Bishop Gregory

субпродукты (но тоже про модальности)

2009-12-18T23:42:21Z

сегодня, наконец, стал подробно вникать в то, что называют словом "модальность" лингвисты. море, конечно, великое и пространное.
но вот что четко, и что, главное, в схемах Чинкве держится строго наряду с настоящими (в логич. смысле) модальностями: modality of volition.
логики этой штукой не занимались вообще (нашел только какого-то странного китайца-любителя). но, видимо, потому, что формально тут неинтересно (все то же самое, что в логике норм и оценок), а практического применения именно этой штуки не нашлось (пока).
но, оглянувшись от лингвистики на нарратологию, я поразился, почему о модальности воли ничего не говорили: ведь она легко может резко отличаться от аксиологической, не говоря уж о деонтической: желание может не только расходиться с долгом, но, как известно, даже с пониманием хорошего у самого же желающего субъекта. напр., сюжет Свидригайлова -- это вполне себе про волю как особую модальность. (про христианские сюжеты ваще молчу).

но вот что интересно и вовсе

если принять во вниманию мою (пока очень сырую) гипотезу, что набор модальностей нарратологии и лингвистики -- это общий набор для всей когнитивной сферы, и, следовательно, нарушения мышления при психических заболеваниях в точности соответствуют нарушению чему-то из этого набора, то

-- выделение желания как особой модальности позволяет решить проблему спецификации schizophrenia simplex.

понятно, что это никакая шизофрения, т.к. нехорошо относить к психозам такие заболевания, при которых нет нарушения тестирования реальности. поэтому DSM-IV права, устранив "простую шизофрению" как класс.

но клинический опыт врачей, которые болезнь "нюхом чуют", не позволяет с этим согласиться до конца: какое-то специфическое заболевание тут есть. мои личные наблюдения заставляют меня принять сторону этих психиатров (хотя без того, чтобы, вместе с ними, цепляться за архаичное определение "шизофрении"). и так же душа не принимает отождествление "простой шизофрении" с "шизотипическим расстройством", хотя на практике диагноз тут почти всегда ставится из социальных соображений, а не по сути заболевания (пациенту важнее право на получение инвалидности, а не научная точность диагноза). но все-таки классическая картина шизотипического расстройства (F 21) -- это целый бульон или компот разнообразных нарушений мышления.

"простая шизофрения" определяется в МКБ-10 (F 20.6), главным образом, по признаку нарушения воли. кто видел, тот знает: это такое "овощение", которое происходит без снижения интеллекта, без нарушения (прочих) мыслительных процессов и даже обычно без депрессии.

но, выходит, что нарушение воли тоже является одним из нарушений мыслительных процессов.

модальности (13)

2009-12-18T13:19:08Z

начинаем сравнение с таблицей Чинкве. подробного пересказа Чинкве не будет, но таблицу воспроизвожу. плюс, в этом же разделе, первые к ней логические пояснения. дальше будет много.
форматирование таблицы сохранить не удается,т.к. слишком большой объем.

17 Modalities and Cinque’s functional projections

Taking in mind the table of narrative modalities, we are in position to compare it with the “universal hierarchy of functional projections” constructed by Cinque (1999).
Cinque’s idea of hierarchy may be productive for the narratological studies as well, but now will be taken aside. We will try to propose a simplified logical interpretation of the Cinque table as if it is a non-ordered set.
The table is the following (Cinque 1999, 130):
Functional head Default Marked
Moodspeech act declarative - declarative
Moodevaluatlve - [ - fortunate] - fortunate
Moodevidentlal direct evidence - direct evidence
Modepistemlc commitment - commitment
T(Past) R1, S R1, S
T(Future) R1,R2 R1, R2
Moodlrrealis realis irrealis
•Modaleth necess - [ - necessary] - necessary
Modaleth possib - [ - possible] - possible
Modvolition - [ - volition] - volition
Modobligation - [ - obligation] - obligation
Modabilityv/permlss - [ - ability/permission] - ability /permission
ASPhapitiual - [ + habitual] + habitual
Asprepetitive(I) - [ + repetitive] + repetitive
ASPfrequentative(I) - [ + frequentative] + frequentative
Aspceleratlve(I) - [ + celerative] + celerative
T(Anterior) E, R2 E, R2
ASPtermmative - [ + terminative] + terminative
ASPcontinuative - [ + continuative] + continuative
AsPperfect imperfect perfect
ASPretrospective - [ + retrospective] + retrospective
ASPproximative - [ + proximative} + proximative
Aspdurative - [ + durative] + durative
ASPprogressive generic progressive
ASPprospective - [ + prospective] + prospective
ASPcompletiveSg - [ + completive] + completive
ASPcompletivePl - [ + completive] + completive
Voice active passive
Aspceperatlve(II) - [ + celerative] + celerative
Asprepetluve(II) - [ + repetitive] + repetitive
Aspfrequentativ(II) - [ + frequentative] + frequentative
Aspcomp|etive(II) - [ + completive] + completive

Some parallels with the narrative modalities are striking. Sometime, Cinque himself calls his “functional projections” modalities in a very philosophical sense of word. His usage of the modal logics is limited to (von Wright 1951) and (Rescher 1968) and that of the generalized quantifiers to the intuitions of (Lewis 1976), but this is enough to recognize alethic, deontic, and epistemic modalities.
Cinque himself is quite aware of the logical nature of his enterprise, while he puts the word “logic” when applied to his table in commas (Cinque 1999, 129). It is logic, nevertheless, while often inexplicit. And, more precisely, a modal logic.
Just now, knowing that the time is also a modal category, we can suppose that the modal nature of the list of functional heads will turn out to be much deeper than it is explicated so far.

иосифляне

2009-12-18T09:04:09Z

про адмирала-иосифлянина
http://vaga-land.livejournal.com/306679.html#cutid1
сказано, что в Спб он был прихожанином Спаса-на-Крови, и был сослан по делу церковников в 1931. это однозначно указывает на истинно-православное вероисповедание.

модальности (12)

2009-12-17T23:08:34Z

Наконец. вся система нарративных модальностей, "как мы ее знаем", в виде таблицы. резюме предыдущих разделов. это то, что подлежит сравнению с таблицей Чинкве 1999.

The system of narrative modalities

Let ussummarize how far from Doležel’s table we are.

Any elementaryplot motive is produced, within the possible world of the narrative, by thequantification Q in the modality Mod,

where Q belongs to either triplet of ‹1,1› type quantifiers (T) or square of ‹1, 1, 1› type quantifiers (S),while Mod is one of the following modalities: alethic, deontic,axiologic, epistemic, and spatiotemporal: QMod = TMod

Thetriplet of ‹1, 1› type quantifiers is formed by the square omitting the innernegation. Thus, it consists from the quantifiers some, none(external negation), any (dual).

