(J. W. L. G.)
1Dr Thomas Smith thus describes the ardour with which Briggs studied theDescriptio: “Hunc in deliciis habuit, in sinu, in manibus, in pectore gestavit, oculisque avidissimis, et mente attentissima, iterum iterumque perlegit,...”Vitae quorundam eruditissimorum et illustrium virorum(London, 1707).2William Lilly’s account of the meeting of Napier and Briggs at Merchiston is quoted in the articleNapier.3It was certainly published after Napier’s death, as Briggs mentions his “librum posthumum.” Thisliber posthumuswas theConstructioreferred to later in this article.4Frisch’sKepleri opera omnia, ii. 834. Frisch thinks Bramer possibly relied on Kepler’s statement quoted in the text (“Quibus forte confisus Kepleri verbis Benj. Bramer....”). See also vol. vii. p. 298.The claims of Byrgius are discussed in Kästner’sGeschichte der Mathematik, ii. 375, and iii. 14; Montucla’sHistoire des mathématiques, ii. 10; Delambre’sHistoire de l’astronomie moderne, i. 560; de Morgan’s article on “Tables” in theEnglish Cyclopaedia; Mark Napier’sMemoirs of John Napier of Merchiston(1834), p. 392, and Cantor’sGeschichte der Mathematik, ii. (1892), 662. See also Gieswald,Justus Byrg als Mathematiker und dessen Einleitung in seine Logarithmen(Danzig, 1856).5See Mark Napier’sMemoirs of John Napier of Merchiston(1834), p. 362.6In theRabdologia(1617) he speaks of the canon of logarithms as “a me longo tempore elaboratum.”7A careful examination of the history of the method is given by Scheibel in hisEinleitung zur mathematischen Bücherkenntniss, Stück vii. (Breslau, 1775), pp. 13-20; and there is also an account in Kästner’sGeschichte der Mathematik, i. 566-569 (1796); in Montucla’sHistoire des mathématiques, i. 583-585 and 617-619; and in Klügel’sWörterbuch(1808), article “Prosthaphaeresis.”8Besides his connexion with logarithms and improvements in the method of prosthaphaeresis, Byrgius has a share in the invention of decimal fractions. See Cantor,Geschichte, ii. 567. Cantor attributes to him (in the use of his prosthaphaeresis) the first introduction of a subsidiary angle into trigonometry (vol. ii. 590).9The title of this work is—Benjaminis Ursini...cursus mathematici practici volumen primum continens illustr. & generosi Dn. Dn. Johannis Neperi Baronis Merchistonij &c. Scoti trigonometriam logarithmicam usibus discentium accommodatam...Coloniae...CIɔ IɔC XIX. At the end, Napier’s table is reprinted, but to two figures less. This work forms the earliest publication of logarithms on the continent.10The title isLogarithmorum canonis descriptio, seu arithmeticarum supputationum mirabilis abbreviatio.Ejusque usus in utraque trigonometria ut etiam in omni logistica mathematica, amplissimi, facillimi & expeditissimi explicatio. Authore ac inventore Ioanne Nepero, Barone Merchistonii, &c. Scoto. Lugduni.... It will be seen that this title is different from that of Napier’s work of 1614; many writers have, however, erroneously given it as the title of the latter.11In describing the contents of the works referred to, the language and notation of the present day have been adopted, so that for example a table to radius 10,000,000 is described as a table to 7 places, and so on. Also, although logarithms have been spoken of as to the basee, &c., it is to be noticed that neither Napier nor Briggs, nor any of their successors till long afterwards, had any idea of connecting logarithms with exponents.12The smallest number of entries which are necessary in a table of logarithms in order that the intermediate logarithms may be calculable by proportional parts has been investigated by J. E. A. Steggall in theProc. Edin. Math. Soc., 1892, 10, p. 35. This number is 1700 in the case of a seven-figure table extending to 100,000.13Accounts of Sang’s calculations are given in theTrans. Roy. Soc. Edin., 1872, 26, p. 521, and in subsequent papers in theProceedingsof the same society.14In vol. xv. (1875) of theVerhandelingenof the Amsterdam Academy of Sciences, Bierens de Haan has given a list of 553 tables of logarithms. A previous paper of the same kind, containing notices of some of the tables, was published by him in theVerslagen en Mededeelingenof the same academy (Afd. Natuurkunde) deel. iv. (1862), p. 15.
1Dr Thomas Smith thus describes the ardour with which Briggs studied theDescriptio: “Hunc in deliciis habuit, in sinu, in manibus, in pectore gestavit, oculisque avidissimis, et mente attentissima, iterum iterumque perlegit,...”Vitae quorundam eruditissimorum et illustrium virorum(London, 1707).
2William Lilly’s account of the meeting of Napier and Briggs at Merchiston is quoted in the articleNapier.
3It was certainly published after Napier’s death, as Briggs mentions his “librum posthumum.” Thisliber posthumuswas theConstructioreferred to later in this article.
4Frisch’sKepleri opera omnia, ii. 834. Frisch thinks Bramer possibly relied on Kepler’s statement quoted in the text (“Quibus forte confisus Kepleri verbis Benj. Bramer....”). See also vol. vii. p. 298.
The claims of Byrgius are discussed in Kästner’sGeschichte der Mathematik, ii. 375, and iii. 14; Montucla’sHistoire des mathématiques, ii. 10; Delambre’sHistoire de l’astronomie moderne, i. 560; de Morgan’s article on “Tables” in theEnglish Cyclopaedia; Mark Napier’sMemoirs of John Napier of Merchiston(1834), p. 392, and Cantor’sGeschichte der Mathematik, ii. (1892), 662. See also Gieswald,Justus Byrg als Mathematiker und dessen Einleitung in seine Logarithmen(Danzig, 1856).
5See Mark Napier’sMemoirs of John Napier of Merchiston(1834), p. 362.
6In theRabdologia(1617) he speaks of the canon of logarithms as “a me longo tempore elaboratum.”
7A careful examination of the history of the method is given by Scheibel in hisEinleitung zur mathematischen Bücherkenntniss, Stück vii. (Breslau, 1775), pp. 13-20; and there is also an account in Kästner’sGeschichte der Mathematik, i. 566-569 (1796); in Montucla’sHistoire des mathématiques, i. 583-585 and 617-619; and in Klügel’sWörterbuch(1808), article “Prosthaphaeresis.”
