楊伯峻《春秋左傳注》考訂六則——以《左傳》隱公至僖公時期為範圍

2021 ◽  
Vol 55 (0) ◽  
pp. 039-056
Author(s):  
黃聖松 黃聖松
Keyword(s):  
Ordinal Number ◽  
Zuo Zhuan

<p>本文討論楊伯峻《春秋左傳注》釋《左傳》魯隱公至魯僖公時期六則有待商榷字詞，計有「季年」、「征伐以討其不然」、「不以阻隘」、「薄而觀之」、「獻狀」、「鄉役之三月」。一、「季年」專指某位國君在位最末年，非泛指最後一段時間。二、「征伐以討其不然」之「不然」有「不如此」義，「征伐以討其不然」指可征伐不遵「會」、「朝」之「禮」之諸侯。三、「不以阻隘」之「阻」、「隘」於傳文相對舉，故仍應從《春秋左傳集解》釋為同義詞。四、「薄而觀之」之「薄」仍應釋為「迫」，表現曹共公欲詳觀重耳駢脅而無禮之狀。五、「獻狀」之「獻」當讀為《說文解字》之「𤅊」，即典籍所見「讞」，有議罪、辨別是非之意。「獻狀」乃如《國語．晉語四》「誅觀狀」，謂議曹共公觀駢脅之罪。六、「鄉役之三月」之「三月」，依《左傳》「某公之某年」、「謚號之某年」句法與僖公二十八年《春秋經》、《左傳》記載，「三月」當為序數，釋為魯僖公二十八年（632 B.C.）三月。</p> <p>&nbsp;</p><p>This article discusses six phrases on Y&aacute;ng B&oacute;-j&ugrave;n’s &quot;Chun Qiu Zuo Zhuan Zhu&quot; which based on the period of Lǔ Yǐn Gōng to Lǔ Xī Gōng in Zuo Zhuan. They are &quot;j&igrave; ni&aacute;n&quot;, &quot;zhēng f&aacute; yǐ tǎo q&iacute; b&ugrave; r&aacute;n&quot;, &quot;b&ugrave; yǐ zǔ &agrave;i&quot;, &quot;b&aacute;o &eacute;r guān zhī&quot;, &quot;xi&agrave;n(獻) zhu&agrave;ng&quot; and &quot;xiāng y&igrave; zhī sān yu&egrave;&quot; 1. The meaning of the phrase &quot;j&igrave; ni&aacute;n&quot; is the last year of a certain monarch’s reign only, not the last period of his reign. 2. The phrase &quot;b&ugrave; r&aacute;n&quot; has the meaning of disobeying the agreement; therefore, the sentence &quot;zhēng f&aacute; yǐ tǎo q&iacute; b&ugrave; r&aacute;n&quot; means to go on a&nbsp;punitive expedition to those vassals who disobeyed the rules of &quot;hu&igrave;&quot; and &quot;ch&aacute;o&quot;. 3. Although the words &quot;zǔ&quot; and &quot;&agrave;i&quot; in the phrase &quot;b&ugrave; yǐ zǔ &agrave;i&quot; are contrastive meanings in &quot;Zhuan&quot;; however, from &quot;Ji Jie&quot;, they should be still interpreted as synonyms. 4. The word &quot;b&aacute;o&quot; should be interpreted as &quot;p&ograve;&quot; in the phrase &quot;b&aacute;o &eacute;r guān zhī&quot;. The whole meaning of this phrase is C&aacute;o G&ograve;ng Gōng heard that Zh&ograve;ng Er’s ribs were connected together, and wanted to take a look at him while he was taking a bath. That was so rude. 5. According to &quot;Shuō W&eacute;n Jiě Z&igrave;&quot;, the word &quot;xi&agrave;n(獻)&quot; should read as &quot;y&agrave;n(𤅊)&quot; in the phrase &quot;xi&agrave;n(獻) zhu&agrave;ng&quot;. The words &quot;y&agrave;n(𤅊)&quot; and &quot;y&agrave;n(讞)&quot; are the same in ancient books and records. It means to judge the cases and distinguish right from wrong. For example, C&aacute;o G&ograve;ng Gōng wanted to take a look at Zh&ograve;ng’ Er’s ribs and that was a case so-called &quot;Zhū guān zhu&agrave;ng&quot; in Gu&oacute; Yǔ. 6. The grammar of the phrase &quot;sān yu&egrave;&quot; in the sentence &quot;xiāng y&igrave; zhī sān yu&egrave;&quot; is quite similar to the sentences &quot;mǒu gōng zhī mǒu ni&aacute;n&quot; and &quot;sh&igrave; h&agrave;o zhī mǒu ni&aacute;n&quot; in Zhun. According to &quot;Jīng&quot; and &quot;Zhu&aacute;n&quot;, &quot;sān yu&egrave;&quot; should be an ordinal number ,and it means the March in 632 B. C.</p> <p>&nbsp;</p>