Thetriplet of ‹1, 1, 1› type quantifiers is formed by the whole square. Thus, itconsists from the quantifiers more than (strong preference), no more than(inversed weak preference = external negation of the strong preference), lessthan (inversed strong preference = internal negation of the strongpreference), no less than (weak preference = dual of the strongpreference).

Thissystem of the narrative modalities can be explicated in the table (representingthe square of more than by the first member only):

Quantifiers	Alethic	Deontic	Axiological	Epistemic	Spatiotemporal
some	possible	permitted	good	known	somewhere
none	impossible	prohibited	bad	unknown	nowhere
any	necessary	obligatory	indifferent	believed	anywhere
more than	more possible	preferred to	preferred to	preferred to	closer than

Two notesto the table above:

The meaning of “preferred to” in the threecases in the bottom row of the table is different. The difference betweendeontic and axiological preferences is well-known and described in thetextbooks. The notion of the epistemic preference was introduced by NicholasRescher as is described above (sect. 7): it deals with the fact that someinformation is more convincing than other.

The spatiotemporal operators (the last column)have both/either spatial and/or temporal value(s). Thus, they can mean “somewherein time,” etc.

Кекелидзе

2009-12-17T16:28:19Z

нет ли у кого в электронном формате Кекелидзе, Этюды...

нужен особ т. 6

K. Kekelidze, Etudebi jveli k'art'uli literaturis istoriidan 6 (Tbilisi 1960)

особ. с. 226-231 (хотя бы), где Petre ierusalimelis homilia.

--------------

и чтоб два раза не вставать: не могут в пдф пока что помочь, поэтому тоже здесь, аще кто имеет доступ к электронному ресурсу:

First Order Predicate Logic with Generalized Quantifiers
PER LINDSTRÖM
Theoria
Volume 32, Issue 3 , Pages186 - 195
1966 Stiftelsen Theoria
www3.interscience.wiley.com/journal/120701005/abstract

модальности (11)

2009-12-17T12:22:43Z

когнитивное время.1 Cognitive time as a dimension of cognitive space

The needs of computer science demanded other kinds of temporal logic. One of them is so-called Linear Temporal Logic (Manna and Pnueli 1992; Manna and Pnueli 1995; Kontchakov, Kurucz, Wolter, Zakharyaschev 2007, 527-528; Kröger, Merz 2008).

In the LTL, there are two symmetrical parts, one for the past and another for the future. The structure of operators is the same for the past and future parts. The flow of time is considered as any strict linear order (W, <), where W is a set of time points w ∈ W and < is the precedence relation. A particular case when W = ℕ is of specific interest (cf. above about the role of graphs in the space representations). The language of the LTL does not allow saying (using Aristotle’s examples which were inspiring the most of modern temporal logicians) “it is necessary that there will be a sea-battle tomorrow” or “it is possibly that there will be a sea-battle tomorrow,” but only “there will be a sea-battle tomorrow.”

The main operators of the LTL are the binary operator U (“until”) for the future part of the LTL and S (“since”) for its past part, “sometime in the future” and “always in future” (⃟_Fand ⃞_F, correspondingly, with symmetrical operators for the past), and the operator “at the next moment” (with its counterpart “at the previous moment”). The operator “always” is dual of the operator “sometime”: ⃞φ= ¬⃟¬φ, where φ is a formula of LTL.

As it has been noted, the operators ⃞ and ⃟ are analogous to the classical quantifiers ∀ and ∃, respectively, and so, a formula ⃟A is the temporal closure of A (Kröger, Merz 2008, 32). We can add, that, in the same sense, a formula ⃞A is the temporal interior of A.

Therefore, leaving aside technical details of the LTL itself, we can summarize its basic ideas as following. The time is considered as a kind of a topological space, where the operators of necessity (any) and possibility (some) are applicable as, respectively, time interior and time closure. The precedence relation is interpreted as a ‹1, 1, 1› type operator analogous to the same type operators of the space and preferences logics.

The ‹1, 1› type operators are presented, though implicitly, as a triplet “somewhere in time,” “anywhere in time,” and “nowhere in time.”

Here we are not interested in practical purposes of the creators of the LTL, and so, need not going deeper into its details. The only basic intuition of the linear approach to time is what we really interested in. Thus, we can see, that the time could be treated as a dimension of the space.

Indeed, in this dimension, the first metrical axiom holds: d (x, y) = 0 iff x = y (identity of indiscernibles). The third axiom (triangle inequality) is inapplicable to a one-dimension space. The second axiom d (x, y) = d (y, x) (symmetry) holds only for some kinds of time perception, as it is the case for the space.

Indeed, for our time thinking, a journey back in time is not a problem, and so, our time thinking logic is not to be divided into past and present parts. Moreover, if we are “speaking about” our present state, then, our present has no preference over other time modalities, and so, there is no need to introduce “at the next moment of time” as a specific operator.

Our final conclusion is that, for the human cognitive sphere, there is no time as something different by nature from the space. Our cognitive time is rather a dimension of our cognitive space. Thus, there is no specific logic of time in the human cognitive sphere. The logic of space is enough.

модальности (10)

2009-12-16T14:48:01Z

почему модальная логика Прайора имеет так мало отношения к логике нашего мышления времени.

расскажу тут и историю. один очень крупный наш логик из старшего поколения, который сам является вехой в развитии модальных логик, недавно писал одну книгу (еще не издана), где о модальной логике времени говорится, примерно, по Прайору. я его спрашиваю: какая же это логика *времени*, если там про алетическую модальность, пусть даже и во времени? -- на это он мне ответил, что он вообще не понимает, как это может быть "просто" логика времени.
но такие логики усиленно разрабатываются с 1980-х годов. computer science простимулировала, хотя в логический мэйнстрим они едва приходят сейчас, уже после 2005 года где-то... (о них -- в след. серии).1 Why Prior is not about time

The logic of time, among other modal logics, ploughed a lonely furrow during the 20^th century. This has drastically affected its development as a logical discipline as well as its applications in other cognitive sciences, including narratology and linguistics.

The first impulse was given by John Ellis McTaggart (1908) who argued that the time in the sense of a series “past—present—future” is non-existent outside our mind, being a derivation of the time in the sense of series “earlier—later.” Arthur Prior in the 1950s answered this philosophical challenge with a theory of time based on then recently published von Wright’s (1951) book on the modal logic (Prior 1969). Prior’s approach consisted in study of “changing truths” rather than the time as such. In his own words, “[c]ertainly there are unchanging truths, but there are changing truths also, and it is a pity if logic ignores these…” (Prior 1996, 46).

Prior’s logic of time, or “Tense Logic,” is a generalization of the alethic modal logic to the changes in time. It is evident from the very beginning, that is, from the nature of Prior’s operators:

P “It has at some time been the case that…”

F “It will at some time be the case that …”

H “It has always been the case that …”

G “It will always be the case that …”

Prior’s logic was, first of all, about causality: necessity and possibility in the past and in the future, a combination of the alethic modal logic with an otherwise unnoticed logic of time. However, until the early 1990s, Prior’s approach (mixing of time modality with alethic modality) remained the predominant style of the logic researches of time (Øhrstrøm, Hastle 1995).