8Besides his connexion with logarithms and improvements in the method of prosthaphaeresis, Byrgius has a share in the invention of decimal fractions. See Cantor,Geschichte, ii. 567. Cantor attributes to him (in the use of his prosthaphaeresis) the first introduction of a subsidiary angle into trigonometry (vol. ii. 590).
9The title of this work is—Benjaminis Ursini...cursus mathematici practici volumen primum continens illustr. & generosi Dn. Dn. Johannis Neperi Baronis Merchistonij &c. Scoti trigonometriam logarithmicam usibus discentium accommodatam...Coloniae...CIɔ IɔC XIX. At the end, Napier’s table is reprinted, but to two figures less. This work forms the earliest publication of logarithms on the continent.
10The title isLogarithmorum canonis descriptio, seu arithmeticarum supputationum mirabilis abbreviatio.Ejusque usus in utraque trigonometria ut etiam in omni logistica mathematica, amplissimi, facillimi & expeditissimi explicatio. Authore ac inventore Ioanne Nepero, Barone Merchistonii, &c. Scoto. Lugduni.... It will be seen that this title is different from that of Napier’s work of 1614; many writers have, however, erroneously given it as the title of the latter.
11In describing the contents of the works referred to, the language and notation of the present day have been adopted, so that for example a table to radius 10,000,000 is described as a table to 7 places, and so on. Also, although logarithms have been spoken of as to the basee, &c., it is to be noticed that neither Napier nor Briggs, nor any of their successors till long afterwards, had any idea of connecting logarithms with exponents.
12The smallest number of entries which are necessary in a table of logarithms in order that the intermediate logarithms may be calculable by proportional parts has been investigated by J. E. A. Steggall in theProc. Edin. Math. Soc., 1892, 10, p. 35. This number is 1700 in the case of a seven-figure table extending to 100,000.
13Accounts of Sang’s calculations are given in theTrans. Roy. Soc. Edin., 1872, 26, p. 521, and in subsequent papers in theProceedingsof the same society.
14In vol. xv. (1875) of theVerhandelingenof the Amsterdam Academy of Sciences, Bierens de Haan has given a list of 553 tables of logarithms. A previous paper of the same kind, containing notices of some of the tables, was published by him in theVerslagen en Mededeelingenof the same academy (Afd. Natuurkunde) deel. iv. (1862), p. 15.
LOGAU, FRIEDRICH,Freiherr von(1604-1655), German epigrammatist, was born at Brockut, near Nimptsch, in Silesia, in June 1604. He was educated at the gymnasium of Brieg and subsequently studied law. He then entered the service of the duke of Brieg. In 1644 he was made “ducal councillor.” He died at Liegnitz on the 24th of July 1655. Logau’s epigrams, which appeared in two collections under the pseudonym “Salomon von Golaw” (an anagram of his real name) in 1638 (Erstes Hundert Teutscher Reimensprüche) and 1654 (Deutscher Sinngedichte drei Tausend), show a marvellous range and variety of expression. He had suffered bitterly under the adverse conditions of the time; but his satire is not merely the outcome of personal feeling. In the turbulent age of the Thirty Years’ War he was one of the few men who preserved intact his intellectual integrity and judged his contemporaries fairly. He satirized with unsparing hand the court life, the useless bloodshed of the war, the lack of national pride in the German people, and their slavish imitation of the French in customs, dress and speech. He belonged to theFruchtbringende Gesellschaftunder the nameDer Verkleinernde, and regarded himself as a follower of Martin Opitz; but he did not allow such ties to influence his independence or originality.
Logau’sSinngedichtewere edited in 1759 by G. E. Lessing and K. W. Ramler, who first drew attention to their merits; a secondedition appeared in 1791. A critical edition was published by G. Eitner in 1872, who also edited a selection of Logau’s epigrams for theDeutsche Dichter des XVII. Jahrhunderts(vol. iii., 1870); there is also a selection by H. Oesterley in Kürschner’sDeutsche Nationalliteratur, vol. xxviii. (1885). See H. Denker,Beiträge zur literarischen Würdigung Logaus(1889); W. Heuschkel,Untersuchungen über Ränders und Lessings Bearbeitung Logauscher Sinngedichte(1901).
Logau’sSinngedichtewere edited in 1759 by G. E. Lessing and K. W. Ramler, who first drew attention to their merits; a secondedition appeared in 1791. A critical edition was published by G. Eitner in 1872, who also edited a selection of Logau’s epigrams for theDeutsche Dichter des XVII. Jahrhunderts(vol. iii., 1870); there is also a selection by H. Oesterley in Kürschner’sDeutsche Nationalliteratur, vol. xxviii. (1885). See H. Denker,Beiträge zur literarischen Würdigung Logaus(1889); W. Heuschkel,Untersuchungen über Ränders und Lessings Bearbeitung Logauscher Sinngedichte(1901).
LOGIA,a title used to describe a collection of the sayings of Jesus Christ (λόγια Ἰησοῦ) and therefore generally applied to the “Sayings of Jesus” discovered in Egypt by B. P. Grenfell and A. S. Hunt. There is some question as to whether the term is rightly used for this purpose. It does not occur in the Papyri in this sense. Each “saying” is introduced by the phrase “Jesus says” (λέγει) and the collection is described in the introductory words of the 1903 series asλόγοιnot asλόγια. Some justification for the employment of the term is found in early Christian literature. Several writers speak of theλόγια τοῦ κυρίουorτὰ κυριακὰ λόγια,i.e.oracles of (or concerning) the Lord. Polycarp, for instance, speaks of “those who pervert the oracles of the Lord.” (Philipp. 7), and Papias, as Eusebius tells us, wrote a work with the title “Expositions of the Oracles of the Lord.” The expression has been variously interpreted. It need mean no more (Lightfoot,Essays on Supernatural Religion, 172 seq.) than narratives of (or concerning) the Lord; on the other hand, the phrase is capable of a much more definite meaning, and there are many scholars who hold that it refers to a document which contained a collection of the sayings of Jesus. Some such document, we know, must lie at the base of our Synoptic Gospels, and it is quite possible that it may have been known to and used by Papias. It is only on this assumption that the use of the term Logia in the sense described above can be justified.