On the Sequentiality of Ordinality and Cardinality

1981 ◽  
Vol 4 (4) ◽  
pp. 391-402 ◽  
Author(s):  
J. Kingma ◽  
W. Koops
Keyword(s):  
Primary School ◽  
Ordinal Number ◽  
Difficulty Level ◽  
School Grade ◽  
The Future ◽  
Task Variables ◽  
Number Development

Some research with Brainerd-like number tasks is reported. 266 subjects (from kindergarten and from primary school grade 1) completed 4 tasks: concrete ordinal correspondence tasks, abstract ordinal correspondence tasks, ordinal number tasks, and cardinal tasks. Results revealed no differences in difficulty level between concrete and abstract ordinal correspondence tasks. The ordinal number tasks were more difficult than the ordinal correspondence tasks. The data also suggest that the child acquires ordinality prior to cardinality. The last finding confirms the conclusion of Brainerd (1978, 1979). Nevertheless, these conclusions are rather weak because of serious differences in psychometric qualities between different kinds of tasks, because of poor operational definitions of cardinality and ordinality, and because of uncontrolled differences in task sensitivity. Only with more refined analyses of task variables will the future of a theory of number development be promising.

Astronomical Evidence for the Bamboo Annals' Chronicle of Early Xia

Early China ◽  
1990 ◽  
Vol 15 ◽  
pp. 87-95 ◽  
Author(s):  
David S. Nivison ◽  
Kevin D. Pang
Keyword(s):  
Chinese History ◽  
The Sun ◽  
Early China ◽  
Western Zhou ◽  
Zuo Zhuan

Tradition says that Yu, first ruler of the Xia Dynasty, was chosen by the “sage emperor” Shun as Shun's successor. The “Modern Text” Bamboo Annals (Jinben Zhushu jinian) dates this act of choice to the fourteenth year of Shun. (With E. L. Shaughnessy, “On the Authenticity of the Bamboo Annals,” Harvard Journal of Asiatic Studies 46 (1986), we accept this text as at least in part the text found in a royal tomb of Wei in A.D. 281.) Following D. Pankenier's argument (“Mozi and the Dates of Xia, Shang and Zhou,” Early China 9–10 [1983–85]), we date this event to 1953 B.C., the year of a dramatic five-planet conjunction. (K. Pang independently dated this conjunction to Yu's reign in his article “Extraordinary Floods in Early Chinese History and their Absolute Dates,” Journal of Hydrology 96 [1987].)We next use K. Pang's discovery (“Extraordinary Floods”) that there was an eclipse of the sun on 16 October 1876 B.C., that exactly satisfies descriptions in the Zuo zhuan (Zhao 17) and in the Bamboo Annals for Xia, Zhong Kang fifth year, of an eclipse associated with the (post-Han Shang shu) “Punitive Expedition of Yin” (except for the day-cycle in the Annals, which we assume to be a later calculation); i.e., it occurred on the first of the ninth lunar month (Xia calendar), the sun's location at the time (188å) was in lunar lodge Fang, and the eclipse was visible in the probable Xia capital area. No other eclipse within many centuries satisfies these criteria.Extending D. Nivison's theory (“The Dates of Western Chou,” Harvard Journal of Asiatic Studies 43 (1983)) that Western Zhou royal calendars began only after completion of mourning, i.e., two years after accession, we then assume that there were similar two-year mourning breaks between Xia royal calendars (possibly reflected in the irregular interregnums in the present Annals). For a demonstration of this chronology, see the chart on page 94.