Prior’s logic as such turned out to be inapplicable to reasoning about time in both narratology and linguistics, even though Prior himself was inspired by the facts related to the natural language. When Alice ter Meulen (1995) proposed a model of time representation in natural language, she preferred to leave aside its logical interpretation. She has been told, however, by Johan van Benthem and Jerry Seligman that a modal logic equivalent to her model should have four-place operators (ter Meulen 1995, 129, n. 1).
Indeed, Prior is more about what we are thinking in time than how we are thinking time. But the structures of language and narrative are about how and not about what. Thus, Prior’s enormous influence after his death (1969) until the early 1990s was rather inhibiting the logical analysis of temporal thinking. However, in about 1990, it was catalyzed by the computer science.

о науке и советской власти

2009-12-16T13:07:23Z

советская власть давала картбланш, которого теперь никто не дает, и, скажем, несохранение Лени Когана на Восточном факультете СПбГУ (в 1990-е) -- это просто приговор факультету. а в советское время всё бы спокойно списали на советскую власть, а наши ученые так бы и оставались учеными.

а тут про картбланш хорошо написал В.Л. Топоров по поводу С.С. Гречишкина:

Отказ в очной аспирантуре был, естественно, списан на происки парткома с гэбухой; мысль о том, что наши профессора — либеральные и либеральнейшие — в сущности, точно такие же гнусные совки, как их идейные антагонисты, не приходила нам в голову поразительно долго; Сергея Сергеевича она так и не осенила, или, вернее, он до самого конца категорически отказывался с нею смириться.

приглашение от Sources chrétiennes

2009-12-16T10:08:43Z

L'Institut des Sources chrétiennes в Лионе проводит курсы для молодых исследователей по подготовке к изданию древних текстов на греческом и на латыни. Курсы бесплатные и на французском.
о. Доминик Гонне попросил меня всем рассказать моим знакомым и позвать, кого можно. вот что он пишет:

I wish to inform you that the Sources Chrétiennes team organizes a session (19th to 23rd April 2010) to learn how to edit old Greek and Latin texts (= Ecdotique). Students and Researchers are warmly welcome. Of course, it is in French. Do you know Students or Researchers who understand enough French to attend such a session ? There is nothing to pay for the inscription to the course itself (= no academic fees). We don't provide lodging, but we can help to find a place in Lyon. Would you be so kind as to tell us if any person is interested?

http://www.sources-chretiennes.mom.fr/index.php?pageid=ecdotique

эфиопский аналог Северной Фиваиды

2009-12-15T18:21:36Z

это острова, на которых монастыри. озеро Тана.
место действия Жития матери нашея Валатта Петрос...
еще картинки и немного слов -- здесь и здесь.
и рядом -- Гондар, эфиопская столица 17 века.

Аракчеев

2009-12-15T11:53:35Z

прекрасная статья Павла Данилина:

В интересах Чечни добиться справедливости по отношению к Аракчееву

Ложь и подлость себя не окупают

модальности (9)

2009-12-15T11:31:49Z

про дистанционную модальность (логика предпочтений применительно к пространству).1 Distance space modality

Presently, there are many logical systems elaborated for reasoning about (different kinds of) space. Normally, all of them consist from two components corresponding to the two mutually irreducible types of quantifiers (‹1, 1› and ‹1, 1, 1›): a kind of the topological modal logic (quantifiers of ‹1, 1› type) and logic of distances in relative coordinates (quantifiers of ‹1, 1, 1› type, often called “ternary” by spatial logicians). The latter is governed by such operators as “nearer than” (van Benthem 1983; van Benthem, Bezhanishvili 2007, 406), “closer-than” (van Benthem, Bezhanishvili 2007, 394-395) or “closer” (Sheremet, Tishkovsky, Wolter, Zakharyaschev, 2005), etc.

Von Wright’s (1979) “logic of elsewhere” (for its recent developments see (van Benthem, Bezhanishvili 2007, 405)) with its main operators “elsewhere” and “everywhere” is especially interesting from the philosophical point of view as an example of clear balancing between the two modal approaches. Indeed, the modal approach to distance presupposes that the observer is involved, but this fact is often implicit and far from being evident. But such categories as “here” and “elsewhere” make it explicit.

The “ternary” operators of the spatial logic are nothing but the main operator of the logic of preferences more than. Indeed, von Wright’s “logic of elsewhere” and, especially, the logic of “closer” (Sheremet, Tishkovsky, Wolter, Zakharyaschev, 2005) are not specifically spatial by nature and could be easily reshaped for other modalities.

Thus, the basic principles of the logic of preferences are applicable to the spatial logic of distances.

To sum up, the logic of space is twofold in the same manner as are alethic, deontic, axiological, and epistemic modal reasoning. One part of it deals with topology, that is, the structure of the modal states of the space. Another part of it deals with distances, that is, the preferences in space.

модальности (8)

2009-12-14T21:04:09Z

простыми человеческими словами о триплете оператора топологической пространственной модальности.
1 Triplet of topological space modality

For the sake of uniformity, it is useful to reformulate our conclusions relating the topological space modality. Its three operators, that is, interior and closure together with negation, no (whose corresponding set is the empty set) form triplet of the quantifiers some, no, any, or, in spatial terms, somewhere, nowhere, and anywhere.

This spatial triplet has spatial sense which is distinct from the existential sense. “Somewhere,” “nowhere,” “anywhere” say nothing about existence, as alethic modal operators do. The spatial operators say about space: somewhere in space, nowhere in space, anywhere in space.

Sometime we can merge existential and spatial contexts, in the same manner as we can merge the axiological and deontic ones (e.g., to perform a duty is good, but duty and goodness belong, nevertheless, to different modalities).

про Эфиопию

2009-12-14T17:11:48Z

http://portal-credo.ru/site/?act=news&id=74961&cf=
только что вывесили на Кредо интервью, которое mitr взяла у Севира Борисовича Чернецова за три недели до его кончины (т.е. где-то в самых первых числах января 2005). он уже не смог прочитать текст, и потом интервью залежалось.
но не потерялось!

точность передачи имен и названий проверяли мы с Денисом Носницыным, но одно имя не смогли восстановить (того сановника, который объяснял Сэмюэлу Рубенсону (по ссылке про его сына, еще более известного среди патрологов) про "неправильную математику", в которой возможно filioque).

эх, много всякого интересного знал Севир Борисович, о чем бы хотелось взять у него не одно такое интервью, а целую книгу. но увы.

заодно в тему: некролог С.Б., написанный С.А. Французовым. там много общих для нас с ним (автором некролога) воспоминаний.

модальности (7)

2009-12-14T13:15:59Z

о пространственных вообще и о топологических в частности.1 Modality of space

Space and time are never considered as modalities in linguistics, but the only probable explanation of this fact is little knowledge of the corresponding logical studies by the linguists. In the narratology, the situation is almost the same but Vadim Rudnev (2000) proposed, while without any appropriate logical apparatus, to consider space and time among the modalities which are shaping the fictional plot. I think his intuition is right.