“The Sayings,” to which the term Logia is generally applied, consist of (a) a papyrus leaf containing seven or eight sayings of Jesus discovered in 1897, (b) a second leaf containing five more sayings discovered in 1903, (c) two fragments of unknown Gospels, the former published in 1903, the latter in 1907. All these were found amongst the great mass of papyri acquired by the Egyptian Exploration Fund from the ruins of Oxyrhynchus, one of the chief early Christian centres in Egypt, situated some 120 m. S. of Cairo.
The eight “sayings” discovered in 1897 are as follows:—
1. ...καὶ τότε διαβλέψεις ἐκβαλεῖν τὸ κάρφος τὸ ἐν τῷ ὀφθαλμῷ τοῦ ἀδελφοῦ σου.2.Λέγει Ἰησοῦς ἐὰν μὴ νηστεύσητε τὸν κόσμον οὐ μὴ εὔρητε τὴν βασίλειαν τοῦ θεοῦ. καὶ ἐὰν μὴ σαββατίσητε τὸ σάββατον οὐκ ὄψεσθε τὸν πατέρα.3.Λέγει Ἰησοῦς ἔ[σ]την ἐν μεσῷ τοῦ κόσμου καὶ ἐν σαρκὶ ὤφθην αὐτοῖς, καὶ εὖρον πάντας μεθύοντας καὶ οὐδένα εὖρον διψῶντα ἐν αὐτοῖς, καὶ πονεῖ ἡ ψυχή μου ἐπὶ τοῖς υὶοῖς τῶν ἀνθρώπων, ὅτι τυφλοί εἰσιν τῇ καρδίᾳ αὐτῶ[ν] κ[αὶ] ο̣ὐ̣ βλ̣έ[πουσιν]....4. [Illegible: possibly joins on to 3] ...[τ]ὴν πτωχείαν.5.[Λέγ]ει [Ἰησοῦς ὄπ]ου ἐὰν ὧσιν [β, οὐκ] ε[ἰσὶ]ν ἄθεοι καὶ [ὅ]που ε[ἶς] ἐστιν μόνος, [λέ]γω, ἐγώ εἰμι μετ᾽ αὐτ[οῦ] ἔγει[ρ]ον τὸν λίθον κἀκεῖ εὑρήσεις με, σχίσον τὸ ξύλον κἀγὼ ἐκεῖ εἰμι.6.Λέγει Ἰησοῦς ούκ ἔστιν δεκτὸς προφήτης ἐν τῇ πατρίδι αὐτ[ο]ῦ, οὐδὲ ἰατρὸς ποιεῖ θεραπείας εἰς τοὺς γινώσκοντας αὐτόν.7.Λέγει Ἰησοῦς πόλιςοἰ κοδομημένη ἐπ᾽ ἄκρον [ὄ]ρους ὑψηλοῦ καὶ ἐστηριγμένη οὔτε πε[σ]εῖν δύναται οὔτε κρυ[β]ῆναι.8.Λέγει Ἰησοῦς ἀκούεις [ε]ἰ̣ς τ̣ὸ ἓ̣ν̣ ᾠ̣τ̣ίον σοῦ τ̣ὸ [δὲ ἕτερον συνέκλεισας].Letters in brackets are missing in the original: letters which are dotted beneath are doubtful.1. “... and then shalt thou see clearly to cast out the mote that is in thy brother’s eye.”2. “Jesus saith, Except ye fast to the world, ye shall in no wise find the kingdom of God; and except ye make the sabbath a real sabbath, ye shall not see the Father.”3. “Jesus saith, I stood in the midst of the world and in the flesh was I seen of them, and I found all men drunken, and none found I athirst among them, and my soul grieveth over the sons of men, because they are blind in their heart, and see not....”4. “... poverty....”5. “Jesus saith, Wherever there are two, they are not without God, and wherever there is one alone, I say, I am with him. Raise the stone and there thou shalt find me, cleave the wood and there am I.”6. “Jesus saith, A prophet is not acceptable in his own country, neither doth a physician work cures upon them that know him.”7. “Jesus saith, A city built upon the top of a high hill and stablished can neither fall nor be hid.”8. “Jesus saith, Thou hearest with one ear [but the other ear hast thou closed].”
1. ...καὶ τότε διαβλέψεις ἐκβαλεῖν τὸ κάρφος τὸ ἐν τῷ ὀφθαλμῷ τοῦ ἀδελφοῦ σου.
2.Λέγει Ἰησοῦς ἐὰν μὴ νηστεύσητε τὸν κόσμον οὐ μὴ εὔρητε τὴν βασίλειαν τοῦ θεοῦ. καὶ ἐὰν μὴ σαββατίσητε τὸ σάββατον οὐκ ὄψεσθε τὸν πατέρα.
3.Λέγει Ἰησοῦς ἔ[σ]την ἐν μεσῷ τοῦ κόσμου καὶ ἐν σαρκὶ ὤφθην αὐτοῖς, καὶ εὖρον πάντας μεθύοντας καὶ οὐδένα εὖρον διψῶντα ἐν αὐτοῖς, καὶ πονεῖ ἡ ψυχή μου ἐπὶ τοῖς υὶοῖς τῶν ἀνθρώπων, ὅτι τυφλοί εἰσιν τῇ καρδίᾳ αὐτῶ[ν] κ[αὶ] ο̣ὐ̣ βλ̣έ[πουσιν]....
4. [Illegible: possibly joins on to 3] ...[τ]ὴν πτωχείαν.
5.[Λέγ]ει [Ἰησοῦς ὄπ]ου ἐὰν ὧσιν [β, οὐκ] ε[ἰσὶ]ν ἄθεοι καὶ [ὅ]που ε[ἶς] ἐστιν μόνος, [λέ]γω, ἐγώ εἰμι μετ᾽ αὐτ[οῦ] ἔγει[ρ]ον τὸν λίθον κἀκεῖ εὑρήσεις με, σχίσον τὸ ξύλον κἀγὼ ἐκεῖ εἰμι.
