the other requirements aresatised. In the European Union critical and scientic editions may be protected also by the relevant neighboring rightthat protects critical and scientic publications of public domain works as made possible by art. 5 of the CopyrightTerm Directive. Not all EU member States have transposed art. 5 into national law.[101]

    9.11 SoftwareSeveral computer programs and standards exist to support the work of the editors of critical editions. These include

  • 36 CHAPTER 9. STEMMATICS

    The Text Encoding Initiative. The Guidelines of the TEI provide much detailed analysis of the proceduresof critical editing, including recommendations about how to mark up a computer le containing a text withcritical apparatus. See especially the following chapters of the Guidelines: 10. Manuscript Description, 11.Representation of Primary Sources, and 12. Critical Apparatus.

    Juxta is an open-source tool for comparing and collating multiple witnesses to a single textual work. It wasdesigned to aid scholars and editors examine the history of a text from manuscript to print versions. Juxtaprovides collation for multiple versions of texts that are marked up in plain text or TEI/XML format.

    The EDMAC macro package for Plain TeX is a set of macros originally developed by John Lavagnino andDominik Wujastyk for typesetting critical editions. EDMAC stands for EDition MACros. EDMAC isin maintenance mode.

    The ledmac package is a development of EDMAC by Peter R. Wilson for typesetting critical editions withLaTeX. ledmac is in maintenance mode.[102]

    The eledmac package is a further development of ledmac by Maeul Rouquette that adds more sophisticatedfeatures and solves more advanced problems. eledmac was forked from ledmac when it became clear that itneeded to develop in ways that would compromise backward-compatibility. eledmac is currently (2014) inactive development.

    ednotes, written by Christian Tapp and Uwe Lck is another package for typesetting critical editions usingLaTeX.

    Classical Text Editor is a word-processor for critical editions, commentaries and parallel texts written by StefanHagel. CTE is designed for use on the Windows operating system, but has been successfully run on Linux andOS/X using Wine. CTE can export les in TEI format. CTE is currently (2014) in active development.

    Critical Edition Typesetter by Bernt Karasch is a system for typesetting critical editions starting from inputinto a word-processor, and ending up with typesetting with TeX and EDMAC. Development opf CET seemsto have stopped in 2004.

    9.12 See also

    9.12.1 Topics Authority (textual criticism) A Historical Account of Two Notable Corruptions of Scripture Biblical manuscript Bible version debate Categories of New Testament manuscripts Close reading Comma Johanneum Dean Burgon Society Diplomatics Biblical glosses Hermeneutics John 21 Kaozheng (Chinese textual criticism)

  • 9.12. SEE ALSO 37

    List of Bible verses