Let us start from the spatial modality because it is the field where we have an about 80-year scholarly tradition to rely on (see now especially (Aiello, Pratt-Hartmann, van Benthem, 2007) with further bibliography).

The modal logic of space was born at the turn of the 1930s and 1940s, when several scholars independently (Stone in 1937, Tarski in 1938, Tsao-Chen in 1938, and McKinsey in 1941) discovered that the most known now (and quite recently developed then) modal logic of predicates, S4, could be interpreted as a logic of topological space (Kontchakov, Kurucz, Wolter, Zakharyaschev 2007, 509). The topological space is distinct from the space(s) of human perceptions but now we need only a rough scheme and so, even topological spaces could provide a satisfying approximation. To be closer to reality, we would need to operate with something like non-metric spaces on the fuzzy graphs, but, even in this case, we will need to construct basic notions analogous to those defined for the topological spaces.

There are two kinds of modal logics of space. The first one (developed first and mentioned above) deals with the topological properties (in a larger sense of word, not restricted to the so-called topological spaces) and, using our previous terminology, is governed by the ‹1, 1› type quantifiers. The second one deals with the distances and is governed by the ‹1, 1, 1› type quantifiers.

2 Modalities of topology

It is necessary to start from, at least, basic definitions (basing on (Kontchakov, Kurucz, Wolter, Zakharyaschev 2007) with minor additions on the graphs).

Space: a pair (Δ, d) where Δ is a nonempty set (of points or vertices of graphs or vertices of fuzzy graphs) and d is a function from Δ × Δ into a set of non-negative real numbers ℝ^³⁰ (or, for spaces on graphs, its subset ℕ [set of natural numbers]), satisfying, at least, the first from the three following axioms:

(1) d (x, y) = 0 iff x = y (identity of indiscernibles),

(2) d (x, y) = d (y, x) (symmetry),

(3) d (x, z) £ d (x, y) + d (y, z) (triangle inequality),

for all x, y, z ∈ Δ.

The value d(x, y) is called the distance between the elements x and y. If these elements are not points but vertices of graph, the distance is defined by the number of the vertices in between, as it is usual in the graph theory.

The metric space is defined on the set of points, its d-function’s range of values is ℝ^³⁰, and it satisfies the whole set of the three axioms.

The distant space is similar to the metric space but does not satisfy the axioms (2) and (3). (On the modal logic for such spaces see, especially (Kurucz, Wolter, Zakharyaschev, 2005).

Examples of breaking condition (2). It is easy to see how, in human perception, the way forward and the way back could differ in length. Not only in human perception, though. The beloved example of Kurucz, Wolter, and Zakharyaschev is the flight from London to Tokyo and back. London is “farer” from Tokyo than Tokyo from London by more than one hour.

Examples of breaking condition (3). The distances are often evaluated in fuzzy terms, such as “short,” “long,” and so on. Short plus short can still be short, but it can also be medium or long. (Here Kurucz–Walter–Zakharyaschev’s example is, in fact, a space on a fuzzy graph).

Main topological operators are those of interior I and closure C. (I omit here the strict definition of the topological space and its interior by means of the four Kuratowski axioms.) C is dual of I. If U is a nonempty set, the universe of the space, and X ⊆ U, then, CX = U – I(U – X). A set X is called open if X = IX and closed if X = CX. The complement of an open set is closed and vice versa. The boundary of X is CX – IX. The self-evident meaning of these definitions is that a set X of the universe of the space U can be considered as either including its boundary (operator C) or excluding it (operator I).

Topological operators for the metric spaces. The main sense of the following definitions consists in the fact that the presence or the absence of the boundary of a set X of the metric space (Δ, d) affects drastically the localization of some element (point) y vis-à-vis an element (point) x ∈ X. If X is open, then, there is a way to formulate a condition that any y ∈ X, too. If X is closed, then, there is a way to formulate a condition that only some y ∈ X. Thus, the interior operator becomes an equivalent of the modal necessity, and the closure operator that of the modal possibility.

The definitions are the following:

IX = {x ∈ X | ∃ε > 0 ∀y (d(x, y) < ε → y ∈ X)},

CX = {x ∈ Δ | ∀ε > 0 ∃y ∈ X d(x, y) < ε}.

These equations can be reformulated in simple words as following: IX is a set whose all elements are internal, while CX is a set whose not all elements are internal but some of them belong to the boundary. Such formulations make self-evident why the operator I is equivalent to the modal operator of necessity (⃞) while the operator C to the operator of possibility (⃟).

For the spaces on the graphs, the notion of ε-vicinity has no sense. However, an analogous definition of the notion of closure is working. Its meaning is to provide the maximum number of links (edges) between the vertices of a given graph. Thus,

· the closure of the graph G having n vertices is a graph C(G) obtained from G by recursively joining pairs of non-adjacent vertices u and v, for which degree (u) + degree (v) ≥ n until no such pair remains (where “degree” of a vertex is the number of the edges adjacent to that vertex).

It follows from the definition of C(G) that I(G) = G (cf. definition of the open set in the topological space. Two graphs C(G) and G differ from each other by the edges: the edges which they have in common are “internal” and the edges proper to C(G) are, so-to-say, “boundary” of the graph. Thus, G (more properly, I(G)) is an equivalent of logical necessity (⃞): it represents a space where any existing path (edge) is internal. C(G) is an equivalent of logical possibility (⃟) given that only some its existing paths (edges) are internal, that is, belonging to G.

помощь зала?

2009-12-14T11:24:23Z

в тех модальных логиках пространства, где рассматривается топология (а не расстояния), всё построено на эквивалентности топологических понятий открытого и замкнутого множеств и, соответственно, понятий необходимости и возможности: т.к. в открытом множестве любая его точка -- внутренняя, то *необходимо* существует такая ее ε-окрестность, любая точка которой будет также принадлежать этому множетсву; если же множество замкнутое, то такая окрестность лишь *возможна*.

но теперь переходим от топологического пространства к пространству на графе.
понятие замыкания на графе определяется аналогично:
если у графа G имеется n вершин, то его замыканием называется граф C(G), полученный последовательным соединением всех тех несмежных вершин, для которых будет выполняться неравенство: сумма степеней обеих вершин больше или равна n.

где здесь эквиваленты модальных "необходимо" и "возможно"? (я уверен, что они есть, но у меня плохо и с математикой, и с пространственным воображением). чтО здесь у нас будет вместо эпсилон-окрестности?

общий смысл мне понятен, но с формализмом торможу.

(а общий смысл такой:
для графа С(G) будет сохраняться различие между степенями для некоторых вершин (тех, к которым достраивались ребра). те, к которым что-то достраивалось, -- это, по-моему, внешние, т.е. дискретный аналог топологической границы. )

УПД кажется, разобрался. тут различаются "внутренние" и "внешние" ребра графа -- т.е. допустимые для данного пространства пути.