6.Λέγει Ἰησοῦς ούκ ἔστιν δεκτὸς προφήτης ἐν τῇ πατρίδι αὐτ[ο]ῦ, οὐδὲ ἰατρὸς ποιεῖ θεραπείας εἰς τοὺς γινώσκοντας αὐτόν.
7.Λέγει Ἰησοῦς πόλιςοἰ κοδομημένη ἐπ᾽ ἄκρον [ὄ]ρους ὑψηλοῦ καὶ ἐστηριγμένη οὔτε πε[σ]εῖν δύναται οὔτε κρυ[β]ῆναι.
8.Λέγει Ἰησοῦς ἀκούεις [ε]ἰ̣ς τ̣ὸ ἓ̣ν̣ ᾠ̣τ̣ίον σοῦ τ̣ὸ [δὲ ἕτερον συνέκλεισας].
Letters in brackets are missing in the original: letters which are dotted beneath are doubtful.
1. “... and then shalt thou see clearly to cast out the mote that is in thy brother’s eye.”
2. “Jesus saith, Except ye fast to the world, ye shall in no wise find the kingdom of God; and except ye make the sabbath a real sabbath, ye shall not see the Father.”
3. “Jesus saith, I stood in the midst of the world and in the flesh was I seen of them, and I found all men drunken, and none found I athirst among them, and my soul grieveth over the sons of men, because they are blind in their heart, and see not....”
4. “... poverty....”
5. “Jesus saith, Wherever there are two, they are not without God, and wherever there is one alone, I say, I am with him. Raise the stone and there thou shalt find me, cleave the wood and there am I.”
6. “Jesus saith, A prophet is not acceptable in his own country, neither doth a physician work cures upon them that know him.”
7. “Jesus saith, A city built upon the top of a high hill and stablished can neither fall nor be hid.”
8. “Jesus saith, Thou hearest with one ear [but the other ear hast thou closed].”
The “sayings” of 1903 were prefaced by the following introductory statement:—
οἱ τοῖοι οἱ λόγοι οἱ [... οὓς ἐλάλησεν Ἰη(σοῦ)ς ὁ ζῶν κ[ύριος? ... καὶ Θωμᾷ καὶ εἶπεν [αὐτοῖς· πᾶς ὅστις ἂν τῶν λόγων τούτ[ων ἀκούσῃ θανάτου οὐ μὴ γεύσηται.“These are the (wonderful?) words which Jesus the living (Lord) spake to ... and Thomas and he said unto (them) every one that hearkens to these words shall never taste of death.”
οἱ τοῖοι οἱ λόγοι οἱ [... οὓς ἐλάλησεν Ἰη(σοῦ)ς ὁ ζῶν κ[ύριος? ... καὶ Θωμᾷ καὶ εἶπεν [αὐτοῖς· πᾶς ὅστις ἂν τῶν λόγων τούτ[ων ἀκούσῃ θανάτου οὐ μὴ γεύσηται.
“These are the (wonderful?) words which Jesus the living (Lord) spake to ... and Thomas and he said unto (them) every one that hearkens to these words shall never taste of death.”
The “sayings” themselves are as follows:—
(1)[λέγει Ἰη(σοῦ)ς· μὴ παυσάσθω ὁ ζη[τῶν...ἕως ἄν εὕρῃ καὶ ὅταν εὔρῃ [θαμβηθήσεαικαὶ θαμβηθεὶς βασιλεύσει κα[ὶ βασιλεύσαςἀναπαήσεται.(2)λέγει Ἰ[η(σοῦς ... τίνες...οἱ ἕλκοντες ἡμᾶς [εἰς τὴν βασιλείαν εἰἡ βασιλεία ἐν οὐρα[νῷ ἐστιν;τὰ πετεινὰ τοῦ οὐρ[ανοῦ καὶ τῶν θηρίων ὅτι ὑπὸ τὴν γῆν ἐστ[ιν ἤ ἐπὶ τῆς γῆς καὶοἱ ἰχθύες τῆς θαλά[σσης οὖτοι οἱ ἕλκον-τες ὑμᾶς καὶ ῇ βασ[ιλεία τῶν οὐρανῶνἐντὸς ὐμῶν [ἐ]στι [καὶ ὅστις ἃν ἑαυτὸνγνῷ ταύτην εὑρή[σει...ἑαυτοὺς γνώσεσθε [καὶ εἰδήσετε ὅτι υἱοὶἔστε ὑμεῖς τοῦ πατρὸς τοῦ τ[ ...γνώσ(εσ)θε ἐαυτοὺς ἐν[ ...καὶ ὑ εῖς ἐστὲ ηπτο̣[(3)[ λέγει Ἰη(σοῦ)ςοὐκ ἀποκνήσει ἄνθ[ρωπος...ρων ἐπερωτῆσαι πα[ ...ρων περὶ τοῦ τόπου τῆ[ς...σετε ὅτι πολλοὶ ἔσονται π[ρῶτοι ἔσχατοι καὶοἱ ἕσχατοι πρῶτοι καὶ[ ...σιν.(4)λέγει Ἰη(σοῦ)ς· [πᾶν τὸ μὴ ἔμπροσ-θεν τῆς ὅψεως σου καὶ[τὸ κεκρυμμένονἀπὸ σοῦ ἀποκαλυφ(θ)ήσετ[αί σοι. οὐ γάρ ἐσ-τιν κρυπτὸν ὃ οὐ φανε[ρὸν γενήσεταικαὶ τεθαμμένον ὃ ο[ὐκ ἐγερθήσεται.(5)[ἐξ] ετάζουσιν αὐτὸν ο[ἱ μαθηταἱ αὐτοῦ καὶ[λέ]γουσιν· πῶς νηστεύ[σομεν καὶ πῶς...[ ... ]μεθα καὶ πῶς[ ...[ ...κ]αὶ τί παρατηρήσ[ομεν...[ ... ]ν; λέγει Ἰη(σοῦ)ς· [ ...[ ... ]ειται μὴ ποεῖτ[ε...[ ... ]ης ἀληθείας ἀν[ ...[ ... ]ν ἀ[π]οκεκρ[υ...[ ...μα] κάρι[ός] ἐστιν[ ...[ ... ]ω ἐστ[ι...[ ... ]ιν[ ...
