The aim of the following brief questionnaire is to gather basic information about those features of various languages which significantly affect expression of mathematical concepts and arguments. I would be most grateful to you if you could provide me with answers in respect of your mother tongue.
- Your answers to this questionnaire – about which language are they? (In my questions, I refer to this language as ‘your language’).
- In your language, are there (a) definite (b) indefinite articles? (English has both, Russian—my mother tongue – neither).
- In your language, is there a distinction between singular, dual (do not be surprised, some languages have dual forms) and plural forms of (a) nouns; (b) verbs? (Russian has singular and plural, both for verbs and nouns, with an additional curious occurrence of plurality markers for two, three, four objects (nouns), which are different for plurality markers for 5+ objects.)
- Is “double negation” used in normative (literate) speech? In English this is usually a sign of some form of slang: “I do not have no knife, man!” In Russian, double negation is used to strengthen the denial: “У меня нет ножа – У меня нет никакого ножа, with two connectives не and ни used as a primary negation (не, нет) and its re-enforcement (ни).
- Is the verb “to be” and its forms routinely omitted from sentences? (This is a prominent feature of Russian.)
- Connective “or” – is it usually understood in inclusive (and/or) or exclusive (either one, or another, but not both) sense? Or can its meaning vary depending on context? In English and Russian, it is mostly inclusive, with an occasional slip into the exclusive mode: “choose – her or me!”, “я или она !”
- I was told that the Japanese language makes use of two different connectives “and”: one for nouns, another for verbs. In your language, are there situations where English connectives “and”, “or”, “but”, “not”, “if … then” have to be translated in two or more different ways depending on context?
- Do you know any traditional proverbial saying which expresses the logical tautology p -> (q -> p)? I discovered that, apparently, students coming from some cultural backgrounds are somewhat uncomfortable with the principle of material implication (which is, in effect, expressed by the tautology above). Russians have such proverbs, for example “туз – он и в Африке туз” (“Ace is the Ace, even in Africa”).
- Any other observations about the logic of your language and peculiarities of its use in mathematics.
In your responses, please do not hesitate to use MS Word, DVI or PDF, if this is necessary for capturing the peculiarities of the alphabet/script of your language – or email me a handwritten graphics file (I could have difficulty with hieroglyphs, though!).
With warmest thanks
Please send your answers and comments to borovik “at” manchester.ac.uk.
Letter from David Pierce about Turkish language:
Let me address Turkish as I understand it (from my experience, from talking with Ayşe, and from reading Geoffrey Lewis, Turkish Grammar, Oxford, 2nd ed., 2000):
- Language: Turkish.
- Articles. Short answer: there is an optional indefinite article, but no definite article.Longer answer: The word bir “one” can serve as an indefinite article. Used like “one”, it precedes adjectives; used like “a(n)”, it follows them:
bir güzel gün “one fine day”
güzel bir gün “a fine day”
But the indefinite article is not required. Its omission may express even more indefiniteness:
Her hafta kitap okuyorum “Every week I read a book” (that is, every week I spend time reading a book).
Her hafta bir kitap okuyorum “I read [and finish] a book every week.”
Moreover, there are two cases for direct objects. An indefinite direct object takes the neutral form, like a subject; a definite direct object carries an ending. But a definite direct object may still take the indefinite article:
Her gün bir gazete okuyorum “Every day I read a newspaper” (not necessarily the same one each day).
Her gün bir gazeteyi okuyorum “Every day I read a newspaper” (a particular newspaper, such as Cumhuriyet).
The 3rd-person pronoun o “he/she/it” serves also as a demonstrative adjective:
o kitap “that book”.
But o is not used as a definite article:
Kitap masada “A book is on the table” or “The book is on the table.”
- Nouns. The numerically neutral form of a noun can be made into an indefinite plural by means of a suffix (-lar or -ler). The suffix is not used if a word for a specific number is used:
beş baş “five head”.
There is at least one example of an Arabic word whose singular and plural forms exist as separate words in Turkish:
şey “thing” (hence şeyler “things”);
eşya (or eşyalar!) “things, belongings”.
Geoffrey Lewis says a few Arabic dual forms survive barely in Turkish:
ebeveyn “[one’s] parents”;
tarafeyn “the two sides [parties]”.
- Verbs. In the first and second persons, there are distinct endings for singular and plural. (I mean for example that a first-person plural ending cannot be analysed into a first-person part and a pluralizing part, though this may have been possible historically.) The second-person plural form is also used as a respectful singular.There is no third-person ending for verbs;—rather, the third-person ending is empty (except in the imperative). However, in case of a plural (third-person) subject, the pluralizing ending -lar/ler is used on the verb (optionally in case of an inanimate subject).
- Double negation. The pronoun hiç “never/nothing” can emphasize negations:
Gerek yok “There is no need”
Hiç gerek yok “There is no need at all”
Perhaps a true “double negation” is shown in the following:
Görmedim “I didn’t see [anything].”
Hiç görmedim “I saw nothing at all” (cf. “I din’t see nuthin’.”)
- “Be”: Routinely omitted. See “my” article Turkish copula in Wikipedia for six ways of…copulating in Turkish.
- Disjunction. For most disjunctions, which may be practically exclusive, but where exclusivity is not the point, there are veya and ya da; where exclusivity is emphasized, there is ya…ya. There is also yoksa “if not”:
Erkek veya kadın, fark etmez “Man or woman, it doesn’t matter.”
Ya sev, ya terk “Love it or leave it.”
Çay isterim, yoksa kahve “I want tea, or, if there is none, coffee.”
- Conjunction. The Arabic borrowing ve “and” is an all-purpose conjunction, usable with nouns and verbs, but it is not spoken much. From its own resources, Turkish has different ways of conjoining nouns and verbs. Nouns can be conjoined with the postposition ile “with”:
Ahmet ile Mehmet “Ahmet and Mehmet” (lit. “Mehmet with Ahmet”).
When two adjacent verbs have the same subject and the same endings, then the ending of the first can be replaced with -ip to denote conjunction:
Kalkıp gittik “We got up and left” (in place of Kalktık ve gittik).
- Material implication. I have no idea.
- In English, the statement
(i) Everything is A
can be formally negated in two ways:
(ii) Something is not A;
(iii) Not everything is A.
But perhaps many people will still write or especially speak the negation as
(iv) Everything is not A.
(Compare the saying, “All that glitters is not gold.”) However, if we are trying to use the language logically, then we prefer to understand (iv) as having the same meaning as
(v) Nothing is A,
which is a negation of
(vi) Something is A.
In Turkish, sentence (iv) is a negation of (i) rather than of (vi), because there is no possibility of writing (iii):
Her muz Asal muz değildir lit. “Every banana Prime banana not-is”, that is, “Not every banana is a Prime banana” (slogan of a banana company in Antalya).
Her muz Asal muzdur “Every banana is a Prime banana.”
Hiçbir muz Asal muz değildir “No [i.e. not-one] banana is a Prime banana.”