но все равно хотелось бы поточнее с формулами. и -- вдруг все-таки появилась литература, которой я пока не заметил?..

модальности (6)

2009-12-12T22:44:26Z

окончание про кванторы. дальше план такой: про пространство-время как модальности, затем начерно сравнить с таблицей Чинкве для естественного языка, а потом подумать, что сделать с рекурсией.
аще бы кто могУщий объяснил мне на пальцах, в чем логический (а не компутерно-сайенсный) смысл статьи про рекурсию как модальность, я был бы весьма благодарен и отметил бы в тексте (который когда-нибудь нескоро превратится в публикацию, а до тех пор будет прочитан разными достойными людьми)...
знак "меньше или равно" превратился в фунт стерлингов. тоже символический, к сожалению.

1 Quantifier more than

The quantifier more than belongs to the ‹1, 1, 1› type because it presupposes a relation (of comparison) between two sets A and C of the same universe M within a given modal state, that is, in respect to the set of the modal states B. In other words, we have to add to the already familiar to us ‹1, 1› type quantifier Q(A, B) the third component C, which results in quantifier Q(A, B, C).

The signs normally used for designation of more than are > (strong preference) and ³ (weak preference = conjunction of strong preference and equality in value). Q(A, B, C) means that A > C (A is strongly preferred to C) in the modal state B. Below I omit “in the modal state B” as meant by default.

A and C are considered as incompatible preferences. The comparison of preferences is considered as a binary relation, that is, there are only two possibilities, either A or C. Thus, the sets A and C are complement sets to each other, non-A = C and vice versa.

Let us consider the negative operations on this quantifier.

External negation: ¬Q = not more than, A £ C (C is weakly preferred to A).

Internal negation: Q¬ = more than non-C = more than A, that is, reversion of “A is strongly preferred to C” to C > A (“C is strongly preferred to A”).

Dual: Q^d = ¬Q¬ = no more than A, that is, C £ A (A is weakly preferred to C).

Strong and weak preferences are duals of each others. Reversion of preference is the operation of inner negation.

The quantifier more than, in its four avatars (that is, the whole square of this quantifier) should be added to the table of Doležel. It is not place here to go into the purely narratological aspects of this addition to the set of quantifiers (cf. my “Theory of Narrative,” forthcoming). It is important here only to mention that the difference between all and not all could be easily comprised as the difference between more and less. Thus, “not completely necessary,” “not completely obligatory,” “not completely indifferent,” and “not completely/exclusively believed” are interpreted as “necessary less than absolutely,” “obligatory less than absolutely,” “indifferent less than completely,” and “less than completely/exclusively believed.” These phrases are sharply distinct in their inner logical structure (by using the quantifiers of different types). Nevertheless, to the human perception, this logical difference is not “phonological.”

Our “phonological” quantifiers are the triplets of the quantifiers of ‹1, 1› type (square of ‹1, 1› minus internal negation) and the whole square of those of ‹1, 1, 1› type.

2 Quantifying in narrative modalities

The list of the narrative modalities is still open, as it was in Doležel’s studies. However, it is not too short even now when it contains four items. Some generalizations would be at place.

The events in the narrative are either changes of modal states or changes of preferences within the same modal state. In the first case, these changes are governed by the quantifiers of ‹1, 1› type (forming a triplet structure = square minus internal negation), in the second case by the quantifiers of ‹1, 1, 1› type (forming the full square of quantifier).

Thus, the formula of any motive (an elementary part of the plot) looks as

Q(Modality),

where Q is either triplet of ‹1, 1› type or square of ‹1, 1, 1› type.

Probably, some quantifiers of other types play some part in the game, too. However, in any case, our system Q is the basic one.

модальности (5)

2009-12-12T11:26:32Z

изменил нумерацию главок. теперь все будут подряд, с одним уровнем нумерации. сейчас будет про обобщение логики предпочтений.

1 Logic of preferences, a generalization

In the modern context, the logic of preferences was first formulated by von Wright in 1962 (then, see (von Wright 1972) etc.) as a “side-product” of his studies in the logics of values and norms. Indeed, both axiological and deontic preferences are the most evident kinds of preferences, and there is no need of arguing for necessity of their study. Since then, the logic of preferences was studied, also in axiological and deontic contexts, by Rescher (see now (Rescher 2004)) and Ivin (Iwin 1975); see, for a detailed review, (Hansson 2001).

Oddly enough, the role of the logic of preferences is so far ignored in narratology. However, it is obvious that the conflicts between different values and different duties belong to the basic motives of the literature and the human history (e.g., sacrifice of Abraham or that of Jephthah). Therefore, without going into the details, we are allowed legitimately to assume that the modalities of preferences are an important part of the whole logical structure of narrative.

A generalization of the logic of preferences to the logic of knowledge has been undertaken by Nicholas Rescher. The deontic and value logics deals with the “normative-evaluative facts,” while the epistemic logic with the “descriptive facts.” “Values and descriptive facts are both governed by norms.” However, “[o]ur knowledge of both sorts of facts, the descriptively informative and the normative-evaluative hinges on the criteriological bearing of the question: What merits approbation? To be sure, this overarching question bears a very different construction on each side of the issue, with approbation as acceptance on the side of descriptive information, and approbation as preference on the side of evaluative judgment. But acceptance too is a preference of sorts: an epistemic preference” (Rescher 2004, 54).

Presently I don’t know any study of preferences in the alethic modal logic. Nevertheless, a direct result of quantification with more than in the alethic modality is such categories as “more (im)possible” and “less (im)possible,” whose sense is self-evident (and not limited to the probabilistic interpretation).

Generally speaking, the logic of preference establishes relations between two sets of objects (in Mostowski’s sense: set is supposed not to have any relevant internal structure) sharing the same modal state but in a different extent. The comparison on which any preference is grounded makes sense within the same modal state only. Both compared sets must belong to either “good” or “bad,” “known” or “unknown”, etc.

модальности (4)

2009-12-11T23:17:11Z

2.5 Quantifiers and resolving ability of human perception
The number of quantifiers that are denotates of some words of natural languages is very great. And the number of quantifiers described in the logical studies by means of logical symbols is even greater. All these quantifiers are, obviously, understandable to the human mind or, speaking a bit more strictly, to human rational reasoning. This is, however, not the same as if they were acceptable to our immediate perception. Thus, for instance, we are able to use the rays of light with a wide range of wavelength, say, in the electronic microscopes or in the night viewing devices, but the range of wavelength accessible to the human eye directly is much narrower. In linguistics, the same situation is well known in phonology: not all sounds which could be produced by the organs of speech are used by the natural languages, even if we take all the natural languages of the world in their totality. In narratology, it is also obvious that not all understandable modalities are really in use in plot constructing.