(1)[λέγει Ἰη(σοῦ)ς· μὴ παυσάσθω ὁ ζη[τῶν...
ἕως ἄν εὕρῃ καὶ ὅταν εὔρῃ [θαμβηθήσεαι
καὶ θαμβηθεὶς βασιλεύσει κα[ὶ βασιλεύσας
ἀναπαήσεται.
(2)λέγει Ἰ[η(σοῦς ... τίνες...
οἱ ἕλκοντες ἡμᾶς [εἰς τὴν βασιλείαν εἰ
ἡ βασιλεία ἐν οὐρα[νῷ ἐστιν;
τὰ πετεινὰ τοῦ οὐρ[ανοῦ καὶ τῶν θηρίων ὅ
τι ὑπὸ τὴν γῆν ἐστ[ιν ἤ ἐπὶ τῆς γῆς καὶ
οἱ ἰχθύες τῆς θαλά[σσης οὖτοι οἱ ἕλκον-
τες ὑμᾶς καὶ ῇ βασ[ιλεία τῶν οὐρανῶν
ἐντὸς ὐμῶν [ἐ]στι [καὶ ὅστις ἃν ἑαυτὸν
γνῷ ταύτην εὑρή[σει...
ἑαυτοὺς γνώσεσθε [καὶ εἰδήσετε ὅτι υἱοὶ
ἔστε ὑμεῖς τοῦ πατρὸς τοῦ τ[ ...
γνώσ(εσ)θε ἐαυτοὺς ἐν[ ...
καὶ ὑ εῖς ἐστὲ ηπτο̣[
(3)[ λέγει Ἰη(σοῦ)ς
οὐκ ἀποκνήσει ἄνθ[ρωπος...
ρων ἐπερωτῆσαι πα[ ...
ρων περὶ τοῦ τόπου τῆ[ς...
σετε ὅτι πολλοὶ ἔσονται π[ρῶτοι ἔσχατοι καὶ
οἱ ἕσχατοι πρῶτοι καὶ[ ...
σιν.
(4)λέγει Ἰη(σοῦ)ς· [πᾶν τὸ μὴ ἔμπροσ-
θεν τῆς ὅψεως σου καὶ[τὸ κεκρυμμένον
ἀπὸ σοῦ ἀποκαλυφ(θ)ήσετ[αί σοι. οὐ γάρ ἐσ-
τιν κρυπτὸν ὃ οὐ φανε[ρὸν γενήσεται
καὶ τεθαμμένον ὃ ο[ὐκ ἐγερθήσεται.
(5)[ἐξ] ετάζουσιν αὐτὸν ο[ἱ μαθηταἱ αὐτοῦ καὶ
[λέ]γουσιν· πῶς νηστεύ[σομεν καὶ πῶς...
[ ... ]μεθα καὶ πῶς[ ...
[ ...κ]αὶ τί παρατηρήσ[ομεν...
[ ... ]ν; λέγει Ἰη(σοῦ)ς· [ ...
[ ... ]ειται μὴ ποεῖτ[ε...
[ ... ]ης ἀληθείας ἀν[ ...
[ ... ]ν ἀ[π]οκεκρ[υ...
[ ...μα] κάρι[ός] ἐστιν[ ...
[ ... ]ω ἐστ[ι...
[ ... ]ιν[ ...
1. “Jesus saith, Let not him who seeks ... cease until he finds and when he finds he shall be astonished; astonished he shall reach the kingdom and having reached the kingdom he shall rest.”2. “Jesus saith (ye ask? who are those) that draw us (to the kingdom if) the kingdom is in Heaven? ... the fowls of the air and all beasts that are under the earth or upon the earth and the fishes of the sea (these are they which draw) you and the kingdom of Heaven is within you and whosoever shall know himself shall find it. (Strive therefore?) to know yourselves and ye shall be aware that ye are the sons of the (Almighty?) Father; (and?) ye shall know that ye are in (the city of God?) and ye are (the city?).”3. “Jesus saith, A man shall not hesitate ... to ask concerning his place (in the kingdom. Ye shall know) that many that are first shall be last and the last first and (they shall have eternal life?).”4. “Jesus saith, Everything that is not before thy face and that which is hidden from thee shall be revealed to thee. For there is nothing hidden which shall not be made manifest nor buried which shall not be raised.”5. “His disciples question him and say, How shall we fast and how shall we (pray?) ... and what (commandment) shall we keep ... Jesus saith ... do not ... of truth ... blessed is he ...”
1. “Jesus saith, Let not him who seeks ... cease until he finds and when he finds he shall be astonished; astonished he shall reach the kingdom and having reached the kingdom he shall rest.”
2. “Jesus saith (ye ask? who are those) that draw us (to the kingdom if) the kingdom is in Heaven? ... the fowls of the air and all beasts that are under the earth or upon the earth and the fishes of the sea (these are they which draw) you and the kingdom of Heaven is within you and whosoever shall know himself shall find it. (Strive therefore?) to know yourselves and ye shall be aware that ye are the sons of the (Almighty?) Father; (and?) ye shall know that ye are in (the city of God?) and ye are (the city?).”
3. “Jesus saith, A man shall not hesitate ... to ask concerning his place (in the kingdom. Ye shall know) that many that are first shall be last and the last first and (they shall have eternal life?).”
4. “Jesus saith, Everything that is not before thy face and that which is hidden from thee shall be revealed to thee. For there is nothing hidden which shall not be made manifest nor buried which shall not be raised.”
5. “His disciples question him and say, How shall we fast and how shall we (pray?) ... and what (commandment) shall we keep ... Jesus saith ... do not ... of truth ... blessed is he ...”
The fragment of a lost Gospelwhich was discovered in 1903 contained originally about fifty lines, but many of them have perished and others are undecipherable. The translation, as far as it can be made out, is as follows:—
1-7. “(Take no thought) from morning until even nor from evening until morning either for your food what ye shall eat or for your raiment what ye shall put on. 7-13. Ye are far better than the lilies which grow but spin not. Having one garment what do ye (lack)?... 13-15. Who could add to your stature? 15-16. He himself will give you your garment. 17-23. His disciples say unto him, When wilt thou be manifest unto us and when shall we see thee? He saith, When ye shall be stripped and not be ashamed ... 41-46. Hesaid, The key of knowledge ye hid: ye entered not in yourselves, and to them that were entering in, ye opened not.”