scholarly journals “How did the serpent of inconsistency enter Frege’s paradise?”

2019 ◽  
pp. 411-436
Author(s):  
Crispin Wright
Keyword(s):  
Cardinal Number ◽  
Ordinal Number ◽  
Higher Order ◽  
Order Logic ◽  
Higher Order Logic ◽  
Indefinite Extensibility ◽  
Basic Law ◽  
Per Se

The paper explores the alleged connection between indefinite extensibility and the classic paradoxes of Russell, Burali-Forti, and Cantor. It is argued that while indefinite extensibility is not per se a source of paradox, there is a degenerate subspecies—reflexive indefinite extensibility—which is. The result is a threefold distinction in the roles played by indefinite extensibility in generating paradoxes for the notions of ordinal number, cardinal number, and set respectively. Ordinal number, intuitively understood, is a reflexively indefinitely extensible concept. Cardinal number is not. And Set becomes so only in the setting of impredicative higher-order logic—so that Frege’s Basic Law V is guilty at worst of partnership in crime, rather than the sole offender.

scholarly journals Duration of colonial bird species egg incubation

2018 ◽  
Vol 7 (1) ◽  
pp. 58-64
Author(s):  
Yuri Gennadievich Lamekhov
Keyword(s):  
Ordinal Number ◽  
Bird Species ◽  
Early Ontogeny ◽  
Egg Laying ◽  
Early Ontogenesis ◽  
Time Interval ◽  
Egg Incubation ◽  
Colonial Bird ◽  
Incubation Duration ◽  
Colonial Settlement

The paper deals with one of the aspects of bird early ontogenesis biology - egg incubation duration, which was defined as the time interval between egg laying and hatching from it. The oomorphological parameters are determined taking into account the ordinal number of the laid eggs. Parameters of early ontogeny of birds are studied on the example of colonially nesting species: blackberry toadstool ( Podiceps nigricollis C.L. Brehm.) and lake gull ( Larus ridibundus L.). Within the colonial settlement of these species, the biological center and the periphery of the colony were isolated. When studying the parameters of early ontogeny of birds and oomorphological characteristics, the same number of eggs was taken into account. During field and laboratory studies it was found that the incubation of eggs lasts longer in eggs from the nests of the biological center of the colony. The first eggs are incubated longer. These features clearly manifested in the early ontogeny of the gull. The increase in the egg incubation duration occurs against the background of an increase in their mass and a decrease in the concentration of lysozyme in the protein shell of the egg. Egg incubation duration is one of the results of embryonalization as a way of evolution of ontogeny. The manifestation of the results of embryogenesis was revealed for the first eggs in the nests of the biological center of the colony. Embryonalization leads to an increase in egg incubation duration as well as to a decrease in the intensity of elimination in early ontogenesis, which affects the number of individuals breeding in the colony and, accordingly, the structure of the colonial settlement of birds.

scholarly journals Гадание по хулилам среди монголов

2021 ◽  
Vol 14 (3) ◽  
pp. 550-567
Author(s):  
Anna D. Tsendina ◽  
◽  
Keyword(s):  
Present Article ◽  
Russian Translation ◽  
Ordinal Number ◽  
Seventh Century ◽  
I Ching ◽  
Book Of Changes ◽  
The Subject