Thus, it would be reasonable to suppose that the situation with quantification is the same. Only a relatively narrow class of quantifiers is really in use when the narrative or the language “work.” These “working” quantifiers are only those whose set is a part of the generative grammar of natural language or the “grammar” of narrative. Of course, their number is much smaller than the number of quantifiers which have their corresponding lexical expressions.

This consideration leads us to answer the question at the end of the previous section: why the “working” modalities of narrative apparently ignore quantifier not all, the inner negation of the quantifier some, being, in the same time, heavenly relying on a derivate of the inner negation of some, quantifier all?

This is not a question of narratology. The triplet structure of the corresponding modalities was described by logicians for different situations, but all of them were not interested in subtle distinction in the quantifying with either all or not all.

My answer is that the opposition between all and not all, in human perception, is completely overshadowed by the much more powerful opposition corresponding to the quantifier more than. This quantifier is of type ‹1, 1, 1›, and so, is irreducible to the quantifiers of type ‹1, 1›. It represents, using an Alexander Ivin’s bon mot, a different worldview.

Just now, it is easy to see that the difference between all and not all is easily perceivable in terms of more than. The quantifier more than has basic significance for the logic of preferences, but, outside some specific contexts, its significance is so far mostly overlooked.

APPELS À CONTRIBUTIONS / CALL FOR PAPERS

2009-12-11T22:25:29Z

пока еще немного черновой текст циркуляра. но дело уже пошло. я это воспринимаю как проект, прямо завещанный мне МвЭ.

The Coming of the Comforter: When, Where, and to Whom? Studies on the Rise of Islam in Memory of John Wansbrough
Edited by Carlos A. Segovia, Alessandro Bausi, and Basil Lourié
(Orientalia Judaica Christiana; Piscataway, NJ: Gorgias Press)

Dear Colleagues and Friends,

We would wish to publish a volume in memory of John Wansbrough on the “sectarian milieu” out of which Islam presumably emerged prior to becoming an autonomous religious entity. Our main concern is to explore the different chronologies and geographies one should alternatively look at and those religious components one should likewise take into account if attempting to define both the boundaries of and some of the conceptual, exegetical, and liturgical elements taken and reworked by formative Islam from that hypothetical “sectarian milieu.” In rigour, we are not only interested in the historical-critical study of Islamic origins, but also in the study of the Christian and Jewish milieus that could have influenced the rise of Islam between the 6th and the 8th centuries. Accordingly, our projected volume shall cover different fields of study.

Such an approach is especially helpful in the frame of the series where we are planning to publish our volume, “Orientalia Judaica Christiana” (http://www.gorgiaspress.com/bookshop/c-104-orientalia-judaica-christiana-1942-1281.aspx). This series is published as a supplement to Scrinium: Revue de patrologie, d’hagiographie critique et d’histoire ecclésiastique (http://scrinium.ru and http://www.gorgiaspress.com/bookshop/c-126-scrinium-revue-de-patrologie-dhagiographie-critique-et-dhistoire-ecclsiastique-1817-7530.aspx).

We would be highly honoured if you accept to contribute in our collective work. Moreover, we would also appreciate if you could provide us with your generous advice regarding other possible authors which in your view could be interested in and thus become part of our project.

Please let us know your impressions and suggestions.

Yours most sincerely,

Carlos A. Segovia, Ph.D.
Visiting Professor in Islamic Studies
UCJC/UNED, Spain

Alessandro Bausi, Ph.D.
Universitäts Professor für „Äthiopistik“
Asien-Afrika-Institut
Hamburg, Germany

Basile Lourié, Dr. habil.
Rédacteur en chef
Scrinium. Revue de patrologie, d’hagiographie critique et d’histoire ecclésiastique

продолжаем про модальности (3)

2009-12-11T13:40:10Z

здесь будет про обобщенные кванторы -- только то, что будет нужно в дальнейшем. к сож., соответствующий раздел недавно переведенной и изданной у нас (усилиями жж-юзеров!) книжки Эммона Баха написан на уровне 1970х годов (это курс лекций 1984 г.), когда из этой области логики лишь очень мало что успело попасть в лингвистику. сейчас дела обстоят, может быть, лучше, но вот, например, книжка Чинкве 1999, которая по сути весьма затрагивает тему, тоже абсолютно невинная в данном вопросе...
...1.1 Generalization of quantifiers

First of all, one can see in the table above that it was composed in the frame of the logic of the 1960s, when the generalized quantifiers were a new and not widely applicable branch of the logical studies. Indeed, the very idea of generalized quantifiers is going back to Andrzej Mostowski’s (1957) seminal paper “On Generalization of Quantifiers”, and, in its present form, to Per Lindström (1966). The application of (Fregean, not generalized) quantifiers to the structures of natural languages is the famous idea of Richard Montague (1970). The recent development in the field was provoked, in a great extent, by needs of natural language studies; see now (Peters, Westerståhl 2006).

First of all, the generalized quantifiers are considered as free from the so-called existential import. This is important from the philosophical viewpoint, too, because, philosophically, the procedure of quantification over the objects has a transparent (Fregean) sense, but the sense of the quantification in modalities is somewhat obscure, or, as Quine (1953) coined this problem, such quantification is “ontologically opaque”: in modalities, it is some states of objects rather than to the objects themselves which are quantified. Quine believed that such quantification is applied to intensionals and that it misses denotates. This difficulty could be avoided in the semantics of possible worlds by means of presupposition that the domain of quantification is limited to the worlds where the appropriate objects do really exist. Dealing with the generalized quantifiers, we do not need, however, any reference to the semantics of possible worlds. Instead, we exempt the quantifiers from any ontological commitment at all.

This condition means that the quantifier “all” (") could be defined on the empty set as well as on a non-empty one. Thus, if an existential import takes place, all (A, B) means that all As are B and there are some As. However, if our all is a generalized quantifier, then, all (A, B) means only that all As are B, without any supposition about the existence of As. Thus, taking an example from a medieval logician (Paul of Venice’s Logica Magna (c. 1400)), the phrase “Some man who is a donkey is not a donkey” is true since the subject term is empty (Peters, Westerståhl 2006, 25).

For our practical purpose, we need take into account only three kinds of the generalized quantifiers. The corresponding types are designated, in Lindström’s terms, as ‹1›, ‹1, 1›, and ‹1, 1, 1›.

The quantifiers of type ‹1› define sets within a given universe, e.g., a quantifier Q defines set A. The quantifiers of types ‹1, 1› and ‹1, 1, 1› define the relations between two or three sets, correspondingly, e.g., Q (A, B) and Q (A, B, C). Everywhere in these designations number “1” means “first order” in a generalized sense. This “first order” is not excluding the functions, as it is the case in the logic of predicates. Instead, it includes any kind of objects whose internal structure is irrelevant, that is, any kind of set considered as lacking any internal structure of relations. Such a generalization of the Fregean notion of quantifier was proposed by Mostowski. Mostowski’s generalization of the notion of quantifier was first applied to the natural language by David Lewis (in his 1975 paper “Adverbs of quantification”), while without knowing neither Mostowski’s nor Lindström’s works. Lewis observed that such adverbs as “often,” “usually,” “seldom” etc. are quantifying over neither time nor events but something called by Lewis “cases.” These “cases” are analogous to Mostowski’s sets and can conclude times, events, and many other things.