1-7. “(Take no thought) from morning until even nor from evening until morning either for your food what ye shall eat or for your raiment what ye shall put on. 7-13. Ye are far better than the lilies which grow but spin not. Having one garment what do ye (lack)?... 13-15. Who could add to your stature? 15-16. He himself will give you your garment. 17-23. His disciples say unto him, When wilt thou be manifest unto us and when shall we see thee? He saith, When ye shall be stripped and not be ashamed ... 41-46. Hesaid, The key of knowledge ye hid: ye entered not in yourselves, and to them that were entering in, ye opened not.”
The second Gospel fragmentdiscovered in 1907 “consists of a single vellum leaf, practically complete except at one of the lower corners and here most of the lacunae admit of a satisfactory solution.” The translation is as follows:—
... before he does wrong makes all manner of subtle excuse. But give heed lest ye also suffer the same things as they: for the evil doers among men receive their reward not among the living only, but also await punishment and much torment. And he took them and brought them into the very place of purification and was walking in the temple. And a certain Pharisee, a chief priest, whose name was Levi, met them and said to the Saviour, Who gave thee leave to walk in this place of purification, and to see these holy vessels when thou hast not washed nor yet have thy disciples bathed their feet? But defiled thou hast walked in this temple, which is a pure place, wherein no other man walks except he has washed himself and changed his garments neither does he venture to see these holy vessels. And the Saviour straightway stood still with his disciples and answered him, Art thou then, being here in the temple, clean? He saith unto him, I am clean; for I washed in the pool of David and having descended by one staircase, I ascended by another and I put on white and clean garments, and then I came and looked upon these holy vessels. The Saviour answered and said unto him, Woe ye blind, who see not. Thou hast washed in these running waters wherein dogs and swine have been cast night and day and hast cleansed and wiped the outside skin which also the harlots and flute-girls anoint and wash and wipe and beautify for the lust of men; but within they are full of scorpions and all wickedness. But I and my disciples who thou sayest have not bathed have been dipped in the waters of eternal life which come from.... But woe unto thee....
... before he does wrong makes all manner of subtle excuse. But give heed lest ye also suffer the same things as they: for the evil doers among men receive their reward not among the living only, but also await punishment and much torment. And he took them and brought them into the very place of purification and was walking in the temple. And a certain Pharisee, a chief priest, whose name was Levi, met them and said to the Saviour, Who gave thee leave to walk in this place of purification, and to see these holy vessels when thou hast not washed nor yet have thy disciples bathed their feet? But defiled thou hast walked in this temple, which is a pure place, wherein no other man walks except he has washed himself and changed his garments neither does he venture to see these holy vessels. And the Saviour straightway stood still with his disciples and answered him, Art thou then, being here in the temple, clean? He saith unto him, I am clean; for I washed in the pool of David and having descended by one staircase, I ascended by another and I put on white and clean garments, and then I came and looked upon these holy vessels. The Saviour answered and said unto him, Woe ye blind, who see not. Thou hast washed in these running waters wherein dogs and swine have been cast night and day and hast cleansed and wiped the outside skin which also the harlots and flute-girls anoint and wash and wipe and beautify for the lust of men; but within they are full of scorpions and all wickedness. But I and my disciples who thou sayest have not bathed have been dipped in the waters of eternal life which come from.... But woe unto thee....
These documents have naturally excited considerable interest and raised many questions. The papyri of the “sayings” date from the 3rd century and most scholars agree that the “sayings” themselves go back to the 2nd. The yearA.D.140 is generally assigned as theterminus ad quem. The problem as to their origin has been keenly discussed. There are two main types of theory. (1) Some suppose that they are excerpts from an uncanonical Gospel. (2) Others think that they represent an independent and original collection of sayings. The first theory has assumed three main forms. (a) Harnack maintains that they were taken from the Gospel according to the Egyptians. This theory, however, is based upon a hypothetical reconstruction of the Gospel in question which has found very few supporters. (b) Others have advocated the Gospel of the Hebrews as the source of the “sayings,” on the ground of the resemblance between the first “saying” of the 1903 series and a well-authenticated fragment of that Gospel. The resemblance, however, is not sufficiently clear to support the conclusion. (c) A third view supposes that they are extracts from the Gospel of Thomas—an apocryphal Gospel dealing with the boyhood of Jesus. Beyond the allusion to Thomas in the introductory paragraph to the 1903 series, there seems to be no tangible evidence in support of this view. The second theory, which maintains that the papyri represent an independent collection of “sayings,” seems to be the opinion which has found greatest favour. It has won the support of W. Sanday, H. B. Swete, Rendel Harris, W. Lock, Heinrici, &c. There is a considerable diversity of judgment, however, with regard to the value of the collection. (a) Some scholars maintain that the collection goes back to the 1st century and represents one of the earliest attempts to construct an account of the teaching of Jesus. They are therefore disposed to admit to a greater or less extent and with widely varying degrees of confidence the presence of genuine elements in the new matter. (b) Sanday and many others regard the sayings as originating early in the 2nd century and think that, though not “directly dependent on the Canonical Gospels,” they have “their origin under conditions of thought which these Gospels had created.” The “sayings” must be regarded as expansions of the true tradition, and little value is therefore to be attached to the new material.
With the knowledge at our disposal, it is impossible to reach an assured conclusion between these two views. The real problem, to which at present no solution has been found, is to account for the new material in the “sayings.” There seems to be no motive sufficient to explain the additions that have been made to the text of the Gospels. It cannot be proved that the expansions have been made in the interests of any sect or heresy. Unless new discoveries provide the clue, or some reasonable explanation can otherwise be found, there seems to be no reason why we should not regard the “sayings” as containing material which ought to be taken into account in the critical study of the teaching of Jesus.
The 1903 Gospel fragment is so mutilated in many of its parts that it is difficult to decide upon its character and value. It appears to be earlier than 150, and to be taken from a Gospel which followed more or less closely the version of the teaching of Jesus given by Matthew and Luke. The phrase “when ye shall be stripped and not be ashamed” contains an idea which has some affinity with two passages found respectively in the Gospel according to the Egyptians and the so-called Second Epistle of Clement. The resemblance, however, is not sufficiently close to warrant the deduction that either the Gospel of the Egyptians or the Gospel from which the citation in 2 Clement is taken (if these two are distinct) is the source from which our fragment is derived.