Introduction. Various collections of Mongolian xylographs and manuscripts may contain works on divination practice with eight khulils. What does the word khulil mean? Why does one use eight khulils? What are the texts devoted to the khulil divination? This article deals with the practice of khulil divination in Mongolia, while introducing a Mongolian text devoted to this form of divination. Results. The divination practice goes back to the oldest Chinese source on divination Yijing (I Ching, Book of Changes, about the seventh century BC). Divination is carried out with the help of the trigram, or the three dashes, which are the result of casting coins or of some other method. A combination of trigrams means a particular future. These three lines are called khulil in Mongolian (gua in Chinese). Divination by 8 gua, or 8 khulils, and 64 (8 × 8) or 512 (8 × 8 × 8) combinations is the most common form of divination in China. Later, each trigram was represented by a year of the 12-year animal cycle so that the ninth year was the beginning of the next cycle. Thus, each of the 8 years symbolizes a certain trigram, or khulil, according to the ordinal number of the latter. Granted the number of Mongolian manuscripts on khulil divination in various collections, this divination form was widely practiced by Mongolians. By way of introducing the literature on the subject, the present article presents the Russian translation of the initial fragment of manuscript MN 1145 originating from Ts. Damdinsuren museum in Ulaanbaatar. This is a Mongolian translation from Chinese made relatively late that has few traces of Mongolization or efforts of adaptation to nomadic realia. Besides concerns for the illnesses of relatives or issues of choosing a son-in-law or a bride, which are of a universal character, the most popular topics are questions about farming, such as: should one expect rain? what will be the harvest of grain and raw silk? Also, there are many questions related to promotion and career, e.g., passing exams for the degree of an official. The text contains numerous Sinicisms, including idioms, expressions, and names of Chinese astrological signs; there is also a reference to buying a jins, which points to the Manchu period. Notably, neither Tibetan items nor Buddhist deities are mentioned in the text.

WARFIELD INVARIANTS IN COMMUTATIVE GROUP ALGEBRAS

2008 ◽  
Vol 07 (03) ◽  
pp. 337-346 ◽  
Author(s):  
PETER V. DANCHEV
Keyword(s):  
Abelian Group ◽  
Prime Number ◽  
Group Algebra ◽  
Ordinal Number ◽  
Commutative Group ◽  
Group Algebras

Let F be a field and G an Abelian group. For every prime number q and every ordinal number α we compute only in terms of F and G the Warfield q-invariants Wα, q(VF[G]) of the group VF[G] of all normed units in the group algebra F[G] under some minimal restrictions on F and G. This expands own recent results from (Extracta Mathematicae, 2005) and (Collectanea Mathematicae, 2008).

Products of some special compact spaces and restricted forms of AC

2010 ◽  
Vol 75 (3) ◽  
pp. 996-1006 ◽  
Author(s):  
Kyriakos Keremedis ◽  
Eleftherios Tachtsis
Keyword(s):  
Set Theory ◽  
Closed Subset ◽  
Choice Function ◽  
Ordinal Number ◽  
Axiom Of Choice ◽  
Finite Support ◽  
Compact Spaces ◽  
The Axiom Of Choice ◽  
Infinite Set

AbstractWe establish the following results:1. In ZF (i.e., Zermelo-Fraenkel set theory minus the Axiom of Choice AC), for every set I and for every ordinal number α ≥ ω, the following statements are equivalent:(a) The Tychonoff product of ∣α∣ many non-empty finite discrete subsets of I is compact.(b) The union of ∣α∣ many non-empty finite subsets of I is well orderable.2. The statement: For every infinite set I, every closed subset of the Tychonoff product [0, 1]Iwhich consists offunctions with finite support is compact, is not provable in ZF set theory.3. The statement: For every set I, the principle of dependent choices relativised to I implies the Tychonoff product of countably many non-empty finite discrete subsets of I is compact, is not provable in ZF0 (i.e., ZF minus the Axiom of Regularity).4. The statement: For every set I, every ℵ0-sized family of non-empty finite subsets of I has a choice function implies the Tychonoff product of ℵ0many non-empty finite discrete subsets of I is compact, is not provable in ZF0.

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