Lindström proposed a further step of generalization allowing quantification over relations. Thus, if the quantifier is applicable to the relations between sets, its order is “2”; then, if it is applicable to the relations between relations, its order is “3,” and so on. E.g., quantifier each other is a denotate of the ‹1, 2› type quantifier.

The difference between types ‹1› and ‹1, 1› could be illustrated by difference between two possible denotates of most. The ‹1› denotate of most is the so-called Rescher quantifier Q^R “more than half of the elements of the universe” (as it was introduced in (Rescher 1962)). The ‹1, 1› denotate is “more than half of” that could be applied to the relation between two different subsets A and B of the universe (Peters, Westerståhl 2006, 62), that is, A is the most (“more than half”) of B, not of the whole corresponding universe.

In contrast with the first-order logic of predicates where the most used quantifiers (especially $ and ") are those of type ‹1›, the natural language is operating mostly by the quantifiers of type ‹1, 1› and, not seldom, of type ‹1, 1, 1›. The quantifiers of type ‹1› determine the denotates of the noun phrases, while the verb phrases’ quantifiers are of type ‹1, 1› or higher.

As to the narratology, the quantifiers in Doležel’s table are all of type ‹1, 1›, Q (A, B). They are defined over relations between two sets in the universe of narrative, where the set B is the set of states appropriate to a given universe, and the set A is the set of the elements of the same universe which are able to change their states according to a given modality. Indeed, modality is, by definition, a kind of relation, and so, its corresponding operators must be of types higher than ‹1›.

1.2 Negative operations on the quantifiers

Already in Doležel’s table the quantifiers are presented via the operations of negation. They are almost self evident in the case of operators of type ‹1› and could be not so evident in other cases.

Thus, the operations of negation on the quantifiers of type ‹1› form the square of this quantifier Q(A), where square (Q) is conjunction of four elements, namely, Q, ¬Q, Q¬, and Q^d. The latter three elements mean the following:

¬Q is external negation = complement set of A = M – A, where M is universe,

Q¬ is internal negation = Q(M – A) = Q (complement set of A),

Q^d = ¬Q¬ is dual of Q = external negation of internal negation.

Example: the square of the quantifier some is none (external negation), not all (internal negation), all (dual).

For the quantifiers of type ‹1, 1› Q(A, B) the square is basically the same but with another definition of internal negation: Q¬ = Q(A, M – B).

.

Thus, in our examples from Doležel’s table: Q (A, B) means that the elements of the subset A of the universe of narrative M are possible or permitted or good or known. Its external negation means that, in the set A, everything is either impossible or prohibited or bad or unknown. Its internal negation (Q¬) (A, B) means that the elements of A are, correspondingly, not necessary or not obligatory or not axiologically neutral or “not believed” (in the sense that they are not to be believed, being either known or unknown). Finally, its dual means that the elements of A are either necessary or obligatory or axiologically neutral (neither good nor bad) or believed (epistemically neutral, that is, neither known nor unknown).

It is obviously that the interpretation of the internal negation, when applied to modalities, can be problematic. At first glance, it looks at odd with the fact that a derivation of the internal negation, dual, is one of the fundamental quantifiers in any logical system. We will turn to this problem in the next section.

продолжаем про модальности. (2)

2009-12-08T22:54:00Z

номера разделов тут полетели. все должны начинаться на 2, а не на 1.
1 Modalities in narratology

1.1 Why modalities?

The narrative is about causality but not about an objectivistic causality where the events are independent from the observer. It is rather similar to the explanations in quantum physics where the events themselves and their causality are directly depending on the way of observation. Thus, a novel could bear the title “Crime and Punishment” but it will be not about necessity or probability of the consequence between crime and punishment in any classical logical sense. Instead, it will be about the conditions of the experiment where the logical implication Crime ® Punishment can be testified, taking into account that there are others where it cannot. In this way, the events in the narrative are the quantum events.

Given that an implication of the role of the “observer” is unavoidable, the logic of the plot development in the narrative could be interpreted as modal logic.

The above demonstration why the logic of the plot should be modal logic is rather evident but it became possible only recently, in the light of the interpretation of modal logic within the classical framework. Before this, the question Why?, applied to the narrative modalities, was without answer.

The same demonstration is also applicable to the “logic of grammar” in linguistics. It is difficult to imagine how the speaker could construct his phrases without any implication of his own position. The mere fact of such an implication is enough to make the logical construction of his phrases modal.

1.2 Doležel’s modalities

The logical modalities of narrative were not deduced but were discovered, or, better, recognized in Propp’s “functions” already described for the folktale. The number of Propp’s “functions” (plot’s parts considered as elementary) was 31 for the simplest example of magical folktale. When Étienne Souriau (1950) repeated the work of Propp (independently, without knowing Propp’s (1928) seminal monograph) but for more complicated objects, theatre plays, the number of “situations dramatiques” (analogues of Propp’s “functions”) was two hundred thousand. Looking at these calculations of Propp and Souriau, Greimas (1966) caught the insight that these innumerable “functions” are to be reduced to several modalities.

These modalities were first described in a systematic way by Doležel (1976; 1999). Doležel attributed to the modalities the shaping of the fictional worlds of narratives that gives them “the potential to produce (generate) stories” (Doležel 1998, 113).

Doležel’s main attention was concentred on the three modalities already studied by von Wright, and, after him, especially by Jaakko Hintikka: alethic (von Wright 1951), epistemic (Hintikka 1962; Hintikka and Hintikka 1989), and deontic (von Wright 1968; Hintikka 1971). To these three modalities he added the fourth, axiological (logic of values), whose pioneering study by Nicholas Rescher (1969/2006) appeared several years before (see now also (Rescher 2004)). Unfortunately, Doležel was unaware of the parallel and independent studies of logic of values by Alexander Ivin (Ivin 1970; Iwin 1975).

The four modal logics were chosen just because it was demonstrated that they are really playing some role in story producing. It was moreover important that the formal structure of all the corresponding logical operators corresponds to the triplet structure of logical quantifiers “all” (" or ¬$¬), “some” ($), and “none” (¬$). The formal structure of the modal operators follows from the requirement of modal completeness (which is the modal analogue of the excluded middle principle of the formal logic).

Thus, Doležel proposed the following table (Doležel 1998, 114):

		Operators
Quantifiers		Alethic			Deontic			Axiological		Epistemic
$	some	M	possible			P	permitted	G	good	K	known
¬$	none	¬M	impossible		¬P		prohibited	¬G	bad	¬K	unknown
¬$¬	all	¬M¬	necessary	¬P¬			obligatory	¬G¬	indifferent	K₀	believed

“The number of these systems, four, is not magical. In accordance with the general character of our fictional semantics, narrative modalities are declared an open set. If other semantic categories are identified logically as modalities and proved significant for formation of narrative worlds, then they should be accepted into the set.” (Doležel 1998, 257, n. 3). These worlds should be comprehended in the sense that the list of the relevant modalities is still open, but not in the sense that it is an open list by nature. Doležel does not pronounce himself whether the number of the narrative modalities is limited or not.