The second Gospel fragment (1907) seems to be of later origin than the documents already mentioned. Grenfell and Hunt date the Gospel, from which it is an excerpt, about 200. There is considerable difficulty with regard to some of the details. The statement that an ordinary Jew was required to wash and change his clothes before visiting the inner court of the temple is quite unsupported by any other evidence. Nothing is known about “the place of purification” (ἁγνευτήριον) nor “the pool of David” (λίμνη τοῦ Δαυείδ). Nor does the statement that “the sacred vessels” were visible from the place where Jesus was standing seem at all probable. Grenfell and Hunt conclude therefore—“So great indeed are the divergences between this account and the extant and no doubt well-informed authorities with regard to the topography and ritual of the Temple that it is hardly possible to avoid the conclusion that much of the local colour is due to the imagination of the author who was aiming chiefly at dramatic effect and was not really well acquainted with the Temple. But if the inaccuracy of the fragment in this important respect is admitted the historical character of the whole episode breaks down and it is probably to be regarded as an apocryphal elaboration of Matt. xv. 1-20 and Mark vii. 1-23.”
See theOxyrhynchus Papyri, part i. (1897), part iv. (1904), part v. (1908).
See theOxyrhynchus Papyri, part i. (1897), part iv. (1904), part v. (1908).
(H. T. A.)
LOGIC(λογική, sc.τέχνη, the art of reasoning), the name given to one of the four main departments of philosophy, though its sphere is very variously delimited. The present article is divided into 1.The Problems of Logic, II.History.
I.The Problems of Logic.
Introduction.—Logic is the science of the processes of inference, what, then, is inference? It is that mental operation which proceeds by combining two premises so as to cause a consequent conclusion. Some suppose that we may infer from one premise by a so-called “immediate inference.” But one premise can only reproduce itself in another form,e.g.all men are some animals; therefore some animals are men. It requires the combination of at least two premises to infer a conclusion different from both. There are as many kinds of inference as there are different ways of combining premises, and in the main three types:—
1.Analogical Inference, from particular to particular:e.g.border-war between Thebes and Phocis is evil; border-war between Thebes and Athens is similar to that between Thebes and Phocis; therefore, border-war between Thebes and Athens is evil.
2.Inductive Inference, from particular to universal:e.g.border-war between Thebes and Phocis is evil; all border-war is like that between Thebes and Phocis; therefore, all border-war is evil.
3.Deductive or Syllogistic Inference, from universal to particular,e.g.all border-war is evil; border-war between Thebes and Athens is border-war; therefore border-war between Thebes and Athens is evil.
In each of these kinds of inference there are three mental judgments capable of being expressed as above in three linguistic propositions; and the two first are the premises which are combined, while the third is the conclusion which is consequent on their combination. Each proposition consists of two terms, the subject and its predicate, united by the copula. Each inference contains three terms. In syllogistic inference the subject of the conclusion is the minor term, and its predicate the major term, while between these two extremes the term common to the two premises is the middle term, and the premise containing the middle and major terms is the major premise, the premise containing the middle and minor terms the minor premise. Thus in the example of syllogism given above, “border-war between Thebes and Athens” is the minor term, “evil” the major term, and “border-war” the middle term. Using S for minor, P for major and M for middle, and preserving these signs for corresponding terms in analogical and inductive inferences, we obtain the following formula of the three inferences:—
The love of unity has often made logicians attempt to resolve these three processes into one. But each process has a peculiarity of its own; they are similar, not the same. Analogical and inductive inference alike begin with a particular premise containing one or more instances; but the former adds a particular premise to draw a particular conclusion, the latter requires a universal premise to draw a universal conclusion. A citizen of Athens, who had known the evils of the border-war between Thebes and Phocis, would readily perceive the analogy of a similar war between Thebes and Athens, and conclude analogously that it would be evil; but he would have to generalize the similarity of all border-wars in order to draw the inductive conclusion that all alike are evil. Induction and deduction differ still more, and are in fact opposed, as one makes a particular premise the evidence of a universal conclusion, the other makes a universal premise evidence of a particular conclusion. Yet they are alike in requiring the generalization of the universal and the belief that there are classes which are whole numbers of similars. On this point both differ from inference by analogy, which proceeds entirely from particular premises to a particular conclusion. Hence we may redivide inference into particular inference by analogy and universal inference by induction and deduction. Universal inference is what we call reasoning; and its two species are very closely connected, because universal conclusions of induction become universal premises of deduction. Indeed, we often induce in order to deduce, ascending from particular to universal and descending from universal to particular in one act as it were; so that we may proceed either directly from particular to particular by analogical inference, or indirectly from particular through universal to particular by an inductive-deductive inference which might be called “perduction.” On the whole, then, analogical, inductive and deductive inferences are not the same but three similar and closely connected processes.
The three processes of inference, though different from one another, rest on a common principle of similarity of which each is a different application. Analogical inference requires that one particular is similar to another, induction that a whole number or class is similar to its particular instances, deduction that each particular is similar to the whole number or class. Not that these inferences require us to believe, or assume, or premise or formulate this principle either in general, or in its applied forms: the premises are all that any inference needs the mind to assume. The principle of similarity is used, not assumed by the inferring mind, which in accordance with the similarity of things and the parity of inference spontaneously concludes in the form that similars are similarly determined (“similia similibus convenire”). In applying this principle of similarity, each of the three processes in its own way has to premise both that something is somehow determined and that something is similar, and by combining these premises to conclude that this is similarly determined to that. Thus the very principle of inference by similarity requires it to be a combination of premises in order to draw a conclusion.