против страшилок

2009-12-08T22:43:03Z

очень поучительная история о том, что не надо "предполагать самое худшее" :
http://geish-a.livejournal.com/630490.html?view=11604442#t11604442

модальные логики, нарратив и Чинкве

2009-12-07T23:57:48Z

после кое-каких бесед с добрыми лингвистическими самаритянами начал потихоньку писать даже не нулевую, а минусовую версию будущей статьи. буду понемногу писать и выкладывать. не исключаю, что окончательный вариант будет написан в соавторстве...

The Modal Logic in the Narrative and the Natural Language

1 Preliminaries

1.1 Introduction

The revival of the modal logic studies in the 1950s has echoed in both narratology and linguistics. At first, in the narratology, Algirdas Julien Greimas (1966) noticed that the logical elements of the plot, as they were specified by Vladimir Propp (1928/1963) and some others after him are, in fact, modalities. Then, John Lyons (1978) identified as logical modalities some properties of the language. Both Greimas and Lyons were especially influenced, first of all, by Georg Henrik von Wright (1951) with his analysis of the alethic, deontic, and epistemic modalities.

Then, in the narratology, Lubomir Doležel (1976; 1998) proposed the first systematic review of the modalities used in the construction of the fictional plot. Independently, Frank Ankersmith (1983), following some ideas of Arthur Danto (1965), discovered the role of the modal logics in the historiography. In the same time, Paul Ricœur (1984-1985) argued for the “grande narratologie” that includes both fiction and historiography. Finally, in the studies of the syntax of natural languages, Guglielmo Cinque (1999) described a system of “functional heads” whose meaning is identified as modal by Cinque himself, while only for a part of them. It seems to me, however, that Cinque describes as a whole the system of logical modalities which can be expressed in the syntax structures, which has been previously fragmentary detected by Lyons. However, this Cinque’s system has never been studied from a logical point of view.

This system of Cinque’s linguistic modalities has striking similarity with that of the narratology. Without being able to explore Cinque’s argumentation at length, I would prefer to describe the modalities of the narratology and to pose them alongside with Cinque’s system.

1.2. Logical modalities: definition and interpretations

The discussion of the problem of modalities in the narratology and the linguistics suffers from a vagueness of terminology and concepts. Therefore, we have to start from the definitions of the basic terms.

“Ask three modal logicians what modal logic is, and you are likely to get at least three different answers.” (Blackburn et al. 2002, viii). Indeed, it is difficult to find out a definition of the very notion of “modality.” Very often, it is introduced in an intuitive way or within a mathematical formalism, in both cases without any explicit connection to the other branches of logics and philosophy. Of course, there are other approaches. Among them, the most popular is the interpretation of “modality” as a state of things in some of the possible worlds. However, the semantics of possible worlds, being a powerful tool of making clear the meaning of the alethic and some other modalities, turns out to be an obstacle in understanding of other modalities, e.g., spatial (cf. (von Wright 1979)). This is one of the (many!) causes which make desirable to present the modal logic with no relation to the semantics of possible worlds and within the context of other (classical) logical systems.

Alternatively to the possible worlds approach, the modal logics can be presented as particular cases of classical logic. The main line of reasoning is the following (Blackburn et al. 2002; 2006). The basic notion is that of “relational structure” that is defined as a set together with collection of relations on that set. Obviously, such structures are to be found everywhere. The relational structures could be approached from an external viewpoint, as normally the modern scholarship does, and this will be the objectivist, so-to-say, approach used by classical logic. Alternatively, the relational structures could be approached from an internal viewpoint, from within. This way of observation where the presence of the observer himself is implied is that of modal logic. Thus, “... modal languages talk about relational structures in a special way: 'from the inside' and 'locally.' Rather than standing outside a relational structure and scanning the information it contains from some celestial vantage point, modal formulas are evaluated inside structures, at a particular state. The function of the modal operators is to permit the information stored at other states to be scanned — but, crucially, only the states accessible from the current point via an appropriate transition may be accessed in this way. <...> the reader who pictures a modal formula as a little automaton standing at some state in a relational structure, and only permitted to explore the structure by making journeys to neighboring states, will have grasped one of the key intuitions of modal model theory.” (Blackburn et al. 2002, ix).

From this perspective, “...modal logic can be regarded as a fragment of first- and second-order classical logic.” (Ibid., xi). What we are the most interested in, however, is an evident usability of modal logic in interpretation of both thinking process itself and its resulting activities such as discourse (that produces narratives) and language.

To sum up, one can say that modal logic considers the states of relational systems from an insider point of view.

1.3. Modal logic approach in the cognitive science

The number of states that are discernible from some internal viewpoint is unlimited. Moreover, any kind of modal logic can be combined with some another and/or a kind of classical logical reasoning. As a result, the number of possible modal logical systems is infinite. Dealing with a given kind of problems, that is, with a given kind of relational systems, we have to choose only the appropriate kinds of logical reasoning.

Thus, it is a priori likely that the number of logical modes of the psychological process of human thinking is far from being unlimited. It is likely that human thinking operates with a limited number of elementary logical modalities to be able to understand any other modalities that it is able to understand. These modes are natural logical tools given to the human cognitive sphere to work. However, so far, no study of the logical modalities of the human cognitive sphere is performed.

The studies of natural language’s syntax and structure of narrative are two of the most natural areas where such study might be initiated. Some congruency of the modal logic systems at work in both would be not to wonder and could be explained by some mechanisms of the human thinking as such. In this way, the studies of modalities of narratology and syntax are both means of investigation of the human cognitive sphere.

Here, I shall limit myself to a review of application of the modal logic approach to the narratology with remarks on the possible use of this approach in the theoretical linguistics, especially in the light of Cinque’s treatment of the functional heads.

Богоматерь Одигитрия

2009-12-07T18:31:44Z

появление этой иконы в К.поле связывается с деятельностью императрицы Евдокии в 430-е годы в Палестине.
я уже интерпретировал эту деятельность в русле переключения богородичного культа с Ефеса на К.поль. тут моя подробная статья, где про Евдокию ближе к концу).

но вот что я совершенно упустил -- это именование этой иконы "Ефесской". с т.зр. К.польского культа Одигитрии во Влахернах, ее следовало бы называть "Палестинской".

вопрос(ы): 1. есть ли об этом исследования (статью Шалиной я не читал пока, но не уверен, что там поднимается слой 5 века), 2. в каких источниках это название сейчас фиксируется впервые? есть ли что-нибудь на греческом (или в древнем восточном переводе на любой язык, но тоже с греческого)?