The three processes, as different applications of the principle of similarity, consisting of different combinations of premises, cause different degrees of cogency in their several conclusions. Analogy hardly requires as much evidence as induction. Men speculate about the analogy between Mars and the earth, and infer that it is inhabited, without troubling about all the planets. Induction has to consider more instances, and the similarity of a whole number or class. Even so, however, it starts from a particular premise which only contains many instances, and leaves room to doubt the universality of its conclusions. But deduction, starting from a premise about all the members of a class, compels a conclusion about every and each of necessity. One border-war may be similar to another, and the whole number may be similar, without being similarly evil; but if all alike are evil, each is evil of necessity. Deduction or syllogism is superior to analogy and induction in combining premises so as to involve or contain the conclusion. For this reason it has been elevated by some logicians above all other inferences, and for this very same reason attacked by others as no inference at all. The truth is that, though the premises contain the conclusion, neither premise alone contains it, and a man who knows both but does not combine them does not draw the conclusion; it is the synthesis of the two premises which at once contains the conclusion and advances our knowledge; and as syllogism consists, not indeed in the discovery, but essentially in the synthesis of two premises, it is an inference and an advance on each premise and on both taken separately. As again the synthesis contains or involves the conclusion, syllogism has the advantage of compelling assent to the consequences of the premises. Inference in general is a combination of premises to cause a conclusion; deduction is such a combination as to compel a conclusion involved in the combination, and following from the premises of necessity.
Nevertheless, deduction or syllogism is not independent of the other processes of inference. It is not the primary inference of its own premises, but constantly converts analogical and inductive conclusions into its particular and universal premises. Of itself it causes a necessity of consequence, but only a hypothetical necessity; if these premises are true, then this conclusion necessarily follows. To eliminate this “if” ultimately requires other inferences before deduction. Especially, induction to universals is the warrant and measure of deduction from universals. So far as it is inductively true that all border-war is evil, it is deductively true that a given border-war is therefore evil. Now, as an inductive combination of premises does not necessarily involve the inductive conclusion, induction normally leads, not to a necessary, but to a probable conclusion; and whenever its probable conclusions become deductive premises, the deduction only involves a probable conclusion. Can we then infer any certainty at all? In order to answer this question we must remember that there are many degrees of probability, and that induction, and therefore deduction, draw conclusions more or less probable, and rise to the point at which probability becomes moral certainty, or that high degree of probability which is sufficient to guide our lives, and even condemn murderers to death. But can we rise still higher and infer real necessity? This is a difficult question, which has received many answers. Some noölogists suppose a mental power of forming necessary principles of deduction a priori; but fail to show how we can apply principles of mind to things beyond mind. Some empiricists, on the other hand, suppose that induction only infers probable conclusions which are premises of probable deductions; but they give up all exact science. Between these extremes there is room for a third theory, empirical yet providing a knowledge of the really necessary. In some cases of induction concerned with objects capable of abstraction and simplification, we have a power of identification, by which, not a priori but in the act of inducing a conclusion, we apprehend that the things signifiedby its subject and predicate are one and the same thing which cannot exist apart from itself. Thus by combined induction and identification we apprehend that one and one are the same as two, that there is no difference between a triangle and a three-sided rectilineal figure, that a whole must be greater than its part by being the whole, that inter-resisting bodies necessarily force one another apart, otherwise they would not be inter-resisting but occupy the same place at the same moment. Necessary principles, discovered by this process of induction and identification, become premises of deductive demonstration to conclusions which are not only necessary consequents on the premises, but also equally necessary in reality. Induction thus is the source of deduction, of its truth, of its probability, of its moral certainty; and induction, combined with identification, is the origin of the necessary principles of demonstration or deduction to necessary conclusions.
Analogical inference in its turn is as closely allied with induction. Like induction, it starts from a particular premise, containing one or more examples or instances; but, as it is easier to infer a particular than a universal conclusion, it supplies particular conclusions which in their turn become further particular premises of induction. Its second premise is indeed merely a particular apprehension that one particular is similar to another, whereas the second premise of induction is a universal apprehension that a whole number of particulars is similar to those from which the inference starts; but at bottom these two apprehensions of similarity are so alike as to suggest that the universal premise of induction has arisen as a generalized analogy. It seems likely that man has arrived at the apprehension of a whole individual,e.g.a whole animal including all its parts, and thence has inferred by analogy a whole number, or class,e.g.of animals including all individual animals; and accordingly that the particular analogy of one individual to another has given rise to the general analogy of every to each individual in a class, or whole number of individuals, contained in the second premise of induction. In this case, analogical inference has led to induction, as induction to deduction. Further, analogical inference from particular to particular suggests inductive-deductive inference from particular through universal to particular.
Newton, according to Dr Pemberton, thought in 1666 that the moon moves so like a falling body that it has a similar centripetal force to the earth, 20 years before he demonstrated this conclusion from the laws of motion in thePrincipia. In fact, analogical, inductive and deductive inferences, though different processes of combining premises to cause different conclusions, are so similar and related, so united in principle and interdependent, so consolidated into a system of inference, that they cannot be completely investigated apart, but together constitute a single subject of science. This science of inference in general is logic.
Logic, however, did not begin as a science of all inference. Rather it began as a science of reasoning (λόγος), of syllogism (συλλογισμός), of deductive inference. Aristotle was its founder. He was anticipated of course by many generations of spontaneous thinking (logica naturalis). Many of the higher animals infer by analogy: otherwise we cannot explain their thinking. Man so infers at first: otherwise we cannot explain the actions of young children, who before they begin to speak give no evidence of universal thinking. It is likely that man began with particular inference and with particular language; and that, gradually generalizing thought and language, he learnt at last to think and say “all,” to infer universally, to induce and deduce, to reason, in short, and raise himself above other animals. In ancient times, and especially in Egypt, Babylon and Greece, he went on to develop reason into science or the systematic investigation of definite subjects,e.g.arithmetic of number, geometry of magnitude, astronomy of stars, politics of government, ethics of goods. In Greece he became more and more reflective and conscious of himself, of his body and soul, his manners and morals, his mental operations and especially his reason. One of the characteristics of Greek philosophers is their growing tendency, in investigating any subject, to turn round and ask themselves what should be the method of investigation. In this way the Presocratics and Sophists, and still more Socrates and Plato, threw out hints on sense and reason, on inferential processes and scientific methods which may be called anticipations of logic. But Aristotle was the first to conceive of reasoning itself as a definite subject of a special science, which he called analytics or analytic science, specially designed to analyse syllogism and especially demonstrative syllogism, or science, and to be in fact a science of sciences. He was therefore the founder of the science of logic.